Abstract：The main source of vibration and acoustic noise of low-speed permanent magnet synchronous motors (PMSMs) is the alternating electromagnetic force of the stator, which is caused by the permanent magnetic field and the armature magnetic field. This paper proposes a stator force calculation model of a surface-mounted permanent magnet motor under the action of armature magnetic field. Taking the physical boundary of the stator and the conductor in the slot as the analysis object, the magnetic permeability distribution function of the stator tooth boundary is extracted through two-dimensional finite element analysis, and its relationship with the basic inductance parameters of the motor is deduced. According to the actual phase current of the motor, the magnetic density distribution and force distribution of the motor tooth boundary and the conductor in the slot are obtained by applying the superposition principle and the Maxwell stress tensor method. Finally, the correctness of the above calculation model is verified by two-dimensional finite element analysis.
吕亚军, 程思为, 王东, 陈俊全. 表贴式永磁电机在电枢磁场作用下的定子受力计算模型[J]. 电工技术学报, 2019, 34(15): 3124-3135.
LüYajun, ChengSiwei, Wang Dong, Chen Junquan. The Stator Force Calculation Model for Surface Mounted Permanent Magnet Motor under the Action of Armature Magnetic Field. Transactions of China Electrotechnical Society, 2019, 34(15): 3124-3135.
[1] 唐任远. 现代永磁电机[M].北京:机械工业出版社, 1997. [2] 马伟明, 王东, 程思为,等. 高性能电机系统的共性基础科学问题与技术发展前沿[J]. 中国电机工程学报, 2016, 36(8):2025-2035. MaWeiming, Wang Dong, Cheng Siwei, et al. Common basic scientific problems and development of leading-edge technology of high performance motor system[J]. Proceedings of the CSEE,2016, 36(8):2025-2035. [3] Chu W Q, Zhu Z Q.On-load cogging torque calculation in permanent magnet machines[J]. IEEE Transactions on Magnetics, 2013, 49(6):2982-2989. [4] Chu W Q, Zhu Z Q.Investigation of torque ripples in permanent magnet synchronous machines with skewing[J]. IEEE Transactions on Magnetics, 2013, 49(3):1211-1220. [5] Lee S K, Kang G H, Jin H, et al.Stator and rotor shape designs of interior permanent magnet type brushless DC motor for reducing torque fluctuation[J]. IEEE Transactions on Magnetics, 2012, 48(11):4662-4665. [6] Li Guangjin, Ren Bo, Zhu Z Q, et al.Cogging torque mitigation of modular permanent magnet machines[J]. IEEE Transactions on Magnetics, 2015, 52(1):1-10. [7] 张海洋, 许海平, 方程, 等. 基于比例积分-准谐振控制器的直驱式永磁同步电机转矩脉动抑制方法[J]. 电工技术学报, 2017, 32(19): 41-51. Zhang Haiyang, XuHaiping, Fang Cheng, et al. Torque ripple suppression method of direct-drive permanent magnet synchronous motor based on proportional-integral and quasi resonant controller[J]. Transactions of China Electrotechnical Society, 2017, 32(19): 41-51. [8] 王东, 马伟明, 郭云珺,等. 基于非正弦供电方式的多相感应电动机建模[J]. 电工技术学报, 2010, 25(2):6-14. Wang Dong, Ma Weiming, Guo Yunjun, et al.Modelling of multiphase induction motor with non-sinusoidal supply[J].Transactions of China Electrotechnical Society,2010, 25(2):6-14. [9] 方程, 许海平, 薛劭申,等. 直驱型多相永磁同步电机定子磁动势与气隙磁密特性分析[J]. 中国电机工程学报, 2013, 33(24):106-113. Fang Cheng, XuHaiping, XueShaoshen, et al. Analysis of stator MMF and air gap flux density characteristics of direct-drive multi-phase permanent magnet synchronous machines[J].Proceedings of the CSEE, 2013, 33(24):106-113. [10] Li Yong, Xing Jingwei, Wang Tianbao, et al.Programmable design of magnet shape for permanent-magnet synchronous motors with sinusoidal back EMF waveforms[J]. IEEE Transactions on Magnetics, 2008, 44(9):2163-2167. [11] Shen Yang, Hu Pengfei, Jin Shuanbao, et al.Design of novel shaftless pump-jet propulsor for multi-purpose long-range and high-speed autonomous underwater vehicle[J]. IEEE Transactions on Magnetics, 2016, 52(7):1-4. [12] El-Refaie A M. Fractional-slot concentrated-windings synchronous permanent magnet machines: opportunities and challenges[J]. IEEE Transactions on Industrial Electronics, 2009, 57(1):107-121. [13] 艾胜, 程思为, 肖飞,等. 