high torque density machines - global events · usa hts motor 36.5mw 120rpm alstom advanced...

Center for Advanced Electrical Machines and Drives (CAEMD) Huazhong University of Science amp Technology China

Ronghai Qu amp Dawei Li

RonghaiQuhusteducn

High Torque Density Machines

CAEMD Web httpwwwcaemdcn

Outline

High torque density (HTD) machines

- Introduction and Ways to achieve HTD

Flux modulation machines

- Principle Features Topologies and family members

Vernier machines Topologies Analysis Design Prototypes

Challenges and Opportunities

Conclusions

2

CAEMD Web httpwwwcaemdcn 3

Introduction

Torque density is a main research topic and important index of electrical machines from the first day

The Development of Electrical Machines

The torque density is improved by 40 times


Reduction gearbox

High-speed machines coupled with reduction gearbox

Regular high-speed machine

Frequent maintenance

Break tooth at overload

Mechanical gears are widely used in mechanical transmission chains moving towards heavy loads and micro-precision

High Speed Motors with Gearbox

A Direct-drive machine is often a preferred solution

Gearbox makes the two rotors in physical contact resulting in vibration amp noise the need for lubricating grease and the risk of breaking teeth at overload condition

4


High torque density is an required feature for direct-drive machines

2e i e

PeT D LΩ

= prop

Direct-drive

Regular Direct-Drive Machines

USA HTS motor 365MW 120RPM Alstom Advanced Induction Motor 20MW 180RPM

Problems in manufacture transportation maintenance

Bulky and heavy

Requires high torque at low speed

Increase torque density


2[ ] cose e i e g gT K D L AB ABη φ= propClassic Torque Equation

Increase magnetic loading

Increase electric loading



Increase linearity of torque vs loading

Ways to Improve Torque Density

Optimizing aspect ratio

Increasing cooling capability

Superconducting wires

Increasing loading utilization

New technics

New materials

New topologies

Reducing armature reaction

6


Peak power density 67kWkgPeak torque density16Nmkg

High efficient oil channel (direct cooling)rated current density 20Amm2

Increase the heat capacity

Reduce the thermal resistance

Winding Potting

Auxiliary Heat Path

Water Channel within the Slot

Direct Oil Cooling

Improved thermal performance

Advanced Cooling Solutions

H Li 2017 Advanced MotorampLord

M Galea 2012 Nottingham

S A Semidey 2014 GIT

Temperature 22 D Howey 2016 YASA Rated current density 246Am2

7


Lightweight ironless-stator PM generators E Spooner etc 2005

Ironless Dual stator axial Flux motor F Caricchi etc 1996

Novel Mechanical Structures

Novel Structure motor S Engstroumlm S Lindgren 2007

Proposed Gear and high-speed generator

Conventional Direct drive

8


Flux Path Seperation

Flux lines (PM field) Flux lines (armature field)

Aver

age

torq

ue (N

m)

Electric loading (Acm)

The flux paths of excitation and armature field are separated using the Halbach array magnets and the armature reaction is weakened

9


Theory

Realization

Instance

SC materials can carry large current Nearly no loss under DC condition T

SC DC excitation Matching structure vacuum cooler refrigerator etc

σLDTe2

2π

= BA=σ

Material cooling system

Copper no extra cooling 45-6

Copper forced air cooling 75-9

Copper liquid cooling

SC material liquid helium

10 MW wind generator SC generator compared to conventional generator volume decrease to 12 weight decrease to 13

High Electric Loading-Superconducting Machines

10


Liu Y Noe M 2016

R Fair 2012

132MW Superconducting wind generator R QU et al 2015

Yubin Wang etc 2013

Superconducting wires are nice but not free


11


TpropABS AmdashElectric loading BmdashMagnetic loading SmdashAir gap area

A small PM motor nested inside a large PM motor The torque and power densities are boosted by doubling the air gap

surface area

bull Higher torque per volume bull Doubled airgap area amp weight bull Unchanged volume

bull Higher torque per volumeweight bull Doubled airgap area bull Coreless rotor bull Unchanged volume

High Torque Density Machine Topology I

12


Dual-rotor radial flux two airgaps Ronghai Qu 2003

Dual-rotor axial flux two airgaps Ion Boldea 2011

Dual-stator radial flux two airgaps Tae-Uk Jung 2013

Radial amp Axial flux three airgaps Masafumi Namba 2017


13


High Torque Density Machine Topology II

Transverse flux machine(TFM) H Weh 1986

pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=

Equivalent model of PMSM amp TFM

The flux linkage of TFM is N times that of PMSM

The torque density of TFM is proportional to N


Separated rotor TFM G Henneberge 1997

Double side TFM H Weh 1995

C-core TFM S M Husband 2003 R Qu T Lipo etc 2002

In recent years a few topologies with high torque density have been obtained and gain lots of attention


Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13


Flux Modulation Machines

For flux modulation machines their pole number of armature windings and excitation MMF are different (For special cases the two values can be same)

They have potential to be with high torque density so that they are very competitive

16

Flux Modulation a new way to improve torque density


Stator

Ferromagnetic pole pieces

Magnets

Rotor

Regular PM machine Flux modulation PM machine

There are three components in a flux-modulation machine ie 1 flux modulator 2 armature and 3 excitation field exciters


17


MMF

Flux modulator

Flux density

Space PWM

Flux Modulation Effect

0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB

Psprop A electrical loading

Bg magnetic loading

The flux modulation PM machine works as an integrator constituted of a magnetic gear and a regular PM machine

Ferromagnetic pole pieces work as a flux modulator to transform the speed of flux from Ω to PrPs Ω

Magnetic gear Flux modulation machine Regular machine

19


l hT Tβ= plusmn

hT

(1 )f hT Tβ= minus plusmn

Positivedirection Magnets

Low speed PM rotor

High speed Armature field

Ferromagnetic pole piece rotor

MMF

Flux modulator

Flux density distribution

Pe=11

Pa=1

Pf=12

Flux modulation PM machine

= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus

Ω Ω minusΩ Ω + Ω = = = minus +

Features

Pe magnet pole pair number Pa armature winding pole pair Pf flux modulator pole pair

20


There are three components in a flux-modulation machine ie flux modulator armature and excitation field exciters

The pole number of the two MMFs is different and the flux modulation is requisite to work as a pole number transformer through air-gap permeance function

Among flux modulator armature and excitation fields only one component can be but not necessary stationary


Stationary Flux Modulator

(SFM)

Stationary Excitation Field

(SEF)

Stationary Armature Field

(SAF)

All the three parts are Rotary

Features

General topology theory for flux modulation machine 21


Stator

Flux modulatorMagnet

s

Rotor

Flux modulator

Rotor WindingWinding

Magnets Magnets

Flux modulator PM rotor

Stator WindingWinding

Vernier PM machine

Harmonic PM machine Transverse flux PM machine

Pf=Z

Pf=kZ

Pr=Z Pr Pole pairs of magnets Z Slot number

Phase coil Stator

Magnet

Flux

Direction of rotation

Magnet

PM rotor PM rotor

B1 B2

Laxial

Flux-Modulation Machines with SFM

22


Magnets

Flux modulator rotor

Armature winding

Armature winding Magnets Armature

winding


Flux reversal machine

Flux switching PM machines


MagnetsStator

Winding

Stator Magnets

Winding

Flux-Modulation Machines with SEF I

Stator

Flux modulatorRotor

Magnets

Stationary magnet

23


Flux-Modulation Machines with SEF II

Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding

Hybrid excitation vernier reluctance machine

StatorMagnets

ArmatureWindingDC+AC

Hybrid excitation vernier reluctance machine with DC-bias current

Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time

CurrentSwitched reluctance machine

Dc-bias vernier reluctance machine

DC field winding is used to replace

the magnets

Stator excitation vernier reluctance machine or variable reluctance machine SRMampDC- bias vernier reluctance machine

