A Comparative Study of Two Permanent Magnet Motors Structures with Interior and Exterior Rotor

Journal of Asian Electric Vehicles, Volume 8, Number 1, June 2010

Mohamed Chaieb 1, Naourez Ben Hadj 2, Jalila Kaouthar Kammoun 3, and Rafik Neji 4

1 Electrical Engineering Department, University of Sfax, [email protected] 2 Electrical Engineering Department, University of Sfax, [email protected] 3 Electrical Engineering Department, University of Sfax, [email protected] 4 Electrical Engineering Department, University of Sfax, [email protected]

Abstract Currently, the permanent magnet motors PMM represent an attractive solution in the electric traction field, thanks to their higher performances than other electric motors. In this context, this work represents an analytical study and validation by the finite element method of two configurations, the radial flux permanent magnet synchronous motors with exterior rotor PMSMER and with interior rotor PMSMIR. This paper is divided into two sections: In the first section, we represent the analytical study based on electromagnetic law of the two structures PMSMER and PMSMIR. In the second section, we represent a comparative study of the two structure performances.

Keywords 2. MODELLING OF THE TWO PMM STRUC- permanent magnet motors design, radial flux, finite TURES element method, modelling, performance 2.1 Structural data The motors structure allowing the determination of 1. INTRODUCTION the studied geometry is based on three relationships. Considering the large variety of electric motors, such The ratio β is the relationship between the magnet an- as asynchronous motors, synchronous motors with gular width La and the pole-pitch Lp. This relationship variable reluctances, permanent magnet motors with is used to adjust the magnet angular width according radial or axial flux, the committed firms try to find the to the motor pole-pitch. best choice of the motor conceived for electric vehicle L field. β = a (1) There are different criteria of selection in order to Lp solve this problem such as the power-to-weight ratio, π the efficiency and the price. The traction electric mo- Lp = (2) tor is specified by several qualities, such as the flex- P ibility, reliability, cleanliness, facility of maintenance, The ratio Rldla is the relationship between the angular silence etc. Moreover, it must satisfy several require- width of a principal tooth and of the magnet angular ments, for example the possession of a high torque width. This ratio is responsible for the regulation of and an important efficiency [Zire et al., 2003; Gasc, the principal tooth size which has a strong influence 2004; Chan, 2004]. on the electromotive force form. In this context, The PMM is characterized by a high Adent efficiency, very important torque, and power-to- Rldla = (3) weight, so it becomes very interesting for electric La traction. The rotor of the PMM supports several con- The Rdid ratio is the relationship between the principal figurations interesting for the magnets mounted on tooth angular width and the inserted tooth angular surface. width Adenti. This relationship fixes the inserted tooth In the intension, to ensure the most suitable and judi- size. cious choice, we start by a comparative study between Adent the two structures, then, we implement a methodology Rdid = (4) of design based on an analytical modelling and on the La electromagnetism laws.

1363 M. Chaieb et al.: A Comparative Study of Two Permanent Magnet Motors Structures with Interior and Exterior Rotor

2.2 Geometrical structures of the PMSMIR and the • Time of starting td = 4 s

PMSMER • Outside temperature tex = 40 °C

This part is devoted to an analytical sizing allowing • Maximum motor power Pmmax = 21,635 kW calculation of geometrical sizes of the two PMM con- • Winding temperature tb = 95 °C figurations which are the PMSMER and the PMSMIR. • Base speed of the vehicle Vb = 30 km/h

Figure 1 represents the PMSMER and the PMSMIR • Maximum Speed of the vehicle Vmax = 100 km/h with the number of pole pairs is 4 and a number of • Load factor of the slots kr = 0, 44 principal teeth is 6, between two principal teeth, an • Acceptable density of current in the slots δ = 7 A/ inserted tooth is added to improve the form of wave mm2 and to reduce the leakage flux [Hadj et al., 2007]. The slots are right and open in order to facilitate the inser- 2.3.2 Constants specific to materials tion of coils and to reduce the production cost. The The motor is composed by a diversity of materials type of winding is concentric; each winding of phase specified as follows: is made up of two diametrically opposite coils [Mag- • Remanent magnetic induction of the magnets Bm = nussen et al., 2005; Bianchi et al., 2003; Libert and 1,175 T

