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

Transcription

1 Journal of Asian Electric Vehicles, Volue 8, Nuber, June A Coparative Stuy of Two Peranent Magnet Motors Structures with Interior an Exterior Rotor Mohae Chaieb, Naourez Ben Haj, Jalila Kaouthar Kaoun 3, an Rafik Neji 4 Electrical Engineering Departent, University of Sfax, chaieb_e@yahoo.fr Electrical Engineering Departent, University of Sfax, benhaj.naourez@enis.rnu.tn 3 Electrical Engineering Departent, University of Sfax, kaoutharkaoun@yahoo.fr 4 Electrical Engineering Departent, University of Sfax, rafik.neji@enis.rnu.tn Abstract Currently, the peranent agnet otors PMM represent an attractive solution in the electric traction fiel, thanks to their higher perforances than other electric otors. In this context, this work represents an analytical stuy an valiation by the finite eleent etho of two configurations, the raial flux peranent agnet synchronous otors with exterior rotor an with interior rotor PMSMIR. This paper is ivie into two sections: In the first section, we represent the analytical stuy base on electroagnetic law of the two structures an PMSMIR. In the secon section, we represent a coparative stuy of the two structure perforances. Keywors peranent agnet otors esign, raial flux, finite eleent etho, oelling, perforance. INTRODUCTION Consiering the large variety of electric otors, such as asynchronous otors, synchronous otors with variable reluctances, peranent agnet otors with raial or axial flux, the coitte firs try to fin the best choice of the otor conceive for electric vehicle fiel. There are ifferent criteria of selection in orer to solve this proble such as the power-to-weight ratio, the efficiency an the price. The traction electric otor is specifie by several qualities, such as the flexibility, reliability, cleanliness, facility of aintenance, silence etc. Moreover, it ust satisfy several requireents, for exaple the possession of a high torque an an iportant efficiency [Zire et al., 3; Gasc, 4; Chan, 4]. In this context, The PMM is characterize by a high efficiency, very iportant torque, an power-toweight, so it becoes very interesting for electric traction. The rotor of the PMM supports several configurations interesting for the agnets ounte on surface. In the intension, to ensure the ost suitable an juicious choice, we start by a coparative stuy between the two structures, then, we ipleent a ethoology of esign base on an analytical oelling an on the electroagnetis laws.. MODELLING OF THE TWO PMM STRUC- TURES. Structural ata The otors structure allowing the eterination of the stuie geoetry is base on three relationships. The ratio β is the relationship between the agnet angular with L a an the pole-pitch L p. This relationship is use to ajust the agnet angular with accoring to the otor pole-pitch. L a L p β = () π L p = () P The ratio R lla is the relationship between the angular with of a principal tooth an of the agnet angular with. This ratio is responsible for the regulation of the principal tooth size which has a strong influence on the electrootive force for. A ent L a R lla = (3) The R i ratio is the relationship between the principal tooth angular with an the inserte tooth angular with A enti. This relationship fixes the inserte tooth size. A ent L a R i = (4) 363

2 ,8,6,4, -, -,4 -,6 -, Full loa flux Full loa flux Full loa flux 3 M. Chaieb et al.: A Coparative Stuy of Two Peranent Magnet Motors Structures with Interior an Exterior Rotor. Geoetrical structures of the PMSMIR an the This part is evote to an analytical sizing allowing calculation of geoetrical sizes of the two PMM configurations which are the an the PMSMIR. Figure represents the an the PMSMIR with the nuber of pole pairs is 4 an a nuber of principal teeth is 6, between two principal teeth, an inserte tooth is ae to iprove the for of wave an to reuce the leakage flux [Haj et al., 7]. The slots are right an open in orer to facilitate the insertion of coils an to reuce the prouction cost. The type of wining is concentric; each wining of phase is ae up of two iaetrically opposite coils [Magnussen et al., 5; Bianchi et al., 3; Libert an Soular, 4]. Magnets Slots Stator yoke Rotor yoke Principal Teeth Inserte Teeth Fig. Raial flux peranent agnet otors with exterior rotor an interior rotor.3 Analytical sizing of the two otors structures The analytical stuy of otor sizing is base on the scheules conitions paraeters, the constant characterizing aterials, the expert ata an the configuration of the two otors. This Sizing otor approach is represente as follows:.3. The scheules ata conitions Electric vehicle ass M = kg Angle of starting a = 3 Tie of starting t = 4 s Outsie teperature t ex = 4 C Maxiu otor power P ax =,635 kw Wining teperature t b = 95 C Base spee of the vehicle V b = 3 k/h Maxiu Spee of the vehicle V ax = k/h Loa factor of the slots k r =, 44 Acceptable ensity of current in the slots δ = 7 A/.3. Constants specific to aterials The otor is copose by a iversity of aterials specifie as follows: Reanent agnetic inuction of the agnets B =,75 T Inuction of eagnetization B c =,383 T Magnetic inuction in teeth ata base =,9 T Relative pereability of the agnets μ a =,5 H/ Coefficient of echanical losses k = % Resistivity of copper with 95 C R cu = 7, -9 Ω Coefficient of variation of the copper resistivity α =,4 Density of the electrical sheets M vt = 785 kg Density of agnets M va = 74 kg Density of copper M vc = 895 kg Coefficient of quality of the sheets Q =, Density of copper M vc = 895 kg.3.3 Expert ata The expert ata are practically represente by three sizes which are, the agnetic inuction in the air gap Be, the agnetic inuction in the stator yoke Bcs an the agnetic inuction in the rotor yoke B cr. It shoul be note that the zone of variation of these three paraeters varies between, to,6 T [Haj et al., 7]. Scheule ata conitions Specific constants to aterials Analytical oel Geoetrical paraeters Expert ata Structural ata Finite eleent etho Electroagnetic paraeters Data ientifie by the finite eleent etho Fig. Sizing otor approach 364