Stator

Magnets

ArmatureWinding

DC field winding is used to partly replace

the magnets


Flux-Modulation Machines with SEF III

Brushless doubly fed machine


A

B C

Armature winding

Vernier reluctance machine

Flux modulator rotorArmature winding

Synchronous reluctance machine

AC field winding can be removed

Pe=Pa Pf=2Pa Pf=Zr+-Zs


Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25


Flux modulator rotorPM rotor

BrushDC armature winding

+

+- -


PM rotor

Stationary DC winding

Flux-modulation DC commutator machine

Flux-modulation coupling

Flux-Modulation Machines with SAF

26


Winding A

Winding A1

Winding A

Dual Electrical ports Dual mechanical ports

1

A e f

A e

P P PP P

= minus=

Flux-Modulation Machines with Dual Ports

Single electrical ports Dual mechanical ports

27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship

Flux modulation machine

Regular PM machine

Flux modulation machine with

dual ports


dual ports

Winding A1 Pole pair PA1

Winding A Pole pair PA

Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1

The flux modulation PM machine with dual ports can be used in HEV to replace one mechanical planetary gear one torque regular motor and one generator

This topology can also work as one type brushless DFIG 29


Basic Theory for Flux Modulation Machines

General topology theory

Field analysis of flux modulation machine

Winding theory

Performance features

Basic theory

A new perspective ie flux modulation principle on the both flux modulation and regular machines is presented

30


Field Analysis based on MMF-Permeance Model

c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω

πα θ ωπ micro micro

=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o

MMF excited by magnets

31


0 1( ) cos( )s f s fP tθ θ ωΛ asymp Λ +Λ minusPermeance function

Field excited by magnets c

10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s

cici e s e e f s e f

i ici

e f s e fi

B t F tFF iP i t iP P i t

F iP P i t

θ θ θθ ω θ ω ω

θ ω ω= =

=

ΛΛ= Λ minus + minus minus minus

Λ+ + minus +

sum sumsum

Pole pair Speed Frequency Source Permeance Magnet MMF

iPe 2iπωe Pe 2iπωe Λ0 i th harmonic Pf-iPe 120iπ(ωe-ωf)( Pf -iPr) 2iπ(ωe-ωf) Λ1

Pf+iPe 120iπ(ωe+ωf)( Pf +iPr) 2iπ(ωe+ωf) Λ1


32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Winding Function for balanced three-phase winding

Magnet Flux linkage 2

0

( ) ( )a g stk g s a s sr l B t N dπ

ψ θ θ θ= int

Flux Linkage Formula

33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si

a g stk g s a s s ci g stki

e j e e f j e fPe Pf Pej i j iPa Pa Pa

b g stk g s b s s ci g stki

e j

de r l B t N d F r ldt

i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =

ΛΛ + plusmn plusmn

= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3

e e f j e fPe Pf Pej i j iPa Pa Pa

c g stk g s b s s ci g stki

e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π

ω π ω ω ω ω π

θ θ θ π

ω ω π ω ω ω ω π

= = plusmn

=

=

Λminus + plusmn plusmn minus

= minus =

ΛΛ + + plusmn plusmn +

sum sum

sumint

Pe Pej i iPa Pa Pa= plusmn

sum sum

Back EMF Formula

34


Torque Formula (1 sgn )

[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a

PPT e t i t e t i t e t i t

PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132

e g axial s max c wP r L N I F k Λ 21 1 1

3=2

avg g stk s max c wa

ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial

Transverse flux PM machine Flux switching PM machines

Winding

Magnets

Rotor

Vernier PM machine

There is an additional coefficient ie pole ratio in the torque formulas of flux modulation machine This offers flux modulation machines high torque density potential capability with limited current and magnetic loading


2

1PF=1 ( )s

m

L Iψ

+

Power Factor Formula

2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine

SFM flux modulation machine

SEF flux modulation machine

36


Winding Theory for Flux Modulations The vernier magnetic geared flux reversal flux switching and

transverse flux machines share same operation principle ie flux modulation principle

Therefore their winding configurations could be analyzed and designed by the same method ie the classical winding theory

So far some topologies still use specified winding theory especially for flux switching machines whose structures are different from regular machines and this introduces some barriers for researchers to further study those machines

No load flux

density analysis Armature

winding pole pair Decide the winding

configuration amp scheme

Since the pole number of armature winding and PM rotor is same in the regular PM machines this two steps are always neglected

37


Winding Theory for Flux Modulations

1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t

Z Z ZB Z Z t B Z Z t B Z Z t


θ θ θ

θ θ θ

θ θ θ

= Λ

= minus + minus Ω + minus minus Ω + minus + Ω

minus minus + Ω + + minus Ω minus + minus Ω

No-load airgap flux density for flux switching PM machines

Flux switching machine

Rotor Stator

PMs Windings

38


Fortunately all the working flux harmonics of FSPM machines satisfy

1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）

1 1( ) ( )i jGCD Z P GCD Z P=

Summary Each of these harmonics is a slot harmonic of another In other words for FSPM machines the pole pair number of all the working harmonics can be used as the armature winding pole pair number to assign winding connection and check whether the windings of a stator and rotor slot combination is symmetrical or not

Winding Theory for Flux Modulation Machines

39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C

Direction of flux rotation

16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2

25811 Direction of flux rotation

120O

14710

36912

A

B

C

28=3Z12+Z2


120O

A 1210 statorrotor tooth FSPM machine

Star of slots of 1210 statorrotor tooth FSPM machine for different order working flux harmonics (a) 16th (b) 20th (c) 8th (d) 28th

(a) (b)

(c) (d)

40


Winding configurations The slot per pole per phase and winding pitch of FSPM machines are

1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41


Winding type determination

Winding configurations of three-phase FSPM machines


Three-phase FSPM machine

Overlapping winding Nonoverlapping winding

Integer slot distributed winding

Fractional slot distributed winding

Concentrated winding with two-slot pitch

SPPge1 SPP is a fraction SPP is an integer

SPPge1 05ltSPPlt1

The fractional slot distributed winding and concentrated winding with two-slot pitch are naturally discovered for the FSPM machines after that the classical winding theory is used

42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B

Nonoverlapping winding (Type1)

Overlapping winding (Type2)


613

614 Type 1

(Nonoverlapping)

614 Type 2 (Overlapping)

614 Type 3 (Full

pitch) Speed 1200RPM No of stator teeth 6 6 No of rotor teeth 13 14 Outer stator diameter 170mm Stack length 100mm Airgap length 2mm Outer rotor diameter 102mm Pole pitches (slot No) 1 1 2 3 Stator tooth width 85m

m 8mm

Magnet thickness 85mm

8mm

Stator back iron thickness

78mm

Slot area 6900mm2 Rotor pole arc 13 No of turns per phase 26 Magnet remanence 11T Relative recoil permeability