Soulard, 2004]. • Induction of demagnetization Bc = 0,383 T • Magnetic induction in teeth data base = 0,9 T Magnets • Relative permeability of the magnets μ = 1,05 H/m Slots a • Coefficient of mechanical losses k = 1 % Stator yoke m • Resistivity of copper with 95 °C R = 17,2 10-9 Ωm Rotor yoke cu • Coefficient of variation of the copper resistivity α = Principal Teeth Inserted Teeth 0,004

• Density of the electrical sheets Mvt = 7850 kg Fig. 1 Radial flux permanent magnet motors with ex- • Density of magnets Mva = 7400 kg terior rotor and interior rotor • Density of copper Mvc = 8950 kg • Coefficient of quality of the sheets Q = 1,100

2.3 Analytical sizing of the two motors structures • Density of copper Mvc = 8950 kg The analytical study of motor sizing is based on the schedules conditions parameters, the constant charac- 2.3.3 Expert data terizing materials, the expert data and the configura- The expert data are practically represented by three tion of the two motors. This Sizing motor approach is sizes which are, the magnetic induction in the air gap represented as follows: Be, the magnetic induction in the stator yoke Bcs and

the magnetic induction in the rotor yoke Bcr. It should 2.3.1 The schedules data conditions be noted that the zone of variation of these three • Electric vehicle mass M = 1000 kg parameters varies between 0,2 to 1,6 T [Hadj et al.,

• Angle of starting ad = 3 ° 2007].

Schedule data conditions

Analytical model Geometrical parameters Specific constants to materials

Expert data

Finite element method Electromagnetic parameters

Full load flux 1 Structural data 0,008 Full load flux 2 0,006 Full load flux 3 0,004 )

b 0,002 W ( 0 x u l 20 40 60 80 100 F -0,002 -0,004 -0,006 -0,008 Rotor position (°)

Data identified by the finite element method

Fig. 2 Sizing motor approach

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2.3.4 Structural data Dm  e For the two configurations, we adopted the same Sd  Aenc Lm (10) number of pole pairs P = 4, with an air gap thickness 2 equivalent to 2mm, With a relationship β equal to 0,667 The inserted tooth section: Sdi and Rldla equal to 1,2. Dm  e S  Adenti Lm (11) di 2 2.3.5 Data identified by the finite element method

Kfu is the flux leakage coefficient of the PMSMIR The slot section: Se which is fixed to 0,95 whereas for the PMSMER, Kfu is equal to 0,98. Between the principal tooth angular Dm  e 1 2  Dm  e (12) Se  Aenc Lm    Adent Adenti Lm 2 2  N  2 width Adent and the inserted tooth angular width Adenti, d we define a ratio didR equal to 0,2. with Lm is the motor length. 2.4 Geometrical sizes The teeth height Hd of the PMSMIR is expressed by Geometrical parameters of the two structures motors equation 13 with Nsph is the number of turns per phase are defined in Figure 3. and In is the rated current. Hd specific to the PMSMIR is expressed: 3 4 2   1 2 Nsph.In Dm + e Dm + e (13) 5 5 Hd = +   − 2 1 Nd δKrAenc  2  2 4 3 Hd specific to the PMSMER is expressed:

2 1 : The magnet height, h a Nsph.In  Dm - e  Dm - e 2 : The slots height and the tooth height, he, hd Hd      (14) δ 3 : The rotor yoke height, hcr Nd KrAenc  2  2 4 : The stator yoke height, hcs 5 : The air gap thickness, e The stator yoke thickness Hcs is obtained by applica- Fig. 3 PMSMER and PMSMIR parameters tion of the flux conservation theorem.

BdSd Hcs  (15) 2.4.1 Stator geometrical sizes of the PMSMIR 2LmBcs The slot average width: Lenc Stator yoke Dm + e + Hd Lenc = Aenc (5) 2

The principal tooth section: Sd

Rotor yoke Dm + e Sd = Adent Lm (6) 2 Fig. 4 Application of the theorem of the flux conser- The inserted tooth section: Sdi vation Dm + e Sdi = Adenti Lm (7) 2

The slot section: Se 2.4.3 The rotor geometrical sizes of the two structures Dm + e 1 2  Dm  e S A L =   e = enc m Adent Adenti Lm (8) The expression of the magnet height Ha is the same 2 2  Nd  2 one in the two structures; it is obtained by the application of the Ampere theorem:   2.4.2 Stator geometrical sizes of the PMSMER (16)  Hdl = Σ ni  Haha + ehe = 0 The slot average width: Lenc contour