3 Journal of Asian Electric Vehicles, Volue 8, Nuber, June.3.4 Structural ata For the two configurations, we aopte the sae nuber of pole pairs P = 4, with an air gap thickness equivalent to, With a relationship β equal to,667 an R lla equal to,..3.5 Data ientifie by the finite eleent etho K fu is the flux leakage coefficient of the PMSMIR which is fixe to,95 whereas for the, K fu is equal to,98. Between the principal tooth angular with A ent an the inserte tooth angular with A enti, we efine a ratio R i equal to,..4 Geoetrical sizes Geoetrical paraeters of the two structures otors are efine in Figure : The agnet height, h a : The slots height an the tooth height, h e, h 3 : The rotor yoke height, h cr 4 : The stator yoke height, h cs 5 : The air gap thickness, e Fig. 3 an PMSMIR paraeters.4. Stator geoetrical sizes of the PMSMIR The slot average with: L enc D + e + H L = enc A enc (5) D e S A enc L () The inserte tooth section: S i S i D e A enti L () The slot section: S e S D e D e e Aenc L Aent Aenti L () N with L is the otor length. The teeth height H of the PMSMIR is expresse by equation 3 with N sph is the nuber of turns per phase an In is the rate current. H specific to the PMSMIR is expresse: H = Nsph.In N δk A r enc D+ e + D+ e H specific to the is expresse: H Nsph.In N δk A r enc D - e D - e (3) (4) The stator yoke thickness H cs is obtaine by application of the flux conservation theore. B S Hcs (5) LBcs Stator yoke The principal tooth section: S D + e S = A ent L (6) The inserte tooth section: S i D + e S i = A enti L (7) The slot section: S e D + e S e = A enc L = D e A A ent enti L N.4. Stator geoetrical sizes of the The slot average with: L enc L enc (8) D e H Aenc (9) Rotor yoke Fig. 4 Application of the theore of the flux conservation.4.3 The rotor geoetrical sizes of the two structures The expression of the agnet height H a is the sae one in the two structures; it is obtaine by the application of the Apere theore: contour Hl = Σ ni H h + eh = (6) a a e The reanent inuction of the agnet M (Ta) at T a C is efine by: The principal tooth section: S 365

4 M. Chaieb et al.: A Coparative Stuy of Two Peranent Magnet Motors Structures with Interior an Exterior Rotor µ abee Ha = Be M(Ta) K fu (7) M = M + α (T ) (8) ( Ta) a The rotor yoke thickness H cr is efine: Φ BeS = BcsHcrLKf u = H cr BeS = K L B fu cr (9) Fig. 5 Mesh in the PMSMIR.4.4 Electrical sizing The electrootive force in the two structures is expresse by: 8 π π EMF (t) = NsphLDBe sin βsin βrlla π () Ω sin PΩ t ( ) The otor electric constant: K e K e N sph L D B e sin sin R lla The electroagnetic torque: T e T 3 e (t) = EMFi(t).ii(t) Ω i= () () with EMFi an i i respectively represent the electrootive force an the current of the i phase. The otor rate current I n is the ratio between the electroagnetic torque an the otor electric constant Fig. 6 Mesh in the two stuie structures is given by figures 5 an 6, we ake a refine esh in the air gap to obtain a precise result [Ohyaa et al., 5]. Figure 7 an figure 8 show respectively the flux ensity in the an in the PMSMIR. We note that the axial inuction for the otor yokes is equal to.4 T that proves no saturation in agnetic otor circuit. We note the appearance of leakages flux in the otor, this requires the eterination of the leakages flux co- Te I n = (3) K e The phase résistance of the otor: R ph R ph = R cu NsphδL (Tb) I / n sp (4) where R cu (Tb) is the Resistivity of copper at the teperature of wining T b an L sp is the spire average length efine as follow [Haj et al., 7]. Fig. 7 Flux ensity in the R (Tb) = R + α (Tb ) (5) cu cu D+ e + h ( ) L sp = Aenc+ Aent. + L (6) Fig. 8 Flux ensity in the PMSMIR 3. COMPARATIVE STUDY BETWEEN THE TWO STRUCTURES In this stuy, the valiation an coparation between the two structures is base on the finite eleents etho using the software FEMM. The esh in the Fig. 9 Flux lines in the 366

