电磁发射用永磁同步直线电机磁场解析及推力波动优化

doi:10.12382/bgxb.2023.0252

摘要/Abstract

摘要：

针对电磁发射用永磁同步直线电机的磁场解析及推力波动优化问题,建立单边发射电机磁场解析模型,利用矢量磁位及边界条件,分别对次级Halbach永磁阵列及初级六相绕组磁场进行解析,得到气隙磁场分布,进而建立单边发射电机主要结构参数与电磁推力间的函数关系。选取永磁阵列极弧系数及厚度、初级绕组宽度及厚度4个参数作为优化变量,利用遗传算法寻找设计变量的最优组合,使发射电机单边电磁推力波动最小化。分析结果表明:磁场解析结果精度较高,电磁推力计算误差满足工程分析的需要;优化后的单边发射电机平均推力提升1.21%,峰均力比下降62.688%,通过解析及仿真结果的对比验证了理论推导的正确性及优化方法的合理性。

关键词: 永磁同步直线电机, 电磁发射, 磁场解析, 推力计算, 推力波动

Abstract:

The magnetic field analysis and thrust fluctuation optimization of a permanent magnet synchronous linear motor for electromagnetic launch are performed by establishing an analytical model of the magnetic field of a single-sided motor for electromagnetic launch. The magnetic fields of the secondary Halbach permanent magnet array and the primary six-phase winding are analyzed to obtain the air-gap magnetic field distribution by using the vector magnetic potential and boundary conditions, and then the functional relationship between the electromagnetic thrust and the main structural parameters of single-sided motor is established. The pole arc coefficient and thickness of permanent magnet array, and width and thickness of primary winding are selected as optimization variables, and the optimal combination of design variables is found by using genetic algorithm to minimize the ripple of the unilateral electromagnetic thrust of single-sided motor. The analysis shows that the accuracy of magnetic field analysis results is high, and the calculation error of electromagnetic thrust meets the needs of engineering analysis. The average thrust of the optimized single-sided motor is increased by 1.21%, and the peak-to-average force ratio is decreased by 62.688%. The correctness of theoretical derivation and the rationality of the optimization method are verified by comparing the analyzed and simulated results.

Key words: permanent magnet synchronous linear motor, electromagnetic launch, magnetic field analysis, thrust calculation, thrust fluctuation

中图分类号:

TM359.4

贾光勇, 孙兆龙, 黄垂兵, 周炜昶, 卯寅浩, 雷招然. 电磁发射用永磁同步直线电机磁场解析及推力波动优化[J]. 兵工学报, 2024, 45(7): 2159-2170.

JIA Guangyong, SUN Zhaolong, HUANG Chuibing, ZHOU Weichang, MAO Yinhao, LEI Zhaoran. Magnetic Field Analysis and Thrust Fluctuation Optimization of Permanent Magnet Synchronous Linear Motor for Electromagnetic Launch[J]. Acta Armamentarii, 2024, 45(7): 2159-2170.

图/表 24

图1 电磁发射用永磁同步直线电机单边结构

Fig.1 Single-sided structure of permanent magnet synchronous linear motor for electromagnetic launch

表1 发射电机初始结构参数

Table 1 Initial structural parameters of launch motor

参数	数值	参数	数值
相数	6	绕组间距/mm	2
极距/mm	72	气隙长度/mm	5
铁芯长度/mm	3742	永磁阵列极对数	6
铁芯厚度/mm	12	永磁阵列厚度/mm	10
绕组截面积/mm²	30	永磁阵列高度/mm	275
绕组极对数	26	径向充磁永磁体宽度/mm	28.8
绕组宽度/mm	10	轴向充磁永磁体宽度/mm	43.2
绕组厚度/mm	3	绕组高度/mm	259.6

图2 单边发射电机磁场解析模型

Fig.2 Analytical model of single-sided motor magnetic field

图3 Halbach永磁阵列磁场解析模型

Fig.3 Analytical magnetic field model of Halbach permanent magnet array

图4 次级永磁阵列有限元二维静磁场仿真模型

Fig.4 Simulation model of finite element two-dimensional static magnetic field of secondary permanent magnet array

图5 Halbach永磁阵列气隙磁密波形对比

Fig.5 Comparison of air-gap flux density waveforms of Halbach permanent magnet array