Dm  e  Hd The remanent induction of the magnet M(Ta) at Ta °C is Lenc Aenc (9) 2 defined by:

The principal tooth section: Sd

1365 M. Chaieb et al.: A Comparative Study of Two Permanent Magnet Motors Structures with Interior and Exterior Rotor

µ aBee Ha = Be (17) M(Ta) − Kfu

M(Ta) = M1+α m(Ta − 20) (18)

The rotor yoke thickness Hcr is defined: Fig. 5 Mesh in the PMSMIR Φ BeSd BeSd = BcsHcrLmKfu =  Hcr = (19) 2 2 2KfuLmBcr

2.4.4 Electrical sizing The electromotive force in the two structures is expressed by: 8  π   π  EMF1(t) = NsphLmDmBesin βsin β Rldla π  2   2  (20) Fig. 6 Mesh in the PMSMER Ω sin(P Ω t) m m two studied structures is given by figures 5 and 6, we make a refined mesh in the air gap to obtain a precised The motor electric constant: Ke result [Ohyama et al., 2005]. 12   Figure 7 and figure 8 show respectively the flux den- Ke  NsphLmDmBesin  sin  Rldla (21)  2 2 sity in the PMSMER and in the PMSMIR. We note that the maximal induction for the motor The electromagnetic torque: T em yokes is equal to 1.4 T that proves no saturation in 1 3 magnetic motor circuit. Tem (t) = EMFi (t).ii (t) (22) We note the appearance of leakages flux in the motor, Ω i=1 this requires the determination of the leakages flux co- with EMFi and ii respectively represent the electromotive force and the current of the i phase.

The motor rated current In is the ratio between the electromagnetic torque and the motor electric constant

Tem In = (23) Ke

The phase résistance of the motor: Rph Fig. 7 Flux density in the PMSMER Nsphδ Lsp Rph = Rcu(Tb) (24) In / 2 where Rcu(Tb) is the Resistivity of copper at the temperature of winding Tb and Lsp is the spire average length defined as follow [Hadj et al., 2007].

Rcu(Tb) = Rcu1+ α (Tb − 20) (25)

Fig. 8 Flux density in the PMSMIR   Dm + e + hd   Lsp = 2(Aenc+ Adent).  + Lm (26)   2  

3. COMPARATIVE STUDY BETWEEN THE TWO STRUCTURES In this study, the validation and comparation between the two structures is based on the finite elements method using the software FEMM. The mesh in the Fig. 9 Flux lines in the PMSMER

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No load flux 1 No load flux 2 No load flux 3 0,008 0,006 0,004 0,002 0

F l u x ( W b ) -0,002 0 20 40 60 80 100 -0,004 Fig. 10 Flux lines in the PMSMIR -0,006 -0,008 Rotor position (°) efficient to validate the analytical model. Fig. 13 Flux of the three phases at no-load for the 3.1 Electromagnetic parameters PMSMIR 3.1.1 Air gap flux density Figures 11 and 12 show the airgap induction in the Full load flux 1 Full load flux 2 PMSMER and in the PMSMIR, the maximal value is Full load flux 3 about 1 T [Pakdel, 2009]. 0,008 0,006 0,004 1 0,002 Be (T) 0 0 20 40 60 80 100 0.5 F l u x ( W b ) -0,002 -0,004 -0,006 0 -0,008 Rotor position (°) -0.5 Fig. 14 Flux of the three phases at full-load for the PMSMIR -1 0 10 20 30 40 50 60 70 Airgap length (mm) No load flux 1 No load flux 2 Fig. 11 Airgap induction in the PMSMER No load flux 3 0,008 0,006 1 0,004 0,002 Be (T) 0 0.5 0 20 40 60 80 100 F l u x ( W b ) -0,002 -0,004 0 -0,006 -0,008 Rotor position (°) -0.5 Fig. 15 Flux of the three phases at no-load for the -1 PMSMER 0 10 20 30 40 50 60 70 Airgap length (mm) Full load flux 1 Fig. 12 Airgap induction in the PMSMIR Full load flux 2 Full load flux 3 0,008 0,006 3.1.2 Flux 0,004 Figures 13, 14, 15 and 16 illustrate the three phases 0,002 0 flux at no-load and at full load according to the me- 0 20 40 60 80 100 F l u x ( W b ) -0,002 chanical angle for the PMSMIR and PMSMER. -0,004 According to the Figure 17, we can conclude that the -0,006 variation of the flux at no-load and at full-load accord- -0,008 ing to the rotor position is very weak, that originates Rotor position (°) the magnetic reaction. Fig. 16 Flux of the three phases at full-load for the PMSMER

