a novel power-train using coaxial magnetic gear

7/21/2019 A Novel Power-train Using Coaxial Magnetic Gear

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Abstract—This paper proposes a novel power-train for power-

split hybrid electric vehicles (HEVs). The key is to integrate two

permanent magnet motor/generators (M/Gs) together with a

coaxial magnetic gear (CMG). By designing the modulating ring

of the CMG to be rotatable, this integrated machine can achieve

both power splitting and mixing, and therefore, can seamlessly

match the vehicle road load to the engine optimal operating

region. With the one-side-in and one-side-out structure and the

non-contact transmission of the CMG, all the drawbacks aroused

by the mechanical gears and chain existing in the traditional

power-train system can be overcome. Moreover, the proposed

power-train possesses the merits of small size and light weight,

which are vitally important for extending the full-electric drive

range of HEVs. The working principle and the design details are

elaborated. By using the finite element method, the

electromagnetic characteristics are analyzed. Finally, system

modeling and simulation are conducted to evaluate the proposed

system.

Index Terms—hybrid electric vehicle, power-train, coaxial

magnetic gear, power-split, Halbach array.

I. I NTRODUCTION

According to the types of the power-train, hybrid electric

vehicles (HEVs) can be generally classified as series HEVs,

parallel HEVs and power-split HEVs, in which the power-split

HEVs combine the benefits of both the parallel types and the

series types, hence offering the merits of ultralow emissions

and high fuel economy [1]-[2]. The power-train of power-split

HEVs is also termed as electronic-continuously variable

transmission (E-CVT) system, which was firstly adopted by

Toyota Prius in 1997 [3]. Then, several derivatives such as the

GM-Allison compound E-CVT, the Timken compound split

E-CVT and the Renault compound split E-CVT were

introduced [4]-[5].

Fig. 1 depicts the basic architecture of the power-train ofToyota Prius. It mainly consists of a planetary gear set, two

electric motor/generators (M/Gs) and two power electronic

inverters. The engine shaft is connected to the planet carrier,

and the rotor shafts of the two M/Gs are attached to the sun

gear and the ring gear, respectively. The ring gear is connected

to the final driveline through a silent chain and a counter gear

to drive the wheels. By controlling the switching modes of the

inverters, multiple power flows among the engine, the M/Gs

and the battery can be achieved. Thus, this power-train can

seamlessly match the vehicle road load to the engine optimal

operating region. However, the reliance on mechanical gears

(including the planetary gear set and the counter gear) and the

silent chain inevitably causes the drawbacks of transmission

loss, gear noise and regular lubrication. In order to overcome

these shortcomings, the combination of two concentrically

arranged machines was proposed to realize power splitting and

mixing for HEVs [6]-[8]. Unfortunately, slip rings and carbon

brushes have to be equipped to inject/withdraw currentsinto/from the rotating armature windings. With no doubt, this

will degrade the reliability of the whole system.

Fig. 1. Architecture of power-train of Toyota Prius

Recently, a high performance coaxial magnetic gear (CMG)

has been proposed [9]-[11]. It can provide non-contact torque

transmission and speed variation using the modulation effectof permanent magnet (PM) fields. Since all the PMs are

involved to transmit torque, the CMG can offer as the torque

density as high as its mechanical counterpart. Thus, it has

promising industrial applications, such as EV drives [12] and

wind power generation [13]. The purpose of this paper is to

develop a novel power-train for power-split HEVs, in which

the CMG is adopted to supersede the mechanical planetary

gear set. By integrating the two PM M/Gs together with the

CMG, the one-side-in and one-side-out mechanical structure

can be achieved so as to eliminate the silent chain and the

A Novel Power-train Using Coaxial Magnetic

Gear for Power-split Hybrid Electric Vehicles

Linni Jian

1, 2

, Guoqing Xu

1, 2

, Yuanyuan Wu

1, 2

, Zhou Cheng

1, 2, 3

, Jianjian Song

1, 2

1 Shenzhen Institutes of Advanced Technology, Chinese Academy of Science, Shenzhen, China2 The Chinese University of Hong Kong, Hong Kong, China

3 Wuhan University of Technology, Wuhan, China

E-mail: [email protected]



counter gear employed in the traditional power-train. Thus, the

aforementioned drawbacks aroused by the mechanical

planetary gear set can be overcome. Moreover, due to the high

torque density of PM machines and the high extent of

integration, the proposed power-train possesses the merits ofsmall size and light weight, which are vitally important for

extending the full-electric drive range of HEVs.

