COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Article: Design issues of an IPM motor for EPSC.F. Wang, J.X. Shen, P.C.K. Luk, W.Z. Fei, M.J. Jin

Article information:To cite this document: C.F. Wang, J.X. Shen, P.C.K. Luk, W.Z. Fei, M.J. Jin, (2012),"Design issues of an IPM motor for EPS", COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 31 Iss: 1 pp. 71 - 87

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Design issues of an IPMmotor for EPS

C.F. WangCollege of Electrical Engineering, Zhejiang University, Hangzhou, China and

Department of Engineering Systems and Management,Cranfield University, Shrivenham, UK

J.X. ShenCollege of Electrical Engineering, Zhejiang University, Hangzhou, China

P.C.K. Luk and W.Z. FeiDepartment of Engineering Systems and Management, Cranfield University,

Shrivenham, UK, and

M.J. JinCollege of Electrical Engineering, Zhejiang University, Hangzhou, China

Abstract

Purpose The purpose of this paper is to present the design procedure of an interior permanentmagnet (IPM) motor used in electric power steering (EPS), and some critical issues which have considerableimpacts on the machines performance are fully discussed before detailed sizing optimization.

Design/methodology/approach The design specifications are derived according to applicationoverall requirements. Critical issues which have considerable impacts on the machines performance,such as operation mode, rotor structure and slot/pole combination, are analyzed based on literaturereview. The proposed machine is optimized, and the losses and efficiency are computed, using 2-Dfinite element analysis (FEA).

Findings Before detailed sizing optimization, machine type selection is fully discussed. Aspectssuch as brushless ac (BLAC) operation mode, IPM rotor structure and combination of 12-slot/10-poleare quite suitable for EPS application. Consequently, a 12-slot/10-pole sinusoidally excited IPMmachine with concentrated windings is selected, since it is convenient to obtain sinusoidal backelectromotive force (back-EMF), minimum cogging torque and torque ripple, short end windings andhigh efficiency, as well as simple rotor assembly. The estimated excellent performance confirms thatthe proposed machine can be an attractive solution for EPS.

Research limitations/implications The excitation current is ideal sinusoidal, while some harmoniccomponents are neglected. Besides, in future, the experimental test should be carried out for validation.

Originality/value A reasonable design procedure, where the motor type selection should be firstaddressed before detailed sizing design, is carried out. A 12-slot/10-pole sinusoidally excited IPMmachine with concentrated windings is provided as a quite competitive candidate for EPS application.

Keywords Electric power steering, Interior permanent magnet, Motor design, Finite element analysis,Road vehicles

Paper type Research paper

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/0332-1649.htm

The first author gratefully acknowledges the internship supported by the Department ofEngineering Systems and Management, Cranfield University, UK, to which this work relates. Allauthors would like to thank Nanyuan Electric Machinery Co., China for manufacture of theprototype machine, and MagneForce Software Systems Inc., USA for offering evaluation licenseof MagneForce V4.0.

IPM motorfor EPS

71

COMPEL: The International Journalfor Computation and Mathematics inElectrical and Electronic Engineering

Vol. 31 No. 1, 2012pp. 71-87

q Emerald Group Publishing Limited0332-1649

DOI 10.1108/03321641211184832

1. IntroductionGlobal warming is becoming a very important world-wide issue. It was even one of thethree main topics in the recent 2009 G8 Summit. Carbon dioxide (CO2) emission is themain contributor of green house gas which leads to global warming. Transportationaccounts for more than 20 percent of man-made CO2. It is therefore highly desirable toreduce green house gas emission by improving vehicles fuel efficiency. On the otherhand, the number of electric machines installed in modern vehicles has been increasingat a rapid pace. The more luxury the vehicle, the more electric machines will beequipped. Well optimised electric machines with high efficiency will therefore play apivotal role in improving the vehicles overall efficiency, and thus in reducing the CO2emission to mitigate global warming.