105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14

614 FSPM machine with overlapping winding614 FSPM machine with nonoverlapping winding

Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40

1210 FSPM machine613 FSPM machine614 FSPM machine with tooth-coil winding614 FSPM machine with two slot pitches614 FSPM machine with full pitches

Back

EM

F(V)

Rotor position(elecdeg)0 1 2 3 4 5 6 7

0

5

10

15

20

25

30

35

1210 FSPM machine613 FSPM machine614 FSPM machine with nonoverlapping winding614 FSPM machine with two slot-pitch winding614 FSPM machine with overlapping

Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100

613 FSPM machine614 type1 FSPM machine614 type3 FSPM machine

Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90

614 type1 FSPM machine614 type3 FSPM machine

Q-axis current(A)

Torq

ue(N

m)

Phase back EMF of 613 and 614 FSPM machines with nonoverlapping and overlapping windings

Torque vs stack length waveforms of 613 and 614 FSPM machines with nonoverlapping and overlapping windings

Average torque vs iq in 614 FSPM machines with nonoverlapping and overlapping windings (Stack length is 200mm)

44


Conditions for Symmetrical Phase Flux linkage Waveform

The airgap flux density produced by the even harmonics in Λr(θst) and magnet MMF is

1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn

Winding Theory for Flux Modulation Machines Conditions for Symmetrical Phase Flux linkage Waveform

If t the greatest common factor of stator slots and pole pairs and Z1(mt) are odd the back EMF waveform of FSPM machines is asymmetrical

If Z1(mt) is even the number of spokes in star of slots is the integer multiple of 2m In order to get symmetrical back EMF waveform the number of stator and rotor teeth satisfy

46


The Vernier magnetic geared flux reversal flux switching and transverse flux machines share same operation principle ie flux modulation principle or magnetic gear effect

All these topologies can be transferred from the basic flux-modulation machine and classified into the flux-modulation machine family

The basic theory of the flux modulation machine has been presented The classical winding theory is successfully applicable to all flux modulation machines

Among these Flux modulation topologies Vernier PM machines are attracting more and more attentions due to its high torque density and simple mechanical structure

Flux Modulation Machines ndash Summary

47


Vernier PM Machines Magnets

+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance

Airgap Flux Density Fundamental Harmonic

S

Stator

Rotor

No load flux density distribution

Vernier PM machines have same mechanical structrue with that of traditional PM machines

Merits High torque density simple mechanical structure high efficiency and structure compactness

48


Winding Configurations

Three-phase Vernier PM machines






3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=

pole ratio 21 1( )4 2

q

le

lt le

pole ratio 5123q

ge =

2 pole ratio 51( 1)2

q

lt lt

lt lt

For vernier machines

49


Slot amp Pole Combinations

r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0

e= [ ( ) ( ) ]g stk g s s sd r L B t N ddt

π

θ θ θminus int 1 5 10 15 20 25 30 35 40Harmonics order

0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu

Harmonics for regular PM machine

Harmonics for VPM machine

13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis

The back-EMF is determined by the product of winding function and flux density harmonics

The order of flux density harmonics contributing to back-EMF harmonics is large in VPM machines

The back-EMF waveform of VPM machines should be sinusoidal

51


Working Harmonics Vernier PM machines Regular PM machines

No of fundamental magnet MMF Pr Pr

No of airgap permeance Const Z 3Z Const

No of working harmonics Pr Z-Pr Z+Pr 3Z-Pr 3Z+Pr Pr

Frequency PrΩ2π PrΩ2π

12-slot 2-stator pole 22-rotor pole vernier PM machines

12-slot 2-stator pole 2-rotor pole regular PM machines

0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis

The flux density working harmonic is defined as the harmonics which contribute to the average torque

52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)

A sinusoidal Wave Phase A

Time(ms)

For the 22-rotor pole 12-stator teeth VPM machine

57111317191 23aiP =

The pole pair number of magnet field harmonics

The pole pair number of winding function harmonics

The EMF waveform of vernier PM machines is inherently sinusoidal even with the full pitch winding configuration

Other Features - Back EMF Harmonics

Ripple torque Average torque

Winding function Magnet field

25471 4923 71eiP =

53


Other Features - Torque Ripple 1

0

10

+2( )

+2

Pr iPr Z Z iPriPs Ps Ps

Pr Z Pr Z PrPs Ps Ps

N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123

( ) cos( 1)peak ripple ei

avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=

12-slot 22-rotor pole vernier PM machines



16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

VPM machineRegular PM machine

1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA

Rotor position(elecdeg)

Line

bac

k EM

F(V

)

Vernier PM Prototypes

Torque transducer

Gear box Prototype

Magnetic powder brake(mechanical Load)

VPM prototype

Commercial motor

Torque Nm 174 Efficiency 085 08 Stator diameter mm 124 Air-gap length mm 08 Magnet thicknessmm 3 32 Stack length 70 120 Active length mm (including end winding length)

160 150

Weight kg 122 145 Power factor 059 098

0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55


End Winding Reduction

56

To reduce Long End Winding

New winding configuration

Dual rotor topologies

Novel stator structure With auxiliary teeth


Different Winding Configurations

Three-phase Vernier PM machine






Long end windings

ldquoNewrdquo type vernier PM machines are found

57


Two Slot Coil Pitch Winding VPM Machines Slot pole combination


q

le

lt le

pole ratio = 511171 23q

=


q

lt lt

lt lt

18 slots Pr =12 Ps =6 18 slots Pr =14 Ps =4 18 slots Pr =15 Ps =3

A VPM machine with two slot coil pitch winding or tooth winding leads to low pole ratio and may be a cost-effective option

58


Performance Comparison Z=24 Pr=19 Ps=5

0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)

slot opening ratio=058 slot opening ratio=013

3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt

The open slot topology

The half-closed slot topology

The open slot topology achieves ~11 larger EMF than the counterpart 59


Slot-Pole Combinations

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

Optional Slot-Pole Combinations For VPM Machines (Z=Pr+Ps kw ge 086)

241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison

Item 2410 24168 24195 24204 Stator outer diameter 248mm 248mm 248mm 248mm Stator inner diameter 85mm 85mm 85mm 85mm

Airgap length 10mm 10mm 10mm 10mm PM thickness 35mm 30mm 30mm 30mm PM pole arc 09 09 09 09

Slot opening ratio 013 058 058 058 Turns in series per phase 168 168 168 168 Rotating speed (RPM) 300 300 300 300

Magnet remanence 105T 105T 105T 105T 0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio

Main Design Parameters

Main geometric parameters of the four topologies keep the same to make a relatively fair comparison

The back-EMF of the 24195 model is ~18 larger than that of the regular 241010 model while 24 lower than the 24204 case

61


Output Torque and Power Factor

0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)

Pole Ratio The average torque values of 24195 and 24168 models are ~18 higher and ~73 lower than that of the 2410 case respectively

62


Prototype and Experiments

Back EMF waveform of the vernier PM machine with two slot pitch winding is also sinusoidal

