考虑绕制不对称性的螺线管线圈磁场计算方法

doi:10.19595/j.cnki.1000-6753.tces.251300

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Abstract Solenoid coils, made by spirally winding wires, are key components for converting electro-magnetic energy. Due to their advantages of stable structure, simple manufacturing process, and easy reinforcement, they are widely used in electrical equipment such as transformers and motors. In the transient simulation, to reduce modeling complexity and computational time, the coil is modeled as a 2D axisymmetric model with multiple coaxial circular cross-sections. This model achieves high computational accuracy and extremely fast solution times for multi-turn dense-wound coils, but it does not account for axial asymmetry introduced by the winding process. Thus, large simulation errors occur when solenoid coils with high magnetic field intensity, non-dense windings, and large-cross-section wires are used in high-intensity scenarios.
Therefore, this paper proposes an improved current filament method that accounts for the winding asymmetry. A numerical solution model is established based on the current filament method and introduces an asymmetric correction coefficient matrix to optimize the current filaments. The optimized current is then imported into the model for magnetic field calculation. The structural asymmetry is equivalent to the excitation-current asymmetry in a symmetric structure, improving solution accuracy without incurring excessive computational load.
Taking a single-layer solenoid coil as an example, this paper first subdivides the coil wire into several current filament units, calculates the electromagnetic characteristic parameters between each pair of units, and constructs a numerical solution model. Then, the asymmetry coefficient of the current filament is calculated, and the current is optimized using the asymmetric correction coefficient matrix. Finally, the optimized current is imported into the 2D axisymmetric equivalent model. The results show that the coil magnetic field distribution closely matches the actual situation, verifying the effectiveness and practicability of the proposed method.
The conclusions are as follows.（1）This paper proposes an improved current filament method considering the winding asymmetry of the coil, which effectively equates the structural asymmetry of the coil to the asymmetry of the excitation current under a symmetric structure.（2）This method effectively improves the current calculation accuracy, achieving a magnetic field distribution closer to that of the 3D coil. Meanwhile, the calculation time is significantly shortened. The output current accuracy is less than 2%, and the error at the current peak is reduced from 3.814% to 0.132%. The magnetic flux density distribution of the coil is closer to the comparison reference value.（3）It has good effectiveness and stability for different solenoid coils. By studying the current calculation accuracy under different factors such as the number of turns, wire size, discharge capacitance, and coil pitch, it is found that the errors of this method are within 0%~1%. Moreover, for complex calculation models, the advantage in computational efficiency is pronounced.

Key words： Solenoid coil winding asymmetry current filament method electromagnetic calculations improved current filament method

Received: 22 July 2025

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	Xiong Qi
	Li Yuanyuan
	Cheng Hui
	Wang Lili
	Yan Nuo

Cite this article:

Xiong Qi,Li Yuanyuan,Cheng Hui等. Method for Calculating Magnetic Field of Solenoid Coil Accounting for Winding Asymmetry[J]. Transactions of China Electrotechnical Society, 2026, 41(16): 5402-5413.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.251300 OR https://dgjsxb.ces-transaction.com/EN/Y2026/V41/I16/5402

