Permanent Magnet

Synchronous Motor (PMSM)

Introduction

Permanent Magnet (PM) Motor

Characterized by permanent

magnets on rotor

Known for its simplicity and

low maintenance

No copper loss on rotor

High efficiency

Exploded View of a PM Motor

J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines

2nd Edition, p. 44, Motor Design Books LLC, 2010.

Inner Rotor Possibilities (1)

surface radial

magnet

surface parallel

magnet breadloaf

magnet ring

magnet

Inner Rotor Possibilities (2)

(e) IPM rotor with 2 magnets/pole in a

V-shaped flux concentrating arrangement

MS-TECH Japan

Toyota Prius

Rotor Flux Distribution of IPMs

Toyota Prius Hybrid Electric Vehicle (HEV)

1. Four cylinder combustion engine;

2. Generator/starter;

3. Electric Motor;

4. Power split device (PSD)

2

3

J. F. Gieras, Permanent Magnet Motor Technology -

Design and Applications, 3rd Edition, p. 282, CRC

Press, 2010.

J. R. Hendershot and T. J. E. Miller,

Design of Brushless Permanent Magnet

Machines 2nd Edition, p. 34, Motor

Design Books LLC, 2010.

Segmented Magnets in Large PM Rotor

J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines

2nd Edition, p. 94 & 602, Motor Design Books LLC, 2010.

Rotor Skew

stepped magnet

Magnetization Profile (1)

parallel magnetization radial magnetization

radial sine magnetization sine angle or sine direction

magnetization

most popular

Magnetization Profile (2)

Flux of a 8 pole machine at no load

radial magnetization

air gap flux density profile versus angle

8d

d 45 90 135 180

Magnetization Profile (3)

radial magnetization

parallel magnetization

Flux in 2 Pole Machine at no load

2d

2d

d

d

Magnetization Profile (4)

, g rotorB

mB

mB

22

PM

PM

2

PM

22

PM

de2PM

radial magnetization

parallel magnetization

, g rotorBmB

22

PM

PM

2

PM

22

PM

de2PM

PM embrace: PMemb

electrical angle

PM

Halbach Array (1)

R. Krishnan, Permanent Magnet Synchronous and Brushless DC Motor Drives, p. 25-30,

CRC press, 2010.

Halbach Array (2)

FEA

Halbach Array (3) Airgap Flux Density

Rotor is outside

Permanent Magnet

Synchronous Motor (PMSM)

Design

Part 1 General Considerations

Stator Volume and Size

0

2

VT

lD

The unit for D and L is inch.

3

0 4 ~ 5 in / (ft lb) for 10hp or more (water cooled)V

Typically

3

0 8 ~ 9 in / (ft lb) for 10hp or less (air cooled)V

If we design D=L, we have the stator bore (inner)

diameter estimated

3

1

0 )(TVDestimated

We can pick up D close to Destimated.

m

outPT

Stator Core Design

,= (1)

g pkcorecore

c c

DBB

d l Pd

, (2)

s g pktoothtooth

s s

BB

t l t

,0

( )

tooth g ae i ae g pk sl B rd B l

,

/

0

/2

,0

,

( )

2 cos( )

2

core gap per half pole pitch

P

g a is a

g pk ae ae

g pk

l B r d

Dl B d

P

DlB

P

Take 0.5 , 0.8s s core tootht B B

P

Ddc

6.1

Effect of Pole Number on Yoke Flux Density

J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines

2nd Edition, p. 106, Motor Design Books LLC, 2010.

Finite Element Analysis

with the same dc

Number of Turns per Coil

pkgaepkgaerated NfNfV ,,,44.42

P

DlB pkgpk

,2

1.1/ awa NkN

sdpw kkkk

where

DlBqkf

CVN

pkgwe

rated

c

,

,

22

1.1

Na is the number of series turns per phase of armature winding

C is the number of parallel circuits of armature winding

CPqNN ca /

Consider leakage flux

Stator Slot Design

S

Ds

3 7s s st d t

0.4 0.6s s st

0 (0.1 ~ 0.5)s sb b

General Consideration

sdst

s

0sb0sd

1sd

Define s s sb t

0 (0.1 ~ 0.5)s sd b

1 (0.1 ~ 0.5)s sd b

Stator Conductor Size

Stator current density

a

rateda

coppersS

CIJ

/,,

where Sa is stator (armature) conductor cross section

area and can be determined from the above formula

together with:

2

,

2 A/cm 800400A/cm :cooled-Air coppersJ

coppers

rateda

aJ

CIS

,

, /

Permanent Magnets

Samarian Cobalt (SmCo)

Operating temperature of up to 350C

2nd strongest rare earth magnet

Neodymium Iron Boron (NdFeB)

Operating temperature of up to 150C

Strongest rare earth magnet

From Yeadon Handbook of Small Electric Motors

Permanent Magnet Properties

Rotor Peripheral Speed

The maximum allowable peripheral speed of the rotor is a central consideration in

machine design. With present-day steel alloys, rotor peripheral speeds of 50,000

ft/min (or about 250 m/s) represent the design limit.

