永磁轮毂电机磁场解析建模
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摘要
利用谐波建模法提出一种可以在永磁电机研究中考虑导磁材料磁导率为有限值的永磁轮毂电机解析模型,分析了电机的电磁性能。在二维极坐标系下,将电机划分为永磁体、气隙、定子齿/槽、定子齿尖/槽开口四个求解域。在各求解域建立泊松方程和拉普拉斯方程,并联立边界条件求得通解中的谐波系数,从而得出各求解域矢量磁位解析表达式。计算了电机气隙磁感应强度、空载反电动势、输出转矩,通过有限元计算和样机实验验证了解析模型的正确性,并利用该模型研究了极弧系数和槽开口宽度对输出转矩的影响规律。
One exact analytical model method for considering the magnetic permeability of magnetically conductive material in a permanent magnetic motor was given by using harmonic modeling, and the electromagnetic performance of the motor was analyzed. In the two-dimensional polar coordinate, the motor was divided into four domains: the permanent magnet, the air gap, the stator tooth/slot and the stator tooth tip/slot opening. The Poisson and Laplace equations were established in each solution domain, and the harmonic coefficients in the general solution were obtained by the boundary conditions, and the analytical expression of vector magnetic potential in each domain was obtained. The electromagnetic performance of air gap magnetic flux density, no-load back EMF, output torque and so on were calculated. The correctness of this analytical model method was verified by comparison with the finite element method and experiment test results.The model was used to study the influence of the pole arc coefficient and slot opening width on the output torque.
One exact analytical model method for considering the magnetic permeability of magnetically conductive material in a permanent magnetic motor was given by using harmonic modeling, and the electromagnetic performance of the motor was analyzed. In the two-dimensional polar coordinate, the motor was divided into four domains: the permanent magnet, the air gap, the stator tooth/slot and the stator tooth tip/slot opening. The Poisson and Laplace equations were established in each solution domain, and the harmonic coefficients in the general solution were obtained by the boundary conditions, and the analytical expression of vector magnetic potential in each domain was obtained. The electromagnetic performance of air gap magnetic flux density, no-load back EMF, output torque and so on were calculated. The correctness of this analytical model method was verified by comparison with the finite element method and experiment test results.The model was used to study the influence of the pole arc coefficient and slot opening width on the output torque.
引文
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[8]Zhu Li,Shan Jiang,Zhu Ziqiang,et al.Comparison of alternate analytical models for predicting cogging torque in surface-mounted permanent magnet machines[C]//2008 IEEE Vehicle Power and Propulsion Conference,Harbin,China,2008:1-6.
[9]Chao Bi,Liu Zhejie,Low T S.Analysis of unbalanced-magnetic-pulls in hard disk drive spindle motors using a hybrid method[J].IEEE Transactions on Magnetics,1996,32(5):4308-4310.
[10]郭思源,周理兵.表面埋入式永磁电机磁场解析[J].中国电机工程学报,2015,35(3):710-718.Guo Siyuan,Zhou Libing.Analytical solution of magnetic field in surface-inset permanent magnet machines[J].Proceedings of the CSEE,2015,35(3):710-718.
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[13]Zhu Ziqiang,Howe D,Bolte E,et al.Instantaneous magnetic field distribution in brushless permanent magnet DC motors.I.open-circuit field[J].IEEETransactions on Magnetics,1993,29(1):124-135.
[14]Zhu Ziqiang,Howe D.Instantaneous magnetic field distribution in brushless permanent magnet DC motors.II.armature-reaction field[J].IEEE Transactions on Magnetics,1993,29(1):136-142.
[15]Hannon B,Sergeant P,Dupre L.Two-dimensional fourier-based modeling of electric machines[C]//2017IEEE International Electric Machines and Drives Conference(IEMDC),Miami,FL,USA,2017:1-8.
[16]王兴华,励庆孚,王曙鸿.永磁无刷直流电机空载气隙磁场和绕组反电势的解析计算[J].中国电机工程学报,2003,23(3):126-130.Wang Xinghua,Li Qingfu,Wang Shuhong.Analytical calculation of no-load air-gap magnetic field and back electromotive force in brushless DC motor[J].Proceedings of the CSEE,2003,23(3):126-130.
[17]Dubas F,Espanet C.Analytical solution of the magnetic field in permanent-magnet motors taking into account slotting effect:no-load vector potential and flux density calculation[J].IEEE Transactions on Magnetics,2009,45(5):2097-2109.
[18]Zhu Ziqiang,Wu Lijian,Xia Zhenping.An accurate subdomain model for magnetic field computation in slotted surface-mounted permanent-magnet machines[J].IEEE Transactions on Magnetics,2010,46(4):1100-1115.
[19]Wu Lijian,Zhu Ziqiang,Staton D,et al.Subdomain model for predicting armature reaction field of surfacemounted permanent-magnet machines accounting for tooth-tips[J].IEEE Transactions on Magnetics,2011,47(4):812-822.