An apparent trend that electric power steering (EPS) is becoming an alternative tothe hydraulic power steering (HPS) can be seen in recent developments in automotiveindustry. In the HPS system, a pump driven by the engine is constantly running tokeep the hydraulic pressure, no matter assistance is required or not. While in the EPSsystem, the electric motor is driven only when the steering wheel is turned. EPS thusoffers much better fuel economy, which can account for 3 percent improvements in fuelefficiency (Yoneda et al., 2006).

Electric machines, the key actuators in the EPS system, are crucial in influencingthe vehicles steering performance. A brushed DC motor was equipped in the worldsfirst EPS system in 1993 by Honda, on Acura NSX (Oprea and Martis, 2008). Presenceof brushes limits its performance especially at higher speeds, and the sparks may causesafety and electromagnetic interference problem. A much more competitive solutionbased on permanent magnet (PM) brushless machines has drawn considerableinterests from both industrial and academic research communities. The hightorque/volume ratio, high dynamics, high speed due to field-weakening capability,elimination of brushes, simple machine structure and high efficiency are some of theadvantages of PM machines. For the disadvantages, the magnets will subject to therisk of irreversible demagnetization in overloading or high temperature conditions.Various PM machine topologies have been developed for EPS applications. Researchhave been focusing on some particular aspects, such as cogging torque reduction andtorque ripple minimization (Jahns and Soong, 1996; Bianchi and Bolognani, 2002; Islamet al., 2003, 2004; Ombach et al., 2006), saturation effect (Seong et al., 2009; Stumbergeret al., 2003; Chedot and Friedrich, 2004), losses (Yamazaki and Ishigami, 2010;Zivotic-Kukolji et al., 2006), and fault tolerance (Oprea and Martis, 2008; Bianchi et al.,2006; Aroquiadassou et al., 2005). Whereas most studies principally focus on theelectromagnetic design level on the size and shape of the magnets of the machine, itappears that few studies emphasize on machine topology selection level prior todetailed machine electromagnetic design. For a complete EPS system designprocedure, it is strongly felt that essential issues for machine characteristics, includingmachine topology, operation mode, and slot/pole combination, should be first decided.

This paper concerns the design of a PM machine for EPS applications. Therequirements of the EPS application are introduced and the specifications of thedesired machine are then derived. Before detailed design, some critical issues whichessentially affect the final performance, viz., operation mode of either brushlessalternating current (BLAC) or brushless direct current (BLDC), rotor structure of eithersurface-mounted permanent magnet (SPM) or interior permanent magnet (IPM), as

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well as slot/pole combination, are analyzed in details. Subsequently, a 12-slot/10-polesinusoidally excited IPM machine with concentrated windings is optimally designedand verified with finite element analysis (FEA). A prototype has been built forvalidation.

2. Application requirements and design specificationsA. Application overall requirementsEPS is an important subsystem on vehicles, which works extremely frequently duringdriving. In such a safety critical application, high reliability must be fully consideredduring the whole design process. Besides, in terms of limited available space and thedemanded working environments, the desired electric machine is to have followingfeatures: compact size, low weight, low cost, variable speed over wide torque-speedareas, low acoustic and electromagnetic noise, high efficiency, as well as smooth torqueoutput for the precision steering and driving comfort.

B. Design specificationsFor small and middle sized vehicles, the electric machine is mounted on the pinionsteering gear or on the steering column. Assistant torque is applied to the steeringcolumn via a worm-gear. Therefore, the electric machine can run at relatively higherspeed. About 6-8 kN column force is required in this EPS system, which corresponds to7 Nm torque demand for electric machine (Ombach and Junak, 2007, 2008). Thespecifications for the desired electric machine under study, which is to be used in acolumn-type EPS, are summarized in Table I. The required torque-speed curve isshown in Figure 1.

DC-bus voltage 42 VStall torque 7 NmBase speed 600 rpmMaximum speed 2,000 rpmTorque ripple ,3%

Table I.Specifications of desiredelectric machine for EPS

application

Figure 1.Torque-speed curve of

desired electric machinefor EPS application

01

2

34

567

8

0 500 1,000 1,500 2,000 2,500speed (rpm)

torq

ue (N

m)IPM motor

for EPS

73

3. Discussion on critical design issuesGreat attention should be paid to certain critical issues which primarily impact themachines output characteristics. These critical issues mainly include operation mode,rotor structure and slot/pole combination.

