Influence of Structural Parameters of Electromagnetic Harmonic Movable Teeth Transmission on System Loss

Transcription

1 Send Orders for Reprnts to 778 The Open Mechancal Engneerng Journal, 014, 8, Open Access Influence of Structural Parameters of Electromagnetc Harmonc Movable Teeth Transmsson on System Loss Yubo Ren *, Lzhong Xu and Yongl Lang Parallel Robot and Electromechancal System Laboratory, Yanshan Unversty, Qnghuangdao, Hebe, , Chna Abstract: In vew of the characterstcs of electromagnetc harmonc movable teeth transmsson system, the heat loss has been analyzed n ths paper based on basc assumptons. At the same tme, the calculaton methods of electromagnetc loss and mechancal loss n system have been also dscussed. Moreover, the nfluence of changes of system parameters on electromagnetc loss and mechancal loss has been analyzed through employng the feld-crcut couplng fnte element method. Accordng to the analyss results, the numercal calculaton model of the three-dmensonal temperature feld of system can be establshed. And the theoretcal bass can be provded for the optmzaton desgn of electromagnetc harmonc movable teeth transmsson system and the mprovement of transmsson effcency of transmsson system. Keywords: Electromagnetc harmoncs, electromagnetc loss, mechancal loss, structural parameters. 1. INTRODUCTION As electronc and control technology contnues to penetrate the mechancal feld, the generalzed complex mechancal transmsson has become a leadng nternatonal subject n mechancal felds [1-4] for ths concept s anttradton and could acheve the organc combnaton of mechancs, electrcty and control. The electromagnetc harmonc movable tooth transmsson system nvolved n ths paper s a knd of organc combnaton of harmonc transmsson technology, electromagnetc transmsson technology, movable tooth transmsson technology and control technology, that s, a new electromechancal ntegrated complex transmsson system [5, 6]. The electromagnetc harmonc movable tooth transmsson motor s an electromagnetc -mechancal energy converson devce. Due to ts long-term contnuous operaton, energy loss s an essental part of the operaton. The lost energy has a great nfluence on the electromagnetc harmonc movable tooth transmsson motor and ts structure desgn. Such as, the lost energy s eventually converted to heat, so that the temperature of each part of the motor ncreases whch has a drect mpact on the lfe of all the nsulatng materals. Meanwhle, the vscosty of lubrcatng ol of the motor may decrease, whch may damage the lubrcaton state between the movable tooth, center wheel and tooth holder, and ultmately lmt the output of the system. And the electromagnetc harmonc transmsson s operatng at a low speed, ts runnng state corresponds to the operatng state of startng or brakng and the effcency dstrbuton has a great nfluence on the electromagnetc motor and ts desgn and structure. Therefore, the study of the losses of electromagnetc harmonc movable teeth transmsson s of great sgnfcance *Address correspondence to ths author at the Parallel Robot and Electromechancal System Laboratory, Yanshan Unversty, Qnghuangdao, Hebe, , Chna; Tel: ; E-mal: ryb@ysu.edu.cn X/14 to analyze the falure mechansm of electromagnetc harmonc movable teeth transmsson system and mprove the operatng performance as well as effectvely control the lubrcatng and the coolng. Experts and scholars have conducted extensve researches on motor losses. For example, n lterature [7], the motor losses of sne-wave drve and square-wave drve have been analyzed and t was found that the motor losses would be mnmzed when the optmal leadng angle s controlled; n lterature [8], the mportance of space harmonc magnetc feld on rotor losses has been revealed and the concept of harmonc losses has been proposed; at the same tme, the motor stator loss, the rotor copper loss, the ron loss and the eddy current loss under dfferent operatng condtons have been also analyzed n detal; n lterature [9], the concepts of stator and rotor regonalzaton have been proposed and the losses as well as the flux densty of each regon have been calculated; meanwhle, the varaton prncples of losses n each part of motor have been analyzed, whch provded a bass for reducng the motor loss; n lterature [10], the radal flux densty and the tangental