II. SYSTEM CONFIGURATION AND OPERATING PRINCIPLE

Fig. 2 shows the architecture of the proposed power-train.

The key is to integrate the two M/Gs into a CMG. PMs are

mounted on both the inside and outside surfaces of the rotor of

M/G1, which also serves as the inner rotor of the CMG.

Similarly, PMs are mounted on both the inside and outside

surfaces of the rotor of M/G2, which also serves as the outer

rotor of the CMG. The stator of M/G1 is deployed in the inner

bore of the CMG and the stator of M/G2 is located at the periphery of the CMG.

The engine shaft is connected to the modulating ring of the

CMG, and the rotor shaft of the M/G2 is attached to the final

driveline. The working principle of the CMG lies on the

magnetic field modulation of the modulating ring [10]. This

modulating ring consists of several ferromagnetic segments

which are symmetrically deployed in the airspace between its

inner rotor and outer rotor. By defining p1 and p2 as the pole-

pair numbers of the inner and outer rotors of the CMG,

respectively, and n s as the number of ferromagnetic segments

on the modulation ring, the CMG can achieve stable torque

transmission when they satisfy the following relationship:

21 p pn s += (1)

When the modulating ring is fabricated as a stationarycomponent, the CMG can offer fixed-ratio variable speed

transmission, and the corresponding speed relationship is

given by:

22

1

21 ω ω ω r G

p

p−=−= (2)

where ω1, ω2 are the rotational speeds of the outer rotor and

inner rotor respectively, Gr is the so-called gear ratio, and the

minus sign indicates that the two rotors rotate in opposite

directions.

In order to achieve multi-port power flow distribution,

herein, the modulating ring is purposely designed as another

rotational component. The corresponding speed relationship is

governed by:

( ) 01 321 =+−+ ω ω ω r r GG (3)

where ω3 is the rotational speed of the modulating ring.

Without considering the power losses occurred in the CMG, it

yields:

0332211 =++ ω ω ω T T T (4)

(a) (b)

(c)

Fig. 2. Proposed power-train. (a) Architecture. (b) Cross-section of integrated machine. (c) Constitution of integrated machine.



0321 =++ T T T (5)

where T 1, T 2 and T 3 are the developed magnetic torques on the

inner rotor, the outer rotor and the modulating ring,

respectively.

Equations (3)-(5) demonstrate that when the modulating

ring is designed to be rotatable, the CMG possesses similar

functions as the planetary gear set [3], thus offering the

capability of both power splitting and mixing.

TABLE I. POWER SPECIFICATIONS OF M/GS

Rated power of M/G1 15 kW

Rated speed of M/G1 2500 rpm

Rated phase voltage of M/G1 100 V

Rated power of M/G2 30 kW

Rated speed of M/G2 950 rpm

Rated phase voltage of M/G2 100 V

III. MACHINE DESIGN

The gear ratio Gr of the CMG and the power specificationsof the two M/Gs are governed by the expected performance of

the vehicle to be designed. Herein, Gr =2.6 which is the same

with that in Toyota Prius is adopted and the power

specifications of the two M/Gs are listed in Table I.

Fig. 3. Construction of PM poles and rotors.

The pole-pair numbers of the CMG are governed by (2).

Hence, p1 and p2 equal to 5 and 13, respectively, are chosen to

result in the gear ratio of 2.6. Consequently, n s equals 18 can

be deduced from (1). For this integrated machine, thedecoupling of electromagnetic fields in the CMG and the two

M/Gs is very important since it can directly affect the

controllability of the system. Thus, the Halbach arrays are

employed to constitute the PM poles on the two rotors. Asshown in Fig. 3, each pole of PM is divided into 4 and 2

segments for the inner rotor and the outer rotor, respectively.

The corresponding magnetization directions are indicated by

the arrow lines. It is well known that the Halbach arrays canoffer the merit of self-shielding. Therefore, the back iron of

the two rotors can be designed to have small thickness, leading

to save iron material and reduce the system size. Moreover,

non-magnetic shielding cases are sandwiched within the tworotors so as to offer further decoupling. The adoption of

Halbach arrays can also help reduce the cogging torque and

increase the torque transmission capability of the CMG [14].

(a)

(b)

Fig. 4. Slots and winding connections of two M/Gs. (a) M/G1. (b) M/G2.

