Analytical Calculation and Optimization Analysis of Electromagnetic Performance of Halbach Partially-Segmented Permanent Magnet Synchronous Motors with Unequal Width and Thickness
Gao Fengyang1, Qi Xiaodong1, Li Xiaofeng1, Tao Caixia1, Gao Peng2
1. College of Automation and Electrical Engineering Lanzhou Jiaotong University Lanzhou 730070 China; 2. College of Electrical Engineering and Information Tianjin University Tianjin 300072 China
Abstract：In order to suppress the electromagnetic torque ripple and reduce the permanent magnet eddy current loss in high power-density permanent magnet synchronous motor, a partially-segmented structure of Halbach is proposed. The permanent magnets is magnetized with Halbach pattern and each pole consists of three sections. The main magnetic pole is segmented on single side. The border magnetic pole and the main magnetic pole are not equal in thickness and width, and the permanent magnet is expanded to Hat type and T type. Using a precise subdomain model method, the solution domain is divided into four regions: slot, slot-opening, air gap and permanent magnet. The magnetic field density of airgap with load and electromagnetic torque is calculated under two-dimensional polar coordinates. A 10-pole/12-slot three-dimensional motor model is established to perform electromagnetic simulation, hierarchical optimization and comparative analysis on Hat-type, T-type and other related five motor structures for finding the optimal Hat-type and T-type structures. The results show that partially-segmented structure of Halbach can reduce the permanent magnet eddy current loss, electromagnetic torque ripple and magnetic field density of airgap with loading. The electromagnetic performance of the partially-segmented structure of the T-type Halbach is higher than that of the Hat type, while the partially-segmented structure of the Hat type Halbach can further reduce the volume of the permanent magnet and save the production cost. Moreover, the equivalent stress and total deformations are calculated based on the three-dimensional finite element stress model of permanent magnetic synchronous motor, which are also in the tolerant range of mechanical strength.
[1] 李勇, 徐兴, 孙晓东, 等. 轮毂电机驱动技术研究概况及发展综述[J]. 电机与控制应用, 2017, 44(6): 1-7, 18. Li Yong, Xu Xing, Sun Xiaodong, et al.Review and future development of in-wheel motor drive technology[J]. Electric Machines and Control Applications, 2017, 44(6): 1-7, 18. [2] 石玉君, 程子活, 蹇林旎. 两种典型的场调制型永磁电机的对比分析[J]. 电工技术学报, 2021, 36(1): 120-130. Shi Yujun, Cheng Zihuo, Jian Linwei.Comparative analysis of two typical field modulated permanentmagnet machines[J]. Transactions of China Electrotechnical Society, 2021, 36(1): 120-130. [3] 孔垂毅, 代颖, 罗建. 电动汽车轮毂电机技术的发展现状与发展趋势[J]. 电机与控制应用, 2019, 46(2): 105-112, 117. Kong Chuiyi, Dai Ying, Luo Jian.Development status and trend of in-wheel motor technology for electric vehicles[J]. Electric Machines and Control Applications, 2019, 46(2): 105-112, 117. [4] 程明, 文宏辉, 曾煜, 等. 电机气隙磁场调制行为及其转矩分析[J]. 电工技术学报, 2020, 35(5): 921-930. Cheng Ming, Wen Honghui, Zeng Yu, et al.Analysis of airgap field modulation behavior and torque component in electric machines[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 921-930. [5] 陈萍, 唐任远, 佟文明, 等. 高功率密度永磁同步电机永磁体涡流损耗分布规律及其影响[J]. 电工技术学报, 2015, 30(6): 1-9. Chen Ping, Tang Renyuan, Tong Wenming, et al.Permanent magnet eddy current loss and its influence of high power density permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2015, 30(6): 1-9. [6] 任庆, 桂祈祯. 基于永磁体温度对车用电机性能影响分析[J]. 机械制造与自动化, 2018, 47(2): 213-217. Ren Qing, Gui Qizhen.Influence analysis of temperature of permanent magnet on performance of vehicle motor[J]. Mechanical Engineering & Automation, 2018, 47(2): 213-217. [7] 张磊, 高春侠. 永磁同步电机磁钢涡流损耗模型及其衡量指标[J]. 电机与控制学报, 2013, 17(7): 46-53. Zhang Lei, Gao Chunxia.Eddy-current loss model and index for magnets of permanent magnet synchronous motors[J]. Electric Machines and Control, 2013, 17(7): 46-53. [8] 范坚坚, 吴建华. 计及齿槽极间隔断Halbach型磁钢的PMSM气隙磁场解析分析[J]. 中国电机工程学报, 2010, 30(12): 98-105. Fan Jianjian, Wu Jianhua.Analytical solution and analysis of airgap magnetic field of PMSM with partition-between-poles Halbach magnet considering effect of slotting[J]. Proceedings of the CSEE, 2010, 30(12): 98-105. [9] 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. [10] 李深, 章跃进, 周晓燕, 等. 