It power factor is larger than 08 63


Relationship between VPM and FSCW Machines

Pr=8 Pr=7 Pr=5

Open Slot Half Closed

Slot

Model Z Pr Slot type Ps Ps regular PrPs

1

12

5 Open slot 7 5 57

2 5 Half closed slot 7 5 57

3 7 Open slot 5 7 12


5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0

Spectra of airgap permeance harmonics

64


0

8

16

24

Torq

ue (N

m)

Half Closed Slot Opening Slot

1284 1275 1257PR=2 PR=14 PR=07

VPM and FSCW Machine Relationship

0

1

2

3

4

5

PR=07PR=14PR=2

Open SlotHalf Closed Slot

12571275

times10(-4)

k conv

+kve

r

Modulated part Regular part

1284

Predicted by analytical method Predicted by FEA

The fractional slot concentrated winding (FSCW) PM machines can also be regarded as one type flux modulation machine

The modulated part torque accounts for large proportion in the total torque of the FSCW PM machines

As the pole ratio increases the ratio of the modulated part torque to the total torque increases

65


Non-overlapping Windings with Large Pole Ratio

Lap Winding Toroidal Winding Non-overlapping FSCW

s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP

End winding length is almost independent from slotpole combination

f f e aP Z P P P= = plusmn f e aP P P= plusmn

66


Dual-Airgap Axial Flux VPM Machines Rotor core

Stator core

WindingMagnets

Rotor coreMachine topology

The rotor-stator-rotor structure makes toroidal windings applicable

Due to mirror symmetry of axial flux topology the analyzing process can be simplified by focusing on only one rotor and half the stator

67


Other Optional Configurations

Different winding configurations

(a) (b)

(c) (d)

(a) (b)

Different slot shapes

Different PM configurations

68


Geometric Parameters

Cylindrical view Flux distribution of the AFVPM machine

Symmetrical Axis

+A+A-C-C+B+B-A-A+C+C-B-B

-A-A+C+C-B-B+A+A-C-C+B+B

Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view

The stator teeth on both sides work as flux modulators

Rectangular instead of trapezoidal slots are chosen for the proposed machine due to manufacturing difficulties

69


Quasi-3D and 3D FEA

Item Analytical Quasi-3D 3D Avg Torque Nm 1103 1056 1061

Torque density kNmm3 339 327 326 Torque ripple - 05 23

Calculation time lt1s 40min 8hour

Sketch of Quasi-3D method Magnetic field plot of quasi-3D and 3D FEA

70


Prototypes

Stator and rotor cores Stator with windings

PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe

Three phase back-EMF waveforms

Average torque vs current

Performance comparison with different analyzing methods

72


Mutli Working Harmonic Vernier PM machines

Cross section of the proposed vernier topology (APMV machine)

= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator

Cross section of regular topology

The flux modulator pitch is unequal to slot opening width

Regular vernier PM machine is a special case of APMV machine

The flux modulator pitch ratio is defined as

Z=6 Pf=12 Ps=2 Pr=10

73


Permeance and Flux Density Harmonics

0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5

Rotor position(mechdeg)

0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf

Regular vernier PM machine k=1 Airgap permeance Flux density

New working permeance harmonics are introduced

0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT

The APMV machine k=13 Airgap permeance Flux density

0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order

k=10 Semi-analytical k=10 FEA k=13 Semi-analytical k=13 FEA

2


Slot Pole Combinations Optional slot-pole combinations for the proposed APMV machine

r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =

35 0866r s wP P kge ge

1 23f r sP nZ P P n= = plusmn =

75


Case Study on Four FEA Models Topology

Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76


No Load Condition Back EMF

0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)

612102 model 618162 model 624222 model 1224195 model

0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)


The back EMF waveforms of the four models are sinusoidal

Additional flux density harmonics are introduced in the proposed machines

77


Parametersrsquo effect on Performance

06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)

Flux Modulator Ratio k


201

Flux modulator pitch ratio k

06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)



Compared to the regular PMV machine gt20 back EMF improvement can be obtained by using the proposed topology

Pole ratio increase

The optimization of the flux modulator pitch ratio k could achieve significant back-EMF improvement

The optimal values of k for maximum back-EMF of the four models are different

For the topologies with 6 slots cogging torque varies greatly with the value of k while the cogging torque of the 1224195 case remains low



00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)



The optimization of k could achieve more than 20 higher torque capability for each case

The pitch ratio has significant influence on torque ripple

79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)

Auxiliary tooth width ratio

k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)

Magnet Thickness(mm)

Tooth width ratio Magnet thickness

The topology with 6 slot 12 auxiliary teeth 10 rotor pole pair 2 stator pole pair is chosen for further analysis

As k rises from 07 to 15 the optimal auxiliary tooth width ratio for maximum output torque gradually decreases

Increasing magnet thickness may result in torque reduction which is different from that of regular PM machines

80


Prototypes

Stator lamination Stator winding

PM rotor View of the prototype 81


Experimental Test Results

0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine

FEA predicted and measured line back-EMF

FEA predicted and measured torque-current waveforms

Comparison of weight and volume the prototype and regular PM machine

The experimental test results agree well with theoretical analysis and simulation study above

The torque density of the APMV prototype is 2Nmkg ie two times that of the regular PM machine

82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+

Regular PM machine Vernier PM machine00

05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)

The power factor of VPM machines with high pole ratio are much lower than that of regular PM machine

Regular PM Vernier PM

Power Factor of Vernier PM Machines

Pole ratio=11 83


Power Factor Analysis

Regular VPM machine with 11 pole ratio

There are almost only half magnets contributing to the flux per armature field pole pitch during one armature field pole

The other half magnets mainly produce flux leakage

The key method to improve power factor is that 1 increasing magnet flux linkage or 2 reducing inductance

84


Power Factor Improvement

Regular Vernier PM machine

Proposed PMV machine

The consequent pole is employed in the rotor and the Halbach array PMs in the stator slot opening are used to guide flux into the stator

This structure can reduce leakage flux

Parameters Value Unit Outer diameter 124 mm Stator inner diameter 744 mm Airgap length 05 mm Magnet thicknesss 3 mm SlotsPoles 1222 ndash Pole arc 09 ndash Slot depth 148 mm Slot opening width 136 mm Stack length 70 mm

Proposed PM machine

85



= +

Proposed machine Consequent pole Vernier PM machine

Flux reversal PM machine

Proposed machine

Regular vernier machine

The analysis results have shown that this machine could produce 956 larger back-EMF and 548 larger output torque

If the two machines had same torque density ie the current loading is smaller in the proposed machine its power factor is ~089


The proposed DSSA VPM machine has two stators and one rotor which is sandwiched by the two stators

The rotor employs tangential-excitation spoke-array magnets

Dual-Stator Spoke-Array(DSSA) Vernier PM machine

DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator

The inner stator tooth has half teeth pitch displacement compared to the outer stator tooth

Magnet Field of DSSA VPM Machines

-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)

Relative position angleslot pitch angleInner stator

Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O

Inner StatorOuter Stator

A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002

Outer statorInner stator

Time(ms)

Flux

link

age(

Wb)

15o

Relative position of two stators in the DSSA vernier PM machine

88



Rotor

Stator

The DSSA VPM machine can greatly improve the flux density with same magnet usage

The special structure heavily reduce magnet leakage flux

89


Reluctance Torque of DSSA VPM Machines

The spoke-array magnets introduce rotor anisotropy for DSSA VPM topology

The gamma angle varies from 0 to 30 degree the power factor would increase from 076 to 091with almost 2 torque improvement