A. Operation modePM brushless machines could be driven in both BLDC and BLAC modes. Thedefinitions of BLDC and BLAC mode are related to the waveforms of the backelectromotive force (back-EMF) and the driving current (Zhu, 2009), viz.:

. BLDC. Trapezoidal back-EMF with rectangular current.

. BLAC. Sinusoidal back-EMF with sinusoidal current.

The typical torque-speed performances (Shi et al., 2006) of brushless motor driven withBLDC and BLAC modes are shown in Figure 2.

For EPS applications, the electric machine usually runs at low or medium speeds.Then the BLAC mode is preferred as it can achieve a higher torque output at lowerspeed. Additionally, the BLAC mode usually results in much lower torque ripple thanthe BLDC mode (Islam et al., 2004), which is highly desirable in EPS applications.Hence, the BLAC mode should be employed, whilst the sinusoidal back-EMF has to beguaranteed.

B. Rotor structurePM machines provide many possibilities to place magnets on rotors, which can bebroadly divided into the SPM or IPM categories according to the fixtures of the PMonto the rotor core. The main SPM types are shown in Figure 3(a) and (b); whereas themain IPM types are shown in Figure 3(c) and (d).

Based on dq-coordinates, the electromagnetic torque can be calculated as:

Te 32plm iq Ld 2 Lqid iq 1

where p is the number of pole pairs, lm is the PM-excited flux linkage, id, iq, Ld and Lqare d, q-axes currents and inductances, respectively.

Figure 2.Typical torque-speedcurves with differentoperation modes

speed

torq

ue/c

urre

nt

BLDC-120

BLDC-180

BLAC

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For SPMs of type shown in Figure 3(a), where Ld Lq, the last item in equation (1) iszero. On the contrary, Ld , Lq for SPMs of type shown in Figure 3(b) and also for theIPMs. Thus, an extra torque boost can be obtained by applying appropriate id and iq,which is so-called reluctance torque (Otaduy and McKeever, 2006).

Though SPMs can offer slightly better dynamics due to smaller inductances as aresult of low (air-like) permanence of the magnets, IPMs can easily achieve the idealsinusoidal back-EMF which is tremendously required in BLAC mode. Furthermore,IPMs own many other advantages over SPMs, as will be discussed in the next section.

C. Slot/pole combinationThe concentrated windings allow many combinations of slots and poles to PMmachines. Different slot/pole combinations have extensive influence on machinecharacteristics, such as back-EMF, cogging torque, losses and efficiency (Yoneda et al.,2006; Zhu, 2009).

Common slot/pole number combinations for three-phase, non-overlapping windingelectric machines are:

Ns

Np k 3

2

; k 1; 2; 3. . . 2

where Ns and Np are numbers of slots and poles, respectively. These machines, 3s/2p,6s/4p, 9s/6p and 12s/9p, inevitably suffer low usage of windings with a winding factorof 0.866.

In order to maximize the winding flux-linkage and power density, coil-pitch shouldbe equal to pole-pitch, which means slot number is equal to pole number. Thesecombinations present maximum flux-linkage and power density, but also largecogging torque, and are therefore only suitable for single phase motors. Thus, therealistic combination of slots and poles should aim at coil-pitch < pole-pitch ratherthan coil-pitch pole-pitch. Therefore, Ns and Np differing by equations (1) and (2)are the two closest cases:

. Case 1: Ns and Np differed by 1, viz.:

Ns 2 Np 1 3

Electric machines with these slot/pole combinations such as 3s/2p, 3s/4p, 9s/8p, 9s/10p,show a number of merits, including high flux linkage per coil, high torque density andnegligible cogging torque. However, there will be a potential weakness in terms of

Figure 3.Different PM rotor

structures(a) (b) (c) (d)

Notes: (a) and (b): SPM; (c) and (d): IPM

IPM motorfor EPS

75

unbalanced magnetic force, which results in vibration and acoustic noise, as well asdecreased lifecycle.