图6 初级绕组磁场解析模型

Fig.6 Analytical model of primary winding magnetic field

图7 初级六相绕组有限元二维瞬态场仿真模型

Fig.7 Simulation model of finite element two-dimensional transient field of primary six-phase winding

图8 初级六相绕组气隙磁密波形对比

Fig.8 Comparison of air gap magnetic density waveforms of primary six-phase winding

图9 单边发射电机有限元二维瞬态场仿真模型

Fig.9 Simulation model of finite element two-dimensional transient field of single-sided motor

图10 气隙中心线处不同时刻磁密波形对比

Fig.10 Comparison of magnetic flux density waveforms at the center line of air gap at different times

图11 单边发射电机电磁推力计算模型

Fig.11 Model for calculating the electromagnetic thrust of single-sided motor

图12 单边发射电机电磁推力验证

Fig.12 Verification of electromagnetic thrust of single-sided motor

图13 极弧系数与平均推力及推力波动峰峰值的关系

Fig.13 Relationship among polar arc coefficient with average thrust and peak-to-peak thrust fluctuations

图14 永磁阵列高度与平均推力及推力波动峰峰值的关系

Fig.14 Relationship among permanent magnet array height with average thrust and peak-to-peak thrust fluctuations

图15 绕组宽度与平均推力及推力波动峰峰值的关系

Fig.15 Relationship among winding width with average thrust and peak-to-peak thrust fluctuations

图16 绕组高度与平均推力及推力波动峰峰值的关系

Fig.16 Relationship among winding height with average thrust and peak-to-peak thrust fluctuations

表2 设计变量约束范围

Table 2 Design variable constraint scope

最大值与最小值	设计变量
最大值与最小值	α_p	h_m/mm	ω_c/mm	h_c/mm
最大值	0.9	12	11	7
最小值	0.1	8	7	3

图17 相关性矩阵

Fig.17 Relevance matrix

图18 平均推力的响应曲面

Fig.18 Response surface of average thrust

图19 推力波动峰峰值的响应曲面

Fig.19 Response surface of the peak-to-peak of thrust fluctuations

表3 设计变量优化结果组合

Table 3 Design variables to optimise the combination of results

组别	优化变量
组别	α_p	h_m/mm	ω_c/mm	h_c/mm
第1组	0.3203	10.1	11.4	5.1
第2组	0.8605	11.654	11.623	3.508
第3组	0.8553	11.6	7.9	6.7

图20 不同变量最优值组合下单边电磁推力波形

Fig.20 Unilateral electromagnetic thrust waveform under optimal combination of different variables

表4 推力波动优化结果对比

Table 4 Comparison of thrust fluctuation optimization results

组别	设计变量优化值
组别	单边平均推力F_x_avg/kN	峰均力比百分值/%
原始组	19.287 2	0.607 8
第1组	18.956 7	0.173 4
第2组	19.521 8	0.226 8
第3组	19.931 8	0.509 6

