Analytical Calculation and Analysis of Torque for Brushless DC Motors with Halbach Magnet Array
Luo Ling1, Xue Likun1, Wu Xianyu2, Zhang Leyue1
1. School of Automation Northwestern Polytechnical University Xi'an 710072 China; 2. College of Aerospace Science and Engineering National University of Defense Technology Changsha 410073 China
Abstract:Since the Halbach magnet array offers self-shielding magnetization and can easily change the waveform of air gap flux density, in this paper it is used in brushless DC motors to increase the electromagnetic torque and reduce the cogging torque. The model for calculating electromagnetic torque and cogging torque is presented according to the no-load magnetic field and the armature magnetic field calculated by conform transformation. Then, the calculated electromagnetic torque and cogging torque are compared with those calculated by the finite-element method (FEM). For the brushless DC motors with Halbach magnet array, the electromagnetic torque and the cogging torque are analyzed when the arc angle of the main segment of two permanent magnets in one pole is different, and they are also calculated when the arc angle of the main segment and the magnetizing angle of lateral permanent magnet (PM) of three PMs in one pole are changed. Furthermore, when the thickness of the PM is changed, the electromagnetic torque and the cogging torque in the brushless DC motor with Halbach magnet array are compared with those in the brushless DC motor with radial magnetization and parallel magnetization. The results show that, if the arc angle of main segment and the magnetizing angle of lateral PM in the Halbach magnet array are properly chosen, the electromagnetic torque can increase and the cogging torque can decrease. As the PM thickness increases, Halbach permanent magnet array is more conducive to increase the electromagnetic torque.
罗玲, 薛利昆, 吴先宇, 张乐玥. 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, Zhang Leyue. Analytical Calculation and Analysis of Torque for Brushless DC Motors with Halbach Magnet Array. Transactions of China Electrotechnical Society, 2017, 32(16): 124-135.
[1] 徐衍亮, 赵建辉, 房建成. 高速储能飞轮用无铁心永磁无刷直流电动机的分析与设计[J]. 电工技术学报, 2004, 19(12): 24-28. Xu Yanliang, Zhao Jianhui, Fang Jiancheng. Analysis and design of coreless permanent magnet brushless DC machine in high-speed energy storage flywheel application[J]. Transactions of China Electro- technical Society, 2004, 19(12): 24-28. [2] 王晓远, 唐任远, 杜静娟, 等. 基于Halbach阵列盘式无铁心永磁同步电机优化设计——楔形气隙结构电机[J]. 电工技术学报, 2007, 22(3): 2-5. Wang Xiaoyuan, Tang Renyuan, Du Jingjuan, et al. Optimization of disk coreless permanent magnet synchronous motor based on Halbach—the wedgy air gap motor[J]. Transactions of China Electrotechnical Society, 2007, 22(3): 2-5. [3] 夏长亮, 李洪凤, 宋鹏, 等. 基于Halbach阵列的永磁球形电动机磁场[J]. 电工技术学报, 2007, 22(7): 126-130. Xia Changliang, Li Hongfeng, Song Peng, et al. Magnetic field model of a PM spherical motor based on Halbach array[J]. Transactions of China Electro- technical Society, 2007, 22(7): 126-130. [4] 宋玉晶, 张鸣, 朱煜. Halbach永磁阵列磁场解析求解及推力建模[J]. 电工技术学报, 2014, 29(11): 61-67. Song Yujing, Zhang Ming, Zhu Yu. Modeling of Halbach array magnetic field and motor thrust[J]. Transactions of China Electrotechnical Society, 2014, 29(11): 61-67. [5] 耿伟伟, 张卓然. 新型外转子Halbach永磁阵列定子无铁心电机设计与分析[J]. 