TABLE II. SPECIFICATIONS OF PROPOSED MACHINE

No. of stator slots of M/G1 12

No. of pole-pairs of M/G1 5

No. of phases of M/G1 3

No. of stator slots of M/G2 24

No. of pole-pairs of M/G2 13

No. of phases of M/G2 3

No. of ferromagnetic segments 18

Length of airgaps 1 mm

Thickness of PMs 6 mm

Thickness of modulating ring 15 mm

Thickness of shielding cases 4 mm

Thickness of back iron of rotors 4 mm

Inside radius of stator of M/G1 30 mm

Outside radius of stator of M/G1 86.5 mm

Inside radius of stator of M/G2 153.5 mm

Outside radius of stator of M/G2 195 mm

Effective axial length 200 mm

Fractional-slots and concentrated windings are adopted in

the stators of the two M/Gs. The concentrated winding refers

to the armature winding that encircles a single stator tooth. It

can offer several significant advantages over the distributed

winding [15]: 1) Reduction in the coil volume and hence the

copper loss in the end region; 2) Shortened machine axiallength; 3) Reduction in machine manufacturing cost; 4)Compatibility with segmented stator structures that makes it

possible to achieve higher slot fill factor values. Moreover, it

has been proven that by adopting fractional-slots and

concentrated windings, the d -axis inductance of the armature

windings can be dramatically increased, which helps achieve

optimal flux weakening of surface-mounted PM machines [16].This feature is advantageous for widening the speed

adjustment range of the M/Gs. Fig. 4 illustrates the slots and

winding connections on the stators of the two M/Gs. Thenumbers of slots are 12 and 24 on M/G1 and M/G2,



respectively. Thus, the slot-per-phase-per-pole (SPP) of 2/5

and 8/13 are achieved for the M/G1 and M/G2, respectively.

IV. FINITE ELEMENT A NALYSIS

The electromagnetic characteristics of the proposedintegrated machine can be analyzed by using the finite element

method (FEM). The specifications are listed in Table II.

Firstly, the electromagnetic field distributions of the

proposed machine under no-load and full-load are illustratedin Fig. 5. It can be observed that almost no flux line goes

through the shielding cases, which demonstrates that due to

the adoptions of Halbach arrays and shielding cases, excellent

field decoupling among the CMG and the two M/Gs can beachieved. With no doubt, this can help improve the

controllability of the whole system. Therefore, the

electromagnetic behavior of each component (namely theCMG and the two M/Gs) can be analyzed and modeled

individually in spite of its integration.

(a) (b) Fig. 5. Electromagnetic field distributions in integrated machine. (a) No load.

(b) Full load.

(a)

(b)

Fig. 6. Back EMF waveforms at rated speeds. (a) M/G1. (b) M/G2.

Secondly, as shown in Fig. 6, the back electromotive force

(EMF) waveforms can be obtained by rotating the two rotors

of M/Gs at their rated speeds. Thirdly, the torque transmission

capability of the CMG can be assessed by calculating the

Maxwell’s stress tensors in the airgaps while keeping the outerrotor and the modulating ring standstill, and rotating the inner

rotor step by step. Fig. 7 depicts the resulting torque-angle

curves. It can be found that the torque-angle curves vary

sinusoidally, in which the maximum torque values denote the pull-out torques. Thus, the pull-out torques of the inner rotor,

outer rotor and modulating ring are 226.7 Nm, 589.7 Nm and

815.9 Nm, respectively. The ratio of the pull-out torques on

the two rotors is 2.601, which has a very good agreement withthe designed gear ratio of 2.6. In addition, the above three

pull-out torques agree well with (5) since there is a phase

difference of π between the curve of the modulating ring andthe curves of the two rotors.

Fig.7. Torque-angle curves of CMG.

Fig. 8. Vehicle road load.

V. SYSTEM MODELING AND SIMULATION

As shown in Fig. 8, the vehicle road load F l consists ofthree main components: aerodynamic drag force F d , rolling

resistance force F r and climbing force F c [2]:

cr d l F F F F ++= (6)

20386.0 AvC F d d ρ = (7)

α cos Mg C F r r = (8)

α sin Mg F c = (9)

where C d is the aerodynamic drag coefficient, ρ is the air

density, A is the vehicle frontal area, v is the vehicle velocity,

M is the vehicle mass, g is the gravitational acceleration, C r is

the rolling resistance coefficient, and α is the angle of incline.



The motive force F available at the wheels is required to

overcome the above road load F l and to drive the vehicle with

an acceleration a. If F l is greater than F , it becomes a

deceleration and a is a negative value. It is expressed as:

( )l

r

F F M k

a −=1 (10)

where k r denotes a correction factor that there is an apparent

increase in vehicle mass due to the inertia of rotational masses.

