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| Overview on Analysis and Suppression Techniques of Detent Force for Iron-Core Permanent Magnet Linear Synchronous Motor |
| Wu Lize, Li Yanxin, Lu Qinfen |
| College of Electrical Engineering Zhejiang University Hangzhou 310027 China |
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Abstract Iron core permanent magnet linear synchronous motor (PMLSM) is widely used in semicon- ductor processing, precision machine tools, and flexible logistics lines that require high-performance linear motions. It has the advantages of high speed, large thrust force, and high thrust force density. However, due to the two broken ends of the structure, the asymmetry of the magnetic circuit causes large thrust ripple, and reducing thrust ripple has become the main objective of optimization design. Usually, the thrust ripple at no-load (detent force) is chosen as the research object. This paper reviews the three methods for calculating the detent force and discusses how to consider the core saturation, cogging effect, and end effect. Then, the suppression methods of detent force are summarized from two aspects of motor structure optimization and control strategy. In addition, the existing problems and limitations of detent force research are pointed out. The development trends of detent force research are predicted. Firstly, the characteristics and principal components of detent force for an iron-core PMLSM with short primary and short secondary are introduced. For short primary structure, the a-slot PMLSM with all-teeth wound contains a+1 slots due to the broken ends, resulting in the cogging force containing 2nd and 4th harmonic components when taking 2τp (τp is pole pitch) as the fundamental wavelength. The detent force of PMLSM with short secondary operating in the non-end region of the primary contains the teeth harmonic component, similar to the cogging torque of a rotating motor. Secondly, three analysis methods of the detent force are introduced, which are the analytical method, the magnetic network method, and the finite element method. To consider the slotting and end effects, the exact subdomain method and the conformal mapping method are proposed based on the traditional subdomain method. However, the magnetic saturation is ignored. The magnetic network method considers the nonlinearity of iron properties by iterative calculation, taking into account slotting and end effects through the magnetic circuit division method and the mesh generation method. The finite element method is the most widely used numerical method. It has high accuracy, but needs a long computing time with accurate meshing. Thirdly, the suppression technology for the detent force is summarized from two aspects: motor design and motor control. In motor design, the optimization methods can be divided into two kinds. One is separating and decreasing the cogging force and end force, and the other is directly weakening the detent force, considering the coupling effect between the cogging force and end force. The latter is more effective in suppressing the detent force. The methods include end-reversed slots, shifting one of the primary components, unequal slot width design, and auxiliary teeth modulation. Most of them are only suitable for double-sided PMLSM. For motor control, the optimization methods of weakening detent force can be divided into compensation methods with and without the mathematical model of detent force. However, the design with the optimal detent force is not optimal for thrust ripple at load, especially under overload conditions. Thus, taking the thrust ripple at load as an optimization objective is needed. The development trends of detent force research for PMLSM are as follows: (1) Exact analytical model considering core saturation effect. (2) Efficient thrust ripple suppression technologies combined with actual load conditions. (3) System-level thrust ripple suppression optimization combined with structural design and control strategies for high precision control requirements.