. Case 2: Ns and Np differed by 2, viz.:

Ns 2 Np 2 4

Machines with these slot/pole combinations, for instance, 6s/4p, 6s/8p, 12s/10p,12s/14p, indicate similarly remarkable attributes, such as high torque density andsmall cogging torque. Moreover, there is no risk of unbalanced magnetic force.

The analysis shows that case 2 to be the better option, and the 12s/10p combinationhas therefore been chosen for this application. The potential merits are confirmed bythe comparison of back-EMF waveforms with different slot/pole combinations, asshown in Figure 4. It is clearly shown that the 12s/10p offers more sinusoidalback-EMF than others.

4. Proposed machineThe foregoing discussion has led to an initial model selection of a 12s/10p IPMmachine, which is to be driven in BLAC mode. The design of the PMs shape and othermachine parameters can now be effectively completed. The key parameters are listedin Table II, including the winding configuration and rotor shape modification.The proposed machine optimized by FEA is shown in Figure 5.

A. Winding configurationNon-overlapping concentrated windings are adopted, which exhibit outstandingfeatures of high winding factor (0.933) and short end winding. Only phase A is shownin Figure 6.

B. Rotor shape modificationAs mentioned previously, sinusoidal back-EMF is required for the BLAC drivingmode, while the essential condition is to attain the sinusoidal air gap flux densitydistribution. A practical technique of rotor shape modification is employed. One ofIPMs important advantages over SPM can be clearly shown in Figure 7, where it canbe seen that it is much simpler to precisely manufacture the rotor laminations outer

Figure 4.Back-EMF waveformswith different slot/polecombinations

8

6

4

2

0

2

4

6

8

0 60 120 180 240 300 360Angular position (elec deg)

Phas

e ba

ck-E

MF

(V)

10s/10p

15s/10p

12s/10p

12s/14p

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76

Symbol Machine parameter Value Unit

Ns Number of slots 12Np Number of poles 10m Number of phases 3Ncoil Number of turns per coil 30

PM material NdFeB35Magnetization orientation ParallelStator and rotor lamination material 35W470

Kp Slot fill factor 54%Rso Stator outer radius 75.0 mmRsi Stator inner radius 41.0 mmRo Rotor outer radius 40.0 mmg Air gap 0.5-0.95 mmwpm PM width 10.0 mmtpm PM thickness 2.0 mmwst Stator tooth width 5.0 mmla Active axial length 70 mmJpeak Rated peak current density 1.7e7 A/m

2

Udc DC-link voltage 42 VPem Rated power output 435 WIpeak Rated peak phase current 14 ARph Phase resistance (1008C) 0.27 V

Table II.Machine parameters

Figure 5.Cross section of the

proposed machine

IPM motorfor EPS

77

shape in IPMs, than the magnets outer shape in SPMs. This also leads to some otherdesirable characteristics:

. IPMs use simple rectangular-shape magnets with parallel magnetization reducing magnet price and manufacturing cost.

. The magnets are mechanically protected suitable for high speed operationwithout protective rings or retaining sleeves on the rotor.

. Presence of flux bridge makes the magnets better protected againstdemagnetization offering high overloading capability.

Besides, it is noteworthy that cogging torque minimization comes along with the gainof sinusoidal air gap flux density distribution.

Figure 6.Winding configuration ofthe proposed machine

22

23A2

A3

A4

A3+

A4+

Phase AA2+

A1+

A1

24

1

2

310

11

12

13

14

15

Figure 7.Rotor outer shapemodifications forsinusoidal air gap fluxdensity

(a) (b)Notes: (a) IPM; (b) SPM

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5. Performance evaluationA commercial FE software MagneForce is used to evaluate the machine performanceby two-dimensional (2D) FEA.

A. Air gap flux densityAs analyzed before, a non-uniform air gap is introduced to obtain sinusoidal fluxdensity distribution, hence sinusoidal back-EMF and negligible cogging torque. Theair gap flux density distributions at conditions of no load and full load are shown inFigure 8. And the corresponding harmonic components are shown in Figure 9. Sincethe third harmonic will be eradicated across the line windings, the effective higherharmonic contents are seen relatively small compared with the fundamental, and agood sinusoidal back-EMF is expected.

