Magnetic force calculation method of permanent magnet electromagnetic hybrid suspension system considering magnetic saturation
-
摘要: 为提高永磁电磁混合悬浮系统磁力计算的准确性和效率，综合考虑解析法计算速度快和有限元法计算精度高的优势，基于等效面电流法，将系统中的永磁体等效为电磁线圈，进而建立了永磁电磁混合悬浮系统的纯电磁线圈等效模型；基于电磁线圈电感的电流-磁链表达式，即非线性磁饱和模型和虚位移能量平衡法，推导了适用于永磁电磁混合悬浮系统的磁力解析表达式；基于有限元仿真结果拟合了各参数变量-气隙方程，确定了考虑磁饱和的永磁电磁混合悬浮系统磁力计算方法。分析结果表明：电磁线圈电感的非线性磁饱和模型可以有效表示磁饱和对于磁力计算的影响；流过永磁电磁混合悬浮系统电磁线圈的电流分别为0、2.0、8.5和17.0 A时，传统解析计算公式的磁力计算结果与传统有限元仿真结果的平均偏差分别为32.87%、20.02%、29.05%和25.67%，考虑磁饱和的磁力计算方法与传统有限元仿真结果的平均偏差分别为1.68%、1.64%、1.58%和1.37%，与试验结果的平均偏差分别为1.66%、1.77%、0.91%和1.35%，相比于传统解析计算公式，本文所述方法极大提高了磁力计算的准确性，与传统有限元法相比，本文所述方法计算任务量大幅减少，计算效率极大提升。
-
关键词:
- 轨道交通 /
- 磁饱和 /
- 有限元法 /
- 永磁电磁混合悬浮系统 /
- 方程拟合
Abstract: To improve the accuracy and efficiency of magnetic force calculation of permanent magnet electromagnetic hybrid suspension system, the advantages of fast calculation speed of analytical method and high calculation accuracy of finite element method were comprehensively considered. Based on the equivalent surface current method, the permanent magnet in the system was equivalent to an electromagnetic coil. Then, the pure electromagnetic coil equivalent model of permanent magnet electromagnetic hybrid suspension system was established. Based on the current-flux linkage expression of the inductance of electromagnetic coil, namely the nonlinear magnetic saturation model and virtual displacement energy balance method, the analytical expression of the magnetic force for the permanent magnet electromagnetic hybrid suspension system was derived. Based on the finite element simulation results, the parameter variable-air gap equation was fitted, and the magnetic force calculation method of permanent magnet electromagnetic hybrid suspension system considering the magnetic saturation was determined. Analysis results show that the nonlinear magnetic saturation model of the inductance of electromagnetic coil can effectively express the influence of magnetic saturation on magnetic force calculation. When the current flowing through the electromagnetic coil of permanent magnet electromagnetic hybrid suspension system is 0, 2.0, 8.5, and 17.0 A, the average deviations of the magnetic force calculation results obtained by traditional analytical calculation formula and traditional finite element simulation results are 32.87%, 20.02%, 29.05%, and 25.67%, respectively. The average deviations of the magnetic force calculation results obtained by magnetic force calculation method considering the magnetic saturation compared with the traditional finite element simulation results are 1.68%, 1.64%, 1.58%, and 1.37%, respectively, and the average deviations compared with the test results are 1.66%, 1.77%, 0.91%, and 1.35%, respectively. Compared with the traditional analytical calculation formula, the proposed method greatly improves the accuracy of magnetic force calculation. Compared with the traditional finite element simulation method, the amount of calculation tasks of the proposed method reduces greatly, and the calculation efficiency improves greatly. -
图 2 永磁电磁混合悬浮系统磁路
Figure 2. Magnetic circuit of permanent magnet electromagnetic hybrid suspension system
图 7 气隙变化过程中线圈电流-磁链曲线