0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()

Variation of torque and power factor vs gamma angle

Variation of reluctance torquemagnet torque vs gamma angle

90


Torque Density of DSSA VPM Machines

The back-EMF waveform of the regular VPM machine is more sinusoidal than that of regular PM machine

The torque per active machine volume of natural cooling totally-enclosed DSSA VPM machine can reach 66 kNmm3

Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)

Regular vernier DSSA Linear loading in out airgap

Acm 220 120

Linear loading in inner airgap Acm 100

Torque Nm 1156 2000 Power factor 066 091 Magnet volumecm3 8646 801 Torque pu 1 173 Torque density kNmm3 38 66

91


Inner Stator

Outer StatorRotorShaft

ReforcingRing

The support structure example of rotor and inner stator use cantilever structural model

The rotor support should be manufactured by non-magnetic material to reduce the magnet end flux leakage

Auxiliary Mechanical Structure

92


Prototype

93


Simulation value Measured value Torque Nm 2000 Speed 30 RMS line current A

236 246

Power factor 085 083 Efficiency 90 85

TABLE Comparison of Simulation and Measured

Performance Indexes

PrototypeMagnetic powder brake

Torque transducer Thermo detector

0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA


The DSSA VPM topology can greatly reduce the magnet flux leakage and all magnets contribute to the airgap flux density at same time The DSSA VPM topology exhibits high power factor

94


High torque density sinusoidal back EMF waveform and smooth torque waveform are inherently features of vernier PM machines

By introducing additional working flux density harmonic further improvement of the torque density can be obtained

Regular vernier PM machines always suffer from low power factor

The dual stator spoke array (DSSA) vernier PM machine can heavily reduce the leakage flux and improve the working flux density by specific design on the rotor and relative position of the two stators

Power factor of the DSSA vernier PM machine can reach a comparable value with that of the regular PM machines and its torque density is larger than that of the regular veriner PM machine

Vernier Machines ndash Summary

95



96

Flux modulation effect is found and developed and this may introduce significant influence on the electric machine and there are still many challenges to be overcome Low power factor It has been illustrated that the low power

factor is the common issue for flux modulation machines and lots of effort is going on this topic Some topologies have shown promising results but with either complex structure or low pole ratio (lower torque density) Reduction of Rotor losses The main field and rotor have

different mechanical speed and this introduces improvement of torque density and large rotor losses at same time


There are few ways to improve machine torque density Flux modulation is another way to offer higher specific torque and offer more freedom to work with It is found that flux modulation principle can be used to analyze

not only flux modulation machines but regular machines In other words regular machines could be regarded as special cases of flux modulation machines Vernier machines as one type of flux modulation machines

can produce high torque density sinusoidal back EMF and much lower torque ripple Some VPM topologies can greatly reduce the magnet flux

leakage boost power factor further improve torque density and greatly reduce machine volume and cost There are a lot more flux modulation machine topologies to be

discovered more opportunity to improve performance

HUST Private information

Summary Conclusions

97


1 D Li R Qu and T Lipo ldquoHigh power factor vernier permanent magnet machinesrdquo IEEE Trans Ind Appl vol 50 no 6 pp 3664-3674 NovDec 2014

2 D Li R Qu J Li L Wu and W Xu ldquoAnalysis of torque capability and quality in vernier permanent magnet machinesrdquo IEEE Trans Ind Appl vol 52 no 1 pp 125-135

3 D Li T Zou R Qu and D Jiang ldquoAnalysis of fractional-slot concentrated winding PM vernier machines with regular open-slot statorsrdquo IEEE Trans Ind Appl vol 54 no 2 pp 1320ndash1330 MarApr 2018

4 T Zou D Li R Qu J Li and D Jiang ldquoAnalysis of a dual-rotor toroidal-winding axial-flux vernier permanent magnet machine IEEE Trans Ind Appl vol 53 no 3 pp 1920-1930 MayJune 2017

5 T Zou D Li R Qu D Jiang and J Li ldquoAdvanced high torque density PM vernier machine with multiple working harmonicsrdquo IEEE Trans Ind Appl vol 53 no 6 pp 5295ndash5304 NovDec 2017

6 T Zou D Li R Qu and D Jiang ldquoPerformance Comparison of Surface and Spoke-Type Flux-Modulation Machines with Different Pole Ratiosrdquo IEEE Trans Magn vol 53 no 6 pp 7402605 June 2017

7 T Zou D Li C Chen R Qu and D Jiang ldquoA multiple working harmonic PM vernier machine with enhanced flux modulation effectrdquo IEEE Trans Magn accepted for publication 2018

8 X Ren D Li R Qu and T Zou ldquoA Brushless Dual-mechanical-port Dual-electrical-port Machine with Spoke Array Magnets in Flux Modulatorrdquo IEEE Trans Magn vol 53 no 11 pp 8110706 Nov 2017

9 K Xie D Li R Qu and Y Gao ldquoA Novel Permanent Magnet Vernier Machine With Halbach Array Magnets in Stator Slot Openingrdquo rdquo IEEE Trans Magn vol 53 no 6 pp 1-5 June 2017

Selected Reference


Center for Advanced Electrical Machines amp Drives Huazhong University of Science and Technology

Ronghaiquhusteducn


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Outline

High torque density (HTD) machines

- Introduction and Ways to achieve HTD


- Principle Features Topologies and family members

Vernier machines Topologies Analysis Design Prototypes


Conclusions

2


Introduction





Reduction gearbox









4



2e i e

PeT D LΩ

= prop

Direct-drive




Bulky and heavy















New technics

New materials

New topologies


6






Winding Potting

Auxiliary Heat Path


Direct Oil Cooling







7








8




Aver

age

torq

ue (N

m)



9


Theory

Realization

Instance



σLDTe2

2π

= BA=σ








10


Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Introduction





Reduction gearbox









4



2e i e

PeT D LΩ

= prop

Direct-drive




Bulky and heavy















New technics

New materials

New topologies


6






Winding Potting

Auxiliary Heat Path


Direct Oil Cooling







7








8




Aver

age

torq

ue (N

m)



9


Theory

Realization

Instance



σLDTe2

2π

= BA=σ








10


Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Reduction gearbox









4



2e i e

PeT D LΩ

= prop

Direct-drive




Bulky and heavy















New technics

New materials

New topologies


6






Winding Potting

Auxiliary Heat Path


Direct Oil Cooling







7








8




Aver

age

torq

ue (N

m)



9


Theory

Realization

Instance



σLDTe2

2π

= BA=σ








10


Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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2e i e

PeT D LΩ

= prop

Direct-drive




Bulky and heavy















New technics

New materials

New topologies


6






Winding Potting

Auxiliary Heat Path


Direct Oil Cooling







7








8




Aver

age

torq

ue (N

m)



9


Theory

Realization

Instance



σLDTe2

2π

= BA=σ








10


Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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New technics

New materials

New topologies


6






Winding Potting

Auxiliary Heat Path


Direct Oil Cooling







7








8




Aver

age

torq

ue (N

m)



9


Theory

Realization

Instance



σLDTe2

2π

= BA=σ








10


Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Winding Potting

Auxiliary Heat Path


Direct Oil Cooling







7








8




Aver

age

torq

ue (N

m)



