Research on Electromagnetic Performance of a Novel Radial Magnetic-Field-Modulated Brushless

Research on Electromagnetic Performance of a Novel Radial Magnetic-Field-Modulated

Brushless Double-Rotor Machine

Ping Zheng, Jingang Bai, Chengde Tong, Jia Lin, Haipeng Wang

School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin, 150080, China

E-mail: zhengping@https://www.360docs.net/doc/7d2448727.html, , baijingangdiyi@https://www.360docs.net/doc/7d2448727.html,

Abstract — A novel radial magnetic-field-modulated brushless double-rotor machin e (MFM-BDRM), which is the key part of compound-structure permanent-magnet synchronous motor (CS-PMSM), is proposed in this paper. The speed an d torque

relations of the first-stator magnetic field, the first PM rotor and

the modulating ring rotor are investigated by analytical method. The harmon ic compon en ts of magn etic field in the in n er an d

outer air gap are an alyzed by fin ite-elemen t method (FEM),

whe n the PM mag n etic field a n d armature field work in depen den tly. Furthermore, electromagn etic performan ces of two typical schemes are an alyzed, which shows that torque ripples are the major problem of the radial MFM-BDRM. Some methods are proposed to reduce the torque ripples and validated

by FEM.

I.

I NTRODUCTION

The compound-structure permanent-magnet synchronous motor (CS-PMSM) system is a novel power-split solution for hybrid electric vehicles (HEVs) [1]-[3]. But the brushes and slip rings which feed the rotating windings may cause problems such as maintenance, frictional loss, and low reliability. Such problems are quite unfavorable for HEVs [4], [5]. In order to overcome the disadvantages above, a novel brushless CS-PMSM based on the principle of the magnetic field modulation is proposed, as shown in Fig. 1. It is composed of the radial magnetic-field-modulated brushless double-rotor machine (MFM-BDRM) and the torque-regulating machine, which can provide the speed and torque difference between the ICE and the final gear, respectively. The torque-regulating machine is normally a traditional permanent-magnet machine. And this paper mainly focuses on the radial MFM-BDRM.

II. P RINCIPLE A NALYSIS OF THE R ADIAL MFM-BDRM A. Theoretical Analysis of Magnetic Field and Speed equation The radial MFM-BDRM consists of three components: the first stator, the modulating ring rotor and first PM rotor, as

shown in Fig. 2.

regulating machine

MFM-BDRM

Fig. 1 Radial magnetic-field-modulated brushless CS-PMSM system

ring rotor

rotor

Fig. 2 Cross section diagram of the radial MFM-BDRM

It is assumed that the pole-pair number of the first PM rotor is n and that of the rotary magnetic field of the first stator is p with the first-stator windings fed with AC current. Meanwhile, it is supposed that the numbers of magnetic blocks and non-magnetic blocks in the modulating ring rotor are both q .

Suppose the rotary speeds of the first PM rotor, the first-stator magnetic field and modulating ring are ?1, ?2, ?3, respectively. The magnetomotive force (MMF) produced by the first PM rotor is given by

()()()2

212

1,3,5,...

,,cos h

h F r t f r hn t hn θθθ==?Ω+???

?

(1)

∑

where f 2h (r) is the amplitude of the MMF harmonics at radius r , r is radius, 2θ is the initial phase angle, t is time, and θ is the phase angle.

When the modulating ring rotor exists, the flux density distribution in the air gap can be expressed as

()()()22121,3,5,...,,cos h h B r t f r hn t hn θθθ=??

=?Ω+????????

∑()()()0301,2,3,...cos k k r r kq t kq λλθθ=

???Ω+??×+ ???

???∑()()02121,3,5,...()cos h h r f r hn t hn λθθ= ??=?Ω+????????

∑

()()21,3,5,...1,2,3,...

12k h h k r f r λ==+

∑∑() 1320cos hn kq hn kq t hn kq hn kq ?θθθ???

Ω+Ω×+?

++????+????

()()21,3,5,...1,2,3,...

1

2k h h k r f r λ==+

∑∑ ()1320cos hn kq hn kq t hn kq hn kq θθθ???Ω?Ω×??+???????????

(2)

where 0()r λ

is the constant component of the air-gap permeance at radius r , is the harmonic amplitude of the

air-gap permeance at radius r , and ()k r λ0θ is the initial phase angle of air-gap permeance[6]-[8].

According to the principle of electro-mechanical energy conversion, the pole-pair number and speed of the first-stator magnetic field are expressed as p hn jq =+ (3)

31

2jq hn hn jq hn jq

ΩΩΩ=

+

++ (4) The MMF produced by the first stator windings is given by

()()()1121,3,5,...

