Abstract：Inductance gradient, an important parameter of electromagnetic rail launcher, weighs strongly on propulsive force and efficiency. There are two main weaknesses in the previous research of inductance gradient: 1) The general analytical method take the rail dimensions into account regardless of the influence of current diffusion, thus the dynamic characteristics cannot be described; 2) Though the finite element method can analyze the influence of the current diffusion, the calculation process is lack of efficiency. Therefore, considering the influence of both rail dimensions and current diffusion, this paper proposes an analytical method to calculate the inductance gradient, which is based on the skin depth and the principle of magnetic energy equivalence. The results calculated by this method were compared with those from different references, and good agreements were obtained. The proposed method can provide an effective theoretical guidance for the optimization design and performance analysis of electromagnetic rail launcher.
[1] 李军, 严萍, 袁伟群. 电磁轨道发射技术的发展与现状[J]. 高电压技术, 2014, 40(4): 1052-1064. Li Jun, Yan Ping, Yuan Weiqun.Electromagnetic gun technology and its development[J]. High Voltage Engineering, 2014, 40(4): 1052-1064. [2] 鲍晓华, 刘佶炜, 孙跃, 等. 低速大转矩永磁直驱电机研究综述与展望[J]. 电工技术学报, 2019, 34(6): 1148-1160. Bao Xiaohua, Liu Jiwei, Sun Yue, et al.Review and prospect of low-speed high-torque permanent magnet machines[J]. Transactions of China Electrotechnical Society, 2019, 34(6): 1148-1160. [3] 王莹, 肖峰. 电炮原理[M]. 北京: 国防工业出版社, 1995. [4] 吕亚军, 程思为, 王东, 等. 表贴式永磁电机在电枢磁场作用下的定子受力计算模型[J]. 电工技术学报, 2019, 34(15): 3124-3135. Lü Yajun, Cheng Siwei, Wang Dong, et al.The stator force calculation model for surface mounted permanent magnet motor under the action of armature magnetic field[J]. Transactions of China Electrotechnical Society, 2019, 34(15): 3124-3135. [5] Grover F W.Inductance calculations: working formulas and tables[M]. New York: Dover Publications, 1962. [6] Kerrisk J F.Current distribution and inductance calculations for rail-gun conductors[R]. Los Alamos, NM, USA: Los Alamos National Laboratory, 1981. [7] Keshtkar A, Bayati S.Derivation of a formula for inductance gradient using intelligent estimation method[J]. IEEE Transactions on Magnetics, 2009, 45(1): 305-308. [8] Deadrick F, Hawke R, Scudder J.MAGRAC-a electromagnetic rail launcher simulation program[J]. IEEE Transactions on Magnetics, 2003, 18(1): 94-104. [9] Ghassemi M, Barsi Y M, Hamedi M H.Analysis of force distribution acting upon the rails and the armature and prediction of velocity with time in an electromagnetic launcher with new method[J]. IEEE Transactions on Magnetics, 2006, 43(1): 132-136. [10] 杨玉东, 王建新, 薛文. 轨道炮动态负载特性的分析与仿真[J]. 兵工学报, 2010, 31(8): 1026-1031. Yang Yudong, Wang Jianxin, Xue Wen.Simulation and analysis for dynamic load characteristic of electromagnetic rail-gun[J]. Acta Armamentarii, 2010, 31(8): 1026-1031. [11] 李湘平, 鲁军勇, 李玉, 等. 基于解析法的电磁发射弹丸内膛磁场分布特性分析[J]. 兵工学报, 2016, 37(12): 2205-2211. Li XiangPing, Lu Junyong, Li Yu. Analysis of distribution characteristics of in-bore magnetic field of electromagnetically launched projectile based on analytical method[J]. Acta Armamentarii, 2016, 37(12): 2205-2211. [12] Marshall R A, Ying W.Electromagnetic rail launchers: their science and technology[M]. Beijing: China Machine Press, 2004. [13] Lü Qingao, Xiang Hongjun, Lei Bin, et al.Physical principle and relevant restraining methods about velocity skin effect[J]. IEEE Transactions on Plasma Science, 2015, 43(5): 1523-1530. [14] 苏子舟, 国伟, 张涛. 电磁轨道发射装置技术[M]. 北京: 国防工业出版社, 2019. [15] 刘治鑫, 王东, 余中军, 等. 基于磁性槽楔修正模型的感应电动机气隙磁场的分布磁路法[J]. 电工技术学报, 2019, 34(15): 3112-3123. Liu Zhixin, Wang Dong, Yu Zhongjun, et al.Distributed magnetic circuit method for calculating air-gap magnetic field of induction motor based on modified model considering the effect of magnetic slot wedges[J]. Transactions of China Electrotechnical Society, 2019, 34(15): 3112-3123. [16] 彭飞, 杨文英, 翟国富. 基于优化的传输线法的并行静磁场有限元方法[J]. 电工技术学报, 2019, 34(13): 2716-2725. Peng Fei, Yang WenYing, Zhai Guofu. An optimized parallel transmission line iteration for parallel finite element analysis in magnetostatic field[J]. Transactions of China Electrotechnical Society, 2019, 34(13): 2716-2725. [17] Kohlberg I, Coburn W O A. solution for the three dimensional rail gun current distribution and electromagnetic fields of a rail launcher[J]. IEEE Transactions on Magnetics, 1995, 31(1): 413-416. [18] Keshtkar A.Effect of rail dimension on current distribution and inductance gradient[J]. IEEE Transactions on Magnetics, 2005, 41(1): 383-386. [19] 王志增, 袁伟群, 严萍. 瞬态情况下电磁轨道发射器的电感梯度[J]. 高电压技术, 2017, 43(12): 4039-4044. Wang Zhizeng, Yuan Weiqun, Yan Ping.Inductance gradient for rail-type electromagnetic launcher under transient conditions[J]. High Voltage Engineering, 2017, 43(12): 4039-4044.
2020, Vol. 35 