定子开槽表贴式永磁电机转子偏心空载气隙磁场全局解析法[J]. 电机与控制学报, 2014, 18(10): 27-35. Li Shen, Zhang Yuejin, Zhou Xiaoyan, et al.Exact analytical solution of open circuit air-gap magnetic field for slotted surface-mounted permanent-magnet motors with rotor eccentricity[J]. Electric Machines and Control, 2014, 18(10): 27-35. [11] Lubin T, Mezani S, Rezzoug A.Exact analytical method for magnetic field computation in the air gap of cylindrical electrical machines considering slotting effects[J]. IEEE Transactions on Magnetics, 2010, 46(4): 1092-1099. [12] 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. [13] 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.Analysis solution of magnetic field surface-inset permanent magnet machines[J]. Proceedings of the CSEE, 2015, 35(3): 710-718. [14] 杨思雨, 夏长亮, 王慧敏, 等. 磁极分段型表贴式永磁电机建模与分析[J]. 电工技术学报, 2015, 30(增刊2): 49-55. Yang Siyu, Xia Changliang, Wang Huimin, et al.Modeling and analyzing for surface mounted permanent magnet machine with segmented pole[J]. Transactions of China Electrotechnical Society, 2015, 30(S2): 49-55. [15] 李琛, 章跃进, 井立兵. Halbach阵列半闭口槽永磁电机全局解析法研究[J]. 中国电机工程学报, 2013, 33(33): 85-94. Li Chen, Zhang Yuejin, Jing Libing.Researches on an exact analytical method of Halbach-array permanentmagnet motors with semi-closed slots[J]. Proceedings of the CSEE, 2013, 33(33): 85-94. [16] 郭思源, 周理兵, 齐歌. 双三相永磁同步电机电磁性能解析计算[J]. 电工技术学报, 2014, 29(5): 17-28. Guo Siyuan, Zhou Libing, Qi Ge.Analytical calculateon of electromagnetic performance in dual threephase permanent magnet brushless AC machines[J]. Transactions of China Electrotechnical Society, 2014, 29(5): 17-28. [17] Madina P, Poza J, Ugalde G, et al.Analysis of nonuniform circumferential segmentation of magnets to reduce eddy-current losses in SPMSM machines[C]// International Conference on Electrical Machines, Marseille, France, 2012: 79-84. [18] Lee S H, Oh H S, Kim H S.Experiment research on motor efficiency improvement through the eddy current reduction using segmentation of rotor magnet[C]//International Conference on Electrical Machines and Systems, Sydney, Australia, 2017: 1-4. [19] Wang Youhua, Ma Jinguang, Liu Chengcheng, et al.Reduction of magnet eddy current loss in PMSM by using partial magnet segment method[J]. IEEE Transactions on Magnetics, 2019, 55(7): 1-5. [20] Lubin T, Mezani S, Rezzoug A.2-D exact analytical model for surface-mounted permanent-magnet motors with semi-closed slots[J]. IEEE Transactions on Magnetics, 2011, 47(2): 479-492. [21] 倪有源, 王磊, 王群京. 凸形不等厚磁极永磁电机建模与分析[J]. 电工技术学报, 2020, 35(11): 2406-2414. Ni Youyuan, Wang Lei, Wang Qunjing.Modeling and analysis of permanent magnet machines with salient shape unequal thickness magnets[J]. Transactions of China Electrotechnical Society, 2020, 35(11): 2406-2414. [22] 杨定伟, 邓兆祥, 张河山, 等. 永磁轮毂电机磁场解析建模[J]. 电工技术学报, 2019, 34(7): 1423-1433. Yang Dingwei, Deng Zhaoxiang, Zhang Heshan, et al.Exact analytical solution of magnetic field in permanent magnet in-wheel motor[J]. Transactions of China Electrotechnical Society, 2019, 34(7): 1423-1433. [23] 梁子漪, 曲荣海, 李大伟, 等. 一种交替极切向励磁游标永磁电机的分析与设计[J]. 电工技术学报, 2020, 35(15): 3173-3181. Liang Ziyi, Qu Ronghai, Li Dawei, et al.Analysis and design of a vernier permanent magnet motor with alternating pole tangential excitation[J]. Transactions of China Electrotechnical Society, 2020, 35(15): 3173-3181. [24] 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. [25] 倪有源, 刘跃斌, 王群京. 组合磁极结构的永磁电机解析法建模与分析[J]. 电机与控制学报, 2019, 23(1): 52-62. Ni Youyuan, Liu Yuebin, Wang Qunjing.Analytical modeling and analysis of permanent magnet machine with combined magnetic poles[J]. Electric Machines and Control, 2019, 23(1): 52-62. [26] 张守首, 郭思源. 考虑分段斜极和磁性槽楔的永磁同步电机磁场解析方法[J]. 电工技术学报, 2019, 34(1): 15-26. Zhang Shoushou, Guo Siyuan.Analytical magnetic field method of permanent magnet synchronous machine considering step-skewed magnets and magnetic slot wedge[J]. Transactions of China Electrotechnical Society, 2019, 34(1): 15-26. [27] 李咸善, 徐浩, 邹芳, 等. 微电网分级优化故障重构[J]. 中国电机工程学报, 2015, 35(24): 6378-6386. Li Xianshan, Xu Hao, Zou Fang, et al.Micro-grid hierarchical optimization fault reconstruction[J]. Proceedings of the CSEE, 2015, 35(24): 6378-6386. [28] Wills D A, Kamper M J.Reducing PM eddy current rotor losses by partial magnet and rotor yoke segmentation[C]//International Conference on Electrical Machines, Roma, Italy, 2010: 1-6.
2022, Vol. 37 
