Cogging Torque Suppression of Interior Permanent Magnet Synchronous Motor Based on Air-Gap Magnetic Field Reconstruction
Ma Jiyuan1, Zeng Yu1, Zhao Wenxiang2, Ji Jinghua1, Yuan Dongyang1
1. School of Electrical and Information Engineering Jiangsu University Zhenjiang 212013 China; 2. School of Electric Power Engineering Nanjing Institute of Technology Nanjing 211167 China
Abstract：The cogging torque of an interior permanent magnet synchronous motor (IPMSM) is related to its structural parameters. Cogging torque induces torque ripple, vibration, and noise under load conditions. The structural design of low cogging torque in IPMSMs has become a focus of research. Precise prediction of the air-gap magnetic field is crucial for evaluating the rationalization of motor design. However, due to the complex rotor structure and uneven core magnetic saturation, accurately predicting the air-gap magnetic field in IPMSMs is a challenging task. This paper presents an enhanced analytical method that integrates magnetic field modulation with the magnetic equivalent circuit method. The speed and accuracy of magnetic field calculation are improved. Then, the rotor surface is notched to reduce specific harmonics in the air-gap magnetic field. The air-gap topology is created through notching on the rotor surface, which results in the reconstruction of the air-gap magnetic field and the suppression of cogging torque. Firstly, according to the modulation theory, the modulation structure of the air-gap magnetic field is analyzed. A refined magnetic circuit model is developed for the motor's structure. Modulation consists of two aspects: the magnetic motive potential of the permanent magnets is modulated by the rotor bridge; the air-gap magnetic field is modulated through the stator slots. Secondly, the target 44th harmonic is separated from the original air-gap magnetic field to construct the target magnetic field. The modulation function transforms the modulation of the original magnetic field into the target magnetic field. The notch function is analyzed by the proposed magnetic equivalent circuit method. After the proposed notching, the model analyzes that the air-gap harmonics are the ideal harmonics. Finally, the modulation function feeds back on the notch function, which notches the rotor surface. The reconstructed air-gap magnetic field is achieved by optimizing the magnetic field harmonics on the rotor surface topology. In terms of calculating results, the analysis and simulation waveforms are highly overlapping. The waveforms consist of the air-gap flux density distribution of the slotless stator, the slotted stator, and the air-gap reconstruction. For the torque performance, the original motor and the air-gap reconstruction motor are compared. The cogging torque of the air-gap reconstructed motor is reduced from 2.45 N∙m to 0.76 N∙m, which is a reduction of about 68.88%, and a slight increase in output torque from 10.79 N∙m to 11.07 N∙m. The torque ripple is considerably reduced, from 37.09% to 8.58%, under load conditions, specifically at 7.5 A and 700 r/min. The following conclusions can be drawn. (1) With the refined magnetic circuit model and improved modulation analysis method, the modulation can be accurately characterized. Simultaneously, the air-gap magnetic field harmonics are calculated. (2) The harmonics of the air-gap magnetic field are effectively optimized by the method of notching on the rotor surface. The air-gap is reconstructed, and the target harmonic of the air-gap magnetic field is reduced. This method significantly reduces the cogging torque while maintaining the motor's output characteristics. Feasible solutions are offered in the field of industrial servo drives, aerospace, and other high-precision controls.
马纪源, 曾煜, 赵文祥, 吉敬华, 袁东洋. 基于气隙磁场重构的内置式永磁同步电机齿槽转矩抑制[J]. 电工技术学报, 2025, 40(20): 6511-6523.
Ma Jiyuan, Zeng Yu, Zhao Wenxiang, Ji Jinghua, Yuan Dongyang. Cogging Torque Suppression of Interior Permanent Magnet Synchronous Motor Based on Air-Gap Magnetic Field Reconstruction. Transactions of China Electrotechnical Society, 2025, 40(20): 6511-6523.