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Received: 16 December 2024
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[1] 吕刚. 直线电机在轨道交通中的应用与关键技术综述[J]. 中国电机工程学报, 2020, 40(17): 5665-5675. Lü Gang.Review of the application and key tech- nology in the linear motor for the rail transit[J]. Proceedings of the CSEE, 2020, 40(17): 5665-5675. [2] 鲁军勇, 柳应全. 电磁发射用直线电机及其控制技术综述[J]. 电工技术学报, 2024, 39(19): 5899-5913. Lu Junyong, Liu Yingquan.Review on linear motor for electromagnetic launch and its control tech- nology[J]. Transactions of China Electrotechnical Society, 2024, 39(19): 5899-5913. [3] 赵立华, 谭立杰, 黄卫国, 等. 直线电机在半导体设备中的典型应用分析[J]. 电子工业专用设备, 2019, 48(2): 16-19. Zhao Lihua, Tan Lijie, Huang Weiguo, et al.Linear motor analysis in semiconductor equipment appli- cation[J]. Equipment for Electronic Products Manufa- cturing, 2019, 48(2): 16-19. [4] 杨永康. 定子分段式永磁同步直线电机的控制方案及其在门控系统应用研究[D]. 济南: 山东大学, 2022. Yang Yongkang.Research on control strategies of stator-segmented permanent magnet synchronous linear motor and its application to door system[D]. Jinan: Shandong University, 2022. [5] 张美玉. 直线电机作动器在汽车悬架主动控制中的应用研究[D]. 长春: 吉林大学, 2022. Zhang Meiyu.Research on application of linear motor actuator in active control of automobile suspen- sion[D]. Changchun: Jilin University, 2022. [6] Kung Y S.Design and implementation of a high- performance PMLSM drives using DSP chip[J]. IEEE Transactions on Industrial Electronics, 2008, 55(3): 1341-1351. [7] Danielsson O, Leijon M.Flux distribution in linear permanent-magnet synchronous machines including longitudinal end effects[J]. IEEE Transactions on Magnetics, 2007, 43(7): 3197-3201. [8] Zhang Chi, Chen Feixue, Qiu Shuheng, et al.A low detent force DS-PMSLM based on the modulation of cogging and end forces[J]. IEEE Transactions on Industrial Electronics, 2023, 70(1): 721-730. [9] Boff B H B, Eckert P R, Amara Y. A comprehensive review on the end effects of linear permanent magnet machines[C]//2021 13th International Symposium on Linear Drives for Industry Applications (LDIA), Wuhan, China, 2021: 1-6. [10] 卢琴芬, 沈燚明, 叶云岳. 永磁直线电动机结构及研究发展综述[J]. 中国电机工程学报, 2019, 39(9): 2575-2588. Lu Qinfen, Shen Yiming, Ye Yunyue.Development of permanent magnet linear synchronous motors structure and research[J]. Proceedings of the CSEE, 2019, 39(9): 2575-2588. [11] Wang Jiabin, Jewell G W, Howe D.A general framework for the analysis and design of tubular linear permanent magnet machines[J]. IEEE Transa- ctions on Magnetics, 1999, 35(3): 1986-2000. [12] 赵云涛, 卢琴芬, 李焱鑫. 无槽圆筒永磁直线同步电机推力波动的解析模型及抑制方法[J]. 中国电机工程学报, 2023, 43(16): 6453-6464. Zhao Yuntao, Lu Qinfen, Li Yanxin.Analytical model and suppression method of thrust ripple in slot-less tubular permanent magnet linear synchronous machines[J]. Proceedings of the CSEE, 2023, 43(16): 6453-6464. [13] Hu Hengzai, Zhao Jing, Liu Xiangdong, et al.No-load magnetic field and cogging force calculation in linear permanent-magnet synchronous machines with semi- closed slots[J]. IEEE Transactions on Industrial Electronics, 2017, 64(7): 5564-5575. [14] Chen Feixue, Zhang Chi, Chen Jinhua, et al.Accurate subdomain model for computing magnetic field of short moving-magnet linear motor with halbach array[J]. IEEE Transactions on Magnetics, 2020, 56(9): 8200509. [15] Lu Qinfen, Wu Bocheng, Yao Yihua, et al.Analytical model of permanent magnet linear synchronous machines considering end effect and slotting effect[J]. IEEE