[20]Wu Lijian,Zhu Ziqiang,Staton D,et al.An improved subdomain model for predicting magnetic field of surface-mounted permanent magnet machines accounting for tooth-tips[J].IEEE Transactions on Magnetics,2011,47(6):1693-1704.
[21]Teymoori S,Rahideh A,Moayed-Jahromi H,et al.2-D analytical magnetic field prediction for consequentpole permanent magnet synchronous machines[J].IEEE Transactions on Magnetics,2016,52(6):1-14.
[22]杨金歌,邓兆祥,周忆,等.车用永磁轮毂电机解析建模与齿槽转矩削弱[J].西安交通大学学报,2018,52(1):1-8.Yang Jinge,Deng Zhaoxiang,Zhou Yi,et al.Analytical modeling and cogging torque weakening of permanent magnet in-wheel motor for electric vehicles[J].Journal of Xi'an Jiaotong University,2018,52(1):1-8.
[23]Yang Shen,Liu Guiying,Xia Zhenping,et al.Determination of maximum electromagnetic torque in PM brushless machines having two-segment halbach array[J].IEEE Transactions on Industrial Electronics,2014,61(2):718-729.
[24]Sprangers R L J,Paulides J J H,Gysen B L J,et al.Magnetic saturation in semi-analytical harmonic modeling for electric machine analysis[J].IEEETransactions on Magnetics,2016,52(2):1-10.
[25]Djelloul-Khedda Z,Boughrara K,Dubas F,et al.Nonlinear analytical prediction of magnetic field and electromagnetic performances in switched reluctance machines[J].IEEE Transactions on Magnetics,2017,53(7):1-11.
[26]李节宝,井立兵,周晓燕,等.表贴式永磁无刷电机直接解析计算方法[J].电工技术学报,2012,27(11):83-88.Li Jiebao,Jing Libing,Zhou Xiaoyan,et al.Exact analytical method for surface-mounted permanentmagnet brushless motors[J].Transactions of China Electrotechnical Society,2012,27(11):83-88.
[27]张凤阁,陈进华,刘光伟,等.面贴式异向旋转双转子永磁电机的磁场解析计算[J].电工技术学报,2011,26(12):28-36.Zhang Fengge,Chen Jinhua,Liu Guangwei,et al.Analytical solution of magnetic field for surfacemounted permanent magnet machines with antirotation dual rotors[J].Transactions of China Electrotechnical Society,2011,26(12):28-36.
[2]张岳,曹文平,John Morrow.电动车用内置式永磁电机(PMSM)设计[J].电工技术学报,2015,30(14):108-115.Zhang Yue,Cao Wenping,John Morrow.Design of an interior permanent magnet synchronous motor(PMSM)for EV traction[J].Transactions of China Electrotechnical Society,2015,30(14):108-115.
[3]朱高嘉,朱英浩,朱建国,等.基于有限公式法和流固耦合的永磁牵引电动机冷却系统设计与分析[J].电工技术学报,2017,32(5):70-77.Zhu Gaojia,Zhu Yinghao,Zhu Jianguo,et al.Thermal analysis and cooling system design of a permanent magnet traction motor using computational fluid dynamics and cell method[J].Transactions of China Electrotechnical Society,2017,32(5):70-77.
[4]朱高嘉,朱英浩,朱建国,等.永磁电机温度场的改进有限公式迭代算法[J].电工技术学报,2017,32(16):136-144.Zhu Gaojia,Zhu Yinghao,Zhu Jianguo,et al.Amodified thermal rewind model of permanent magnet motors based on finite formulation method[J].Transactions of China Electrotechnical Society,2017,32(16):136-144.
[5]朱军,田淼,付融冰,等.基于载波频率成分的永磁同步电机转子定位研究[J].电力系统保护与控制,2015,43(14):48-54.Zhu Jun,Tian Miao,Fu Rongbing,et al.Research on rotor position of permanent magnet synchronous motor based on carrier frequency component[J].Power System Protection and Control,2015,43(14):48-54.
[6]陈柄任,李颖晖,李哲,等.基于流形学习的PMSM早期匝间短路故障特征提取[J].电力系统保护与控制,2016,44(17):18-24.Chen Bingren,Li Yinghui,Li Zhe,et al.Feature extraction of inchoate interturn short circuit fault for PMSM based on manifold learning[J].Power System Protection and Control,2016,44(17):18-24.
[7]Zhu Ziqiang.Fractional slot permanent magnet brushless machines and drives for electric and hybrid propulsion systems[J].COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering,2011,30(1):9-31.
[8]Zhu Li,Shan Jiang,Zhu Ziqiang,et al.Comparison of alternate analytical models for predicting cogging torque in surface-mounted permanent magnet machines[C]//2008 IEEE Vehicle Power and Propulsion Conference,Harbin,China,2008:1-6.
[9]Chao Bi,Liu Zhejie,Low T S.Analysis of unbalanced-magnetic-pulls in hard disk drive spindle motors using a hybrid method[J].IEEE Transactions on Magnetics,1996,32(5):4308-4310.