B. Back-EMFThe three phase back-EMF at the rated speed of 600 rpm is shown in Figure 10, whichare visually seen very symmetrical. Fourier analysis is then undertaken to evaluate theharmonic content of the spectrum. The total harmonic distortion is found to be 0.67percent, which means that the back-EMF is essentially sinusoidal.

Figure 8.Air gap flux density

distribution1.5

1.0

0.5

0.0

0.5

1.0

1.5

2.0

Br (

T)

no load full load

720 480 240 0 240 480 720Angular position (elec deg)

Figure 9.Harmonic components of

air gap flux density0.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Harmonic order

Br a

mpl

itude

(T)

no load full load

IPM motorfor EPS

79

C. InductanceTaking the saturation effects into account, the load will affect the permeance, whichwill result in inductance variation. Based on FEA, Ld and Lq are calculated withdifferent load conditions, i.e. variation of phase current with different amplitudes andadvanced commutation angles. The results are shown in Figures 11 and 12,respectively. The ratio Lq/Ld represents for the saliency level of a PM machine, which isdetermined by the physical structure and load condition, and is related to thereluctance torque. Figure 13 shows the variation of Lq/Ld.

During operations at higher load, Lq varies in the range of almost 40 percent, whileLd varies in the range of 5 percent only. This can be explained by the cross-couplingeffects between d- and q- axes, as a result of high magnetic saturation. It is generallyknown that operations with high magnetic saturation are inherent design features forelectric machines with high power density (Ombach and Junak, 2008).

Figure 11.Ld as a function of phasecurrent and advancedcommutation angle

15 13 11 9 7 5 3 1 015

3565

3.00

3.20

3.40

3.60

3.80

4.00

Ld (m

H)

gamma

(deg)

Iphase (A)

Figure 10.Back-EMF waveforms ofthe proposed motor atspeed of 600 rpm

18.0

12.0

6.0

0.0

6.0

12.0

18.0

24.0

0 120 240 360 480 600 720Angular position (elec deg)

Bac

k-EM

F (V

)

phase-A phase-B phase-CCOMPEL31,1

80

D. TorqueThe electromagnetic torque is calculated according to equation (1) under different loadconditions, as shown in Figure 14. The maximum torque occurs when the advancedcommutation angle is about 258. And the separated reluctance torque component is alsocomputed according to equation (5) by utilizing the FEA data obtained in calculating theelectromagnetic torque, in order to save simulation time, as shown in Figure 15:

Tr 32pLd 2 Lqid iq 5

Torque ripple should be completely minimized to ensure accurate steering andcomfortable driving experience. In general, torque ripple consists of two components, viz.,

Figure 12.Lq as a function of phase

current and advancedcommutation angle

15 13 11 9 7 5 3 10

1535

653.003.403.804.204.605.005.405.80

Lq (m

H)

Iphase (A) gamma

(deg)

Figure 13.Lq/Ld as a function of

phase current andadvanced commutation

angle

15 13 11 9 7 5 3 10

15

35

651.00

1.10

1.20

1.30

1.40

1.50

Lq/L

d

Iphase (A) gam

ma(de

g)

IPM motorfor EPS

81

the load dependent component and the load independent component. The former can beextensively ameliorated by employing BLAC mode, and the latter is essentially thecogging torque of the machine, which has already been reduced by means of a sinusoidalair gap flux density distribution, as shown in Figure 16. Figure 17 shows the output torquewaveform at full load condition, where the smoothness of the torque is evident. From thezoomed-in view of the torque ripple in Figure 18, it is further confirmed that the peak topeak torque ripple is 0.17 Nm, or 2.2 percent of the average output torque, which wellexceeds the requirement of less than 3 percent.