Figure 7. Current-flux linkage curves of coils during air gap change
图 9 不同电磁线圈电流下电磁力随气隙高度变化的仿真曲线
Figure 9. Simulation curves of electromagnetic force changing with air gap height under different electromagnetic coil currents
图 10 永磁电磁混合悬浮系统试验平台
Figure 10. Experimental platform of permanent magnet electromagnetic hybrid suspension system
图 11 不同电磁线圈电流下电磁力随气隙高度变化的试验曲线
Figure 11. Experimental curves of electromagnetic force changing with air gap height under different electromagnetic coil currents
表 1 仿真结构和求解参数
Table 1. Simulation structure and solution parameters
参数 数值 轨道和U型铁芯材料 纯铁 线圈材料 铜 永磁体材料 NdFe35 永磁体总厚度/mm 6 U型铁芯截尺寸/mm 100×25 绕线窗口尺寸/mm 30×45 线圈匝数 550 永磁体矫顽力/A·m-1 5.8×105 真空磁导率/(H·m-1) 4π×10－7 永磁体相对磁导率/(H·m-1) 1.05 永磁体剩磁/T 1.2 纯铁相对磁导率/(H·m-1) 4 000 铜相对磁导率/(H·m-1) 0.99 额定电磁线圈电流/A 2 启动电磁线圈电流/A 8.5 等效线圈1(2)电流/A 2.67 额定气隙/mm 10 气隙高度/mm 5~15 变量气隙仿真步长/mm 0.1 
下载: 导出CSV
-
[1] 马卫华, 胡俊雄, 李铁, 等. EMS型中低速磁浮列车悬浮架技术研究综述[J]. 西南交通大学学报, 2023, 58(4): 720-733.MA Wei-hua, HU Jun-xiong, LI Tie, et al. Technologies research review of electro-magnetic suspension medium-low-speed maglev train levitation frame[J]. Journal of Southwest Jiaotong University, 2023, 58(4): 720-733. (in Chinese) [2] 邓自刚, 刘宗鑫, 李海涛, 等. 磁悬浮列车发展现状与展望[J]. 西南交通大学学报, 2022, 57(3): 455-474, 530.DENG Zi-gang, LIU Zong-xin, LI Hai-tao, et al. Development status and prospect of maglev train[J]. Journal of Southwest Jiaotong University, 2022, 57(3): 455-474, 530. (in Chinese) [3] GOU Jin-song. Development status and global competition trends analysis of maglev transportation technology based on patent data[J]. Urban Rail Transit, 2018, 4(3): 117-129. doi: 10.1007/s40864-018-0087-3 [4] TZENG Y K, WANG T C. Optimal design of the electromagnetic levitation with permanent and electro magnets[J]. IEEE Transactions on Magnetics, 1994, 30(6): 4731-4733. doi: 10.1109/20.334204 [5] CHO H W, HAN H S, LEE J M, et al. Design considerations of EM-PM hybrid levitation and propulsion device for magnetically levitated vehicle[J]. IEEE Transactions on Magnetics, 2009, 45(10): 4632-4635. doi: 10.1109/TMAG.2009.2023998 [6] 王莉, 张昆仑. 基于零功率控制策略的混合磁悬浮系统[J]. 西南交通大学学报, 2005, 40(5): 667-672. doi: 10.3969/j.issn.0258-2724.2005.05.022WANG Li, ZHANG Kun-lun. Hybrid magnetic suspension system based on zero power control strategy[J]. Journal of Southwest Jiaotong University, 2005, 40(5): 667-672. (in Chinese) doi: 10.3969/j.issn.0258-2724.2005.05.022 [7] GAO Tao, YANG Jie, JIA Li-min, et al. Design of new energy-efficient permanent magnetic maglev vehicle suspension system[J]. IEEE Access, 2019, 7: 135917-135932. doi: 10.1109/ACCESS.2019.2939879 [8] 苏芷玄, 杨杰, 彭月, 等. 单点混合磁悬浮系统的自抗扰控制仿真研究[J]. 铁道科学与工程学报, 2022, 19(4): 864-873.SU Zhi-xuan, YANG Jie, PENG Yue, et al. Simulating active disturbance-resistant control of single-point hybrid magnetic suspension system[J]. Journal of Railway Science and Engineering, 2022, 19(4): 864-873. (in Chinese) [9] 龙鑫林, 佘龙华, 常文森. 电磁永磁混合型EMS磁悬浮非线性控制算法研究[J]. 铁道学报, 2011, 33(9): 36-39. doi: 10.3969/j.issn.1001-8360.2011.09.006LONG Xin-lin, SHE Long-hua, CHANG Wen-seng. Study on nonlinear control method for hybrid EMS maglev train[J]. Journal of the China Railway Society, 2011, 33(9): 36-39. (in Chinese) doi: 10.3969/j.issn.1001-8360.2011.09.006 [10] 徐绍辉, 徐正国, 金能强, 等. 