[1] Liu Guohai, Liu Lu, Chen Qian, et al.Torque calculation of five-phase interior permanent magnet machine using improved analytical method[J]. IEEE Transactions on Energy Conversion, 2019, 34(2): 1023-1032. [2] 吴翔, 李超, 刘志恒, 等. 带有LC正弦波滤波器的内置式永磁同步电机电流控制器谐振抑制参数设计[J]. 电工技术学报, 2023, 38(22): 6082-6093. Wu Xiang, Li Chao, Liu Zhiheng, et al.Parameter design of the current controller for interior permanent magnet synchronous motor with LC sinusoidal filter to suppress resonance[J]. Transactions of China Electrotechnical Society, 2023, 38(22): 6082-6093. [3] 李仕豪, 狄冲, 刘佶炜, 等. 考虑交叉耦合影响的内置式永磁同步电机电感计算及转矩分析[J]. 电工技术学报, 2023, 38(18): 4889-4899, 4931. Li Shihao, Di Chong, Liu Jiwei, et al.Inductance calculation and torque analysis of interior permanent magnet synchronous machine considering cross- coupling effects[J]. Transactions of China Electro- technical Society, 2023, 38(18): 4889-4899, 4931. [4] 贾海媛, 王刚. 双气隙磁场调制式永磁电机气隙磁场仿真分析与优化设计[J]. 微电机, 2024, 57(11): 24-28, 39. Jia Haiyuan, Wang Gang.Theoretical analysis and optimal design of air-gap field for double air-gap field modulation permanent magnet motor[J]. Micromotors, 2024, 57(11): 24-28, 39. [5] 程明, 文宏辉, 花为, 等. 电机气隙磁场调制统一理论及其典型应用[J]. 中国电机工程学报, 2021, 41(24): 8261-8283. Cheng Ming, Wen Honghui, Hua Wei, et al.General airgap field modulation theory for electrical machines and its typical applications[J]. Proceedings of the CSEE, 2021, 41(24): 8261-8283. [6] Zhao Yu, Li Dawei, Liang Ziyi, et al.A high power factor PM vernier machine with segmented stator[J]. IEEE Transactions on Transportation Electrification, 2024, 10(4): 9294-9303. [7] Zeng Yu, Cheng Ming, Liu Guohai, et al.Effects of magnet shape on torque capability of surface-mounted permanent magnet machine for servo applications[J]. IEEE Transactions on Industrial Electronics, 2020, 67(4): 2977-2990. [8] 冯魏, 郭凯凯. 低转矩脉动永磁辅助同步磁阻电机转子结构优化设计[J]. 电机与控制应用, 2024, 51(9): 70-79. Feng Wei, Guo Kaikai.Optimized rotor design for permanent magnet assisted synchronous reluctance motor with low torque ripple[J]. Electric Machines & Control Application, 2024, 51(9): 70-79. [9] Zhao Wenxiang, Hu Qingze, Ji Jinghua, et al.Torque generation mechanism of dual-permanent-magnet- excited vernier machine by air-gap field modulation theory[J]. IEEE Transactions on Industrial Electronics, 2023, 70(10): 9799-9810. [10] 李亚, 周庆林, 丁石川, 等. 表嵌式交替极永磁电机拓扑演化及气隙磁场调制效应研究[J]. 电工技术学报, 2023, 38(12): 3188-3198. Li Ya, Zhou Qinglin, Ding Shichuan, et al.Investigation of topologies evolution and air-gap field modulation effect on surface-inset consequent-pole PM machines[J]. Transactions of China Electro- technical Society, 2023, 38(12): 3188-3198. [11] Wen Honghui, Cheng Ming, Jiang Yunlei, et al.Analysis of airgap field modulation principle of flux guides[C]//2018 IEEE Energy Conversion Congress and Exposition (ECCE), Portland, OR, USA, 2018: 7302-7309. [12] Li Zhaokai, Huang Xiaoyan, Liu Ang, et al.Analytical model of electromagnetic performance for permanent-magnet vernier machines using nonlinear exact conformal model[J]. IEEE Transactions on Transportation Electrification, 2022, 8(2): 2005-2014. [13] Xiang Pengjie, Yan Liang, Guo Yiming, et al.A concentrated-flux-type PM machine with irregular magnets and iron poles[J]. IEEE/ASME Transactions on Mechatronics, 2024, 29(1): 691-702. [14] 李世奇, 佟文明, 贾建国, 等. 考虑磁桥非线性的内置式永磁同步电机空载电磁性能通用解析模型[J]. 