Transactions on Energy Conversion, 2020, 35(1): 139-148. [16] Zhu Z Q, Howe D.Instantaneous magnetic field distribution in brushless permanent magnet DC motors. Ⅱ. armature-reaction field[J]. IEEE Transa- ctions on Magnetics, 1993, 29(1): 136-142. [17] Zhu Z Q, Howe D.Instantaneous magnetic field distribution in brushless permanent magnet DC motors. Ⅲ. effect of stator slotting[J]. IEEE Transa- ctions on Magnetics, 1993, 29(1): 143-151. [18] de la Barrière O, Hlioui S, Ben Ahmed H, et al. Three-dimensional analytical modeling of a permanent- magnet linear actuator with circular magnets[J]. IEEE Transactions on Magnetics, 2010, 46(9): 3608-3616. [19] Liu Guohai, Ding Ling, Zhao Wenxiang, et al.Nonlinear equivalent magnetic network of a linear permanent magnet vernier machine with end effect consideration[J]. IEEE Transactions on Magnetics, 2018, 54(1): 8100209. [20] 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 Indu- strial Electronics, 2017, 64(7): 5323-5332. [21] Hur J, Yoon S B, Hwang D Y, et al.Analysis of PMLSM using three dimensional equivalent magnetic circuit network method[J]. IEEE Transactions on Magnetics, 1997, 33(5): 4143-4145. [22] Boduroglu A, Demir Y, Cumhur B, et al.A novel track structure of double-sided linear PM synchronous motor for low cost and high force density appli- cations[J]. IEEE Transactions on Magnetics, 2021, 57(2): 8201305. [23] Youn S W, Lee J J, Yoon H S, et al.A new cogging-free permanent-magnet linear motor[J]. IEEE Transactions on Magnetics, 2008, 44(7): 1785-1790. [24] 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): 2475-2486. [25] Jahns T M, Soong W L.Pulsating torque minimi- zation techniques for permanent magnet AC motor drives-a review[J]. IEEE Transactions on Industrial Electronics, 1996, 43(2): 321-330. [26] 徐月同, 傅建中, 陈子辰. 永磁直线同步电机推力波动优化及实验研究[J]. 中国电机工程学报, 2005, 25(12): 122-126. Xu Yuetong, Fu Jianzhong, Chen Zichen.Thrust ripple optimization and experiment for PMLSM[J]. Proceedings of the CSEE, 2005, 25(12): 122-126. [27] 程远雄. 永磁同步直线电机推力波动的优化设计研究[D]. 武汉: 华中科技大学, 2011. Cheng Yuanxiong.Study on optimal design of thrust ripple of permanent magnetic synchronous linear motors[D]. Wuhan: Huazhong University of Science and Technology, 2011. [28] 王秀和, 杨玉波, 丁婷婷, 等. 基于极弧系数选择的实心转子永磁同步电动机齿槽转矩削弱方法研究[J]. 中国电机工程学报, 2005, 25(15): 146-149. Wang Xiuhe, Yang Yubo, Ding Tingting, et al.The method for reducing cogging torque by suitable selection of pole-arc coefficient in solid-rotor PM synchronous motors[J]. Proceedings of the CSEE, 2005, 25(15): 146-149. [29] 张颖. 永磁同步直线电机磁阻力分析及控制策略研究[D]. 武汉: 华中科技大学, 2008. Zhang Ying.Research on the analysis of detent force and control strategies of permanent magnetic synchronous linear motors[D]. Wuhan: Huazhong University of Science and Technology, 2008. [30] Kim T W, Chang J H.Analysis of thrust characte- ristics considering step-skew and overhang effects in permanent magnet linear synchronous motor[J]. IEEE Transactions on Magnetics, 2015, 51(3): 8102104. [31] Trapanese M, Cipriani G, Curto D, et al.Optimization of cogging force in a linear permanent magnet generator for the conversion of sea waves energy[C]//2015 IEEE International Electric Machines & Drives Conference (IEMDC), Coeur d’Alene, ID, USA, 2015: 769-773. [32] 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. [33] Chi Song, Yan Jianhu, Shan Liang, et al.Detent force minimizing for moving-magnet-type