Abstract：Axial flux permanent magnet synchronous motors (AFPMSM) have an intrinsic 3-D electromagnetic structure.Its accurate modeling and optimization of torque usually require the use of 3-D finite element analysis (FEA),which is highly time consuming.This paper presents a new torque analytical model and then it was used to optimize the torque of an AFPMSM.Firstly,the analytical model of magnetic field was established by using magnetic potential and relative permeance.Then,electromagnetic torque and cogging torque analytical models were derived based on Maxwell-tensor method.Finally,3-D FEA was presented for verifying the accuracy of the proposed model.The analytical model indicates the criterion to produce electromagnetic torque and cogging torque.It also clears the relationship between the order components of torque and the harmonic field.Based on the analytical model,the torque of a virtual AFPMSM with one stator and one rotor was optimized by triangular skew method.The result shows that the triangular skew method can greatly decrease the cogging torque and electromagnetic torque ripple,and the analytical method is really high efficient
[1] 宫晓,徐衍亮,冯开杰.新型盘式横向磁通永磁电机及其空载电动势波形的解析计算[J].电工技术学报,2014,29(7):77-82. Gong Xiao,Xu Yanliang,Feng Kaijie.A novel disc transverse-flux permanent magnet machine and analytical expression of its no-load EMF waveform[J].Transactions of China Electrotechnical Society,2014,29(7):77-82. [2] 王允凯,周涛.基于等效磁路法的轴向永磁电机效率优化设计[J].电工技术学报,2015,30(2):73-79. Wang Yunkai,Zhou Tao.Efficiency optimization design of axial flux permanent magnet machines using magnetic equivalent circuit[J].Transactions of China Electrotechnical Society,2015,30(2):73-79. [3] 沈健.轴向磁通永磁同步电机转矩特性分析与转矩优化[D].上海:同济大学,2015. [4] Wang Xiuhe,Yang Yubo,Fu Dajin.Study of cogging torque in surface-mounted permanent magnet motors with energy method[J].Journal of Magnetism and Magnetic Material,2003,267(11):80-85. [5] 王秀和,杨玉波,丁婷婷,等.基于极弧系数选择的实心转子永磁同步电动机齿槽转矩削弱方法研究[J].中国电机工程学报,2005,25(15):146-149. Wang Xiuhe,Yang Yubo,Ding Tingting,et al.The method for reducing cogging torque by suitable selection of pole-arc coefficient in solid-rotor PM synchronous motors[J].Proceedings of the CSEE,2005,25(15):146-149. [6] 王兴华,励庆孚,王署鸿.永磁无刷直流电机磁阻转矩的解析计算方法[J].中国电机工程学报,2002,22(10):104-108. Wang Xinghua,Li Qingfu,Wang Shuhong.Analytical calculation of cogging torque in brushless DC motor[J].Proceedings of the CSEE,2002,22(10):104-108. [7] 马琮淦,左曙光,何吕昌,等.分布式驱动用永磁同步电机电磁转矩的解析计算[J].振动与冲击,2013,32(6):38-42. Ma Conggan,Zuo Shuguang,He Lüchang,et al.Analytical calculation of electromagnetic torque in permanent magnet synchronous machine in distributed drive[J].Journal of Vibration and Shock,2013,32(6):38-42. [8] Aydin M,Gulec M.Reduction of cogging torque in double-rotor axial-flux permanent-magnet disk motors:A review of cost-effective magnet-skewing techniques with experimental verification[J].IEEE Transactions on Industrial Electronics,2014,61(9):5025-5034. [9] Caricchi F,Giulii F,Crescimbini F,et al.Experimental study on reducing cogging torque and no-load power loss in axial-flux permanent-magnet machines with slotted winding[J].IEEE Transactions on Industry Applications,2004,40(4):1066-1075. [10]Aydin M,Zhu Z Q,Lipo T,et al.Minimization of cogging torque in axial-flux permanent-magnet machines:Design concepts[J].IEEE Transactions on Magnetics,2007,43(9):3614-3622. [11]郝立,林明耀,徐妲,等.轴向磁场磁通切换型永磁电机齿槽转矩抑制[J].电工技术学报,2015,30(2):21-26. Hao Li,Lin Mingyao,Xu Da,et al.Cogging torque reduction in axial field flux-switching permanent magnet machines[J].Transactions of China Electrotechnical Society,2015,30(2):21-26. [12]Aydin M,Qu R,Lipo T.Cogging torque minimization technique for multiple-rotor,axial-flux,surface-mounted-PM machines:Alternating magnet pole-arcs in facing rotors[C]//38th IAS Annual Meeting,Conference Record of the Industry Applications Conference,2003. [13]Letelier A,González D,Tapia J,et al.Cogging torque reduction in an axial flux PM machine via stator slot displacement and skewing[J].IEEE Transactions on Industry Applications,2007,43(3):685-693. [14]González D,Tapia J,Letelier A.Design consideration to reduce cogging torque in axial flux permanent-magnet machines[J].IEEE Transactions on Magnetics,2007,43(8):3435-3440. [15]Hwang C,Li P,Chuang F,et al.Optimization for reduction of torque ripple in an axial flux permanent magnet machine[J].IEEE Transactions on Magnetics,2009,45(3):1760-1763. [16]Madhavan R,Fernandes B.A novel technique for minimizing torque ripple in axial flux segmented rotor SRM[C]//IEEE Energy Conversion Congress and Exposition,2011. [17]Chan T F,Lai L L,Xie S.Field computation for an axial flux permanent-magnet synchronous generator[J].IEEE Transactions on Energy Conversion,2009,24(1):1-11. [18]Zhang Y J,Ho S L,Wong H C,et al.Analytical prediction of armature-reaction field in disc-type permanent magnet generators[J].IEEE Transactions on Energy Conversion,1999,14(4):1385-1390. [19]Zhu Z Q,Howe D.Instantaneous magnetic field distribution in brushless permanent magnet DC motors,part III,effect of stator slotting[J].IEEE Transactions on Magnetics,1993,29(1):143-151. [20]Yang Y P,Luh Y P,Cheung C H.Design and control of axial-flux brushless DC wheel motors for electric vehicles-part I:multiobjective optimal design and analysis[J].IEEE Transactions on Magnetics,2004,40(4):1873-1882.
2016, Vol. 31 