5 Journal of Asian Electric Vehicles, Volue 8, Nuber, June efficient to valiate the analytical oel. 3. Electroagnetic paraeters 3.. Air gap flux ensity Figures an show the airgap inuction in the an in the PMSMIR, the axial value is about T [Pakel, 9] Fig. Flux lines in the PMSMIR Be (T) Fig. Airgap inuction in the Airgap length () Be (T) Airgap length () Fig. Airgap inuction in the PMSMIR 3.. Flux Figures 3, 4, 5 an 6 illustrate the three phases flux at no-loa an at full loa accoring to the echanical angle for the PMSMIR an. Accoring to the Figure 7, we can conclue that the variation of the flux at no-loa an at full-loa accoring to the rotor position is very weak, that originates the agnetic reaction.,8,6,4, -, -,4 -,6 -, No loa flux No loa flux No loa flux 3 Fig. 3 Flux of the three phases at no-loa for the PMSMIR,8,6,4, -, -,4 -,6 -, Full loa flux Full loa flux Full loa flux 3 Fig. 4 Flux of the three phases at full-loa for the PMSMIR,8,6,4, -, -,4 -,6 -, No loa flux No loa flux No loa flux 3 Fig. 5 Flux of the three phases at no-loa for the,8,6,4, -, -,4 -,6 -, Full loa flux Full loa flux Full loa flux 3 Fig. 6 Flux of the three phases at full-loa for the 367

6 M. Chaieb et al.: A Coparative Stuy of Two Peranent Magnet Motors Structures with Interior an Exterior Rotor Flux(Wb) -,4 -,6 -,8 Fig. 7 Flux at Full-loa an at no-loa of the PMS- MIR 3..3 Electrootive forces EMF The for of EMF represents a very significant paraeter. It is expresse by: EMF = N,6,4, -, sph Φ t Flux at no-loa Flux at full-loa (7) Figures 8, 9, an give an iea on the for of the EMF at no-loa an at full loa accoring to the rotor position. This EMF is generate by the flux evolution through a coil of the stator. EMF (V) No loa EMF No loa EMF No loa EMF3 Fig. 8 EMF at no-loa of the PMSMIR EMF (V) Full loa EMF Full loa EMF Full loa EMF3 Fig. 9 EMF at full-loa of the PMSMIR 3. Torque an Power-to-weight ratio 3.. Calculation of the torque The instantaneous torque is expresse by equation. Figure an 3 represent the torque at full-loa EMF (V) No loa EMF No loa EMF No loa EMF3 Fig. EMF at no-loa of the FEM (V) Full loa EMF Full loa EMF Full loa EMF3 Fig. EMF at full-loa of the an at no loa of the two structures obtaine by the finite eleent etho [Zhu et al., 6; Yee-pien et al., 9]. The obtaine results valiate the analytical oel because the torque oscillates aroun the average value foun analytically which is N. Torque (N) No-loa torque with exterior rotor Full-loa torque with exterior rotor Rotor positopn( ) Fig. Torque at no-loa an at full-loa for the Torque (N) No-loa torque with interior rotor Full-loa torque with interior rotor Fig. 3 Torque at no-loa an at full-loa for the PMSMIR 368

