Abstract：The modular structure of modular permanent magnet linear synchronous motor (MPMLSM) is beneficial to simplify the winding manufacturing process and improve the motor performance and fault tolerance rate. As a motor with high efficiency, high thrust density, and high reliability, it has received extensive attention and application in recent years. However, in mass production, the modular structure is more susceptible to machining tolerances. In order to improve the motor performance and better meet the quality requirements, this paper proposes a thrust robustness optimization method considering manufacturing tolerance, which provides help for the optimization design and application of MPMLSM. First, a robust optimization model is established based on design for six Sigma (DFSS), and the optimization objective function is determined according to the sigma level. Then, the Latin Hypercube Sampling (LHS) method is used to sample within the dimensional tolerance range according to the normal distribution law to simulate possible variations in motor dimensions in mass production. A motor design surrogate model based on the Back Propagation Neural Network (BPNN) can calculate the motor performance required for subsequent optimization quickly and conveniently. The training samples of the model are obtained by uniform sampling, and the thrust performance of the samples is simulated by finite element software. Subsequently, the motor performance of the samples obtained by LHS is calculated by the trained surrogate model, and the mean and variance of the whole sample are solved and substituted into the objective function to obtain the fitness value. Finally, Non-dominated Sorting Genetic Algorithm Ⅱ is used for global optimization to obtain the Pareto front and robust optimization schemes. Compared with the deterministic optimization scheme, the effectiveness of the method is verified. Through finite element verification, the determination coefficient of the surrogate model established by BPNN is 0.999 9, and the mean square error is 1.76×10-3. Thus, the motor performance can be calculated quickly and accurately. Under the harsh condition that the allowable thrust variation range (λ) is 2%, the robust optimization scheme can reduce the probability of failure (POF) from 67.32% to 7.96% under condition 1, and from 53.3% to 1.76% under condition 2. Compared with the deterministic optimization scheme without considering tolerance, although the robust optimization design slightly increases the motor volume and thrust ripple, the robustness is improved. At the same time, it can be inferred that the POF of the robust optimization scheme is 0 when λ≥7% under condition 1 or λ≥5% under condition 2. The reduction of failure probability indicates that the MPMLSM robust optimization schemes have higher qualification rates in mass production and are less affected by tolerances. The following conclusions can be drawn: (1) Under the premise of convergence, reducing manufacturing tolerance can reduce the motor volume and make the motor thrust closer to the set value. However, the manufacturing cost is increased. (2) λ mainly affects the thrust fluctuation, and little affects the volume. Under the same volume condition, the thrust fluctuation increases with the increase of λ. (3) In the optimization results, the tooth height and primary polar distance vary with different tolerance conditions, while the remaining variables are optimized to optimum values. (4) The POF of the robust optimization scheme is lower than that of the deterministic optimization scheme, especially when λ is small. Therefore, the robust optimization scheme has better robustness and is more in line with the quality requirement in mass production.
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.
Gong Xixia, Li Yanxin, Lu Qinfen. Thrust Robustness Optimization of Modular Permanent Magnet Linear Synchronous Motor Accounting for Manufacture Tolerance. Transactions of China Electrotechnical Society, 2024, 39(2): 465-474.
[1] 蒋钱, 卢琴芬, 李焱鑫. 双三相永磁直线同步电机的推力波动及抑制[J]. 电工技术学报, 2021, 36(5): 883-892. Jiang Qian, Lu Qinfen, Li Yanxin.Thrust ripple and depression method of dual three-phase permanent magnet linear synchronous motors[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 883-892. [2] Cui Fengrui, Sun Zhaolong, Xu Wei, et al.Com-parative analysis of bilateral permanent magnet linear synchronous motors with different structures[J]. CES Transactions on Electrical Machines and Systems, 2020, 4(2): 142-150. [3] 沈燚明, 卢琴芬. 初级励磁型永磁直线电机研究现状与展望[J]. 电工技术学报, 2021, 36(11): 2325-2343. Shen Yiming, Lu Qinfen.Overview of permanent magnet linear machines with primary excitation[J]. Transactions of China Electrotechnical Society, 2021, 36(11): 2325-2343. [4] 丁文, 李可, 付海刚. 