Mathematical Model of Parameters for Normal Conducting Magnetic Levitation Motors Considering Magnetic Saturation
-
摘要:
常导磁浮列车提速导致悬浮气隙波动幅度增大，使电机磁场更易进入饱和区，从而加剧铁心磁阻非线性，削弱传统磁路法参数模型的准确性. 为此，提出一种考虑磁饱和影响的常导高速磁浮电机参数解析建模方法，以提升长定子直线同步电机参数模型的计算精度. 首先，基于磁路法构建考虑铁心磁阻变化的等效气隙模型；其次，结合有限元磁场数据，采用基于微分磁导率的磁化效应动态表征方法，获取铁心材料的相对磁导率，实现磁饱和程度的定量描述；最后，将动态微分磁导率与等效气隙模型相结合，建立能够反映铁心饱和、齿槽效应及气隙变化等多重因素的电机参数模型，并对其精度进行验证. 研究结果表明：在磁饱和状态下，传统磁路法参数模型存在显著失真，各电感参数的相对误差普遍超过45%；引入等效气隙与基于微分磁导率的磁化表征方法后，模型对铁心磁阻及不同饱和程度的响应能力增强，参数预测精度提升，以5 mm悬浮高度为例，定子自感、定子与励磁互感以及励磁自感的预测精度分别提高39.43%、30.14%和40.11%.
Abstract:The increase in speed of normal conducting magnetic levitation trains leads to an increased fluctuation range of the levitation air gap, making the motor’s magnetic field more likely to enter the saturation region, which aggravates the nonlinearity of the iron core’s magnetic reluctance and weakens the accuracy of the conventional magnetic circuit method parameter model. Therefore, an analytical parameter modeling method for normal conducting high-speed magnetic levitation motors considering the influence of magnetic saturation was proposed to improve the calculation accuracy of the parameter model for long-stator linear synchronous motors. First, an equivalent air gap model considering the variation in the iron core’s magnetic reluctance was constructed based on the magnetic circuit method. Second, combined with finite element magnetic field data, a dynamic characterization method for the magnetization effect based on differential permeability was adopted to obtain the relative permeability of the iron core material, realizing the quantitative description of the magnetic saturation degree. Finally, the dynamic differential permeability was combined with the equivalent air gap model to establish a motor parameter model capable of reflecting multiple factors such as iron core saturation, slotting effect, and air gap variation, and its accuracy was verified. The research results indicate that under the magnetic saturation state, the parameter model by the conventional magnetic circuit method exhibits significant distortion, with the relative errors of various inductance parameters generally exceeding 45%. After introducing the equivalent air gap and the magnetization characterization method based on differential permeability, the response capability of the model to the iron core’s magnetic reluctance and different saturation degrees is enhanced, and the parameter prediction accuracy is improved. By taking a suspension height of 5 mm as an example, the prediction accuracies of the stator self-inductance, the mutual inductance between stator and excitation, and the excitation self-inductance are improved by 39.43%, 30.14%, and 40.11%, respectively.
-
图 2 定子与励磁中心轴线相对位移较小时的示意
Figure 2. Schematic of small relative displacement between stator and excitation central axis
图 3 电机定子与励磁绕组的梯形波等效气隙磁动势
Figure 3. Trapezoidal wave equivalent air gap magnetomotive force of motor stator and excitation winding
图 4 电机铁心与气隙中的主磁通路径示意
Figure 4. Schematic of main magnetic flux path in motor’s iron core and air gap
图 5 磁化效应的不同方法表征
Figure 5. Characterization of magnetization effect by different methods
图 6 考虑磁饱和的参数模型设计流程
Figure 6. Design flowchart of parameter model considering magnetic saturation
图 7 不同悬浮高度下铁心处磁感应强度
Figure 7. Magnetic induction intensity at iron core under different suspension heights
图 9 定子A相与励磁互感结果比较
Figure 9. Comparison of mutual inductance results between stator phase A and excitation
图 10 励磁绕组自感结果比较
Figure 10. Comparison of self-inductance results of excitation winding
表 1 常导磁浮电机主要结构参数
Table 1. Main structural parameters of normal conducting magnetic levitation motor
符号 描述 取值 τs 定子极距/mm 258 τN 定子槽距/mm 86 bN 定子槽宽/mm 43 be 定子铁心厚度/mm 185 Ns 定子绕组匝数/匝 1 τm 励磁磁极极距/mm 266.5 bm 励磁磁极极宽/mm 166.5 bf 励磁磁极铁心厚度/mm 170 Nm 励磁绕组匝数/匝 270 lair 额定悬浮高度/mm 10 ls 定子槽深的气隙高度/mm 41 lm 励磁铁心槽深的气隙高度/mm 120 