7 Journal of Asian Electric Vehicles, Volue 8, Nuber, June Figures 4 an 5 illustrate the torque ripple in the two structures, we conclue that the torque ripple in the is 6.4 % an in the PMSMIR is 9.43 % [Wang et al., 9]. Torque ripple (N) Torque ripple (N) Fig. 4 Torque ripple in the Fig. 5 Torque ripple in the PMSMIR 3.. Power-to-weight ratio The power-to-weight ratio is efine by the relationship between the power an the ass of the otor active part. Figure 6 represents the power-to-weight ratio specific to the two structures accoring to the power. Accoring to this figure, we notice that the power-toweight ratio of the is slightly lower than the PMSMIR, while the great otor power it is the reverse. Power-to-wight ratio (Kw/Kg),8,6,4, Power-to-wight ratio with interior rotor Power-to-wight ratio with exterior rotor Power-to-wight ratio (Kw) Fig. 6 Power-to-weight ratio 3.3 Losses an efficiency Table represents the efficiency an the losses for the PMSMIR an the. Table Losses an the efficiency of the two structures PMSMIR Joule losses 557,8 547,89 Iron losses 59,66 3,653 Mechanical losses 5,755 6,5 Efficiency,96,964 We can euce that the Joules losses an the iron losses for the are lower than those of the PMSMIR. Moreover, the efficiency of the is ore interesting than the other structure. Figure 7 illustrates the total losses of the two structures. Losses (W) 5 5 Losses for interior rotor Losses for exterior otor 3 Motor power (kw) Fig. 7 Losses accoring to the power We conclue that the losses agnitue is the sae orers for low powers in the two structures. However, for the powers higher than 5kW, the losses in are lower than those prouce by the PMSMIR. Figure 8 represents the efficiency obtaine for the two structures; we note that the offers efficiency better than that evelope by the PMSMIR. As a conclusion, the configuration of the is ost suitable since it offers efficiency higher than that Efficiency efficiency of the interior rotor efficiency of the exterior rotor,966,964,96,96,958,956,954,95, Motor power (kw) Fig. 8 Efficiency accoring to the power 369

8 M. Chaieb et al.: A Coparative Stuy of Two Peranent Magnet Motors Structures with Interior an Exterior Rotor reache by the first structure. This type of configuration is aapte ore to be exploite as a otor-wheel. 4. CONCLUSION We choose the synchronous peranent agnet otor with raial flux. Basing on the scheule ata conitions, sizing approach given by Figure, electroagnetic laws, an analytical oelling of two structures which are the an the PMSMIR is carrie out. We copare efficiency, ass, torques an losses in the two structures of the PMM. In conclusion, the PMS- MER is the ost interesting since it is ore profitable an lighter than the PMSMIR. Finally, the realization of a prototype is necessary to confir our stuy. References Bianchi, B., N. Bolognani, an P. Frare, Design Criteria for High-efficiency SPM Synchronous Motors, IEEE Transactionss on Magnet, Vol., No., , 6. Chan, C. C., The sate of the art of electric vehicles, Journal of Asian Electric Vehicles, Vol., No., 579-6, 4. Gasc, L., Peranent agnet otor esign with low torque ripple for autootive electric power steering: Structure an control approaches, PhD Thesis, Polytechnic National Institute of Toulouse, 4. Haj, N. B., S. Tounsi, R. Neji, an F. Sellai, Real coe Genetic algorith for peranent agnet otor ass iniization for electric vehicle application, Proceeings of 3r International Syposiu on Coputational Intelligence an Intelligent Inforatics, 53-58, 7. Kazuhiro, O., A. Kenichi, N. Mage, F. Nashe, H. Fujii, an H. Uehara, Design using finite eleent analysis of switche reluctance otor for electric vehicle, Journal of Asian Electric Vehicles, Vol. 3, No., 793-8, 5. Libert, F., an J. Soular, Investigation on pole-slot cobinations for peranent agnet achines with concentrate winings, Proceeings of the International Conference on Electrical Machines, Vol., , 4. Magnussen, F., an H. Lenenann, Parasitic effects in PM achines with concentrate winings, IAS5 4th Annual Meeting Hong Kong, Vol., 45-49, 5. Pakel, M., Analysis of the agnetic flux ensity, the agnetic force an the torque in a 3D brushless DC otor, Journal of Electroagnetic Analysis an Applications, Vo., No. -5, 9. Wang, Y., J. Shen, Z. Fang, an W. Fei, Reuction of cogging torque in peranent agnet flux-switching achines, Journal of Electroagnetic Analysis an Applications, Vol., No., -4, 9. Yee-pien, Y., Y. Shih-chin, an L. Jieng-jang, Optial esign an control of a torque otor for achine tools, Journal of Electroagnetic Analysis an Applications, Vol., No. 4, -8, 9. Zhu, Z. Q., Y. F. Shi, an D. Howe, Coparison of torque-spee characteristics of interior-agnet achines in brushless AC an DC oes for EV/HEV applications, Journal of Asian Electric Vehicles, Vol. 4, No., , 6. Zire, H. S., C. Espanet, an A. Miraoui, Perforance coparison of two agnet synchronous otors structures with interior rotor an exterior rotor, Proceeings of Electrotechnique u Futur, EF, 5, 3. (Receive February 5, ; accepte May 3, ) 37