Fig. 9. Rotational parts of integrated machine (from left to right: inner rotor,

modulating ring and outer rotor).

Fig. 9 indicates the rotational parts of the integratedmachine. Their motions are governed by:

dt

d J T T m

1111

ω =+ (11)

dt

d J T T e

333

ω =+ (12)

dt

d J T T T fd m

2

222

ω =−+ (13)

where J 1, J 2, J 3 are the moments of inertia of inner rotor of

CMG (rotor of M/G1), outer rotor of CMG (rotor of M/G2) andmodulating ring of CMG, respectively; T fd , T m1 and T m2 are the

load torque of final driveline, output torque of M/G1, and

output torque of M/G2, respectively. In addition, assuming thatthe initial torques are zero at the time instant t =0, the

developed magnetic torques in the CMG can be given by [17]:

( ) ⎥⎦⎤

⎢⎣⎡ −+−= ∫

t

s P dt N p pT T 0

3221111 sin ω ω ω (14)

( ) ⎥⎦⎤

⎢⎣⎡ −+−= ∫

t

s P dt N p pT T 0

3221122 sin ω ω ω (15)

( ) ⎥⎦⎤

⎢⎣⎡ −+= ∫

t

s P dt N p pT T 0

3221133 sin ω ω ω (16)

where T p1, T p2 and T p3 are the pull-out torques developed on

the inner rotor, outer rotor and modulating ring, respectively.

On the other hand, the M/Gs can be modeled by following

equations:

k

d

k

s

k

qk

q

k k

qdt

d ir v λ ω

λ ++= (17)

k

q

k

s

k

d k

d

k k

d dt

d ir v λ ω

λ −+= (18)

k

q

k

q

k

q i L=λ (19)

k

pm

k

d

k

d

k

d i L λ λ += (20)

( )k

d

k

q

k

q

k

d k mk ii pT λ λ −=2

3 (21)

where superscript k =1 is for the case of M/G1, and k =2 is for

the case of M/G2, subscript q represents the q-axis component,

and d represents the d -axis component; v, i, L and λ are thestator voltage, stator current, stator inductance and stator flux

linkage; ω s is the rotational speed of the stator flux linkageand λ pm is the flux linkage excited by the PMs.

Fig. 10. Power distributions under FUD 48 driving mode.

For simplicity, the engine is assumed to be shut down and

the vehicle is driven under the full-electric mode. As shown inFig. 10, the FUD 48 driving mode is engaged. The maximum

speed is 48 km/h and the time span is 55 s. The power

distribution between the two M/Gs is defined as: 1) during the

time period of 0-18 s, the M/G1 and M/G2 supply 1/3 and 2/3

of the propulsion power; 2) during the time period of 18-48 s,

the M/G2 supply all the power needed; 3) during the time period of 48-55 s, the M/G1 and M/G2 collect 1/3 and 2/3 of

the dynamic power of the vehicle.

(a)



(b)

Fig. 11. Simulated responses of rotational speed, electromagnetic torque andstator current. (a) M/G1. (b) M/G2.

Fig. 11 shows the simulated responses of the M/G1 and

M/G2. It can be observed that the rotational speeds of the two

M/Gs are with opposite directions, and the ratio of theirquantities is consistent with the gear ratio. This is in

accordance with the speeds relationship constrained by (3)

since the engine is shut down during the whole process.

Moreover, during the acceleration stage (0-18 s), the torque

and speed of each M/G are with the same direction, whichmeans that the two M/Gs deliver power to the driveline

simultaneously. Then, when the vehicle runs at the high speed

range (18-48 s), the torque of M/G1 is zero while the M/G2 solely supplies the power needed. Finally, during thedeceleration stage (48-55 s), the torque and speed of each M/G

are with opposite directions, which means that the two M/Gsrecycle the braking power of the vehicle, namely regenerative

braking.

VIII. CONCLUSIONS

In this paper, a new power-train for power-split HEVs has

been designed, analyzed and modeled. The key is to integratetwo PM M/Gs together with a CMG. First, by purposely

designing the modulating ring of the CMG to be rotatable, this

integrated machine can achieve both power splitting and

mixing, and therefore can seamlessly match the vehicle roadload to the engine optimal operating region. Then, with the

one-side-in and one-side-out structure and the non-contact

transmission of the CMG, all the drawbacks aroused by the

mechanical gears and chain existing in the traditional power-

train can be overcome. Finally, the proposed power-trainsystem possesses the merits of small size and light weight,

which are vitally important for extending the full-electric drive

range of HEVs.

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a novel power-train using coaxial magnetic gear

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