9


Theory

Realization

Instance



σLDTe2

2π

= BA=σ








10


Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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8




Aver

age

torq

ue (N

m)



9


Theory

Realization

Instance



σLDTe2

2π

= BA=σ








10


Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Aver

age

torq

ue (N

m)



9


Theory

Realization

Instance



σLDTe2

2π

= BA=σ








10


Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Theory

Realization

Instance



σLDTe2

2π

= BA=σ








10


Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Liu Y Noe M 2016

R Fair 2012


Yubin Wang etc 2013



11




surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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surface area




12







13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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13




pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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pφa pφ φ=

pφ

pφpφ

pφ

a pNφ φ=










Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Magnet13

13

Winding13

13

Rotor Pole13

13

Stator Pole13

13

Shaft13

13

Frame13

13

13





16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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16



Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Stator


Magnets

Rotor




17


MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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MMF

Flux modulator

Flux density

Space PWM


0 40 80 120 160 200 240 280 320 360-05

-04

-03

-02

-01

00

01

02

03

04

05

Rotor position(deg)

-5 0 5 10 15 20 25 300

01

02

03

04

Order

Flux

den

sity

(T)

0 40 80 120 160 200 240 280 320 360-10

-08

-06

-04

-02

00

02

04

06

08

10

Rotor position(deg)

-5 0 5 10 15 20 25 300

05

1

15

Order

Flux modulator

Flux

den

sity

(T)

Flux

den

sity

(T)

Flux

den

sity

(T)

18



PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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PrgTorqueDensity AB


Bg magnetic loading




19


l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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l hT Tβ= plusmn

hT



Low speed PM rotor



MMF

Flux modulator


Pe=11

Pa=1

Pf=12


= sgn

0

sgn

(1 sgn )

re fe e

ra a f a

r re e a a

ee a

a

ef a

a

PP

T TPT TP

PT TP

Ω minusΩΩ= minus


Features


20







(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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(SFM)


(SEF)


(SAF)


Features



Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Stator


s

Rotor

Flux modulator


Magnets Magnets



Vernier PM machine


Pf=Z

Pf=kZ


Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


22


Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Magnets


Armature winding


winding





MagnetsStator

Winding

Stator Magnets

Winding


Stator

Flux modulatorRotor

Magnets

Stationary magnet

23



Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Stator Magnets

Winding

2Pe=Z

StatorMagnets

ArmatureWinding

Stator Magnets

ArmatureWinding

DC-Field Winding


StatorMagnets



Stator Magnets

ArmatureWinding

DC Field Winding

StatorMagnets


DC-bias

Time




the magnets


Stator

Magnets

ArmatureWinding


the magnets





A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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A

B C

Armature winding







Excitation winding

A

B C

CA

B

Armature winding

Pe=Pa Pf=2Pa Pf=Zr


Pf=Pe+-Pa Pf=Zr+-Zs

25




+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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+

+- -


PM rotor





26


Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Winding A

Winding A1

Winding A


1

A e f

A e

P P PP P

= minus=



27


1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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1

1

1 1 1

sgn

(1 sgn )

sgn

mma A

A

mf A

A

m ma ma

m f A

A f m

A m

m m m f f f

A A A A A A

PT TP

PT TP

T T T

PP

f P f Pf P f P

=

= minus +

= +

Ω minusΩ= minus

Ω minusΩΩ = Ω

= Ω = Ω= Ω = Ω


Speed relationship

Torque relationship


Regular PM machine


dual ports


dual ports



Pe=PA1 Pe=PA1

Winding A1

Pole pair PA1


28



Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Converter

fΩrΩ

Grid

Flux modulator

PM rotor

Winding A

Winding A1







Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Winding theory


Basic theory


30



c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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c135

135 0 r

( ) cos( )

4 sin( ) cos( )2

s ci e si

rm e s e

i

F t F iP i t

B h i iP i t

θ θ ω


=

=

= minus

= minus

sum

sum

αmh

MMF Fc

0

rm

r

B hmicro micro

0

rm

r

B hmicro micro

minus

Magnets

Magnet

Stator yoke

0

r mc

r

B hFmicro micro

=0

mm

r m

hRAmicro micro

=0

gr g

gRAmicro micro

=

hm

Rsy

Rry Rotor yoke

g2Rg

Fc

2Rm

2Rg

2Rm

Fc

Rsy

Rry

Airgap

0o 180o


31




10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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10

135 1351

135

( )= ( ) ( )cos( ) cos[( ) ( ) ]

2cos[( ) ( ) ]

2

g s s s


i ici

e f s e fi


F iP P i t


θ ω ω= =

=


Λ+ + minus +

sum sumsum





32


13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j a sj

b s j a sj

c s j a sj

sj wj

a

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum



0


ψ θ θ θ= int


33


2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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2

1350

10

2

1350

0

[ ( ) ( ) ]

sin( ) ( ) sin[( ) ]2

[ ( ) ( ) ]

si




e j


i N i t i N i t


i N

π

π

θ θ θ π

ω ω ω ω ω ω

θ θ θ π

ω

=

= = plusmn

=

= minus =


= minus =

Λ

sumint

sum sum

sumint

1

2

1350

10

2 2n( ) ( ) sin[( ) sgn ]3 2 3

[ ( ) ( ) ]

2 2sin( ) ( ) sin[( ) sgn ]3 2 3



e j e e f j e fPfj

i t j i N i t j


i N i t j i N i t j

π


θ θ θ π


= = plusmn

=

=


= minus =


sum sum

sumint


sum sum

Back EMF Formula

34



[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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[ ( ) ( ) ( ) ( ) ( ) ( )] [ ]sgn

e

ae a a b b c c e f

e

a


PP

+= + + Ω minus Ω

1 1 132

eg stk s max c w

a

P r l N I F kP

Λ 1 1 132


3=2


ZT r l N I F kP

Λ

Magnets


Armature winding

Phase coil Stator

Magnet

Flux


Magnet

PM rotor PM rotor

B1 B2

Laxial


Winding

Magnets

Rotor

Vernier PM machine



2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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2

1PF=1 ( )s

m

L Iψ

+


2

6 1 2

1 11

1 0

1PF15

11 ( )

2e a

end slotj

j k g stk

p p c

L LN I Ir l

N F NN

π= plusmn

=+

+sum+

Λ+

Λ

2

6 1 20

1 1 1

1PF15

21 ( )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sumΛ

+Λ

2

6 1 2

1 1

1PF15

1 (1 )

end slotj

j k g stk

c

L LN I Ir l

F Nπ= plusmn

=+

+sum+

Regular PM machine



36






No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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No load flux





37



1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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1 1 11 2 2 2 2 2 3 2 2

1 1 14 2 2 5 2 2 6 2 2

( ) ( ) ( )

5sin(( ) ) sin(( ) ) sin( ) )

2 2 23 5 3

sin(( ) ) sin(( ) ) sin(( ) )2 2 2

g s s sr s

s s s

s s s

B t F t



θ θ θ

θ θ θ

θ θ θ

= Λ





Rotor Stator

PMs Windings

38



1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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1 1