Figure 14.Electromagnetic torque asa function of phase currentand advancedcommutation angle

0123456789

0 10 20 30 40 50 60 70 80 90gamma (deg)

Torq

ue (N

m)

Iphase from 1 A to 15 A

Figure 15.Reluctance torque as afunction of phase currentand advancedcommutation angle

0

0.3

0.6

0.9

1.2

1.5

1.8

0 10 20 30 40 50 60 70 80 90gamma (deg)

Rel

ucta

nce

torq

ue (N

m)

Iphase from 1 A to 15 A

Figure 16.Cogging torque waveform

6

4

2

0

2

4

6

0 6 12 18 24 30 36Angular position (mech deg)

Cogg

ing

torq

ue (m

Nm)

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E. Losses and efficiencyFor EPS applications, the machine runs at low and moderate speed, whereelectromagnetic losses dominate the total losses. Thus, only the electromagneticlosses are evaluated here. Electromagnetic losses mainly include copper losses in thestator windings PCu, iron losses in the stator and rotor laminations PFe and eddy currentlosses in the magnets PPM. The power flow can be expressed by:

Pin PCu PFe PPM Pout 6Apparently, copper losses are the main part considering that the iron losses and eddycurrent losses are often small or negligible at low speed. Based on these assumptions, theefficiency map of the proposed motor as a function of phase current and advancedcommutation angle is computed and is shown in Figure 19.

F. Frame and prototypeConsiderable efforts have also been spent on the final mechanical design of themachine, which is shown in Figure 20. A prototype, shown in Figure 21, has been builtfor validation, which will be the subject of future work.

6. ConclusionsA full design procedure of a brushless PM motor drive system used for EPS applicationsis proposed. The requirements of the EPS application are first introduced and the

Figure 17.Output torque waveform

0123456789

0 120 240 360 480 600 720Angular position (elec deg)

Torq

ue (N

m)

Figure 18.Zoomed-in view of torque

ripple7.50

7.60

7.70

7.80

7.90

8.00

0 120 240 360 480 600 720Angular position (elec deg)

Torq

ue (N

m)

Peak to peak value is 0.17 Nm

IPM motorfor EPS

83

specifications of the desired machine are then deduced. For correct selection of the rightmachine topology before detailed electromagnetic machine design, critical issuesincluding operation mode, rotor structure and slot/pole combination are first analyzed.Consequently, the IPM rotor type, BLAC operation mode and 12s/10p combination havebeen selected for further design. The final design is fully optimized by FEA.Subsequently, the characteristics of the proposed machine such as air gap flux density,back-EMF, inductance, output torque, cogging torque, torque ripple, losses andefficiency, are evaluated. The comprehensive 2D FEA results verify that the design fullymeets the requirements of the steering system. Finally, the mechanical design is shownand a prototype motor has been built for verification in future work.

Figure 19.Efficiency map as afunction of phase currentand advancedcommutation angle

Figure 20.Frame of the proposedmotor

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References

Aroquiadassou, G., Henao, H., Lanfranchi, V., Betin, F., Nahidmobarakeh, B., Capolino, G.,Biedinger, M. and Friedrich, G. (2005), Design comparison of two rotating electricalmachines for 42 V electric power steering, 2005 IEEE International Conference on ElectricMachines and Drives, pp. 431-6.

Bianchi, N. and Bolognani, S. (2002), Design techniques for reducing the cogging torque insurface-mounted PM motors, IEEE Trans. on Industry Applications, Vol. 38 No. 5,pp. 1259-65.

Bianchi, N., Pre, M.D. and Bolognani, S. (2006), Design of a fault-tolerant IPM motor for electricpower steering, IEEE Trans. on Vehicular Technology, Vol. 55 No. 4, pp. 1102-11.

Chedot, L. and Friedrich, G. (2004), A cross saturation model for interior permanent magnetsynchronous machine. Application to a starter-generator, IEEE Ind. App. Society Annu.Meeting, Seattle, pp. 64-70.

Islam, M.S., Mir, S. and Sebastian, T. (2003), Issues in reducing the cogging torque ofmass-produced permanent magnet brushless dc motor, Proc. 38th IEEE Ind. App. Annu.Meeting, Salt Lake City, UT, USA, pp. 393-400.

Islam, M.S., Mir, S., Sebastian, T. and Underwood, S. (2004), Design considerations ofsinusoidally excited permanent magnet machines for low torque ripple applications, Ind.App. Conf., 2004. 39th IAS Annu. Meeting, Vol. 3, pp. 1723-30.