1367 M. Chaieb et al.: A Comparative Study of Two Permanent Magnet Motors Structures with Interior and Exterior Rotor

Flux at no-load No load EMF1 Flux at full-load No load EMF2 0,006 No load EMF3 250 0,004 200 0,002 150 100 0 50 -0,002 0 20 40 60 80 100 0 F l u x ( W b )

E M F ( V ) -50 0 20 40 60 80 100 -0,004 -100 -0,006 -150 -0,008 -200 Rotor position (°) -250 Rotor position (°) Fig. 17 Flux at Full-load and at no-load of the PMS- Fig. 20 EMF at no-load of the PMSMER MIR

Full load EMF1 3.1.3 Electromotive forces EMF Full load EMF2 Full load EMF3 The form of EMF represents a very significant param- 250 200 eter. It is expressed by: 150 100 50 dΦ 0 EMF = −Nsph (27) dt F E M ( V ) -50 0 20 40 60 80 100 -100 Figures 18, 19, 20 and 21 give an idea on the form of -150 -200 the EMF at no-load and at full load according to the -250 rotor position. This EMF is generated by the flux evo- Rotor position (°) lution through a coil of the stator. Fig. 21 EMF at full-load of the PMSMER

No load EMF1 and at no load of the two structures obtained by the No load EMF2 No load EMF3 finite element method [Zhu et al., 2006; Yee-pien et 250 200 al., 2009]. The obtained results validate the analytical 150 model because the torque oscillates around the aver- 100 50 age value found analytically which is 112 Nm. 0

E M F ( V ) -50 0 20 40 60 80 100 -100 No-load torque with exterior rotor -150 Full-load torque with exterior rotor -200 140 -250 120 Rotor position (°) 100 80 Fig. 18 EMF at no-load of the PMSMIR 60

T o r q u e ( N m ) 40 20 Full load EMF1 0 Full load EMF2 0 20 40 60 80 100 Full load EMF3 250 Rotor positopn(°) 200 150 Fig. 22 Torque at no-load and at full-load for the 100 50 PMSMER 0

E M F ( V ) -50 0 20 40 60 80 100 No-load torque with interior rotor -100 -150 Full-load torque with interior rotor -200 120 -250 100 Rotor position (°) 80 60 Fig. 19 EMF at full-load of the PMSMIR 40

T o r q u e ( N m ) 20 0 0 20 40 60 80 100 3.2 Torque and Power-to-weight ratio Rotor position (°) 3.2.1 Calculation of the torque The instantaneous torque is expressed by equation 22. Fig. 23 Torque at no-load and at full-load for the Figure 22 and 23 represent the torque at full-load PMSMIR

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Figures 24 and 25 illustrate the torque ripple in the 3.3 Losses and efficiency two structures, we conclude that the torque ripple in Table 1 represents the efficiency and the losses for the the PMSMER is 6.14 % and in the PMSMIR is 9.43 PMSMIR and the PMSMER. % [Wang et al., 2009]. Table 1 Losses and the efficiency of the two struc-

112 tures

110 PMSMIR PMSMER 108 Joule losses 557,180 547,089 106 104 Iron losses 59,662 32,653 o r q u e i p l ( N m ) T 102 Mechanical losses 215,755 216,025 100 0 20 40 60 80 100 Efficiency 0,962 0,964 Rotor position (°) Fig. 24 Torque ripple in the PMSMER We can deduce that the Joules losses and the iron losses for the PMSMER are lower than those of the PMSMIR. Moreover, the efficiency of the PMSMER 118 is more interesting than the other structure. Figure 27 116 illustrates the total losses of the two structures. 114 Losses for interior rotor 112 Losses for exterior motor o r q u e i p l ( N m ) T 110 1500

108 1000 0 20 40 60 80 100 500

Rotor position (°) L o s e ( W ) 0 Fig. 25 Torque ripple in the PMSMIR 0 10 20 30 Motor power (kW)

