Abstract:The cogging torque of permanent-magnet machines will cause the torque ripple and reduce the accuracy of motor control. How to reduce the cogging torque has been one of the research hotspots in the field of permanent-magnet machines. The deduction process of traditional analytical method of cogging torque is commonly based on energy method. In this paper, a new cogging torque analysis method for permanent magnet machine is proposed by combining energy method with magnetic field modulation theory. The mechanism of cogging torque is explained, and the expression of cogging torque is deduced. It is proved that cogging torque is the result of the interaction of several modulated magnetic fields. Based on the analysis of the expression of the cogging torque component, the period constraints of the harmonic permanent magnetic field and the harmonic air-gap permeance are obtained to generate each cogging torque component. The integer-slot winding machine and the fractional-slot winding machine are simulated by finite element method. The cogging torques of machines with different pole/slot combinations are studied. The variations of the amplitudes of the harmonic magnetic fields in the air gap with the rotation of the rotor are studied, verifying the theoretical derivation. Finally, based on the analysis method of cogging torque in this paper, the design method of the machine is provided to suppress the cogging torque.
刘家琦, 白金刚, 郑萍, 刘国鹏, 黄家萱. 基于磁场调制原理的齿槽转矩研究[J]. 电工技术学报, 2020, 35(5): 931-941.
Liu Jiaqi, Bai Jingang, Zheng Ping, Liu Guopeng, Huang Jiaxuan. Investigation of Cogging Torque Based on Magnetic Field Modulation Principle. Transactions of China Electrotechnical Society, 2020, 35(5): 931-941.
[1] 胡鹏飞, 王东, 靳栓宝, 等. 偏心磁极永磁电机气隙磁场正弦优化模型[J]. 电工技术学报, 2019, 34(18): 3759-3768. Hu Pengfei, Wang Dong, Jin Shuanbao, et al.Sinusoidal optimization model for air gap magnetic field of eccentric magnetic pole permanent magnet motor[J]. Transactions of China Electrotechnical Society, 2019, 34(18): 3759-3768. [2] 李帅, 孙立志, 刘兴亚, 等. 永磁同步电机电流谐波抑制策略[J]. 电工技术学报, 2019, 34(增刊1): 87-96. Li Shuai, Sun Lizhi, Liu Xingya, et al.Current harmonics suppression strategies of permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2019, 34(S1): 87-96. [3] 刘毓希, 李立毅, 曹继伟, 等. 短时高过载永磁同步电机电磁热研究[J]. 电工技术学报, 2019, 34(11): 2296-2305. Liu Yuxi, Li Liyi, Cao Jiwei, et al.Electromagnetic thermal analysis for short-term high-overload permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2019, 34(11): 2296-2305. [4] 刘平, 王鑫, 孙千志, 等. 永磁同步电机定子绕组温度估计的信号注入策略优化[J]. 电机与控制学报, 2019, 23(11): 18-26. Liu Ping, Wang Xin, Sun Qianzhi, et al.Signal injection strategy optimization of stator winding temperature estimation for permanent magnet synchronous motor[J]. Electric Machines and Control, 2019, 23(11): 18-26. [5] Li Y X, Zhu Z Q.Cogging torque and unbalanced magnetic force prediction in PM machines with axial-varying eccentricity by superposition method[J]. IEEE Transactions on Magnetics, 2017, 53(11): 1-4. [6] Jo I H, Lee H W, Jeong G, et al.A study on the reduction of cogging torque for the skew of a magnetic geared synchronous motor[J]. IEEE Transactions on Magnetics, 2019, 55(2): 1-5. [7] 杨玉波, 刘国鹏, 陈鹏, 等. 基于子域法的游标混合电机电磁性能解析计算[J]. 