[1] 冯波, 彭大为, 杨奕, 等. 改进型扁平螺线管线圈高抗偏移无线电能传输系统[J]. 电工技术学报, 2025, 40(12): 3716-3726.
Feng Bo, Peng Dawei, Yang Yi, et al.Enhanced flat solenoid coil with high misalignment tolerance for wireless power transfer system[J]. Transactions of China Electrotechnical Society, 2025, 40(12): 3716-3726.
[2] Plavec E, Ladisic I, Vidović M.The impact of coil winding angle on the force of DC solenoid electro-magnetic actuator[J]. Advances in Electrical and Electronic Engineering, 2019, 17(3): 244-250.
[3] 邓将华, 黄伍平, 王威. 电磁成形线圈电感计算[J]. 福州大学学报(自然科学版), 2016, 44(6): 789-794.
Deng Jianghua, Huang Wuping, Wang Wei.Indu-ctance computation for electromagnetic forming coil[J]. Journal of Fuzhou University（Natural Science Edition), 2016, 44(6): 789-794.
[4] Bramerdorfer G, Tapia J A, Pyrhönen J J, et al.Modern electrical machine design optimization: techniques, trends, and best practices[J]. IEEE Transactions on Industrial Electronics, 2018, 65(10): 7672-7684.
[5] 何致远, 康敏. 矩形体充磁线圈有限元分析[J]. 系统仿真学报, 2010, 22(12): 2813-2816.
He Zhiyuan, Kang Min.Analysis of a rectangular magnetic charging coil by finite element method[J]. Journal of System Simulation, 2010, 22(12): 2813-2816.
[6] Zhang Wenting, Zhou Hang, Liang Xiaoguang, et al.Pitch effect of helical coils of electromagnetic forming[J]. IEEE Access, 2020, 8: 205162-205169.
[7] 熊奇, 邱爽, 李彦昕, 等. 组合式电磁成形技术研究进展[J]. 电工技术学报, 2024, 39(9): 2710-2729.
Xiong Qi, Qiu Shuang, Li Yanxin, et al.research progress of combined electromagnetic forming tech-nology[J]. Transactions of China Electrotechnical Society, 2024, 39(9): 2710-2729.
[8] 王懿杰, 陆凯兴, 姚友素, 等. 具有强抗偏移性能的电动汽车用无线电能传输系统[J]. 中国电机工程学报, 2019, 39(13): 3907-3917.
Wang Yijie, Lu Kaixing, Yao Yousu, et al.An electric vehicle（EV)-oriented wireless power transfer system featuring high misalignment tolerance[J]. Proceedings of the CSEE, 2019, 39(13): 3907-3917.
[9] 王艺宇, 胡道宇, 吕民东, 等. 阻尼线圈电流控制相序对超导电动悬浮系统振动抑制效果研究[J]. 中国电机工程学报, 2025, 45(22): 9016-9028.
Wang Yiyu, Hu Daoyu, Lü Mindong, et al.Research on the vibration suppression effect of damping coil current control phase sequence in superconducting electrodynamic suspension system[J]. Proceedings of the CSEE, 2025, 45(22): 9016-9028.
[10] 魏文琦, 张绍哲, 谢剑峰, 等. 脉冲强磁场磁感应强度测量技术研究进展[J]. 电工技术学报, 2024, 39(23): 7291-7308.
Wei Wenqi, Zhang Shaozhe, Xie Jianfeng, et al.Progress of magnetic induction intensity measurement techniques in the pulsed high magnetic field[J]. Transactions of China Electrotechnical Society, 2024, 39(23): 7291-7308.
[11] 韩厚祥. CFETR中心螺线管超导模型线圈绕制成形关键技术研究[D]. 合肥: 中国科学技术大学, 2019.
Han Houxiang.Key technical researching for the coil winding of the CFETR CS model coil[D]. Hefei: University of Science and Technology of China, 2019.
[12] Zhu Xuehua, Xing Meng, Ye Juntao, et al.Design and optimization of a novel solenoid with high magnetic uniformity[J]. Scientific Reports, 2024, 14: 24650.
[13] Humphries S, Young D E.Principles of charged particle acceleration[J]. Physics Today, 1988, 41(5): 98-99.
[14] 吴劲斌, 颜国正, 文人庆, 等. 多维无线能量传输系统的设计与优化[J]. 光学精密工程, 2023, 31(15): 2218-2226.