下载: 导出CSV
表 2 不同悬浮高度下的铁心相对磁导率
Table 2. Relative permeability of iron core under different suspension heights
lair/mm μr lair/mm μr 1 6.01 11 924.16 2 10.65 12 1037.81 3 15.41 13 1121.34 4 21.55 14 1233.74 5 25.94 15 1310.31 6 39.37 16 1336.81 7 142.04 17 1466.57 8 374.68 18 1435.90 9 595.27 19 1459.80 10 755.22
下载: 导出CSV
-
[1] 熊嘉阳, 沈志云, 池茂儒, 等. 高速磁悬浮列车技术综述[J]. 交通运输工程学报, 2025, 25(2): 1-23.Xiong Jiayang, Shen Zhiyun, Chi Maoru, et al. Review on high-speed maglev train technology[J]. Journal of Traffic and Transportation Engineering, 2025, 25(2): 1-23. [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 Zigang, Liu Zongxin, Li Haitao, et al. Development status and prospect of maglev train[J]. Journal of Southwest Jiaotong University, 2022, 57(3): 455-474, 530. [3] Ouyang M H, Chen S, Li Q L, et al. Numerical investigation on aerodynamic forces and flow patterns of high-speed trains from open air into long tunnel[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2022, 229: 105142. doi: 10.1016/j.jweia.2022.105142 [4] Zhang L, Gao Y, Lin T T, et al. Comparative analysis of crosswind influence on aerodynamic characteristics of superconducting and normal-conducting high-speed maglev trains[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2025, 265: 106182. doi: 10.1016/j.jweia.2025.106182 [5] 孙友刚, 张丹丹, 吉文, 等. 基于模糊补偿的磁浮列车悬浮系统非奇异终端滑模控制[J]. 西南交通大学学报, 2025, 60(4): 803-811.Sun Yougang, Zhang Dandan, Ji Wen, et al. Fuzzy compensation-based non-singular terminal sliding mode control of maglev vehicle levitation system[J]. Journal of Southwest Jiaotong University, 2025, 60(4): 803-811. [6] 陈绪黎, 向活跃, 田祥富, 等. 连续梁竖向刚度对高速磁浮列车-桥梁动力响应的影响[J]. 西南交通大学学报, 2025, 60(5): 1178-1185.Chen Xuli, Xiang Huoyue, Tian Xiangfu, et al. Influence of vertical stiffness of continuous girder on dynamic responses of high-speed electromagnetic suspension train and bridge[J]. Journal of Southwest Jiaotong University, 2025, 60(5): 1178-1185. [7] 付善强, 吴冬华, 韩伟涛, 等. 基于非线性材料的高速磁浮电磁铁建模与分析[J]. 西南交通大学学报, 2023, 58(4): 879-885.Fu Shanqiang, Wu Donghua, Han Weitao, et al. Modeling and analysis of high-speed maglev electromagnets based on nonlinear materials[J]. Journal of Southwest Jiaotong University, 2023, 58(4): 879-885. [8] Zhu J Q, Cao X Q, Ge Q X, et al. Adaptive-SMO-based traction force fluctuation suppression strategy considering suspension system for high-speed maglev train[J]. IEEE Transactions on Industrial Electronics, 2024, 71(3): 2289-2299. doi: 10.1109/TIE.2023.3270525 [9] 朱进权, 葛琼璇, 张波, 等. 考虑悬浮系统影响的高速磁悬浮列车牵引控制策略[J]. 电工技术学报, 2022, 37(12): 3087-3096.Zhu Jinquan, Ge Qiongxuan, Zhang Bo, et al. Traction control strategy of high-speed maglev considering the influence of suspension system[J]. Transactions of China Electrotechnical Society, 2022, 37(12): 3087-3096. [10] Lv G, Cui L L, Zhi R D. Inductance analysis of transverse flux linear synchronous motor for maglev trains considering three-dimensional operating conditions[J]. IEEE Transactions on Industrial Electronics, 2024, 71(1): 769-776. doi: 10.1109/TIE.2023.3250754 [11] 康劲松, 丁浩, 倪菲, 等. 计及悬浮系统影响的高速磁浮直线同步电机建模方法[J]. 西南交通大学学报, 2024, 59(4): 729-736.Kang Jinsong, Ding Hao, Ni Fei, et al. Modeling of high-speed maglev linear synchronous motors considering influence of suspension system[J]. Journal of Southwest Jiaotong University, 2024, 59(4): 729-736. [12] 孙鹏琨, 葛琼璇, 王晓新, 等. 基于硬件在环实时仿真平台的高速磁悬浮列车牵引控制策略[J]. 电工技术学报, 2020, 35(16): 3426-3435.Sun Pengkun, Ge Qiongxuan, Wang Xiaoxin, et al. Traction control strategy of high-speed maglev train based on hardware-in-the-loop real-time simulation platform[J]. Transactions of China Electrotechnical Society, 2020, 35(16): 3426-3435. [13] Wang H M, Zhao J H, Xiong Y Y, et al. Exact air gap magnetic field calculation of a short primary single-sided linear induction motor considering coupling effects of slot harmonics and longitudinal dynamic end effect[J]. IEEE Transactions on Magnetics, 2025, 61(11): 8203512. doi: 10.1109/tmag.2025.3613661 [14] 王辉煌, 杜玉梅, 张瑞华, 等. 