Analytical Calculation of No-Load Magnetic Field in Permanent Magnet Linear Synchronous Motors Based on an Accurate Subdomain Model
Wang Mingjie1, Xu Wei2, Yang Cunxiang1, Qiu Hongbo1, Zhu Jianguo3
1. School of Electrical and Information Zhengzhou University of Light Industry Zhengzhou 450002 China; 2. School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan 430074 China; 3. School of Electrical and Information University of Sydney Sydney NSW2006 Australia
Abstract:Accurate calculation of the magnetic field distribution in permanent magnet linear synchronous motor (PMLSM) is required to obtain the parameters and performance, and the establishment of an accurate mathematical model is the key to solving the magnetic field problem. To avoid the limitations of the traditional analytical theory of PMLSM in solving the slot effect on air gap magnetic field, an accurate subdomain model of PMLSM is proposed to obtain the accurate magnetic field distribution. By taking into account the relative magnetic permeability of the permanent magnet (PM), slot depth and mutual influence of all slots on the magnetic field distribution, the Laplace equation of permanent magnet subdomain, airgap subdomain and slot subdomain are established in the scalar magnetic potential. According to the boundary conditions of each subdomain interface, all boundary condition equations are set up based on the Fourier series method, and the equivalent model of end area is established. The scalar magnetic potential and no-load flux density distribution of each subdomain are then solved. The slot and end effects on the spatial distribution of air gap magnetic field are discussed. The accuracy of analytical model is validated by the finite element method (FEM) results.
王明杰, 徐伟, 杨存祥, 邱洪波, 朱建国. 基于精确子域模型的永磁直线同步电机空载磁场解析计算[J]. 电工技术学报, 2020, 35(5): 942-953.
Wang Mingjie, Xu Wei, Yang Cunxiang, Qiu Hongbo, Zhu Jianguo. Analytical Calculation of No-Load Magnetic Field in Permanent Magnet Linear Synchronous Motors Based on an Accurate Subdomain Model. Transactions of China Electrotechnical Society, 2020, 35(5): 942-953.
[1] Boldea Ion, Tutelea L N, Xu Wei, et al.Linear electric machines, drives, and MAGLEVs: an overview[J]. IEEE Transactions on Industrial Electronics, 2018, 65(9): 7504-7515. [2] 许孝卓, 孙震, 汪旭东, 等. Halbach交替极永磁同步直线电机特性分析[J]. 电工技术学报, 2019, 34(9): 1825-1833. Xu Xiaozhuo, Sun Zhen, Wang Xudong, et al.Characteristic of a novel permanent magnet linear synchronous motor with halbach array consequent-pole[J]. Transactions of China Electrotechnical Society, 2019, 34(9): 1825-1833. [3] Zhang He, Kou Baoquan, Zhu Ziqiang, et al.Thrust ripple analysis on toroidal-winding linear permanent magnet vernier machine[J]. IEEE Transactions on Industrial Electronics, 2018, 65(12): 9853-9862. [4] Sheikh-Ghalavand B, Vaez-Zadeh S, Hassanpour I A.An improved magnetic equivalent circuit model for iron-core linear permanent-magnet synchronous motors[J]. IEEE Transactions on Magnetics, 2010, 46(1): 112-120. [5] 杜怿, 程明, 邹国棠. 初级永磁型游标直线电机设计与静态特性分析[J]. 