linear synchronous motor[J]. IEEE Transactions on Magnetics, 2019, 55(6): 8102005. [34] Kimoulakis N M, Kladas A G, Tegopoulos J A.Cogging force minimization in a coupled permanent magnet linear generator for sea wave energy extraction applications[J]. IEEE Transactions on Magnetics, 2009, 45(3): 1246-1249. [35] Xu Xiaozhuo, Sun Zhen, Du Baoyu, et al.Pole optimization and thrust ripple suppression of new halbach consequent-pole PMLSM for ropeless elevator propulsion[J]. IEEE Access, 2020, 8: 62042-62052. [36] Zhu Yuwu, Lee Sanggun, Chung K S, et al.Investi- gation of auxiliary poles design criteria on reduction of end effect of detent force for PMLSM[J]. IEEE Transactions on Magnetics, 2009, 45(6): 2863-2866. [37] Zhang Chao, Zhang Liwei, Huang Xianjin, et al.Research on the method of suppressing the end detent force of permanent magnet linear synchronous motor based on stepped double auxiliary pole[J]. IEEE Access, 2020, 8: 112539-112552. [38] 彭兵, 刘铁法, 张囡, 等. 凹型端齿削弱永磁直线电机端部力波动方法[J]. 电工技术学报, 2015, 30(7): 119-124. Peng Bing, Liu Tiefa, Zhang Nan, et al.A method for reducing the end effect force fluctuation by the concave profile end-tooth in permanent magnet linear motors[J]. Transactions of China Electrotechnical Society, 2015, 30(7): 119-124. [39] Zhu Z O, Xia Z P, Howe D.Reduction of cogging force in slotless linear permanent magnet motors[J]. IEE Proceedings-Electric Power Applications, 1997, 144(4): 277-282. [40] Inoue M, Sato K.An approach to a suitable stator length for minimizing the detent force of permanent magnet linear synchronous motors[J]. IEEE Transa- ctions on Magnetics, 2000, 36(4): 1890-1893. [41] Zhang He, Kou Baoquan, Jin Yinxi, et al.Investi- gation of auxiliary poles optimal design on reduction of end effect detent force for PMLSM with typical slot-pole combinations[J]. IEEE Transactions on Magnetics, 2015, 51(11): 8203904. [42] 寇宝泉, 张赫, 郭守仑, 等. 辅助极一体式永磁同步直线电机端部定位力抑制技术[J]. 电工技术学报, 2015, 30(6): 106-113. Kou Baoquan, Zhang He, Guo Shoulun, et al.End effect detent force reduction for permanent magnet linear synchronous motors with auxiliary poles one-piece structure[J]. Transactions of China Elec- trotechnical Society, 2015, 30(6): 106-113. [43] 杨岳. 低速大推力分数槽绕组圆筒型永磁直线电机设计与优化[D]. 哈尔滨: 哈尔滨理工大学, 2019. Yang Yue.Design and optimization of cylindrical permanent magnet linear motor with low-speed and large-thrust fractional-slot winding[D]. Harbin: Harbin University of Science and Technology, 2019. [44] Baatar N, Yoon H S, Pham M T, et al.Shape optimal design of a 9-pole 10-slot PMLSM for detent force reduction using adaptive response surface method[J]. IEEE Transactions on Magnetics, 2009, 45(10): 4562-4565. [45] Yao Yihua, Chen Yi, Lu Qinfen, et al.Analysis of thrust ripple of permanent magnet linear synchronous motor with skewed PMs[C]//2015 18th International Conference on Electrical Machines and Systems (ICEMS), Pattaya, Thailand, 2015: 1141-1146. [46] Zhao Jing, Mou Quansong, Zhu Congcong, et al.Study on a double-sided permanent-magnet linear synchronous motor with reversed slots[J]. IEEE/ ASME Transactions on Mechatronics, 2021, 26(1): 3-12. [47] Huang Xuzhen, Yu Hanchuan, Zhou Bo, et al.Detent-force minimization of double-sided permanent magnet linear synchronous motor by shifting one of the primary components[J]. IEEE Transactions on Industrial Electronics, 2020, 67(1): 180-191. [48] Chung S U, Kim J M.Double-sided iron-core PMLSM mover