flux densty n dfferent parts of motor have been analyzed; t was proposed that the motor loss could be dvded nto alternatng loss and rotatonal loss; at the same tme, the nfluences of torque and speed on motor loss have been compared. The motor loss has been analyzed from a certan perspectve n above lteratures and the feld-crcut couplng fnte element method s rarely employed to study the electromagnetc losses; moreover, the lteratures about the nfluence of operatng parameters on system losses are less. In vew of the operatng characterstcs of electromagnetc harmonc movable teeth transmsson and the system condtons at dfferent frequences, the electromagnetc losses and the mechancal losses of electromagnetc harmonc movable teeth transmsson have been dscussed n ths paper. At the same tme, the nfluence prncples of structural parameters on electromagnetc losses and mechancal losses have been analyzed through takng the 014 Bentham Open

2 Electromagnetc Harmonc Movable Teeth Transmsson on System Loss The Open Mechancal Engneerng Journal, 014, Volume prototype as example, whch provdes a theoretcal bass for the optmal desgn of system structure.. LOSS ANALYSIS Electromagnetc harmonc tooth transmsson s an electromagnetc - mechancal energy converson devce. Energy loss n acton s eventually converted to heat energy and t fnally reaches steady state equlbrum by the heat exchange between the motor components wth the envronment. The loss of the electromagnetc harmonc tooth transmsson s comprsed of electromagnetc loss and mechancal loss..1. Electromagnetc Loss Part of system nput electrc power s consumed n the stator resstance, producng the electron copper loss, whle the other part of the consumpton s n the resstance feld, resultng n the stator ron loss. Besdes, the addtonal loss ncludng flexsplne eddy current loss and hysteress loss should also be consdered. The remanng power s appled to flexsplne through the ar gap magnetc feld- P M Electronc Copper Loss In the harmonc electromagnetc tooth transmsson process, the alternatng electrc current flows through a conductor whch wll lead to the skn effect and proxmty effect n the surroundng magnetc feld [11]. The addtonal losses caused by them are defned as eddy-current loss, whle the eddy-current loss and DC loss are collectvely known as AC loss (copper loss) [1], namely P cu = P z + P w (1) P cu s the AC loss; P z s the DC loss; P z = I R z ; P w s eddycurrent loss; I s the vrtual value of current; R z s DC resstance. Assumng that the magnetc feld n the harmonc motor slot s parallel to ts bottom, gnore the effects of eddy current of the conductor on the magnetc feld and the eddycurrent loss of the conductor s shown as follows [1]: P w =!" B l d d 4 18# c () d s the dameter of the conductor; l d s the length of the conductor; ρ c s the resstvty of the conductor; B s the ampltude of flux densty; ω s the frequency of flux densty angular..1.. Iron Core Loss The stator core loss s one of the man losses of harmonc electromagnetc tooth transmsson system, whch accounts for a large proporton of the total losses. It s usually refered to the sum of tooth ron loss and ron loss of the yoke part. P Fe = P c + P a () and P c = k z p 0 B c f 1 G c P a = k a p 0 B a f 1 G a! # " $# k z, k a s the coeffcent wth addtonal loss; p 0 s the specfc losses of core materal; B c s the tooth flux densty; B a s the yoke flux densty; f means the frequency; G c means the tooth weght; G a means the yoke weght... Mechancal Power Loss..1. The Power Loss of Engagement Par The analyss ndcates that there s relatve rollng moton between the movable tooth and flexble wheel, there s relatve sldng between the movable tooth and the tooth carrer, and there are both relatve rollng and relatve sldng between the tooth and the center wheel P 1, P, P respectvely referng to the power loss when the th movable tooth contacts wth the flexble wheel, the tooth carrer and the center wheel. The meshng power loss of a sngle tooth s: P f = P 1 + P + P n Pf = P! f +! P f f " =m q = p n the formula, F 1f!, F f!, F f! means the frcton between the movable tooth and the flexble wheel, tooth rack and center wheel; f and f 1 s the frcton coeffcent of the movable tooth wth the flexble wheel and tooth rack;! 