电工技术学报, 2012, 27(11) : 22-30. Du Yi, Cheng Ming, Chau K T.Design and analysis of a new linear primary permanent magnet vernier machine[J]. Transactions of China Electrotechnical Society, 2012, 27(11): 22-30. [6] Liu Guohai, Jiang Shan, Zhao Wenxiang, et al.Modular reluctance network simulation of a linear permanent-magnet vernier machine using new mesh generation methods[J]. IEEE Transactions on Industrial Electronics, 2017, 64(7): 5323-5332. [7] Asfirane S, Hlioui S, Amara Y.Global quantities computation using mesh-based generated reluctance networks[J]. IEEE Transactions on Magnetics, 2018, 1(1): 1-4. [8] Chung M J, Gweon D G.Modeling of the armature slotting effect in the magnetic field distribution of a linear permanent magnet motor[J]. IEEE Transactions on Magnetics, 2002, 84(2): 101-108. [9] 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. [10] Zhu Ziqiang, Howe D.Instantaneous magnetic field distribution in brushless permanent magnet DC motors. III. Effect of stator slotting[J]. IEEE Transactions on Magnetics, 1993, 29(1): 143-151. [11] 王明杰, 李彦彦, 焦留成, 等. 永磁游标直线电机磁场解析计算[J].电机与控制学报, 2017, 21(10): 54-61. Wang Mingjie, Li Yanyan, Jiao Liucheng, et al.Analytical magnetic field calculation of linear permanent magnet vernier motor[J]. Electric Machines and Control, 2017, 21(10): 54-61. [12] Krop D C J, Lomonova E A, Vandenput A J A. Application of Schwarz-Christoffel mapping to permanent magnet linear motor analysis[J]. IEEE Transactions on Magnetics, 2008, 44(3): 352-359. [13] Zeng Lizhan, Chen Xuedong, Li Xiaoqing, et al.A thrust force analysis method for permanent magnet linear motor using Schwarz-Christoffel mapping and considering slotting effect, end effect, and magnet shape[J]. IEEE Transactions on Magnetics, 2015, 51(9): 101-108. [14] 于吉坤, 李立毅, 张江鹏, 等. 定子开槽永磁同步电机气隙比磁导解析计算[J]. 电工技术学报, 2016, 31(增刊1): 45-52. Yu Jikun, Li Liyi, Zhang Jiangpeng, et al.Analytical calculation of air-gap relative permeance in slotted permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2016, 31(S1): 45-52. [15] Liu Z J, Li J T.Analytical solution of air-gap field in permanent magnet motors taking into account the effect of pole transition over slots[J]. IEEE Transactions on Magnetics, 2007, 43(10): 3872-3883. [16] Dubas F, Espanet C.Analytical solution of the magnetic field in permanent-magnet motors taking into account slotting effect: no-load vector potential and flux density calculation[J]. IEEE Transactions on Magnetics, 2009, 45(5): 2097-2109. [17] Zhu Ziqiang, 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. [18] 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 calculation of electromagnetic performance in dual three-phase permanent magnet brushless AC machines[J]. Transactions of China Electrotechnical Society, 2014, 29(5): 17-28. [19] Wu Lijian, Zhu Ziqiang, Staton D, et al.An improved subdomain model for predicting magnetic field of surface-mounted permanent magnet machines accounting for tooth-tips[J]. IEEE Transactions on Magnetics, 2011, 47(6): 1693-1704. [20] 薛志强, 周羽, 李槐树. 考虑定转子双边开槽时表贴式永磁电机空载磁场解析计算[J]. 中国电机工程学报, 2016, 37(8): 2399-2408. Xue Zhiqiang, Zhou Yu, Li Huaishu.Analytical calculation of open-circuit field in surface-mounted permanent-magnet machines accounting for slots in stator and rotor[J]. Proceedings of the CSEE, 2016, 37(8): 2399-2408. [21] 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): 11-22. 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): 11-22. [22] Hu Hengzai, Zhao Jing, Liu Xiangdong, et al.Magnetic field and force calculation in linear permanent-magnet synchronous machines accounting for longitudinal end effect[J]. IEEE Transactions on Industrial Electronics, 2016, 63(12): 7632-7643. [23] Hu Hengzai, Liu Xiangdong, Zhao Jing, et al.Analysis and minimization of detent end force in linear permanent magnet synchronous machines[J]. IEEE Transactions on Industrial Electronics, 2018, 65(3): 2475-2485. [24] 唐勇斌. 精密运动平台用永磁直线同步电机的磁场分析与电磁力研究[D]. 哈尔滨: 哈尔滨工业大学, 2014.