参考文献 32

[1]	孙兆龙, 马伟明, 吴旭升, 等. 双初级耦合直线感应电动机电磁参数计算[J]. 中国电机工程学报, 2019, 39(7):1878-1886.
	SUN Z L, MA W M, WU X S, et al. Calculation of electromagnetic parameters for double primary coupled linear induction motors[J]. Proceedings of the CSEE, 2019, 39(7): 1878-1886. (in Chinese)
[2]	孙兆龙, 刘德志, 马伟明, 等. 双初级耦合直线感应电动机研究[J]. 中国电机工程学报, 2010, 30(27):1-6.
	SUN Z L, LIU D Z, MA W M, et al. Study of double primary coupled linear induction motors[J]. Proceedings of the CSEE, 2010, 30(27):1-6. (in Chinese)
[3]	黄垂兵, 许金, 吴振兴, 等. 分段供电六相圆筒式直线感应电动机阻抗矩阵及参数辨识方法[J]. 中国电机工程学报, 2018, 38(10):3087-3093,3160.
	HUANG C B, XU J, WU Z X, et al. Impedance matrix and parameter identification method for six-phase cylindrical linear induction motors with segmented power supply[J]. Proceedings of the CSEE, 2018, 38(10):3087-3093,3160. (in Chinese)
[4]	黄垂兵, 马伟明, 许金, 等. 六相圆筒式直线感应电机磁路计算及饱和特性分析[J]. 电工技术学报, 2018, 33(5):1032-1039.
	HUANG C B, MA W M, XU J, et al. Six-phase cylindrical linear induction motor magnetic circuit calculation and saturation characteristics analysis[J]. Transactions of China Electrotechnical Society, 2018, 33(5):1032-1039. (in Chinese)
[5]	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 X S, CUI H S, HU C F, et al. Optimized design of thrust characteristics of flat plate permanent magnet linear synchronous motor[J]. Transactions of China Electrotechnical Society, 2021, 36(5):916-923. (in Chinese)
[6]	杨归, 许金, 朱俊杰, 等. 六相永磁直线同步电机电磁特性分析及数学模型建立[J]. 电机与控制应用, 2022, 49(11):22-28.
	YANG G, XU J, ZHU J J, et al. Analysis of electromagnetic characteristics and mathematical model establishment of six-phase permanent magnet linear synchronous motor[J]. Electric Machines and Control Application, 2022, 49(11):22-28. (in Chinese)
[7]	WU T, FENG Z N, WU C, et al. Multiobjective optimization of a tubular coreless LPMSM based on adaptive multiobjective black hole algorithm[J]. IEEE Transactions on Industrial Electronics, 2020, 67(5): 3901-3910.
[8]	陈永波, 燕延, 王伟明, 等. 磁悬浮直线电机三维有限元分析及优化设计研究[J]. 组合机床与自动化加工技术, 2017(1):31-34. doi: 10.13462/j.cnki.mmtamt.2017.01.009
	CHEN Y B, YAN Y, WANG W M, et al. Three-dimensional finite element analysis and optimization design of magnetic suspension linear motor[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2017(1):31-34. (in Chinese)
[9]	CAO D H, ZHAO W X, JI J H, et al. Parametric equivalent magnetic network modeling approach for multiobjective optimization of PM machine[J]. IEEE Transactions on Industrial Electronics, 2021, 68(8): 6619-6629.
[10]	LU Q F, WU B C, YAO Y H, 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.
[11]	ZHANG H S, WANG Y P, TUO J Y, et al. Magnetic field and electromagnetic performance analysis of permanent magnet machines with segmented Halbach array[J]. COMPEL-The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2022, 41(1): 357-380.
[12]	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 B Q, CAO H C, LI W L, et al. Analytical analysis of a novel bilayer Halbach permanent magnet array[J]. Transactions of China Electrotechnical Society, 2015, 30(10):68-76. (in Chinese)
[13]	于雅莉, 张国胜, 吴迪. 低噪声屏蔽电机定子屏蔽套激振力和受迫振动分析[J]. 电工技术学报, 2017, 32(增刊1):160-168.
	YU Y L, ZHANG G S, WU D. Low noise shielded motor stator shield sleeve excitation force and forced vibration analysis[J]. Transactions of China Electrotechnical Society, 2017, 32(S1):160-168. (in Chinese)
[14]	PILE R, DEVILLERS E, BESNERAIS J L. Comparison of main magnetic force computation methods for nise and vibration assessment in electrical machines[J]. IEEE Transactions on Magnetics, 2018, 54(7): 1-13.
[15]	GE Q W, KOU B Q, ZHANG Y Q, et al. 3-D electromagnetic force characteristics and modeling of double-sided air-cored superconducting linear synchronous motor for EDS train[J]. IEEE Transactions on Magnetics, 2018, 54(7):1-13.
[16]	CHI S, YAN J H, SHAN L, et al. Detent force minimizing for moving-magnet-type linear synchronous motor[J]. IEEE Transactions on Magnetics, 2019, 55(6):1-5.
[17]	KIM K H, CHO H K, WOO D K. 3D Characteristic analysis of 3-leg linear permanent magnet motor with magnet skew and overhang structure[J]. IEEE Access, 2021(9):153863-153874.