,,cos g g F r t f r gp t gp 1θθ==

?Ω??∑

θ+??

(5) where f 1g (r) is the MMF harmonic amplitude of the first-stator

magnetic field at radius r , 1θ is the initial phase angle. With

the influence of the modulating ring rotor, the flux density

distribution in the air gap can be expressed as

()()()1

121,3,5,...,,cos g g B r t f r gp t gp θθ=??

=?Ω?????

???

∑1θ+0q θ??1

()()031,2,3,...()cos k k r r kq t k λλθ=??×+?Ω+????

??∑()()0121,3,5,...()cos g g r f r gp t gp λθθ=??=??????

???

∑Ω+

()()11,3,5,...1,2,3,...

12k g g k r f r λ==+∑∑ ()2310cos gp kq gp kq t gp kq gp kq θθθ????Ω+Ω×+?++????+????

()()11,3,5,...1,2,3,...12k g g k r f r λ==+∑∑ ()2310cos gp kq gp kq t gp kq gp kq θθθ????Ω?Ω×??+??????????

(6)

Similarly, the pole-pair number and speed of the first PM rotor are expressed as

n gp jq =+ (7)

32

1jq gp gp jq gp jq

ΩΩΩ=+

++ (8) From equations (3), (4), (7) and (8), the relation of p , q and n is deduced as

q p n =+ (9)

The relation of ?1, ?2 and ?3 is deduced as

312

q n n q n q

?ΩΩΩ=+

?? (10) B. Analysis of Torque

According to the equilibrium of torque, the relation of the torque of the first PM rotor, first stator and modulating ring rotor is expressed as

(11)

312(T T T =?+)12312233T T T where T , T and T are the torque of the first PM rotor, the first stator and the modulating ring rotor, respectively.

Based on the principle of energy conservation, the relation of the torques and speeds of the first PM rotor, the first stator and the modulating ring rotor are expressed as

Ω=Ω+Ω (12)

From equations (9), (10), (11) and (12), the relation of T 1,

T 2 and T 3 is deduced as

21p T T n = (13)

31q

T T n

=?0

100200300-0.4

-0.20.0

0.20.4 (14) III. F INITE -E LEMENT A NALYSIS OF R ADIAL MFM-BDRM A. Finite-element Analysis of Magnetic Field

In this selection p=20, q=24, n=4 are employed. When the windings of the first stator are not electrified, i.e., only the first PM rotor acts, the flux density distributions in the inner and outer air gap are calculated by FEM, as shown in Figs. 4 and 5, respectively.

F l u x d e n s i t y (T )

Mechanical degree

F l u x d e n s i t y a m p l i t u d e (T )

Pole pairs

100200300

-0.8

-0.40.0

0.40.8

(a) (b)

F l u x d e n s i t y (T )

M echanical de

g ree

F l u x d e n s i t y a m p l i t u d e (T )

Pole pairs

100200300-1.0

-0.50.0

0.51.0

(c) (d)

F l u x d e n s i t y (T )

M echanical degree

F l u x d e n s i t y a m p l i t u d e (T )

Pole pairs

100200300-0.4

-0.20.0

0.20.4

(e) (f)

Fig. 4: Flux density distribution in the inner air gap: (a), (b): the modulating ring is air; (c), (d): the modulating ring is magnetic material; (e), (f): the modulating ring is the alternate placement of magnetic and nonmagnetic material.

F l u x d e n s i t y (T )

Mechanical degree

e (T )

t u d l i t y a m p e n s i d F l u x Pole pairs

(a) (b)

-0.6

-0.30.0

0.30.6

F l u x d e n s i t y (T )

M echanical degree

F l u x d e n s i t y a m p l i t u d e (T )

Pole pairs

(c) (d)

100200300-1.0

-0.50.0

0.51.0

F l u x d e n s i t y (T )

M echanical degree

F l u x d e n s i t y a m p l i t u d e (T )

Pole pairs

(e) (f)

Fig. 5: Flux density distribution in the outer air gap: (a), (d): the modulating ring is air; (b), (e): the modulating ring is magnetic material; (c), (f): the modulating ring is the alternate placement of magnetic and nonmagnetic material.