中速磁浮无铁心永磁直线同步电机的结构优化[J]. 电机与控制学报, 2023, 27(5): 46-55.Wang Huihuang, Du Yumei, Zhang Ruihua, et al. Structure improvement of ironless permanent magnet linear synchronous motor with Halbach array for middle speed maglev trains[J]. Electric Machines and Control, 2023, 27(5): 46-55. [15] Liu J P, Wang X H, Li X L, et al. Electromagnetic and stress performance analysis for synchronous reluctance motor using a new hybrid subdomain method[J]. IEEE Transactions on Industrial Electronics, 2024, 71(8): 8548-8559. doi: 10.1109/TIE.2023.3327333 [16] Zhu X K, Qi G Y, Cheng M, et al. Equivalent magnetic network model of electrical machine based on three elements: magnetic flux source, reluctance, and magductance[J]. IEEE Transactions on Transportation Electrification, 2025, 11(1): 3538-3548. doi: 10.1109/TTE.2024.3443521 [17] Ayhan U, Gurleyen H. Advanced modeling of a 12/10 variable flux reluctance machine using winding and air-gap permeance functions considering saturation and skew effects[J]. IEEE Transactions on Transportation Electrification, 2025, 11(4): 10001-10011. doi: 10.1109/TTE.2025.3548479 [18] Kang J S, Mu S Y, Ni F. Improved EL model of long stator linear synchronous motor via analytical magnetic coenergy reconstruction method[J]. IEEE Transactions on Magnetics, 2020, 56(8): 8300213. doi: 10.1109/tmag.2020.3002964 [19] 章九鼎, 卢琴芬. 长定子直线同步电机齿槽效应的计算与影响[J]. 电工技术学报, 2021, 36(5): 964-972, 1026.Zhang Jiuding, Lu Qinfen. Calculation and influences of cogging effects in long-stator linear synchronous motor[J]. Transactions of China Electrotechnical Society, 2021, 36(5): 964-972,1026. [20] Feng Y, Zhao C F, Bai Z, et al. A modified electromagnetic force calculation method has high accuracy and applicability for EMS maglev vehicle dynamics simulation[J]. ISA Transactions, 2023, 137: 186-198. doi: 10.1016/j.isatra.2023.01.019 [21] Cao J C, Deng X Q, Li D, et al. Electromagnetic analysis and optimization of high-speed maglev linear synchronous motor based on field-circuit coupling[J]. CES Transactions on Electrical Machines and Systems, 2022, 6(2): 118-123. doi: 10.30941/CESTEMS.2022.00017 [22] Ma C G, Li J M, Zhao H C, et al. 3-D analytical model of armature reaction field of IPMSM with multi-segmented skewed poles and multi-layered flat wire winding considering current harmonics[J]. IEEE Access, 2020, 8: 151116-151124. doi: 10.1109/ACCESS.2020.3017005 [23] 王娟. 磁悬浮列车用长定子直线同步电机特性研究与故障分析[D]. 北京: 中国科学院电工研究所. 2004. [24] 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. doi: 10.3969/j.issn.0258-2724.20210843Li Songqi, Luo Cheng, Zhang Kunlun. Correction of magnetic force of hybrid electromagnet based on magnetic flux leakage compensation[J]. Journal of Southwest Jiaotong University, 2022, 57(3): 604-609. doi: 10.3969/j.issn.0258-2724.20210843 [25] 张育兴, 马名中, 马伟明, 等. 双定子直线感应电机饱和特性分析[J]. 中国电机工程学报, 2012, 32(36): 102-108, 7.Zhang Yuxing, Ma Mingzhong, Ma Weiming, et al. Analysis of saturation characteristics of double-stator linear induction motors[J]. Proceedings of the Chinese Society for Electrical Engineering, 2012, 32(36): 102-108, 7. [26] Nguyen M D, Yang J W, Hoang D T, et al. Electromagnetic analysis of YASA axial flux motor using harmonic modeling considering non-linear core permeability[J]. IEEE Transactions on Magnetics, 2025, 61(9): 8203412. doi: 10.1109/tmag.2025.3578655 [27] 王树宏, 高锋, 高定刚, 等. 基于UM仿真软件的高速磁浮列车轨道不平顺的动力学响应研究[J]. 城市轨道交通研究, 2022, 25(9): 69-73, 78. doi: 10.16037/j.1007-869x.2022.09.014Wang Shuhong, Gao Feng, Gao Dinggang, et al. Research on dynamic response of high-speed maglev train track irregularity based on UM simulation software[J]. Urban Mass Transit, 2022, 25(9): 69-73, 78. doi: 10.16037/j.1007-869x.2022.09.014 -
下载:
点击查看大图
计量
- 文章访问数: 29
- HTML全文浏览量: 25
- PDF下载量: 8
- 被引次数: 0