teeth arrangement design for redu- ction of detent force and speed ripple[J]. IEEE Transactions on Industrial Electronics, 2016, 63(5): 3000-3008. [49] Wu Qingle, Yang Guolai, Tang Enling, et al.A slotted double-primaries permanent magnet syn- chronous linear motor with a low thrust ripple[J]. IEEE/ASME Transactions on Mechatronics, 2024, 29(5): 3786-3798. [50] Wu Lize, Li Yanxin, Lu Qinfen.Detent force fast optimization method of modular permanent-magnet linear synchronous motors[J]. IEEE Transactions on Industrial Electronics, 2024, 71(12): 16191-16199. [51] 张晓文. 基于卡尔曼滤波器的永磁直线同步电机定位力补偿策略研究[D]. 哈尔滨: 哈尔滨工业大学, 2021. Zhang Xiaowen.Research on compensation strategy of detent force of permanent magnet linear syn- chronous motor based on Kalman filter[D]. Harbin: Harbin Institute of Technology, 2021. [52] 夏加宽, 董婷, 王贵子. 抑制永磁直线电机推力波动的电流补偿控制策略[J]. 沈阳工业大学学报, 2006, 28(4): 379-383, 400. Xia Jiakuan, Dong Ting, Wang Guizi.Current compensation control strategy for restraining thrust fluctuation of PMLSM[J]. Journal of Shenyang University of Technology, 2006, 28(4): 379-383, 400. [53] Zhu Yuwu, Cho Y H.Thrust ripples suppression of permanent magnet linear synchronous motor[J]. IEEE Transactions on Magnetics, 2007, 43(6): 2537-2539. [54] Zhu Yuwu, Koo D H, Cho Y H.Detent force minimization of permanent magnet linear syn- chronous motor by means of two different methods[J]. IEEE Transactions on Magnetics, 2008, 44(11): 4345-4348. [55] Zhu Yuwu, Jin Sangmin, Chung K S, et al.Control- based reduction of detent force for permanent magnet linear synchronous motor[J]. IEEE Transactions on Magnetics, 2009, 45(6): 2827-2830. [56] 陆华才, 江明, 郭兴众, 等. 永磁直线同步电机推力波动约束[J]. 电工技术学报, 2012, 27(3): 128-132. Lu Huacai, Jiang Ming, Guo Xingzhong, et al.Thrust ripple suppression for permanent magnet linear syn- chronous motor[J]. Transactions of China Electro- technical Society, 2012, 27(3): 128-132. [57] Ahn H S, Chen Yangquan, Dou Huifang.State- periodic adaptive compensation of cogging and Coulomb friction in permanent-magnet linear motors[J]. IEEE Transactions on Magnetics, 2005, 41(1): 90-98. [58] 陈兴林, 杨天博, 刘杨. 直线电机定位力波动的辨识及迭代补偿方法[J]. 电机与控制学报, 2015, 19(2): 60-65. Chen Xinglin, Yang Tianbo, Liu Yang.Method of cogging force compensation for linear motor based on model identification and iterative learning[J]. Electric Machines and Control, 2015, 19(2): 60-65. [59] 唐明, 吴凯, 李龙, 等. 永磁直线同步电机端部效应补偿的扰动观测器设计与仿真[J]. 微电机, 2016, 49(5): 40-44, 67. Tang Ming, Wu Kai, Li Long, et al.End effects disturbance observer design and simulation of per- manent magnet linear synchronous motor[J]. Micro- motors, 2016, 49(5): 40-44, 67. [60] Wang Mingyi, Li Liyi, Pan Donghua.Detent force compensation for PMLSM systems based on structural design and control method combination[J]. IEEE Transactions on Industrial Electronics, 2015, 62(11): 6845-6854. [61] Kim J, Cho K, Jung H, et al.A novel method on disturbance analysis and feed-forward compensation in permanent magnet linear motor system[C]//2014 5th International Conference on Intelligent Systems, Modelling and Simulation, Langkawi, Malaysia, 2014: 394-399. [62] 张国强, 赵新茹, 张恒, 等. 基于比例谐振内模扩张状态观测器的PMLSM推力波动抑制策略[J]. 电工技术学报, 2024, 39(8): 2449-2458. Zhang Guoqiang, Zhao Xinru, Zhang Heng, et al.Proportional resonant internal model extended state observer based thrust ripple suppression strategy of PMLSM drives[J]. Transactions of China Electro- technical Society, 2024, 39(8): 2449-2458. [63] 赵鑫宇, 王丽梅. 