电工技术学报, 2023, 38(6): 1421-1432. Li Shiqi, Tong Wenming, Jia Jianguo, et al.General analytical model of no-load electromagnetic perfor- mance of interior permanent magnet synchronous motors considering nonlinearity of magnetic bridges[J]. Transactions of China Electrotechnical Society, 2023, 38(6): 1421-1432. [15] Guo Baocheng, Huang Yunkai, Peng Fei, et al.A new hybrid method for magnetic field calculation in IPMSM accounting for any rotor configuration[J]. IEEE Transactions on Industrial Electronics, 2019, 66(7): 5015-5024. [16] 翟凤晨, 于慎波, 何庆桡. V型内置式永磁同步电机空载气隙磁场解析计算[J]. 电机与控制学报, 2023, 27(9): 73-81. Zhai Fengchen, Yu Shenbo, He Qingrao.Analytical calculation of no-load air gap magnetic field of V-type interior permanent magnet synchronous motors[J]. Electric Machines and Control, 2023, 27(9): 73-81. [17] Faradonbeh V Z, Rahideh A, Boroujeni S T, et al.2-D analytical no-load electromagnetic model for slotted interior permanent magnet synchronous machines[J]. IEEE Transactions on Energy Conversion, 2021, 36(4): 3118-3126. [18] Wei Qiang, Zhu Z Q, Jia Yan, et al.Electromagnetic performance analysis of variable flux memory machines with series-magnetic-circuit and different rotor topologies[J]. CES Transactions on Electrical Machines and Systems, 2024, 8(1): 3-11. [19] Zhuang Haijun, Zuo Shuguang, Ma Zhixun, et al.Analytical modeling of open-circuit air-gap flux density in interior permanent magnet machine[J]. IEEE Transactions on Magnetics, 2023, 59(6): 8101112. [20] Dajaku G, Gerling D.Stator slotting effect on the magnetic field distribution of salient pole syn- chronous permanent-magnet machines[J]. IEEE Transactions on Magnetics, 2010, 46(9): 3676-3683. [21] Wu Shuang, Shi Tingna, Guo Liyan, et al.Accurate analytical method for magnetic field calculation of interior PM motors[J]. IEEE Transactions on Energy Conversion, 2021, 36(1): 325-337. [22] Ma Conggan, Zhang Jingjing, Wang Jianfeng, et al.Analytical model of open-circuit air-gap field distribution in interior permanent magnet machines based on magnetic equivalent circuit method and boundary conditions of macroscopic equations[J]. IEEE Transactions on Magnetics, 2021, 57(3): 8104209. [23] 王群京, 郑耀达, 刘先增. 基于结构参数优化的电机振动噪声的抑制研究[J]. 电气工程学报, 2023, 18(2): 16-25. Wang Qunjing, Zheng Yaoda, Liu Xianzeng.Research on suppression of motor vibration and noise based on structural parameter optimization[J]. Journal of Electrical Engineering, 2023, 18(2): 16-25. [24] 王力新, 王晓远, 高鹏, 等. 电动汽车用内置式永磁同步电机转矩脉动分析及抑制[J]. 电工技术学报, 2024, 39(20): 6386-6396. Wang Lixin, Wang Xiaoyuan, Gao Peng, et al.Torque ripple reduction analysis of interior permanent magnet synchronous motor for electric vehicle[J]. Transa- ctions of China Electrotechnical Society, 2024, 39(20): 6386-6396. [25] Jia Lun, Lin Mingyao, Le Wei, et al.Dual-skew magnet for cogging torque minimization of axial flux PMSM with segmented stator[J]. IEEE Transactions on Magnetics, 2020, 56(2): 7507306. [26] Won Y J, Kim J H, An S M, et al.Comparative study of cogging torque, torque ripple, and vibration on stator tooth chamfer types in permanent magnet synchronous motors[J]. IEEE Transactions on Mag- netics, 2024, 60(9): 8202905. [27] Gao Jian, Xiang Zhiman, Dai Litao, et al.Cogging torque dynamic reduction based on harmonic torque counteract[J]. IEEE Transactions on Magnetics, 2022, 58(2): 8103405. [28] 郭培遥, 梁建伟, 王昕华, 等. 辐条式磁齿轮电机齿槽转矩抑制[J]. 电机与控制应用, 2023, 50(7): 66-73, 80. Guo Peiyao, Liang Jianwei, Wang Xinhua, et al.Cogging torque suppression of spoke magnetic gear motor[J]. Electric Machines & Control Application, 2023, 50(7): 66-73, 80.
2025, Vol. 40 