电机与控制学报, 2019, 23(9): 9-17, 25. Yang Yubo, Liu Guopeng, Chen Peng, et al.Electromagnetic performance investigation of vernier hybrid machine[J]. Electric Machines and Control, 2019, 23(9): 9-17, 25. [8] 罗玲, 薛利昆, 吴先宇, 等. Halbach永磁阵列无刷直流电机转矩的解析计算和分析[J]. 电工技术学报, 2017, 32(16): 124-135. Luo Ling, Xue Likun, Wu Xianyu, et al.Analytical calculation and analysis of torque for brushless dc motors with Halbach magnet array[J]. Transactions of China Electrotechnical Society, 2017, 32(16): 124-135. [9] 唐旭, 王秀和, 田蒙蒙, 等. 基于改变定子齿槽参数的异步起动永磁同步电动机齿槽转矩削弱措施研究[J]. 电工技术学报, 2016, 31(23): 1-8. Tang Xu, Wang Xiuhe, Tian Mengmeng, et al.Study of reduction methods of cogging torque in line-start permanent magnet synchronous motor by changing the parameters of stator teeth and slots[J]. Transactions of China Electrotechnical Society, 2016, 31(23): 1-8. [10] 杨玉波, 王秀和, 陈谢杰, 等. 基于不等槽口宽配合的永磁电动机齿槽转矩削弱方法[J]. 电工技术学报, 2005, 20(3): 40-44. Yang Yubo, Wang Xiuhe, Chen Xiejie, et al.A method for reducing cogging torque by different slot widths in permanent magnet motors[J]. Transactions of China Electrotechnical Society, 2005, 20(3): 40-44. [11] Zhu Z Q, Li H Y, Deodhar R, et al.Recent developments and comparative study of magnetically geared machines[J]. CES Transactions on Electrical Machines and Systems, 2018, 2(1): 13-22. [12] 付兴贺, 王标, 林明耀. 磁力齿轮发展综述[J]. 电工技术学报, 2016, 31(18): 1-12. Fu Xinghe, Wang Biao, Lin Mingyao.Overview and recent developments of magnetic gears[J]. Transactions of China Electrotechnical Society, 2016, 31(18): 1-12. [13] Wu Fan, El-Refaie A M. Permanent magnet vernier machine: a review[J]. IET Electric Power Applications, 2019, 13(2): 127-137. [14] Liu Guohai, Jiang Shan, Zhao Wenxiang, et al.A new modeling approach for permanent magnet vernier machine with modulation effect consideration[J]. IEEE Transactions on Magnetics, 2017, 53(1): 1-12. [15] Zhu Xiaofeng, Hua Wei, Zhang Gan.An improved configuration for cogging torque reduction in flux-reversal permanent magnet machines[J]. IEEE Transactions on Magnetics, 2017, 53(6): 1-4. [16] Gao Yuting, Qu Ronghai, Li Dawei, et al.Design of three-phase flux-reversal machines with fractional-slot windings[J]. IEEE Transactions on Industry Applications, 2016, 52(4): 2856-2864. [17] Bai Jingang, Liu Jiaqi, Zheng Ping, et al.Design and analysis of a magnetic-field modulated brushless double-rotor machine—part I: pole pair combination of stator, PM rotor and magnetic blocks[J]. IEEE Transactions on Industrial Electronics, 2019, 66(4): 2540-2549. [18] Liu Yulong, Niu Shuangxia, Fu Weinong.Design of an electrical continuously variable transmission based wind energy conversion system[J]. IEEE Transactions on Industrial Electronics, 2016, 63(11): 6745-6755. [19] Cheng Ming, Han Peng, Hua Wei.General airgap field modulation theory for electrical machines[J]. IEEE Transactions on Industrial Electronics, 2017, 64(8): 6063-6074. [20] Cheng Ming, Wen Honghui, Han Peng, et al.Analysis of airgap field modulation principle of simple salient poles[J]. IEEE Transactions on Industrial Electronics, 2019, 66(4): 2628-2638. [21] 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. [22] Toba A, Lipo T A.Generic torque-maximizing design methodology of surface permanent-magnet vernier machine[J]. IEEE Transactions on Industry Applications, 2000, 36(6): 1539-1546.