As shown in Figs. 4 and 5, when the modulating ring rotor

employs the alternative magnetic and nonmagnetic material,

the flux density distribution is obviously changed in the inner and outer air gap. Especially in the outer air gap, the 4 pole-pair PM magnetic field is modulated into the magnetic field with a significant 20 pole-pair component. The FEM simulation result is in agreement with the former analysis. When the windings of the first stator are fed with m -phase AC current in the absence of PMs on the first PM rotor, the flux density distributions in the inner and outer air gaps are shown in Figs. 6 and 7, respectively. -0.020.000.02

F l u x d e n s i t y (T )

M echanical degree

F l u x d e n s i t y a m p l i t u d e (T )

Pole pairs

(a) (b)

100200300-0.004

-0.0020.0000.0020.004

F l u x d e n s i t y (T )

Mechanical degree

F l u x d e n s i t y a m p l i t u d e (T )

Pole pairs

(c) (d)

100200300-0.10

-0.050.00

0.050.10

F l u x d e n s i t y (T )

Mechanical degree

F l u x d e n s i t y a m p l i t u d e (T )

Pole pairs

(e) (f)

Fig. 6: Flux density distribution in the inner air gap: (a), (d): the modulating ring is air; (b), (e): the modulating ring is magnetic material; (c), (f): the modulating ring is the alternate placement of magnetic and nonmagnetic material

100200300-0.10

-0.050.00

0.050.1

F l u x d e n s i t y (T )

M echanical deg ree

F l u x d e n s i t y a m p l i t u d e (T )

Pole p irs

100200300-0.2

0.0

0.2a (a) (b)

F l u x d e n s i t y (T )

M echanical degree

F l u x d e n s i t y a m p l i t u d e (T )

Pole airs

010*******-0.2-0.10.0

0.10.2 p (c) (d)

F l u x d e n s i t y (T )

Mechanical degree

F l u x d e n s i t y a m p l i t u d e (T )

Pole pairs (e) (f) Fig. 7: Flux density distribution in the outer air gap: (a), (d): the modulating

ring is air; (b), (e): the modulating ring is magnetic material; (c), (f): the modulating ring is the alternate placement of magnetic and nonmagnetic material As shown in Figs. 6 and 7, when the modulating ring rotor employs the alternative magnetic and nonmagnetic material, the flux density distribution is also obviously changed in the

inner and outer air gap. And the 20 pole-pair PM magnetic

field is modulated into the inner magnetic field with a

significant 4 pole-pair component. The FEM simulation result is in agreement with the former analysis.

B. Finite-element Analysis of Electromagnetic Performance With p=20, q=24 and n=4, equation (10) is expressed as

23161

55

Ω=Ω?Ω

(15)

With ?1=1200 rpm, ?2= -240 rpm, ?3=0 rpm, the no-load back electromotive force (EMF) is shown in Fig. 8, and the electromagnetic torque of the radial MFM-BDRM is shown in

Fig. 9.

B a c k E M F (V )

Time(ms)

T o r q u e (N m )

Time(ms)

Fig. 8 No-load back EMF Fig. 9 Electromagnetic torque

With ?1=3000 rpm, ?2= 1800 rpm and ?3=2000 rpm, the no-load EMF is shown in Fig. 10, and the electromagnetic torque of the radial MFM-BDRM is shown in Fig. 11.

B a c k E M F (V )

Time(ms)

T o r q u e (N m )Time(ms)

Fig. 10 No-load back EMF Fig. 11 Electromagnetic torque

With ?1=5000 rpm, ?2= 6200 rpm and ?3=6000 rpm, the

no-load EMF is shown in Fig. 12, and the electromagnetic torque of the radial MFM-BDRM is shown in Fig. 13.

B a c k E M F (V )

Time(ms)

T o r q u e (N m )

Time(ms) Fig. 12 No-load back EMF Fig. 13 Electromagnetic torque As can be seen from the comparison of Figs. 8, 10 and 12, when the first-PM rotor and the modulating ring rotor are working at different speeds, the amplitude of the no-load back EMF is obviously different from each other. With ?1=5000 rpm and ?3=6000 rpm, the amplitude of the no-load back EMF is largest. However, the waveform of back EFM in the three-phase windings is seriously distorted, even asymmetrical.

From Figs. 9, 11 and 13, the torque ripples of the first-PM rotor and modulating ring rotor are especially serious, which

can’t meet requirement of the electric vehicles. In further study of the feasibility of the radial MFM-BDRM,

p=4, q=24, n=20 are selected. And equation (10) is expressed as

2365Ω=Ω?Ω1 (16) With ?1=1200 rpm, ?

2= -6000 rpm, ?3=0 rpm, the no-load back EMF is shown in Fig. 14, and the electromagnetic torque

of the radial MFM-BDRM is shown in Fig. 15.