一种12/10极模块化定子混合励磁开关磁阻电机分析[J]. 电工技术学报, 2022, 37(8): 1948-1958. Ding Wen, Li Ke, Fu Haigang.Analysis of a 12/10-pole modular-stator hybrid-excited switched relu-ctance machine[J]. Transactions of China Electro-technical Society, 2022, 37(8): 1948-1958. [5] 王宇, 张成糕, 郝雯娟. 永磁电机及其驱动系统容错技术综述[J]. 中国电机工程学报, 2022, 42(1): 351-372. Wang Yu, Zhang Chenggao, Hao Wenjuan.Overview of fault-tolerant technologies of permanent magnet brushless machine and its control system[J]. Pro-ceedings of the CSEE, 2022, 42(1): 351-372. [6] Lei Gang, Bramerdorfer G, Liu Chengcheng, et al.Robust design optimization of electrical machines: a comparative study and space reduction strategy[J]. IEEE Transactions on Energy Conversion, 2021, 36(1): 300-313. [7] Bramerdorfer G.Effect of the manufacturing impact on the optimal electric machine design and perfor-mance[J]. IEEE Transactions on Energy Conversion, 2020, 35(4): 1935-1943. [8] Xu Gaohong, Jia Zexin, Zhao Wenxiang, et al.Multi-objective optimization design of inset-surface per-manent magnet machine considering deterministic and robust performances[J]. Chinese Journal of Elec-trical Engineering, 2021, 7(3): 73-87. [9] Yao Zheng, Zhao Jiwen, Song Juncai, et al.Research on selection criterion of design tolerance for air-core permanent magnet synchronous linear motor[J]. IEEE Transactions on Industrial Electronics, 2021, 68(4): 3336-3347. [10] Lei Gang, Wang Tianshi, Zhu Jianguo, et al.Robust multiobjective and multidisciplinary design optimi-zation of electrical drive systems[J]. CES Transa-ctions on Electrical Machines and Systems, 2018, 2(4): 409-416. [11] Lei Gang, Liu Chengcheng, Li Yanbin, et al.Robust design optimization of a high-temperature supercon-ducting linear synchronous motor based on taguchi method[J]. IEEE Transactions on Applied Supercon-ductivity, 2019, 29(2): 1-6. [12] Sun Ke, Tian Shaopeng.Multiobjective optimization of IPMSM with FSCW applying rotor Notch design for torque performance improvement[J]. IEEE Transa-ctions on Magnetics, 2022, 58(5): 1-9. [13] Skarmoutsos G A, Gyftakis K N, Mueller M.Analyti-cal prediction of the MCSA signatures under dynamic eccentricity in PM machines with concentrated non-overlapping windings[J]. IEEE Transactions on Energy Conversion, 2022, 37(2): 1011-1019. [14] 丁强, 王晓琳, 邓智泉, 等. 大气隙磁通切换无轴承永磁电机径向力绕组设计与比较[J]. 电工技术学报, 2018, 33(11): 2403-2413. Ding Qiang, Wang Xiaolin, Deng Zhiquan, et al.Design and comparison of radial force winding configurations for wide air-gap flux-switching bearingless permanent-magnet motor[J]. Transactions of China Electrotechnical Society, 2018, 33(11): 2403-2413. [15] 隋义, 尹佐生, 郑萍, 等. 单双层混合绕组型低互感五相容错永磁电机的电磁问题研究[J]. 中国电机工程学报, 2022, 42(1): 329-340. Sui Yi, Yin Zuosheng, Zheng Ping, et al.Research on electromagnetic problems of low-mutual-inductance five-phase fault-tolerant PMSM with hybrid single/ double-layer FSCW[J]. Proceedings of the CSEE, 2022, 42(1): 329-340. [16] Mehta S, Kabir M A, Pramod P, et al.Segmented rotor mutually coupled switched reluctance machine for low torque ripple applications[J]. IEEE Transa-ctions on Industry Applications, 2021, 57(4): 3582-3594. [17] Deb K, Pratap A, Agarwal S, et al.A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197. [18] Ma Yiming, Xiao Yang, Wang Jin, et al.Multicriteria optimal Latin hypercube design-based surrogate-assisted design optimization for a permanent-magnet vernier machine[J]. IEEE Transactions on Magnetics, 2022, 58(2): 1-5. [19] Koch P N, Yang R, Gu L.Design for six sigma through robust optimization[J]. Structural and Multi-disciplinary Optimization, 2004, 26(3): 235-248. [20] 唐晓芬主编, 上海质量管理科学研究院编著. 六西格玛核心教程: 黑带读本[M]. 修订版. 北京: 中国标准出版社, 2006. [21] 谢冰川, 张岳, 徐振耀, 等. 基于代理模型的电机多学科优化关键技术综述[J]. 电工技术学报, 2022, 37(20): 5117-5143. Xie Bingchuan, Zhang Yue, Xu Zhenyao, et al.Review on multidisciplinary optimization key tech-nology of electrical machine based on surrogate models[J]. Transactions of China Electrotechnical Society, 2022, 37(20): 5117-5143. [22] Wu Jiangling, Sun Xiaodong, Zhu Jianguo.Accurate torque modeling with PSO-based recursive robust LSSVR for a segmented-rotor switched reluctance motor[J]. CES Transactions on Electrical Machines and Systems, 2020, 4(2): 96-104. [23] 李雄松, 崔鹤松, 胡纯福, 等. 平板型永磁直线同步电机推力特性的优化设计[J]. 电工技术学报, 2021, 36(5): 916-923. Li Xiongsong, Cui Hesong, Hu Chunfu, et al.Optimal design of thrust characteristics of flat-type permanent magnet linear synchronous motor[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 916-923. [24] 何海婷, 柳亦兵, 巴黎明, 等. 基于BP神经网络的飞轮储能系统主动磁轴承非线性动力学模型[J]. 中国电机工程学报, 2022, 42(3): 1184-1198. He Haiting, Liu Yibing, Ba Liming, et al.Nonlinear dynamic model of active magnetic bearing in flywheel system based on BP neural network[J]. Proceedings of the CSEE, 2022, 42(3): 1184-1198.
2024, Vol. 39 
