﻿ 电磁轨道炮馈电方式分析及耦合仿真研究
 舰船科学技术  2021, Vol. 43 Issue (12): 166-169    DOI: 10.3404/j.issn.1672-7649.2021.12.030 PDF

Research on the feed mode and coupling simulation of electromagnetic rail gun
LIU Ke-ke, WU Li-zhou, CHEN Liang, QIU Qun-xian
The 713 Research Institute of CSSC, Zhengzhou 450015, China
Abstract: The gun tail feeder is one of the key parts of the electromagnetic rail gun, the choice of feeding mode plays a crucial role in the current convergence and overall layout of the electromagnetic tailgun. This paper discusses the square type, T type and ring type feeding mode, and mainly establishes a simple 3d model based on the T type feeing mode, the electromagnetic field-stress field coupling theory is described, and the busbar copper plate and coaxial cable are electrified by Ansys simulation software flow distribution law and electromagnetic stress field coupling simulation, the results agree with theoretical analysis., The research results of this paper have important reference for the further design of the gun tail feeding mode.
Key words: cannon tail feed     T feeding     the current simulation     coupling simulation
0 引　言

1 炮尾馈电方式分析

 图 1 炮尾馈电装置简易模型 Fig. 1 A simple model of gun tail feeder

2 电磁场及应力场计算理论 2.1 Maxwell方程描述

Maxwell方程组的微分形式可表示为：

 $\nabla \times \vec H = \vec J + \frac{{\partial \vec D}}{{\partial t}} ，$ (1)
 $\nabla \times \vec E = - \frac{{\partial \vec B}}{{\partial t}} ，$ (2)
 $\nabla \cdot \vec{B} = 0 ，$ (3)
 $\nabla \cdot \vec D = \rho 。$ (4)

 $\nabla \cdot \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {J} = - \frac{{\partial \rho }}{{\partial t}}，$ (5)

 $\left\{ \begin{gathered} {\boldsymbol{B}} = \nabla \times {\boldsymbol{A}}，\hfill \\ {\boldsymbol{E}} = - \nabla \varphi - \frac{{\partial {\boldsymbol{A}}}}{{\partial t}}。\hfill \\ \end{gathered} \right.$ (6)

 $\boldsymbol{B}=\nabla \times \boldsymbol{A}，$ (7)

 $\nabla \cdot {\boldsymbol{A}} = 0，$ (8)

 $VOLT(t,x,y,z) = \int_{ - \infty }^t {\phi (\tau ,x,y,z){\rm{d}}\tau }。$ (9)

 $\left\{ \begin{gathered} \nabla \times \frac{1}{{{\mu _1}}}\nabla \times {\boldsymbol{A}} - \nabla \frac{1}{{{\mu _1}}}(\nabla \cdot {\boldsymbol{A}}) +\hfill \\ \qquad {\sigma _1}\left( {\nabla \frac{{\partial V}}{{\partial t}} + \frac{{\partial {\boldsymbol{A}}}}{{\partial t}} - {\mathbf{v}} \times \nabla \times {\boldsymbol{A}}} \right) = 0 ，\hfill \\ \nabla \cdot {\sigma _1}\left( { - \nabla \frac{{\partial V}}{{\partial t}} - \frac{{\partial {\boldsymbol{A}}}}{{\partial t}} + {\mathbf{v}} \times \nabla \times {\boldsymbol{A}}} \right) = 0。\hfill \\ \end{gathered} \right.$ (10)

 $\left\{ \begin{gathered} \nabla \times \frac{1}{{{\mu _2}}}\nabla \times {\boldsymbol{A}} - \nabla \frac{1}{{{\mu _2}}}(\nabla \cdot {\boldsymbol{A}}) + {\sigma _2}\left( {\nabla \frac{{\partial V}}{{\partial t}} + \frac{{\partial {\boldsymbol{A}}}}{{\partial t}}} \right) = 0 ，\hfill \\ \nabla \cdot {\sigma _2}\left( { - \nabla \frac{{\partial V}}{{\partial t}} - \frac{{\partial {\boldsymbol{A}}}}{{\partial t}}} \right) = 0。\hfill \\ \end{gathered} \right.$ (11)

 $\nabla \times \frac{1}{{{\mu _3}}}\nabla \times {\boldsymbol{A}} - \nabla \frac{1}{{{\mu _3}}}(\nabla \cdot {\boldsymbol{A}})\; = 0，$ (12)

 $\left\{ \begin{gathered} {{\boldsymbol{A}}_{1t}} - {{\boldsymbol{A}}_{2t}} = 0 ，\hfill \\ \frac{1}{{{\mu _1}}}{(\nabla \times {{\boldsymbol{A}}_1})_t} - \frac{1}{{{\mu _2}}}{(\nabla \times {{\boldsymbol{A}}_2})_t} = 0 ，\hfill \\ {\sigma _2}{\left( - \nabla \frac{{\partial {V_2}}}{{\partial t}} - \frac{{\partial {{\boldsymbol{A}}_2}}}{{\partial t}}\right)_n} -\hfill \\ \qquad{\sigma _1}{\left( - \nabla \frac{{\partial {V_1}}}{{\partial t}} - \frac{{\partial {{\boldsymbol{A}}_1}}}{{\partial t}} + {\mathbf{\upsilon }} \times \nabla \times {{\mathbf{A}}_1}\right)_n} = 0 ，\hfill \\ \end{gathered} \right. \in {\varGamma _{1,2}}。$ (13)

2.2 静力学基础及耦合方式

 ${\boldsymbol{M}}x''+ {\boldsymbol{C}}x'+ {\boldsymbol{K}} x= F(t)。$ (14)

 ${\boldsymbol{K}}x = F。$ (15)

Ansys软件能实现前后处理、分析求解及多场耦合分析一体化，能实现前后处理、分析求解及多场耦合分析统一数据库。利用Ansys软件可以进行结构静力分析（包括线性分析及非线性分析）、结构动力学分析（瞬态动力学分析谐响应分析和随机振动响应分析）等。

3 T型馈电装置电磁场有限元仿真模型 3.1 基于Ansoft Maxwell涡流场的电流密度仿真

 图 2 母线铜板电流密度分布图 Fig. 2 Current density distribution diagram of bus copper plate

 图 3 左侧同轴电缆内芯电流分布云图 Fig. 3 Left coaxial cable core current distribution cloud diagram
3.2 基于Ansys的馈电装置应力场仿真结果及分析

 图 4 同轴电缆内芯应力分布云图 Fig. 4 Stress distribution cloud diagram of coaxial cable inner core

 图 5 母线铜板应力分布云图 Fig. 5 Stress distribution cloud diagram of bus copper plate

 图 6 同轴电缆内芯应变图 Fig. 6 Strain diagram of coaxial cable inner core

 图 7 母线铜板应变图 Fig. 7 Strain diagram of bus copper plate
4 结　语

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