永磁直线同步电机自适应分数阶终端滑模控制[J]. 电工技术学报, 2023, 38(20): 5434-5443. Zhao Xinyu, Wang Limei.Adaptive fractional-order terminal sliding mode control for permanent magnet linear synchronous motor[J]. Transactions of China Electrotechnical Society, 2023, 38(20): 5434-5443. [64] 方馨, 王丽梅, 张康. 基于扰动观测器的永磁直线电机高阶非奇异快速终端滑模控制[J]. 电工技术学报, 2023, 38(2): 409-421. Fang Xin, Wang Limei, Zhang Kang.High order nonsingular fast terminal sliding mode control of permanent magnet linear motor based on disturbance observer[J]. Transactions of China Electrotechnical Society, 2023, 38(2): 409-421. [65] Wang Yiming, Wang Xiuping, Xu X.Backstepping control of primary permanent magnet linear syn- chronous motor based on adaptive RBF obser- ver[C]//2021 IEEE International Conference on Power Electronics, Computer Applications (ICPECA), Shenyang, China, 2021: 957-961. [66] 宋琳, 聂子玲, 孙军, 等. 基于参数辨识的永磁同步直线电机循环神经网络多维观测器[J]. 电工技术学报, 2024, 39(22): 7059-7072. Song Lin, Nie Ziling, Sun Jun, et al.Multidi- mensional observer of permanent magnet synchronous linear motor recurrent neural network based on parameter identification[J]. Transactions of China Electrotechnical Society, 2024, 39(22): 7059-7072. [67] 魏惠芳, 王丽梅. 永磁直线同步电机自适应模糊神经网络时变滑模控制[J]. 电工技术学报, 2022, 37(4): 861-869. Wei Huifang, Wang Limei.Adaptive fuzzy neural network time-varying sliding mode control for per- manent magnet linear synchronous motor[J]. Transa- ctions of China Electrotechnical Society, 2022, 37(4): 861-869. [68] Guo Liang, Zheng Chao.Optimization of fuzzy sliding mode controller with improved genetic algo- rithm[C]//2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 2019: 1-5. [69] Sun Che, Fang Youtong, Pfister P D.Comparison of two finite-permeability subdomain models for surface-mounted permanent-magnet machines con- sidering magnetic saturation[J]. IEEE Transactions on Energy Conversion, 2024, 39(4): 2758-2768. [70] Li Zhaokai, Wu Lize, Li Yanxin, et al.Hybrid analytical model of permanent magnet linear motor considering iron saturation and end effect[J]. IEEE Transactions on Energy Conversion, 2024, 39(3): 2008-2017. [71] Liu C T, Hwang C C, Li Pinglun, et al.Design optimization of a double-sided hybrid excited linear flux switching PM motor with low force ripple[J]. IEEE Transactions on Magnetics, 2014, 50(11): 8102704. [72] Dong Fei, Zhao Jiwen, Song Juncai, et al.Optimal design of permanent magnet linear synchronous motors at multispeed based on particle swarm optimization combined with SN ratio method[J]. IEEE Transactions on Energy Conversion, 2018, 33(4): 1943-1954. [73] Wang Mingyi, Li Liyi, Pan Donghua, et al.High-bandwidth and strong robust current regulation for PMLSM drives considering thrust ripple[J]. IEEE Transactions on Power Electronics, 2016, 31(9): 6646-6657. [74] Yang Ye, Mizushima K, Matsuba S, et al.Topology optimization using a normalized Gaussian network of iron yoke for magnetic field design of an accelerator superconducting magnet[J]. IEEE Transactions on Applied Superconductivity, 2023, 33(5): 4000105. [75] 龚夕霞, 李焱鑫, 卢琴芬. 模块化永磁直线同步电机考虑制造公差的推力鲁棒性优化[J]. 电工技术学报, 2024, 39(2): 465-474, 513. Gong Xixia, Li Yanxin, Lu Qinfen.Thrust robustness optimization of modular permanent magnet linear synchronous motor accounting for manufacture tolerance[J]. Transactions of China Electrotechnical Society, 2024, 39(2): 465-474, 513. |
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