1 23456

i jj

ZP k PP

i j i j

= plusmn

= ne

（）




39


Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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Winding connection

determination

1

67

2

34

5

8

910

11

12

30o


14710

25811

36912

A

B

C


16=Z2+Z12

120O

14710

25811

36912

A

B

C


20=3Z12-Z2

120O

14710

36912

A

B

C

8=3Z12-Z2


120O

14710

36912

A

B

C

28=3Z12+Z2


120O



(a) (b)

(c) (d)

40



1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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1

1

SPP=2

2

a

aa

ZmP

ZP

τ

=


41











SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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SPPge1 05ltSPPlt1


42


Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Winding type

+A

-A+B

-B

-C

-C

-C

-C

-A

+A

+B

-B




613

614 Type 1

(Nonoverlapping)


614 Type 3 (Full


m 8mm


8mm


78mm


105

Rated current 32A 0 1 2 3 4 5 6 7 80

02

04

06

08

1

12

14


Order

Mag

nitu

de(V

)

43



0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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0 50 100 150 200 250 300 350-40

-30

-20

-10

0

10

20

30

40


Back

EM

F(V)


0

5

10

15

20

25

30

35


Order

Back

EM

F(V)

200 250 300 350 400 450 500 550 60010

20

30

40

50

60

70

80

90

100


Stack length(mm)

Torq

ue(N

m)

0 20 40 60 80 100 120 140-10

0

10

20

30

40

50

60

70

80

90


Q-axis current(A)

Torq

ue(N

m)




44




1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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1 21 11 3 1 2 2

0

0 2 2 2

3( ) [ sin( ) sin( )][ cos((2 2 ) 2 )

2 2 2cos(2 2 )]

s rg s c s c s s

s r s

Z ZgB t F F Z Z Z t

Z Z t

θ θ θ θmicro

θ

Λ Λ= + plusmn Ω

minusΛ Λ minus Ω


45


14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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14710

25811

36912

A

B

C

4=Z2-Z12

120O 17

511

39

+A

+B

+C

14=2Z2-Z12

60O

410

28

612

+A

+C

+B1210 FSPM machine

2 2 1Z kt= plusmn




46







47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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47



+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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+A

A-

+A

A-

+B

+B

-B-B+C +C

-C-C

Stator

Rotor

NSNSNSNSN N

Rotor PM MMF

Airgap Permeance


S

Stator

Rotor




48









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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幻灯片编号 98

幻灯片编号 99









3 1 23(Z )

=a

e a

e

a

Z k kGCD PZ P P

PPoleRatioP

= = +

=


q

le

lt le

pole ratio 5123q

ge =


q

lt lt

lt lt


49



r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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r sZ P P= plusmn ( 1 23) ( )

s r

s r s

P P mk kG C D P P P

plusmn = =plusmn

50


Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Back-EMF

2

0


π


0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



13 5

13 5

13 5

( ) cos( )

2( ) cos( )32( ) cos( )3

2

a s j s sj

b s j s sj

c s j s sj

sj wj

s

N N jP

N N jP j

N N jP j

NN kj P

θ θ

θ θ π

θ θ π

π

=

=

=

= = minus = + =

sumsumsum

Win

ding

Fun

ctio

n Back EMF Analysis




51









0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40 45 50

Harmonics order0

01

02

03

04

05

06

07

Flux

den

sity

(T)

Harmonics

Working harmonics

Field Analysis


52


0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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0 5 10 15 20 25 30 35 40 45 500

01

02

03

04

05

06

07

Flux

den

sity

(T) Working

harmonics

Harmonics

Harmonics order1 5 10 15 20 25 30 35 40

Harmonics order0

01

02

03

04

05

06

07

08

09

1

Win

ding

func

tion

pu



0 2 4 6 8 10 12

-600

-400

-200

0

200

400

600

Back

-EM

F(V)


Time(ms)


57111317191 23aiP =







25471 4923 71eiP =

53



0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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0

10

+2( )

+2



N N NTRI vernier i

N N N

minus +

minus +

ΛΛ=

ΛΛ

（ + ）

（ + ）

16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum

1(regular) iNTRI i

N=




16 1=123


avg ei kk

T FTRI i tT F

ω= plusmn

= sum


1 5 7 11 13 17 19 23 25 29Harmonics index

0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 290

02

04

06

08

1

12

14


Harmonics index

Tor

que

ripp

le In

dex


0

02

04

06

08

1

12

14

Tor

que

ripp

le In

dex

1 5 7 11 13 17 19 23 25 29Harmonics index

54


0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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0 40 80 120 160 200 240 280 320 360-80

-60

-40

-20

0

20

40

60

80

Measured 2D FEA


Line

bac

k EM

F(V

)


Torque transducer

Gear box Prototype


VPM prototype

Commercial motor


160 150


0 1 2 3 4 5 6 7 8 9

0

5

10

15

20

2D FEA Measured

Input current(A)

Tor

que(

Nm

)

Long end winding

55



56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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56













Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Long end windings


57




q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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q

le

lt le


=


q

lt lt

lt lt



58



0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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0 50 100 150 200 250 300 350

-300

-200

-100

0

100

200

300

back

-EM

F (V

)

Elec Angle (degree)


3 123(Z )

=10866 ( 1)2 6r

s

r s

Ps

Z k kGCD PZ P P

ZkP

= = + gt hArr lt lt






1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24


241010 24168 24195 24204

1

2

3

4

5678

910

11

12

13

14

15

16

1718 19 20

2122

23

24

60


Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Back-EMF Comparison





-300

-200

-100

0

100

200

300

back

-EM

F (k

V)

Elec Angle (degree)

24168 24195 24204 241010

Pole Ratio




61



0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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0 1 2 3 40

30

60

90

120

24168 24195 24204 2410

Torq

ue (N

m)

Time (ms)

Pole Ratio

0 20 40 60 80 1000

200

400

600

800

24168 24195 24204 241010

Ave

rage

Tor

que

(Nm

)

Phase current (A)

Pole Ratio

0 20 40 60 80 10000

02

04

06

08

10

24168 24195 24204 241010

Pow

er F

acto

r

Phase current (A)


62







Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Pr=8 Pr=7 Pr=5


Slot


1

12

5 Open slot 7 5 57




5 8 Open slot 4 8 2


0 2 4 6 8 10 12 140

1

2

3

4

times10(-4)

ΛZ

Airg

ap P

erm

eanc

e

Order


Λ0


64


0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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0

8

16

24

Torq

ue (N

m)


1284 1275 1257PR=2 PR=14 PR=07


0

1

2

3

4

5

PR=07PR=14PR=2


12571275

times10(-4)

k conv

+kve

r


1284





65




s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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s

Z 1 1q = = 2mP 4 2s

Zq = = 1232mP



66



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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幻灯片编号 99



Stator core

WindingMagnets




67




(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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(a) (b)

(c) (d)

(a) (b)



68




Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Symmetrical Axis



Stator yoke

N N N

N N NS S

S S

Rotor yoke

Rotor yoke

ghm

ws wp(r)

hys

hyr

hss

Lt

ws

wp(r)

Slot

Slot

Ri

Ro

N

N

S

S

N

Ri

Ro

pα

θs

θs

Top view



69


Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Quasi-3D and 3D FEA





70


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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幻灯片编号 99


Prototypes


PM rotor Prototype

71


Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Experimental Test

Test bench

Oscilloscope

Torque transducer

Prototype

Dyno machine

Current probe




72




= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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= 2fk Pτ π