1 means the relatve rollng angular velocty between the movable tooth and the flexble wheel; V means the relatve sldng angular velocty between the movable tooth and the tooth rack;! means the relatve rollng-sldng angular velocty; f means the rollng-sldng frcton coeffcent between the movable tooth and the flexble wheel. The electromagnetc harmonc movable tooth transmsson has mult-tooth engagement smultaneously; at any tme, the frcton power loss on each movable tooth s not the same, coupled wth the nput power, whch s because there are always half of the movable teeth n two regons of engagement operatng, so the power loss at any moment s shown as follows: n P f = P! f +! P f (5) =m q = p m, n and p, q respectvely represents the number of movable tooth n two dfferent regons of engagement.... The Power Loss of the Bearng The power loss of a sngle bearng (4)

3 780 The Open Mechancal Engneerng Journal, 014, Volume 8 Ren et al. P zc =!n z M f 0 (6) n z s the rotaton speed of the nner rng of the bearng; M f s the frcton torque of the bearng. + ( ) M = Yf1Fa Dm 10 f0 νnz D νn m z 10 f Yf1Fa Dm + 16 f0d νnz 10 m Y and F a respectvely represents the axal coeffcent and axal load of the bearng; v s the knematc vscosty of the lubrcant; D m s the average dameter of the bearng; f and f 0 1 are the coeffcents related to the bearng type and lubrcaton methods.... Power Loss Due to Ol Agtaton The power loss due to ol agtaton manly ncludes that of flexsplne and movable tooth. For the sphercal surface (radus of r! and the effectve area A) rotatng at the angular velocty of "! n the vscous flud medum (densty "!, knematc vscosty v and frcton coeffcent f! ), the power loss due to ol agtaton s shown as follows: 1 8 P y = ρ f Aω r In the above formula f = ( Re 500) ( 16 Re ) 0.59 ( T 41) ( 16 R ) a 16 R e The Reynolds number R e = ω r C ν, the Taylor number Ta = R C r e, C s the characterstc gap surroundng the ball surface. The total losses of mechancal power s shown as follows: P = P + P + P f z y..4. Rollng-Sldng Frcton Coeffcent e T < 41 e a R 500 T 41 a Based on the prevous analyss, there are both rollng and sldng when the tooth contacts wth the center wheel, so the correspondng frcton s referred to as rollng-sldng frcton. The work done by the rollng frcton, sldng frcton and rollng-sldng frcton, s respectvely shown as (7) (8) follows: w w w = µ 1 1 F S1 = µ F S = f F S (9) (10) (11) µ refers to the rollng frcton coeffcent; µ 1 s the sldng frcton coeffcent; f s the rollng-sldng frcton coeffcent; F s the postve pressure mposed on the movable tooth by the center wheel; S 1 refers to the arc length of engagement of movable tooth, that s, the rollng dstance; S refers to the sldng dstance; S refers to the arc length of engagement of center wheel, that s, the rollng-sldng dstance. The work done by the rollng-sldng frcton s equal to the sum of the work done by rollng frcton and sldng frcton; therefore f S = µ 1 S1 + µ S (1) S 1 can be approxmately calculated by the followng formula: S 1 rb r b ϕ v s the radus of the movable tooth; s the wrap angle of the centered tooth; z z s the wave number of the centered tooth. ( r r b ) S = + ϕ r s the radus of flexsplne. S + = S1 S Fnally [( µ 1 µ ) rbϕ v + µ ϕ ( r + rb )] ( r rb ) ϕ f + = (1). INFLUENCE OF SYSTEM PARAMETERS ON ELECTROMAGNETIC LOSS In ths part, the nfluence of system parameters on electromagnetc loss has been analyzed through takng twopole 4-slot harmonc transmsson as example. The man parameters of system are shown n Table 1. ϕ v Table 1. Harmonc electromagnetc movable teeth transmsson motor parameters. Item Value Item Value Rated power P e 100 W Rated voltage U e 0 V Number of pole pars p 1 Stator slots m 4 Number of turns per slot N z 81 Rated current I 0.56 A Outer dameter of stator D (mm) 118 Inner dameter of stator d (mm) 68 Length of ron core lt (mm) 6 Flexsplne length l (mm) 17 Outer dameter of flexsplne r (mm) 67 Flexsplne thckness t (mm) 0. ar gap δ (mm) 0.5 Core materal of stator 5WW70 Phase Resstance R (Ω) Phase nductance L 0.4 mh