Wu Jinbin, Yan Guozheng, Wen Renqing, et al.Design and optimization of multi-dimensional wire-less power transmission system[J]. Optics and Precision Engineering, 2023, 31(15): 2218-2226.
[15] Nunio F, Torre A, Zani L.Mechanical analysis of the European DEMO central solenoid pre-load structure and coils[J]. Fusion Engineering and Design, 2019, 146: 168-172.
[16] 叶毅, 龙全红, 廖树清, 等. 1.5 T磁感应强度水冷式螺线管线圈结构设计及仿真研究[J]. 强激光与粒子束, 2023, 35(2): 024003.
Ye Yi, Long Quanhong, Liao Shuqing, et al.Structure design and simulation research for the water-cooled solenoid with 1.5 T magnetic field[J]. High Power Laser and Particle Beams, 2023, 35(2): 024003.
[17] Wu A Y, Sun K S.Formulation and implementation of the current filament method for the analysis of current diffusion and heating in conductors in railguns and homopolar generators[J]. IEEE Transactions on Magnetics, 1989, 25(1): 610-615.
[18] Luo Jing, Novac B M, Smith I R, et al.Fast and accurate two-dimensional modelling of high-current, high-voltage air-cored transformers[J]. Journal of Physics D: Applied Physics, 2005, 38(6): 955.
[19] 刘守豹, 阮江军, 彭迎, 等. 改进电流丝法及其在感应线圈炮场路结合分析中的应用[J]. 中国电机工程学报, 2010, 30(30): 128-134.
Liu Shoubao, Ruan Jiangjun, Peng Ying, et al.Improvement of current filament method and its application in field-circuit analysis of induction coil Gun[J]. Proceedings of the CSEE, 2010, 30(30): 128-134.
[20] 黎镇浩, 曹全梁, 赖智鹏, 等. 电流丝法在电磁成形线圈电流和工件电磁力计算中的应用[J]. 电工技术学报, 2018, 33(18): 4181-4190.
Li Zhenhao, Cao Quanliang, Lai Zhipeng, et al.Application of current filament method on the calculation of current and force in electromagnetic forming[J]. Transactions of China Electrotechnical Society, 2018, 33(18): 4181-4190.
[21] 熊奇, 阎诺, 邱爽, 等. 吸引力电磁成形上下同轴组合线圈受力分析[J]. 中国电机工程学报, 2025, 45(19): 7831-7841.
Xiong Qi, Yan Nuo, Qiu Shuang, et al.Force analysis of upper and lower coaxial combined coils for attractive electromagnetic forming[J]. Proceedings of the CSEE, 2025, 45(19): 7831-7841.
[22] 张宇娇, 赵志涛, 徐斌, 等. 基于U-net卷积神经网络的电磁场快速计算方法[J]. 电工技术学报, 2024, 39(9): 2730-2742.
Zhang Yujiao, Zhao Zhitao, Xu Bin, et al.Fast calculation method of electromagnetic field based on U-net convolutional neural network[J]. Transactions of China Electrotechnical Society, 2024, 39(9): 2730-2742.
[23] Montgomery D B, Weggel R J.Solenoid Magnet Design[M]. USA: Krigier Publishing Company, 1980.
[24] Özüpak Y, Teke İ H, Mamiş M S.Analysis of electronic circuit transformer with experimental and finite elements[J]. International Journal of Energy Applications and Technologies, 2021, 8(1): 21-26.
[25] 张骁. 脉冲强磁场作用下管件胀拉成形数值模拟与实验研究[D]. 武汉: 华中科技大学, 2017.
Zhang Xiao.Numerical Simulation and experimental study of tube bulging-drawing forming under pulsed high magnetic fields[D]. Wuhan: Huazhong University of Science and Technology, 2017.
[26] 刘扬, 白庆伟, 张恺华, 等. 电磁脉冲波形对ZL114A铝合金凝固过程的影响[J]. 材料开发与应用, 2025, 40(1): 111-124.
Liu Yang, Bai Qingwei, Zhang Kaihua, et al.Effect of electromagnetic pulse waveform on solidification process of ZL114A aluminum alloys[J]. Materials Development and Application, 2025, 40(1): 111-124.