电工技术学报, 2015, 30(14): 130-137. Geng Weiwei, Zhang Zhuoran. Design and analysis of external rotor coreless permanent magnet motor with Halbach magnet array[J]. Transactions of China Electrotechnical Society, 2015, 30(14): 130-137. [6] Zhu Z Q, Howe D. Halbach permanent magnet machines and applications: a review[J]. IEE Pro- ceedings—Electric Power Applications, 2001, 148(4): 299-308. [7] Guler F, Ergene L T, Ekin C. Halbach array variations on BLDC motor under magnet constraint[C]//IEEE Fourth International Conference on Power Engineering, Energy and Electrical Drives (POWERENG), 2013: 1509-1513. [8] Młot A, Łukaniszyn M. Torque characteristics of a BLDC motor with multipolar excitation[J]. COMPEL, 1982, 28(1): 178-187. [9] 雷银照. 关于电磁场解析方法的一些认识[J]. 电工技术学报, 2016, 31(19): 11-25. Lei Yinzhao. Reviews of analytical methods for electromagnetic fields[J]. Transactions of China Electrotechnical Society, 2016, 31(19): 11-25. [10] Zhu Z Q, Howe D. Instantaneous magnetic field distribution in brushless permanent magnet DC motors, I. open-circuit field[J]. IEEE Transactions on Magnetics, 1993, 29(1): 124-135. [11] Wang X, Li Q, Wang S, et al. Analytical calculation of air-gap magnetic field distribution and instantaneous characteristics of brushless DC motors[J]. IEEE Transactions on Energy Conversion, 2003, 18(3): 424-432. [12] Žarko D, Ban D, Lipo T A. Analytical solution for cogging torque in surface permanent-magnet motors using conformal mapping[J]. IEEE Transactions on Magnetics, 2008, 44(1): 52-65. [13] Žarko D, Ban D, Lipo T A. Analytical solution for electromagnetic torque in surface permanent-magnet motors using conformal mapping[J]. IEEE Transa- ctions on Magnetics, 2009, 45(7): 2943-2954. [14] 仇志坚, 李琛, 周晓燕, 等. 表贴式永磁电机转子偏心空载气隙磁场解析[J]. 电工技术学报, 2013, 28(3): 114-121. Qiu Zhijian, Li Chen, Zhou Xiaoyan, et al. Analytical calculation of no-load air-gap magnetic field in surface-mounted permanent magnet motors with rotor eccentricity[J]. Transactions of China Electro- technical Society, 2013, 28(3): 114-121. [15] 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. [16] 范坚坚, 吴建华, 李创平, 等. 分块式Halbach型磁钢的永磁同步电机解析[J]. 电工技术学报, 2013, 28(3): 35-42. Fan Jianjian, Wu Jianhua, Li Chuangping, et al. Solution of permanent magnet synchronous motors with partition between poles Halbach magnet[J]. Transactions of China Electrotechnical Society, 2013, 28(3): 35-42. [17] 郭思源, 周理兵, 曲荣海, 等. 基于精确子域模型的游标永磁电机解析磁场计算[J]. 中国电机工程学报, 2013, 33(30): 71-80. Guo Siyuan, Zhou Libing, Qu Ronghai, et al. Analytical magnetic field calculation of vernier permanent-magnet machines based on accurate subdomain model[J]. Proceedings of the CSEE, 2013, 33(30): 71-80. [18] Tiang T L, Ishak D, Lim C P, et al. A comprehensive analytical subdomain model and its field solutions for surface-mounted permanent magnet machines[J]. IEEE Transactions on Magnetics, 2015, 51(4): 1-14. [19] 寇宝泉, 曹海川, 李伟力, 等. 新型双层Halbach永磁阵列的解析分析[J]. 电工技术学报, 2015, 30(10): 68-76. Kou Baoquan, Cao Haichuan, Li Weili, et al. Analytical analysis of a novel double layer Halbach permanent array[J]. Transactions of China Electro- technical Society, 2015, 30(10): 68-76. [20] Zarko D, Ban G, Lipo T A. Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance[J]. IEEE Transactions on Magnetics, 2006, 42(7):1828-1837. [21] 许孝卓, 汪旭东, 封海潮, 等. 分数槽集中绕组永磁同步直线电机磁场解析计算[J]. 电工技术学报, 2015, 30(14): 122-129. Xu Xiaozhuo, Wang Xudong, Feng Haichao, et al. Magnetic field calculation of the permanent magnet synchronous linear motor with fractional-slot concentrated windings[J]. Transactions of China Electrotechnical Society, 2015, 30(14): 122-129. [22] 汤蕴璆. 电机内的电磁场[M]. 北京: 科学出版社, 1981.