4 Electromagnetc Harmonc Movable Teeth Transmsson on System Loss The Open Mechancal Engneerng Journal, 014, Volume Influence of Frequency on Iron Core Loss In order to save energy and reduce stator losses, the most drect way s to use the low-loss ron core materals. The stator core adopted n ths paper uses the ultra-thn, low-loss and cold-rolled slcon steel. The specfc loss curve of coldrolled non-orented slcon steel of 5ww70 under dfferent frequences whch s measured by AC magnetc gauge as shown n Fg. (1). It s requred to employ the specfc loss curve under each frequency, analyze the software SAP and adopt the best estmaton method to ft the loss coeffcents. Then, the relatonshp between core loss coeffcent and frequency under alternatng magnetc condton can be obtaned, whch s shown n Fg. (). magnetc feld rotates 0.6 electrcal angle. It s demanded to calculate the magnetc feld dstrbuton of 1000 magnetc feld postons. Then, the waveforms of magnetc flux densty of the central teeth and the yoke part of stator core n (a) Loss coeffcent k z (b) Loss coeffcent k a Fg. (1). The specfc core loss of 5WW70 slcon steel sheet wth dfferent frequences. In Fg. (), t s found that the loss coeffcent of slcon s not a constant, but a functon of magnetc frequency. As the frequency of motor system studed n ths paper s low, the relatonshp between loss coeffcent and frequency under low and ntermedate frequences s only analyzed. Under the low frequency (less than 400 Hz) and the ntermedate frequency (from 400 Hz to 1000 Hz), the loss coeffcents k z and k a have lttle changes wth the changes of frequency. The loss coeffcent can be consdered as a constant when calculatng the losses, whch can be obtaned by the loss curve fttng provded by manufacturers... Influence of the Waveforms of Magnetc Feld on Iron Core Loss The waveform of the man magnetc feld can drectly affect the dstrbuton of flux densty n stator core. Therefore, the losses of stator core losses are related to the waveform of magnetc feld. From the perspectve of reducng the ron core losses, the nfluence of hgher harmoncs of flux densty waveform has been analyzed under the exstence of power n ths paper. In order to accurately calculate the core loss, frstly, t s requred to employ the fnte element to analyze the magnetc feld of system. The sne-wave magnetc feld and the thrd harmonc magnetc feld should be nlet under related load. It s necessary to conduct a calculaton when the motor Fg. (). The loss coeffcents varaton wth frequency. a cycle should be extracted, whch s shown n Fg. (). In ths fgure, the magnetc flux densty waveforms of snewave magnetc feld are represented as long dotted lne and the magnetc flux densty waveforms of the thrd harmonc magnetc feld are represented as contnuous sold lne. In Fg. (), t s found that the magnetc flux densty waveforms n teeth part and the yoke part have great changes under the sne-wave magnetc feld and the thrd harmonc magnetc feld. The contents of stator flux densty harmoncs under the thrd harmonc magnetc feld are hgher than the ones under the sne-wave magnetc feld. Therefore, the stator core losses are also greater. For the great harmonc contents, there s a bg dsadvantage on the stator core loss. It s requred to take measures to reduce the armature current harmonc contents so as to reduce the core losses.

5 78 The Open Mechancal Engneerng Journal, 014, Volume 8 Ren et al... Influence of Groove Sze of Stator on Core Loss Accordng to the above analyss, t s found that the stator core loss s proportonal to the square of flux densty and the flux densty n stator groove s related to the groove sze. Therefore, the stator core loss s also related to the groove sze. (a) Magnetc flux densty waveforms n teeth part Based on the motor loss calculaton model of feld-crcut couplng fnte element, the nfluences of the slot wdth, the slot heght, the groove humeral angle, the groove wdth, the groove heght and the radus sze of stator have been analyzed, whch s shown n Fg. (5). (a) Influence of changes of slot wdth on loss (b) Magnetc flux densty waveforms n yoke part (b) Influence of changes of slot heght on loss Fg. (). Stator core flux densty waveform. In ths paper, the prototype power s 0.5 kw and the structure of stator groove as well as the sze s shown n Fg. (4). Rs (c) Influence of groove humeral angle on loss s h b 0 α 0 hb Fg. (4). Basc szes of stator slots. s