[10]郭思源,周理兵.表面埋入式永磁电机磁场解析[J].中国电机工程学报,2015,35(3):710-718.Guo Siyuan,Zhou Libing.Analytical solution of magnetic field in surface-inset permanent magnet machines[J].Proceedings of the CSEE,2015,35(3):710-718.
[11]Boules N.Prediction of no-load flux density distribution in permanent magnet machines[J].IEEETransactions on Industry Applications,1985,IA-21(3):633-643.
[12]Lee K,DeBortoli M J,Lee M J,et al.Coupling finite elements and analytical solution in the airgap of electric machines[J].IEEE Transactions on Magnetics,1991,27(5):3955-3957.
[13]Zhu Ziqiang,Howe D,Bolte E,et al.Instantaneous magnetic field distribution in brushless permanent magnet DC motors.I.open-circuit field[J].IEEETransactions on Magnetics,1993,29(1):124-135.
[14]Zhu Ziqiang,Howe D.Instantaneous magnetic field distribution in brushless permanent magnet DC motors.II.armature-reaction field[J].IEEE Transactions on Magnetics,1993,29(1):136-142.
[15]Hannon B,Sergeant P,Dupre L.Two-dimensional fourier-based modeling of electric machines[C]//2017IEEE International Electric Machines and Drives Conference(IEMDC),Miami,FL,USA,2017:1-8.
[16]王兴华,励庆孚,王曙鸿.永磁无刷直流电机空载气隙磁场和绕组反电势的解析计算[J].中国电机工程学报,2003,23(3):126-130.Wang Xinghua,Li Qingfu,Wang Shuhong.Analytical calculation of no-load air-gap magnetic field and back electromotive force in brushless DC motor[J].Proceedings of the CSEE,2003,23(3):126-130.
[17]Dubas F,Espanet C.Analytical solution of the magnetic field in permanent-magnet motors taking into account slotting effect:no-load vector potential and flux density calculation[J].IEEE Transactions on Magnetics,2009,45(5):2097-2109.
[18]Zhu Ziqiang,Wu Lijian,Xia Zhenping.An accurate subdomain model for magnetic field computation in slotted surface-mounted permanent-magnet machines[J].IEEE Transactions on Magnetics,2010,46(4):1100-1115.
[19]Wu Lijian,Zhu Ziqiang,Staton D,et al.Subdomain model for predicting armature reaction field of surfacemounted permanent-magnet machines accounting for tooth-tips[J].IEEE Transactions on Magnetics,2011,47(4):812-822.
[20]Wu Lijian,Zhu Ziqiang,Staton D,et al.An improved subdomain model for predicting magnetic field of surface-mounted permanent magnet machines accounting for tooth-tips[J].IEEE Transactions on Magnetics,2011,47(6):1693-1704.
[21]Teymoori S,Rahideh A,Moayed-Jahromi H,et al.2-D analytical magnetic field prediction for consequentpole permanent magnet synchronous machines[J].IEEE Transactions on Magnetics,2016,52(6):1-14.
[22]杨金歌,邓兆祥,周忆,等.车用永磁轮毂电机解析建模与齿槽转矩削弱[J].西安交通大学学报,2018,52(1):1-8.Yang Jinge,Deng Zhaoxiang,Zhou Yi,et al.Analytical modeling and cogging torque weakening of permanent magnet in-wheel motor for electric vehicles[J].Journal of Xi'an Jiaotong University,2018,52(1):1-8.
[23]Yang Shen,Liu Guiying,Xia Zhenping,et al.Determination of maximum electromagnetic torque in PM brushless machines having two-segment halbach array[J].IEEE Transactions on Industrial Electronics,2014,61(2):718-729.
[24]Sprangers R L J,Paulides J J H,Gysen B L J,et al.Magnetic saturation in semi-analytical harmonic modeling for electric machine analysis[J].IEEETransactions on Magnetics,2016,52(2):1-10.
[25]Djelloul-Khedda Z,Boughrara K,Dubas F,et al.Nonlinear analytical prediction of magnetic field and electromagnetic performances in switched reluctance machines[J].IEEE Transactions on Magnetics,2017,53(7):1-11.
[26]李节宝,井立兵,周晓燕,等.表贴式永磁无刷电机直接解析计算方法[J].电工技术学报,2012,27(11):83-88.Li Jiebao,Jing Libing,Zhou Xiaoyan,et al.Exact analytical method for surface-mounted permanentmagnet brushless motors[J].Transactions of China Electrotechnical Society,2012,27(11):83-88.
[27]张凤阁,陈进华,刘光伟,等.面贴式异向旋转双转子永磁电机的磁场解析计算[J].电工技术学报,2011,26(12):28-36.Zhang Fengge,Chen Jinhua,Liu Guangwei,et al.Analytical solution of magnetic field for surfacemounted permanent magnet machines with antirotation dual rotors[J].Transactions of China Electrotechnical Society,2011,26(12):28-36.