Figure 21.Prototype of theproposed motor

IPM motorfor EPS

85

Jahns, T.M. and Soong, W.L. (1996), Pulsating torque minimization techniques for permanentmagnet AC motor drives a review, IEEETrans. on Ind. Electronics, Vol. 43 No. 2, pp. 321-30.

Ombach, G. and Junak, J. (2007), Two rotors designs comparison of permanent magnetbrushless synchronous motor for an electric power steering application, EuropeanConference on Power Electronics and Applications, pp. 1-9.

Ombach, G. and Junak, J. (2008), Comparison of double-layer interior permanent magnetsynchronous motor design with two different pole numbers, 18th InternationalConference on Electrical Machines (ICEM 2008), pp. 1-6.

Ombach, G., Junak, J. and Ackva, A. (2006), Vibrations optimization of brushless power steeringmotor with taking into account magnetostriction effects, paper presented at 17thInternational Conference on Electrical Machines, Chania, Greece.

Oprea, C. and Martis, C. (2008), Fault tolerant permanent magnet synchronous machine forelectric power steering systems, International Symposium on Power Electronics, ElectricalDrives, Automation and Motion (SPEEDAM 2008), pp. 256-61.

Otaduy, P.J. and McKeever, J.W. (2006), Modeling Reluctance-Assisted PM Motors, Oak RidgeNational Laboratory, Oak Ridge, TN.

Seong, T.L., Burress, T.A. and Tolbert, L.M. (2009), Power-factor and torque calculation withconsideration of cross saturation of the interior permanent magnet synchronous motorwith brushless field excitation, IEEE International Electric Machines and DrivesConference (IEMDC09), pp. 317-22.

Shi, Y., Zhu, Z.Q. and Howe, D. (2006), Torque-speed characteristics of interior-magnet machinesin brushless AC and DC modes, with particular reference to their flux-weakeningperformance, CES/IEEE 5th International Power Electronics and Motion ControlConference (IPEMC 2006), Vol. 3, pp. 1-5.

Stumberger, B., Stumberger, G., Dolinar, D., Hamler, A. and Trlep, M. (2003), Evaluation ofsaturation and cross-magnetization effects in interior permanent-magnet synchronousmotor, IEEE Trans. on Ind. App., Vol. 39 No. 5, pp. 1264-71.

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About the authors

C.F. Wang is a PhD student at Zhejiang University, China. He received the BEngdegree from Zhejiang University in 2007, and took an internship at CranfieldUniversity, UK, in 2009.

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J.X. Shen is a Professor at Zhejiang University, China. He received the BEng andMEng degrees from Xian Jiaotong University, China, in 1991 and 1994,respectively, and a PhD degree from Zhejiang University in 1997. He was withNanyang Technological University, Singapore (1997-1999), University ofSheffield, UK (1999-2002), and IMRA Europe SAS, UK (2002-2004). His mainresearch interests include design and applications of permanent-magnetmachines and drives. J.X. Shen is the corresponding author and can becontacted at: J_X_Shen@zju.edu.cn

P.C.K. Luk is a Senior Lecturer and the Head of Power and Drive Systems Groupat Cranfield University, UK. He received his high diploma with merit fromPolytechnic University (PolyU), HK, in 1983, MPhil from Sheffield University,UK, in 1989, and PhD from Glamorgan University, UK, in 1992. He was with GEC(HK), PolyU, and Universities of Glamorgan, Robert Gordon and Hertfordshire,UK. His current main research interests are in electrical drives for electric vehiclesand renewable energy applications.

W.Z. Fei is working towards a PhD degree at Cranfield University, UK, andmeanwhile doing joint projects under an MOU between Zhejiang University,China and Cranfield University. He received the BEng and MEng degrees fromZhejiang University, in 2004 and 2006, respectively.

M.J. Jin received the B.S. degree and PhD degree from Zhejiang University,Hangzhou, China, in 2001 and 2006, respectively. Since 2006, he has been with thedepartment of Electrical Engineering, Zhejiang University, where he currently isa lecturer. His research interests are electrical machine design and drives. Dr Jinis a member of IEEE Industry Applications.

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