6 Electromagnetc Harmonc Movable Teeth Transmsson on System Loss The Open Mechancal Engneerng Journal, 014, Volume 8 78 (Fg. 5) contd.. (d) Influence of groove wdth on loss (e) Influence of groove heght on loss harmonc magnetc feld. The larger the slot wdth s, the greater the nfluence of harmoncs on loss wll be. () The nfluence of slot heght on loss s slght due to ts smaller sze. () The groove humeral angle selected n ths paper s among 0.9~1.1 tmes 7 ~ of 0. The greater the groove humeral angel, the smaller the loss wll be. However, the changes are gentle. (4) The larger the groove wdth s, the greater the loss wll be. That s because the larger sze of groove wdth wll lead to the reducton of teeth wdth. When the magnetc flux of each fundamental wave s unchanged, the magnetc crcut wll be more saturated and the loss wll be ncreased. (5) The ncrease of groove heght wll lead to the reducton of the magnetc crcut area n yoke part. The magnetc crcut s easly saturated and the loss s ncreased. (6) The ncrease of groove radus can cause the reducton of magnetc crcut area n yoke area. The saturaton degree wll be ncreased, whch s not conducve to the reducton of loss. However, the dfference n the nfluence of each groove sze on loss can drectly affect the sze of groove area. The phenomenon that the szes whch greatly affect the loss are blndly mproved to reduce the loss can lead to the hgh groove fllng rate and ncrease the offlne dffculty. Therefore, under the premse of understandng the nfluence of each sze on loss, t s requred to reasonably select the groove sze so as to reduce the losses to some extent. (f) Influence of groove radus on loss.4. Proportonal Changes of Copper Loss and Iron Loss n Electromagnetc Loss The electromagnetc loss n electromagnetc harmonc movable teeth transmsson can be dvded nto electronc copper loss and ron core loss. The addtonal losses caused by harmonc magnetc potental and leakage magnetc feld should be added nto the copper loss and the ron loss through the coeffcent. When the power changes from small to large, the proportonal changes of the copper loss P cu and the ron loss P Fe on total electromagnetc losses are shown n Fg. (6). Fg. (5). Impact of dfferent slot szes on core losses. In Fg. (5), t s found that: (1) The larger the slot wdth s, the greater the loss wll be. That s because the slottng of stator wll cause the uneven gap presence and produce the presence harmoncs. The presence harmoncs and the magnetc potental fundamental wave can cause the presence Fg. (6). Proporton of copper losses and ron losses n electromagnetc losses.

7 784 The Open Mechancal Engneerng Journal, 014, Volume 8 Ren et al. In Fg. (6), t s found that: (1) When the motor power changes from small to large, the proporton of copper loss s changng. The changes are from large to small whch shows a declnng trend; () When the motor power changes from small to large, the proporton of ron loss s changng. The changes are from small to large, whch shows an upward trend; when the power s greater than 0.75 kw, the changes of copper loss are more than 50%, whch s greater than the ones of copper loss. For the electromagnetc harmonc movable teeth transmsson motor wth small power, the proporton of copper loss n electromagnetc loss s hgh. It s requred to take measures to control copper loss based on the factors to affect copper loss; however, for the electromagnetc harmonc movable teeth transmsson motor wth great power, the proporton of ron loss s greater than the one of copper loss. Therefore, t s necessary to pay attenton to the flux densty dstrbuton of each part of stator so as to reduce the ron loss. Fg. (9). Varaton of loss wth transmsson rato. (a) Relatonshp between Loss and Lubrcaton Condton under Dfferent r b. 4. INFLUENCE FACTORS AND INFLUENCE PRINCIPLES OF MECHANICAL POWER LOSS The mechancal power loss of electromagnetc harmonc movable teeth transmsson s nfluenced by the teeth radus, the rato of long shaft and short shaft of flexble gear after deformaton, the transmsson rato and the lubrcaton effects, etc. In ths paper, the change prncples of the mechancal power loss affected by above factors have been analyzed and calculated. Some calculaton results can be shown n Fgs. (7-10). (b) Relatonshp between loss and lubrcaton condton under dfferent a/b (c) Relatonshp between loss and lubrcaton condton under dfferent Fg. (7). Varaton of Loss wth Movable Tooth Radus r b. Fg. (8). Varaton of Loss wth a/b. Fg. (10). Relatonshp curve of loss and lubrcaton status.