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

k=13θ=30degtimesk

A+

A-B+

B-

C+

C-

A+

A-

B-

B+C-

C+

Rotor

Magnets

30o

Stator

Flux modulator





Z=6 Pf=12 Ps=2 Pr=10

73



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order Pf

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08

Rotor positionmm

Order

Flux

den

sity

TFl

ux d

ensi

tyT

Pf-Pr

Pf



0 20 40 60 80 100 120 140 160 180 2001

2

3

4x 10

-5


0 2 4 6 8 10 12 14 160

1

2

3x 10

-5

Order

Airg

ap p

erm

eanc

eAi

rgap

per

mea

nce

Pf05Pf

0 50 100 150 200 250-2

-1

0

1

2

0 2 4 6 8 10 12 14 16 18 200

02

04

06

08Rotor positionmm

Order

Pf-Pr Pr-Pf2 Pr+Pf2

Flux

den

sity

TFl

ux d

ensi

tyT


0

10

20

30

2014104 8

Bac

k-EM

F(V)

Harmonic Order


2



r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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r rcom

f r s

P PPRP P P

= =minus

1r

addf

r ff

PPRnP P

n

=minusminus

3 123(Z )s

Z k kGCD P

= =



75



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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幻灯片编号 99



Z=6 Pf =12 Pr =10 Ps =2 Z=6 Pf =18 Pr =16 Ps =2

Z=6 Pf =24 Pr =22 Ps =2 Z=12 Pf =24 Pr =19 Ps =5

Tooth width

Flux modulatorpitch

PM thickness

76



0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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0 60 120 180 240 300 360

-60-40-20

0204060

Phas

e B

ack-

EMF(

V)

ElecAngle(Degree)


0 60 120 180-15

-10

-05

00

05

10

15

Airg

ap fl

ux d

ensi

ty(T

)

ElecAngle(Degree)


Airgap Flux Density

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

Phas

e B

ack-

EMF(

V)

Harmonic


0 2 4 6 8 10 12 14 16 18 20 22 2400

04

08

12

Harmonic

Airg

ap fl

ux d

ensi

ty(V

)




77



06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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06 07 08 09 10 11 12 13 14 15 160

10

20

30

40

50

60

415

343

31

Ph

ase

Bac

k-EM

F(V)



201


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Cog

ging

Tor

que(

Nm

)




Pole ratio increase






00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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幻灯片编号 99



00 02 04 06 08 10

12

14

16

18

20

22

00 02 04 06 08 10

12

14

16

18

20

22

Time(Period)

Torq

ue(N

m)

Time(Period)

612102 k=1 618162 k=1 624222 k=1 1224195 k=1

612102 k=126 618162 k=114 624222 k=108 1224195 k=134


06 07 08 09 10 11 12 13 14 15 16

0

1

2

3

Toru

qe ri

pple

(Nm

)





79



030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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030 035 040 045 050 055 0600

4

8

12

16

20

Torq

ue(N

m)


k=070 k=086 k=102 k=118 k=134 k=150

05 10 15 20 25 30 35 40 458

10

12

14

16

18

20

22

612102 k=126 618162 k=114 624222 k=108 1224195 k=134

Torq

ue(N

m)






80


Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Prototypes





0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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0 1 2 3 4 5 6-300

-200

-100

0

100

200

300

FEAMeasured

Time ms

Back

EM

F V

1 2 3 4 5 6 72

4

6

8

10

12

14

16

18

20

22

FEAMeasured

Current A

Torq

ueN

m

21Nm104kg

14Nm1435kg

APMV machine

RegularPM machine






82


Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Armature only

Magnet only

Flux linkageamp

Inductance

2

1

1 ( )s

m

PowerFactorL Iψ

=

+


05

10

15

20

25

Sync

hron

ous

Indu

ctan

ce(m

H)




Pole ratio=11 83







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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幻灯片编号 86

幻灯片编号 87

幻灯片编号 88

幻灯片编号 89

幻灯片编号 90

幻灯片编号 91

幻灯片编号 92

幻灯片编号 93

幻灯片编号 94

幻灯片编号 95

幻灯片编号 96

幻灯片编号 97

幻灯片编号 98

幻灯片编号 99







84








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

幻灯片编号 3

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幻灯片编号 92

幻灯片编号 93

幻灯片编号 94

幻灯片编号 95

幻灯片编号 96

幻灯片编号 97

幻灯片编号 98

幻灯片编号 99








Proposed PM machine

85



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

幻灯片编号 3

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幻灯片编号 92

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幻灯片编号 94

幻灯片编号 95

幻灯片编号 96

幻灯片编号 97

幻灯片编号 98

幻灯片编号 99



= +



Proposed machine








DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

幻灯片编号 3

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幻灯片编号 94

幻灯片编号 95

幻灯片编号 96

幻灯片编号 97

幻灯片编号 98

幻灯片编号 99





DSSA VPM Topology

A+

-C

A-

-C

-C

-C

B+

B-

+B

B-

A+

A-

+A

+A

-C-C

+B

-A

+C

-B

-B

MagnetWinding

Stator Rotor

+C

-A

+B

87


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

幻灯片编号 3

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幻灯片编号 99


Outer Stator

Magnet

Winding

Innerstator



-05 -04 -03 -02 -01 00 01 02 03 04 0500

02

04

06

08

10

Back

-EM

F(p

u)


Outer stator

Aouter+

Aouter+

A+ A+

Aouter-

Aouter-

A-A-

mioα

1

2

34

5

6 7

8

910

11

12

12

34

5

6 78

910

11

12

O


A A1 A2

B B1 B2

C C1 C2

0 10 20 30 40 50 60 70 80 90-002

-0015

-001

-0005

0

0005

001

0015

002


Time(ms)

Flux

link

age(

Wb)

15o


88



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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幻灯片编号 95

幻灯片编号 96

幻灯片编号 97

幻灯片编号 98

幻灯片编号 99



Rotor

Stator



89





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

幻灯片编号 3

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幻灯片编号 95

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幻灯片编号 97

幻灯片编号 98

幻灯片编号 99





0 5 10 15 20 25 30980

990

1000

1010

1020

1030

0 5 10 15 20 25 3007

075

08

085

09

095

0 5 10 15 20 25 3007

075

08

085

09

095

Power FactorTorque

gamma angle(deg)

Power FactorT

orqu

e(N

m)

gamma angle(deg)0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

Rat

io o

f rel

ucta

nce

torq

ue

to m

agne

t tor

que

()



90





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

幻灯片编号 3

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幻灯片编号 95

幻灯片编号 96

幻灯片编号 97

幻灯片编号 98

幻灯片编号 99





Back-EMF waveform

Time(ms)

Bac

k-E

MF

(V)


Acm 220 120



91


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

幻灯片编号 3

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幻灯片编号 95

幻灯片编号 96

幻灯片编号 97

幻灯片编号 98

幻灯片编号 99


Inner Stator


ReforcingRing




92


Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

幻灯片编号 3

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Prototype

93



236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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236 246



Performance Indexes



0 5 10 15 20 25 300

500

1000

1500

2000

2500

Outp

ut T

orqu

e(Nm

)Phase Current (A)

Measured 2-D FEA



94








95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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95



96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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96











Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


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Summary Conclusions

97











Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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Selected Reference



Ronghaiquhusteducn


幻灯片编号 2

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