电磁永磁混合悬浮系统的建模仿真与实验[J]. 辽宁工程技术大学学报, 2006, 25(4): 553-555. doi: 10.3969/j.issn.1008-0562.2006.04.022XU Shao-hui, XU Zheng-guo, JIN Neng-qiang, et al. Modeling, simulation and experiments for the hybrid maglev system[J]. Journal of Liaoning Technical University, 2006, 25(4): 553-555. (in Chinese) doi: 10.3969/j.issn.1008-0562.2006.04.022 [11] 黎松奇, 罗成, 张昆仑. 基于漏磁补偿的混合电磁铁磁力修正研究[J]. 西南交通大学学报, 2022, 57(3): 604-609.LI Song-qi, LUO Cheng, ZHANG Kun-lun. Correction of magnetic force of hybrid electromagnet based on magnetic flux leakage compensation[J]. Journal of Southwest Jiaotong University, 2022, 57(3): 604-609. (in Chinese) [12] 薛毓强, 吴金龙. 基于分布参数磁路模型的永磁接触器吸力特性[J]. 电工技术学报, 2014, 29(7): 222-228.XUE Yu-qiang, WU Jin-long. Study of attractive force characteristics based on magnetic distributed parameter circuit model of permanent magnet contactors[J]. Transactions of China Electrotechnical Society, 2014, 29(7): 222-228. (in Chinese) [13] KERDTUAD P, KITTIRATSATCHA S. Tractive force estimation for hybrid pm-electromagnetic suspension system maglev train prototype[C]//IEEE. 2020 6th International Conference on Engineering, Applied Sciences and Technology (ICEAST). New York: IEEE, 2020: 1-4. [14] 王志涛, 蔡尧, 龚天勇, 等. 基于场-路-运动耦合模型的超导电动悬浮列车特性研究[J]. 中国电机工程学报, 2019, 39(4): 1162-1170.WANG Zhi-tao, CAI Yao, GONG Tian-yong, et al. Characteristic studies of the superconducting electrodynamic suspension train with a field-circuit-motion coupled model[J]. Proceedings of the CSEE, 2019, 39(4): 1162-1170. (in Chinese) [15] 巫川, 李冠醇, 王东. 永磁电动悬浮系统三维解析建模与电磁力优化分析[J]. 电工技术学报, 2021, 36(5): 924-934.WU Chuan, LI Guan-chun, WANG Dong. 3-D analytical modeling and electromagnetic force optimization of permanent magnet electrodynamic suspension system[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 924-934. (in Chinese) [16] LIU Ya-ping, XU Xiao-zhou, WANG Xu-dong, et al. Mechanism analysis and modeling research of novel hybrid excitation guiding system[C]//IEEE. 2016 IEEE 11th Conference on Industrial Electronics and Applications (ICIEA). New York: IEEE, 2016: 2251-2256. [17] 高元鑫, 路勇, 苗立贤, 等. 基于COMSOL＿Mutiphysics的高频电磁阀电磁力动态仿真[J]. 哈尔滨工程大学学报, 2021, 42(11): 1641-1646.GAO Yuan-xin, LU Yong, MIAO Li-xian, et al. Dynamic simulation of the electromagnetic force of a high-frequency solenoid valve based on COMSOL_Multiphysics[J]. Journal of Harbin Engineering University, 2021, 42(11): 1641-1646. (in Chinese) [18] 程志勇, 卢东方, 薛子兴, 等. 基于COMSOL Mutiphysics的履带式磁选机平面磁系磁场仿真与参数优化[J]. 中南大学学报(自然科学版), 2021, 52(4): 1049-1057.CHENG Zhi-yong, LU Dong-fang, XUE Zi-xing, et al. COMSOL Mutiphysics-based magnetic field simulation and parameter optimization of planar magnetic system of crawler magnetic separator[J]. Journal of Central South University (Science and Technology), 2021, 52(4): 1049-1057. (in Chinese) [19] RAJ R, RAM B S, BHAT R, et al. A novel cost-effective magnetic characterization tool for soft magnetic materials used in electrical machines[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 6009508. [20] LI Ping-yuan, LIU Chuan, WANG Bao-xin, et al. The investigation of strategy to suppress thrust fluctuations in electromagnetic halbach coreless linear motor[J]. IEEE Transactions on Applied Superconductivity, 2024, 34(8): 3603804. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10737297 [21] LONG Gang, SHEN Jin-song, HU Zu-zhi, et al. 3-D numerical modeling of transient electromagnetic responses in anisotropic formation with cement-coated steel casing borehole[J]. IEEE Transactions on Geoscience and Remote Sensing, 2024, 62: 5931912. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10716689 [22] 刘泽旭, 胥光申, 盛晓超, 等. 洛伦兹力磁悬浮织针驱动器设计与仿真[J]. 纺织学报, 2021, 42(11): 159-165.LIU Ze-xu, XU Guang-shen, SHENG Xiao-chao, et al. Design and simulation of Lorentz force actuated maglev knitting needle actuator[J]. Journal of Textile Research, 2021, 42(11): 159-165. (in Chinese) [23] NI Fei, MU Si-yuan, KANG Jin-song, et al. Robust controller design for maglev suspension systems based on improved suspension force model[J]. IEEE Transactions on Transportation Electrification, 2021, 7(3): 1765-1779. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9350649 [24] WANG X B, LIN H Y, HO S L, et al. Analysis of dynamic characteristics of permanent magnet contactor with sensorless displacement profile control[J]. IEEE Transactions on Magnetics, 2010, 46(6): 1633-1636. http://www.researchgate.net/profile/SL_Ho/publication/224139386_Analysis_of_Dynamic_Characteristics_of_Permanent_Magnet_Contactor_With_Sensorless_Displacement_Profile_Control/links/00b4952baaa7f12f6d000000 [25] 汤龙飞, 柯昌辉, 许志红. 智能单稳态永磁接触器动作特性的联合仿真[J]. 中国电机工程学报, 2023, 43(4): 1641-1650.TANG Long-fei, KE Chang-hui, XU Zhi-hong. Co-simulation of action characteristics of intelligent monostable permanent magnet contactor[J]. Proceedings of the CSEE, 2023, 43(4): 1641-1650. (in Chinese) [26] 邵立雪. 大功率永磁直流接触器电磁设计及控制研究[D]. 南京: 东南大学, 2018.SHAO Li-xue. Research on electromagnetic design and control of high power DC permanent magnet contactor[D]. Nanjing: Southeast University, 2018. (in Chinese) [27] RONG Ming-zhe, LOU Jian-yong, LIU Yi-ying, et al. Static and dynamic analysis for contactor with a new type of permanent magnet actuator[J]. IEICE Transactions on Electronics, 2006, 89(8): 1210-1216. http://www.researchgate.net/profile/Jianyong_Lou/publication/220242049_Static_and_Dynamic_Analysis_for_Contactor_with_a_New_Type_of_Permanent_Magnet_Actuator/links/0046352898e1f93b6f000000 [28] FANG S H, LIN H Y, HO S L. Magnetic field analysis and dynamic characteristic prediction of AC permanent-magnet contactor[J]. IEEE Transactions on Magnetics, 2009, 45(7): 2990-2995. http://www.onacademic.com/detail/journal_1000035162248210_070b.html [29] 贺湘琰, 李靖. 电器学[M]. 北京: 机械工业出版社, 2012.HE Xiang-yan, LI Jing. Electrical Engineering[M]. Beijing: China Machine Press, 2012. (in Chinese) [30] 王秀和. 永磁电机[M]. 北京: 中国电力出版社, 2007.WANG Xiu-he. Permanent Magnet Motor[M]. Beijing: China Electric Power Press, 2007. (in Chinese) [31] 陈春涛, 吴新振, 郑晓钦, 等. 基于改进等效面电流法的永磁电机气隙磁场解析计算[J]. 中国电机工程学报, 2021, 41(增1): 315-323.CHEN Chun-tao, WU Xin-zhen, ZHENG Xiao-qin, et al. Analytical calculation of air-gap magnetic field of permanent-magnet motor based on improved equivalent surface current method[J]. Proceedings of the CSEE, 2021, 41(S1): 315-323. (in Chinese) -
点击查看大图
图(11) / 表(1)
计量
- 文章访问数: 44
- HTML全文浏览量: 11
- PDF下载量: 7
- 被引次数: 0