3.2.2 Power-to-weight ratio Fig. 27 Losses according to the power The power-to-weight ratio is defined by the relationship between the power and the mass of the motor We conclude that the losses magnitude is the same or- active part. Figure 26 represents the power-to-weight ders for low powers in the two structures. ratio specific to the two structures according to the However, for the powers higher than 15kW, the losses power. in PMSMER are lower than those produced by the According to this figure, we notice that the power-to- PMSMIR. weight ratio of the PMSMER is slightly lower than Figure 28 represents the efficiency obtained for the the PMSMIR, while the great motor power it is the two structures; we note that the PMSMER offers ef- reverse. ficiency better than that developed by the PMSMIR. As a conclusion, the configuration of the PMSMER is most suitable since it offers efficiency higher than that Power-to-wight ratio with interior rotor Power-to-wight ratio with exterior rotor 1 efficiency of the interior rotor efficiency of the exterior rotor 0,8 0,966 0,6 0,964 0,962 0,4 0,96 0,958 0,2

E f i c e n y 0,956 0 0,954 0 5 10 15 20 25 30 0,952 0,95 P o w e r - t i g h a ( K / ) Power-to-wight ratio (Kw) 0 5 10 15 20 25 30 Motor power (kW) Fig. 26 Power-to-weight ratio Fig. 28 Efficiency according to the power

1369 M. Chaieb et al.: A Comparative Study of Two Permanent Magnet Motors Structures with Interior and Exterior Rotor

reached by the first structure. This type of configura- machines, Journal of Electromagnetic Analysis and tion is adapted more to be exploited as a motor-wheel. Applications, Vol. 1, No. 1, 11-14, 2009. Yee-pien, Y., Y. Shih-chin, and L. Jieng-jang, Optimal 4. CONCLUSION design and control of a torque motor for machine We choose the synchronous permanent magnet motor tools, Journal of Electromagnetic Analysis and Ap- with radial flux. Basing on the schedule data condi- plications, Vol. 1, No. 4, 220-228, 2009. tions, sizing approach given by Figure 2, electromag- Zhu, Z. Q., Y. F. Shi, and D. Howe, Comparison of netic laws, an analytical modelling of two structures torque-speed characteristics of interior-magnet ma- which are the PMSMER and the PMSMIR is carried chines in brushless AC and DC modes for EV/HEV out. applications, Journal of Asian Electric Vehicles, We compare efficiency, mass, torques and losses in the Vol. 4, No. 1, 843-850, 2006. two structures of the PMM. In conclusion, the PMS- Zire, H. S., C. Espanet, and A. Miraoui, Performance MER is the most interesting since it is more profitable comparison of two magnet synchronous motors and lighter than the PMSMIR. Finally, the realization structures with interior rotor and exterior rotor, of a prototype is necessary to confirm our study. Proceedings of Electrotechnique du Futur, EF, 51, 2003. References Bianchi, B., N. Bolognani, and P. Frare, Design Crite- (Received February 5, 2010; accepted May 3, 2010) ria for High-efficiency SPM Synchronous Motors, IEEE Transactionss on Magnet, Vol. 21, No. 2, 396-404, 2006. Chan, C. C., The sate of the art of electric vehicles, Journal of Asian Electric Vehicles, Vol. 2, No. 2, 579-600, 2004. Gasc, L., Permanent magnet motor design with low torque ripple for automotive electric power steer- ing: Structure and control approaches, PhD Thesis, Polytechnic National Institute of Toulouse, 2004. Hadj, N. B., S. Tounsi, R. Neji, and F. Sellami, Real coded Genetic algorithm for permanent magnet motor mass minimization for electric vehicle application, Proceedings of 3rd International Sympo- sium on Computational Intelligence and Intelligent Informatics, 153-158, 2007. Kazuhiro, O., A. Kenichi, N. Maged, F. Nashed, H. Fujii, and H. Uehara, Design using finite element analysis of switched reluctance motor for electric vehicle, Journal of Asian Electric Vehicles, Vol. 3, No. 2, 793-800, 2005. Libert, F., and J. Soulard, Investigation on pole-slot combinations for permanent magnet machines with concentrated windings, Proceedings of the Interna- tional Conference on Electrical Machines, Vol. 1, 530-535, 2004. Magnussen, F., and H. Lendenmann, Parasitic ef- fects in PM machines with concentrated windings, IAS2005 40th Annual Meeting Hong Kong, Vol. 2, 1045-1049, 2005. Pakdel, M., Analysis of the magnetic flux density, the magnetic force and the torque in a 3D brushless DC motor, Journal of Electromagnetic Analysis and Applications, Vo. 1, No. 1-5, 2009. Wang, Y., J. Shen, Z. Fang, and W. Fei, Reduction of cogging torque in permanent magnet flux-switching

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