B a c k E M F (V )

Time(ms)

T o r q u e (N m )

Time(ms)

Fig. 14 No-load back EMF Fig. 15 Electromagnetic torque

With ?1=3000 rpm, ?2= -3000 rpm, ?3=2000 rpm, the no-load back EMF is shown in Fig. 16, and the electromagnetic torque of the radial MFM-BDRM is shown in Fig. 17.

B a c k E M F (V )

Time(ms)

T o r q u e (N m )Time(ms)

Fig. 16 No-load back EMF Fig. 17 Electromagnetic torque

With ?1=5000 rpm, ?2= 11000 rpm, ?3=6000 rpm, the no-load back electromotive force (EMF) is shown in Fig. 18. And the electromagnetic torque of the radial MFM-BDRM is shown in Fig. 19.

B a c k e l e c t r o m

o t i v e f o r c e (V )Time(ms)

T o r q u e (N m )

Time(ms)

Fig. 18 No-load back EMF Fig. 19 Load torque

Compared with the former scheme, the waveforms of back EFM in the three-phase windings are symmetrical, as shown in Figs. 14, 16 and 18. However, the waveforms of back EMF is modestly distorted, especially when the speeds of the first PM rotor and the modulating ring rotor are 3000 rpm and 2000 rpm. From Figs. 15, 17 and 19, the average electromagnetic torque is calculated, as shown in Table I. It is obvious that the

torque of the modulating ring rotor approximately equals the addition of those of the first PM rotor and the first stator. And the ratios of T 2/ T 1 and T 3/ T 1 approximately equal the theoretical values. However, torque ripples are still serious, especially when the modulating ring rotor and the first PM rotor work at different speeds. TABLE I

T ORQUE P ERFORMANCE OF THE R ADIAL MFM-BDRM T 1 （Nm ）T 2

（Nm ） T 3 （Nm ）

T 2/ T 1T 3/ T 1

?1=1200 rpm ?3=0 rpm 31.7 9 -40 0.28-1.26?1=3000 rpm ?3=2000 rpm -34.6 -7.1 42.9 0.21-1.24?1=5000 rpm ?3=6000 rpm

-44.9 -9.2 53.2 0.20-1.18IV.

T ORQUE -R IPPLE A NALYSIS

Due to rich harmonics in the magnetic field, as shown in Figs. 4, 5, 6 and 7, the torque ripples of the modulating ring rotor and the first PM rotor are serious [9], [10]. Efforts are made to reduce torque ripples of MFM-BDRM in this section. A. Matches of Magnetic Blocks and Pole Pairs of the First PM Rotor

For a given pole pair number of the first-stator, the torque ripple is analyzed with respect to different number matches of magnetic blocks and pole pairs of the first PM rotor, as shown in Figs. 20 and 21.

)

T o r q u e R i p p l e o f F i r s t P M R o t o r (%Numbers of Magnetic Blocks/Pole Pairs of PM Rotor

Fig. 20 PM-rotor torque ripple verses different combinations

T o r q u e R i p p l e o f M o d u l a t i n g R i n g R

o t o r (%)

Numbers of Magnetic Blocks/Pole Pairs of PM Rotor

T r o q u e R i p p l e o f M o d u l a t i n g R i n g R o t o r (%)

Thickness of Magnetic Blocks(mm)

Fig. 21 Torque ripple of modulating ring rotor verses different combinations

The lowest torque ripples of the first PM rotor and the modulating ring rotor are achieved when the numbers of magnetic blocks and pole pairs are 23 and 19, respectively.

B. Optimization of Magnetic Blocks As the harmonic components in the magnetic field led by the magnetic blocks also result in a high torque ripple, the circumferential span and radial thickness of the magnetic blocks are optimized by FEM, as shown in Figs. 22, 23, 24 and 25. The lowest torque ripples of the first PM rotor and the modulating ring rotor take place when the span and the thickness are 0.5, 7mm and 0.5, 6mm respectively. T o r q u e R i p p l

e o

f F i r s t P M R o t o r (%)

Span of Magnetic Blocks

Fig. 22 Torque ripple of PM rotor verses span of magnetic blocks

T o r q u e R i p p l e o f M o d u l a t i n g R i n g R o t o r (%)

Span of Magnetic Blocks

Fig. 23 Torque ripple of modulating ring rotor verses

span of magnetic blocks

T o r q u e R i p p l e o f F i r s t P M R o t o r (%)

Thickness of Magnetic Blocks(mm)

Fig. 24 Torque ripple of PM rotor verses thickness of magnetic blocks

Fig. 25 Torque ripple of modulating ring rotor verses

thickness of magnetic blocks

C. Optimization of Slot Opening

The torque ripples of the first PM rotor and the modulating

ring rotor are further decreased by optimizing the slot opening, as shown in Figs. 26 and 27. It is obvious that the torque ripple of the first PM rotor is low and almost unchanged with the slot opening varying from 1 mm to 5 mm. However, the torque ripple of the modulating ring rotor can reach the lowest value under condition of the closed slot.