永磁同步电机转子位置检测滤波方法研究[J]. 电机与控制学报, 2018, 22(3):66-73. Ai Sheng, Cheng Siwei, Xiao Fei, et al.A study on position signal filtering method for permanentmagnet synchronous machines[J]. Electical Machines and Control, 2018, 22(3):66-73. [14] 艾胜,任强,程思为,等.一种大功率永磁电机旋转变压器位置补偿方法[J].电力电子技,2018,52(2):13-15. Ai Sheng, RenQiang, Cheng Siwei, et al. A resolver position compensation method for high-power permanent-magment machine[J]. Power Electronics, 2018,52(2):13-15. [15] 杨光, 杨明发, 赵参. 基于电流斩波的开关磁阻电机转矩脉动减小策略研究[J]. 电气技术, 2016, 17(7): 20-23. Yang Guang, Yang Mingfa, Zhao Can.Torque ripple reduction of switched reluctance motors based on current chopping control[J]. Electrical Engineering, 2016, 17(7): 20-23. [16] 荣智林, 陈启军. 具有死区补偿的自抗扰控制下PMSM转矩脉动抑制方法[J]. 控制与决策, 2016, 31(4):667-672. RongZhilin, Chen Qijun. Torque ripple suppression method of PMSM based on ADRC with dead-time compensation[J]. Control and Decision, 2016, 31(4):667-672. [17] 林福, 左曙光, 毛钰,等. 考虑电流谐波的永磁同步电机电磁振动和噪声半解析模型[J]. 电工技术学报, 2017, 32(9):24-31. Lin Fu,ZuoShuguang,Mao Yu, et al. Semi-analytical model of vibration and noise for permanent magnet synchronous motor considering current harmonics[J]. Transactions of China Electrotechnical Society, 2017, 32(9):24-31. [18] 钟鸿敏, 左曙光, 吴旭东,等. 电励磁爪极发电机气隙磁场与径向电磁力的解析计算模型[J]. 电工技术学报, 2017, 32(7):49-58. ZhongHongmin,ZuoShuguang,Wu Xudong, et al. Analytic model of air gap magnetic field and radial electromagnetic force for electric excitation claw pole alternators[J]. Transactions of China Electrotechnical Society, 2017, 32(7):49-58. [19] 陈益广, 韩柏然, 沈勇环,等. 永磁同步推进电机电磁振动分析[J]. 电工技术学报, 2017, 32(23):16-22. Chen Yiguang, Han Boran,Shen Yonghuan, et al.Electromagnetic vibration analysis of permanent magnet synchronous propulsion motor[J]. Transactionsof China Electrotechnical Society, 2017, 32(23):16-22. [20] 谢颖, 李飞, 黎志伟,等. 内置永磁同步电机减振设计与研究[J]. 中国电机工程学报, 2017, 37(18):5437-5445. Xie Ying, Li Fei, Li Zhiwei, et al.Optimized design and research of vibration reduction with an interior permanent magnet synchronous motor[J]. Proceedings of the CSEE, 2017, 37(18):5437-5445. [21] 左曙光, 刘晓璇, 于明湖,等. 永磁同步电机电磁振动数值预测与分析[J]. 电工技术学报, 2017, 32(1):159-167. ZuoShuguang,Liu Xiaoxuan,Yu Minghu,et al.Numerical prediction and analysis of electromagnetic vibration inpermanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society,2017, 32(1):159-167. [22] 郑江, 代颖, 石坚. 车用永磁同步电机的电磁噪声特性[J]. 电工技术学报,2016, 31(增刊1):53-59. Zheng Jiang, Dai Ying, Shi Jian.Electromagnetic noise characteristics of permanent magnet synchronousmotor applied in electric vehicle[J]. Transactions of China Electrotechnical Society, 2016, 31(S1):53-59. [23] Zhu Z Q, 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. [24] Zhu Z Q, Xia Zhenping, Wu Lijian, et al.Analytical modeling and finite-element computation of radial vibration force in fractional-slot permanent-magnet brushless machines[J]. IEEE Transactions on Industry Applications, 2010, 46(5):1908-1918. [25] Cavagnino A.Accuracy-enhanced algorithms for the slot leakage inductance computation of double-layer windings[J]. IEEE Transactions on Industry Applications, 2017, 53(5): 4422-4430.
2019, Vol. 34 