8 Electromagnetc Harmonc Movable Teeth Transmsson on System Loss The Open Mechancal Engneerng Journal, 014, Volume In Fgs. (7-10), t s found that: (1) Wth the ncrease of teeth radus r b, the frcton losses between movable teeth and teeth rack and between center gear and flexble gear are both reduced. That s because the teeth radus s ncreased, the number of movable teeth s few and the frcton par s reduced wth the certan whole sze of system. () Wth the ncrease of the rato a/b between long shaft and short shaft of flexble gear after deformaton, the frcton losses between movable teeth and teeth rack and between center gear and flexble gear are both ncreased. That s because the ncrease of a/b represents the ncrease of radal deformaton of flexble gear. If the radal deformaton of flexble gear s ncreased, the force of flexble, center gear and teeth rack on movable teeth wll be great. Therefore, the frcton loss s great. () Wth the ncrease of transmsson rato, the frcton losses between movable teeth and teeth rack and between center gear and flexble gear are both ncreased. That s because the transmsson rato s ncreased and the number of movable teeth s ncreased, the frcton par wll be ncreased. Although force on each movable tooth s reduced, the frcton loss produced by the ncrease of frcton par can not be offset. (4) The nfluence of lubrcaton condton on the frcton loss of electromagnetc harmonc movable teeth transmsson s great. The frcton loss of electromagnetc harmonc movable teeth transmsson can be reduced by more than 95% through achevng the lqud lubrcaton. And the frcton loss of harmonc movable teeth transmsson can be reduced by 90% ~ 94% under boundary lubrcaton stuaton. The reason s that the frcton coeffcents between movable teeth and teeth rack and between center gear and flexble gear are low under lqud lubrcaton condton, whch are generally between 0.001~ 0.008; n the boundary lubrcaton condton, the frcton coeffcents are generally between 0.0 ~ 0.1. Therefore, the good lubrcaton s very mportant to mprove the workng effcency of electromagnetc harmonc movable teeth transmsson system. (5) The proportons of the three frcton losses n overall frcton losses are bascally: the frcton loss between movable teeth and center gear s the greatest, accountng for 40% ~ 50% of total frcton losses, followed by the frcton loss between movable teeth and teeth rack, whch accounts for 0% ~ 50% of total frcton loss; the frcton loss between movable teeth and flexble gear s the smallest, accountng for 0% ~ 0% of total frcton loss. CONCLUSION In ths paper, the electromagnetc loss and the mechancal loss of electromagnetc harmonc movable teeth transmsson have been studed and the nfluence prncples of changes of system parameters on electromagnetc loss and mechancal loss have been analyzed. The results show that: (1) The electromagnetc loss of system s greater than the mechancal loss. () The proporton of electronc copper loss n total electromagnetc loss s hgh under low power. It s requred to take measures to control the copper loss accordng to the factors that affect the copper loss. () When the power s more than 0.75 kw, the proporton of ron loss n electromagnetc loss s hgher than the one of copper loss. It s necessary to pay attenton to the dstrbuton of flux densty n each part of stator so as to reduce the ron loss. (4) In order to reduce the loss of mechancal power, the dameter of movable teeth and flexble gear can be determned accordng to the proportons of frcton losses between movable teeth and center gear, between movable teeth and teeth rack and between movable teeth and flexble gear. Under the certan radal dsplacement, t s requred to reduce the frcton par and mprove the lubrcaton effcency. CONFLICT OF INTEREST The authors confrm that ths artcle content has no conflct of nterest. ACKNOWLEDGEMENTS Declared none. REFERENCES [1] M. A. Delucch, and M. Z. Jacobson, "Provdng all global energy wth wnd, water, and solar power, Part II: Relablty, system and transmsson costs, and polces", Energy Polcy, vol. 9, no., pp , 011. [] N. L, S. M. Wang, and J. J. Du, "Natural characterstcs and dynamc load coeffcent of power four embranchments gear transmsson," Journal of Aerospace Power, vol. 8, no., pp , 01. [] Y. Ren, L. Xu, and Y. 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9 786 The Open Mechancal Engneerng Journal, 014, Volume 8 Ren et al. [10] L. L, X. Huang, B. Kao, B. Kao, and B. Yan, Research of core loss of permanent magnet synchronous motor (PMSM) n AC servo system, In: Internatonal Conference on Electrcal Machnes and Systenms. Pscataway, USA: IEEE, 008, pp [11] Y. Q. Wang, G. Wu, and S. Wang, Engneerng Electromagnetc Felds Introducton, Electronc Industry Press, Bejng, 005, pp [1] S. Iwasak, and R. Deodhar, Influence of PWM on the proxmty loss n permanent-magnet brushless AC machnes," IEEE Transactons on Industry Applcatons, vol. 45, no. 4, pp , 009. [1] M. Hu, and X. Huang, Method and Applcaton of Numercal Calculaton of Motor Performance, Southeast Unversty Press, Nanjng, 00, pp Receved: January 8, 015 Revsed: January 15, 015 Accepted: January 16, 015 Ren et al.; Lcensee Bentham Open. Ths s an open access artcle lcensed under the terms of the Creatve Commons Attrbuton Non-Commercal Lcense ( whch permts unrestrcted, non-commercal use, dstrbuton and reproducton n any medum, provded the work s properly cted.