1 ft/min = 0.0051 m/s

Motor Losses (1)

Copper loss

Typical

Stray losses

Electrical phenomenon such as skin and proximity

effect

RIPCu2

Motor Losses (2)

Core (Iron) Loss

Hysteresis loss

Eddy Current loss

Mechanical loss

Windage loss

Friction loss

2/32 )()( BfBffBP ecn

hIron

Finite Element Analysis

Fundamental harmonic

J. R. Hendershot and T. J. E. Miller, Design of Brushless Permanent Magnet Machines

2nd Edition, p. 174-175, Motor Design Books LLC, 2010.

Part 2 Surface Mount Round

Rotor Multi-Pole PM Motor

Design

Magnetic Circuit Analysis

For a multi-pole surface mount rotor

md

Poles

aD

D

2 2 0g m mH g H d 0 0g m mgB H d

g

0

m m l m

m g

d B k A

g H A

g g gB A

m m mB A

g l mk

: Leakage Coefficientlk

Working Point for Permanent Magnetics (1)

B

0H0 cH

rB

)( cc

r HHH

BB HHH

H

BBH c

c

r )(

max

( )To get (BH) 0 ,

2 2

r cm m

BH B HB H

H

0 mRH

mRB

Maximum Energy Point

Working Point for Permanent Magnetics (2)

Load Line:

0

0

gmm m

l m

c m

AdB H

g k A

P H

1 1.2rm

Pc is called permeance coefficient

0

/

/

g g gm m mc

m l m l m m g m

A A gB dP

H g k A k A d

R

R

P

P

Define: (1 )m m r m m cB B H H

0.6 0.9m Typically pick up:

0

rrm

c

B

H

0 1

m mc rm

m m

BP

H

Airgap Magnetic Field from PM Rotor

/2 /2

/2 /2

2cos( ) ( )cos( )

2

sin4 2

PM PM

PM PMrh m ae ae m ae ae

PM

m

B B h d B h d

h

Bh

,

1,3,5...

cos( ) cos( )2

g rotor Rh

h

Rh rh de rh d

B B

PB B h B h

sin2

PMphk h

pitch factor for the

hth harmonic

, g rotorB

mB

mB

22

PM

PM

2

PM

22

PM

de2PM

2de d

P

2

PM

PM embrace: PMemb

electrical angle

Phasor Diagram

V

AE

ASjX I

full-load pull out

Typically, design cos 1 at full-load for PMSM.

Need to specify torque angle, if sin 1/3 ( =19.47 ),

T (1 / 3) .T

, , ,

, , ,

cos 0.94

sin 0.33

g pk r pk r pk

a pk r pk r pk

B B B

B B B

netB

RB

SB

,

4sin

2

PMr pk mB B

Air Gap Size and PM Thickness

Initial total effective air gap size:

0, ,

41.5 2

a

a pk A rated

total

NB I

g P

' ' /ctotal total total m rm

g k g g g d

0,

,

4 1.5 2atotal A rated

a pk

Ng I

B P

From:

From:

can obtain and mg d

1

mc rm

m

P

Carters coefficient

m l mc mg

g

d k AP r

g A

totalg

sdst

s

0sb0sd

1sd

Effective Air Gap

'total c totalg k gwhere the Carters coefficient

2

0 0 0

0

2 'atan ln 1

2 ' 2 '

sc

s s total ss

total s total

k

b b g b

g b g

2

0

05 '

sc

ss

total s

kb

g b

approximately

Rotor Sizing

Total rotor diameter, including magnet

Rotor inner diameter

gDDr 2

2i r mD D d

Part 3 Two Pole Super High

Speed PM Motor with Magnet

Inserted in Rotor Shaft

Prototype

Rotor is assembled by

heating and cooling.

Rotor is welded and

well balanced after

assembly.

Air Gap Size

For a 2-pole PM rotor 2 0eff g m rg H H D

02 0eff m m rg B H D

0

/ 2r mc

eff m

D BP

g H

S

rDeffg

2 2

rD Dg

( )g mA A

1 1 1( ) (1 )

2 2 2

r rc c

c rm rm

D D Dk k

P

Define: (1 )m m r m m cB B H H

0.6 0.9m Typically pick up: 0 1

m mc rm

m m

BP

H

1 1c

rc

c

c rm

kD D

kk

P

( )2 2

r reff c

rm rm

D Dg k g

2

rD Dg

Carters coefficient

N

totalg

sdst

s

0sb0sd

1sd

Effective Air Gap

'total c totalg k g

where the Carters coefficient

2

0 0 0

0

2 'atan ln 1

2 ' 2 '

sc

s s total ss

total s total

k

b b g b

g b g

2

0

05 '

sc

ss

total s

kb

g b

approximately

, '2 2

r rtotal eff total

rm rm

D Dg g g g

Example - Specifications

Design a 2kW, 100krpm, NdFeB-38 PMSM, 2 pole

36 V terminal voltage, Y connected, 90% efficiency.