[18]	SONG Z X, LIU C H, FENG K, et al. Field prediction and validation of a slotless segmented-halbach permanent magnet synchronous machine for more electric aircraft[J]. IEEE Transactions on Transportation Electrification, 2020, 6(4):1577-1591.
[19]	ZHAO J, MOU Q S, GUO K Y, et al. Reduction of the detent force in a flux-switching permanent magnet linear motor[J]. IEEE Transactions on Energy Conversion, 2019, 34(3):1695-1705.
[20]	汪旭东, 翟中飞, 许孝卓, 等. 一种大推力凸极永磁直线同步电机特性分析[J]. 机电工程, 2018, 35(10):1100-1105.
	WANG X D, ZHAI Z F, XU X Z, et al. Characterization of a high thrust convex pole permanent magnet linear synchronous motor[J]. Journal of Mechanical & Electrical Engineering, 2018, 35(10):1100-1105. (in Chinese)
[21]	CHENG Z H, XU Q W, LONG S, et al. Thrust force ripple optimization of MEMS permanent magnet linear motor based on harmonic current injection[C]// Proceedings of the 2021 IEEE International Electrical and Energy Conference.Wuhan, China:IEEE, 2021:1-6.
[22]	LIU X, LI X S, HUANG S D, et al. Parameters optimization of the permanent magnet linear synchronous machine using kriging-based genetic algorithm[C]// Proceedings of the 2019 International Conference on Electrical Machines and Systems.Harbin, China:IEEE, 2019: 1-6.
[23]	JIANG Q, LU Q F, LI Y X, et al. Design optimisation and performance investigation of novel dual three-phase permanent-magnet linear synchronous machines for a ropeless elevator system[J]. IET Electric Power Applications, 2020, 14(14):2788-2797.
[24]	周汉秦, 黄晓艳, 方攸同. 基于改进遗传算法的表贴式永磁同步电机优化设计[J]. 微电机, 2017, 50(5):1-4,16.
	ZHOU H Q, HUANG X Y, FANG Y T. Optimal design of surface-mounted permanent magnet synchronous motor based on improved genetic algorithm[J]. Micromotors, 2017, 50(5):1-4,16. (in Chinese)
[25]	李立毅, 唐勇斌, 刘家曦, 等. 多种群遗传算法在无铁心永磁直线同步电机优化设计中的应用[J]. 中国电机工程学报, 2013, 33(15): 69-77,14.
	LI L Y, TANG Y B, LIU J X, et al. Application of multiple group genetic algorithms in the optimization design of ironless permanent magnet linear synchronous motors[J]. Proceedings of the CSEE, 2013, 33(15):69-77,14. (in Chinese)
[26]	LEE T H, KANG Y R, SON J C, et al. Optimized design of permanent magnet assisted synchronous reluctance motor using oriented auto-tuning niching algorithm[J]. Journal of Electrical Engineering & Technology, 2021, 16:1495-1503.
[27]	MIAO Z C, SU Y. Analysis of detent force in flat-type permanent magnet linear synchronous motor and multi-objective optimization based on parameter classification[J]. IEEJ Transactions on Electrical and Electronic Engineering, 2022, 17(12):1772-1782.
[28]	ZHAO W X, MA A Q, JI J H, et al. Multiobjective optimization of a double-side linear vernier PM motor using response surface method and differential evolution[J]. IEEE Transactions on Industrial Electronics, 2020, 67(1):80-90.
[29]	HUSSAIN S, KHAN F, ULLAH W, et al. Optimization and experimentation of fault-tolerant field excited linear flux switching machine with concentrated and toroidal windings for rail transportation system[J]. IEEE Transactions on Industry Applications, 2023, 59(2):1361-1371.
[30]	刘文奇, 崔皆凡, 李柏昕, 等. 分数槽永磁同步直线电机空载气隙磁密解析[J]. 电机与控制应用, 2021, 48(4):65-70,109.
	LIU W Q, CUI J F, LI B X, et al. Fractional slot permanent magnet synchronous linear motor no-carrier air gap magnetic density analysis[J]. Electric Machines and Control Application, 2021, 48(4): 65-70,109. (in Chinese)
[31]	颜建虎, 李彪, 时岩, 等. 主动悬架用非均匀齿圆筒型永磁直线电机多目标分层优化设计[J]. 兵工学报, 2023, 44(1):40-50. doi: 10.12382/bgxb.2022.0756
	YAN J H, LI B, SHI Y, et al. Multi-objective hierarchical optimization of non-uniformly toothed cylindrical permanent magnet linear motors for active suspensions[J]. Acta Armamentarii, 2023, 44(1):40-50. (in Chinese)
[32]	王鹤翔, 毛晓东, 庞丽萍, 等. 基于多目标遗传算法的特种车舱室送风系统优化设计[J]. 兵工学报, 2022, 43(12):2981-2988. doi: 10.12382/bgxb.2021.0632
	WANG H X, MAO X D, PANG L P, et al. Optimization of air supply systems for special vehicle cabins based on multi-objective genetic algorithms[J]. Acta Armamentarii, 2022, 43(12):2981-2988. (in Chinese)