T o r q u e R i p p l e o f F i r s t P M R o t o r (%)

Slot Opening(mm)

Fig. 26 Torque ripple of PM rotor verses slot opening

T o r q u e R i p p l e o f M o d u l a t i n g R i n g R o t o r (%)

Slot Opening(mm)

Fig. 27 Torque ripple of modulating ring rotor verses slot opening

V.

C ONCLUSIONS

(1) A novel brushless double-rotor machine (radial MFM-BDRM) is proposed for HEV application based on the magnetic field modulation principle, which can solve winding overheating and problems caused by brushes and slips in traditional DRM.

(2) Analysis of electromagnetic performances of two typical schemes shows the low PM pole-pair scheme is more suitable for HEV application.

(3)The torque ripples of the first PM rotor and the modulating ring rotor are comparatively high in the initial scheme, which is reduced by selecting favorable matches of

magnetic blocks and PM pole pairs, and optimizing magnetic blocks and the slot opening.

A CKNOWLEDGMENT

This work was supported in part by National Natural Science Foundation of China under Project 50877013 and 51077026, and in part by the Fundamental Research Funds for the Central Universities (Grant No. HIT.BRET1.2010013).

R EFERENCES

[1] E. Nordlund and S. Eriksson, “Test and verification of a four-quadrant

transducer for HEV applications,” Proceedings of IEEE Vehicle Power and Propulsion Conference, 2005, pp. 37-41.

[2]Ping Zheng, Peter Thelin, Anyuan Chen and Erik Nordlund, “ Influence

of Saturation and Saliency on the Inductance of a Four-Quadrant Transducer Prototype Machine,” IEEE Trans. on magnetics., vol.42, no.

4, Apr., 2007, pp. 1319-1322.

[3]Longya Xu, Yuan Zhang and Xuhui Wen, “Multioperational Modes and

Control Strategies of Dual-Mechanical-Port Machine for Hybrid Electrical Vehicles,” IEEE Trans. on Industry Applications, vol.45, no. 2, Apr., 2009, pp. 747-755.

[4]T. Fan, X. H. Wen, S. Xue, and L. Kong, “A brushless permanent

magnet dual mechanical port machine for hybrid electric vehicle application,” ICEMS, Oct. 2008, pp. 3604-3607.

[5]P. Zheng, R. R. Liu, P. Thelin, E. Nordlund, and C. Sadarangani,

“Research on the parameters and performances of a 4QT prototype machine used for HEV,” IEEE Trans. on magnetics., vol.43, no.1, Jan., 2007, pp. 443-446.

[6]L.L.Wang, J.X.Shen, “Development of a Magnetic-Geared Permanent-

Magnet Brushless Motor,” IEEE Transactions on magnetics, Vol. 45, No. 1 Oct, 2009, pp. 4578-4581.

[7]Thierry Lubin, Smail Mezani and Abderrezak Rezzoug, “Analytical

Computation of the Magnetic Field Distribution in a Magnetic gear,”

IEEE Trans. on magnetics., vol.46, no.7, Jun., 2010, pp. 2611-2621. [8]Linni Jian, K. T. Chau, “A Coaxial Magnetic Gear With Halbach

Permanent-Magnet Arrays,” IEEE Transactions on Energy Conversion, Vol. 25, No. 2 June, 2010, pp. 319-328.

[9]Mohammad S. Islam, Rakib Islam and Tomy Sebastian, “Experimental

Verification of Design Techniques of Permanent-Magnet Synchronous Machine for Low-Torque-Ripple Applications,” IEEE Transactions on Industry Applications, Vol. 47, No. 1 Jan., 2011, pp. 88-95.

[10]Dong-Hee Lee, Jianing Liang, Zhen-Guo Lee and Jin-Woo Ahn, “A

Simple Nonlinear Logical Torque Sharing Function for Low-Torque Ripple SR Drive,” IEEE Transactions on Industrial Electronics, Vol. 56, No. 8 Aug., 2009, pp. 3021-3028.