电磁轨道炮瞬态电磁场变步长微分求积法研究

Research on Transient Electromagnetic Field of Electromagnetic Rail Gun with Variable Step-size Differential Quadrature Method

摘要

瞬态电磁场数值模拟是电磁轨道炮发射动力学研究的热点问题。为了提升电磁轨道炮发射动力学仿真速度,针对电磁轨道炮发射过程瞬态电磁场快速计算问题,采用有限元和边界元耦合方法,建立了三维瞬态电磁场微分方程,利用高阶微分求积时间积分法对该微分方程在时间域上离散,提出基于圆频率的微分求积变步长策略,形成了有限元边界元-变步长微分求积时间积分瞬态电磁场分析方法。针对经典三维瞬态电磁场时空演化问题,对比定步长、变步长微分求积时间积分法和欧拉向后差分法计算结果,发现变步长微分求积时间积分法具有更高的计算效率和计算精度。将提出的方法和形成的计算模型用于电磁轨道炮发射过程瞬态电磁场分析,得到了轨道炮电枢的速度、位移以及轨道和电枢的电流密度分布、磁感应强度分布,并与LS-DYNA计算结果进行对比,验证了计算模型的有效性。有限元边界元-变步长微分求积时间积分瞬态电磁场分析方法为电磁轨道炮发射动力学分析提供了高效求解策略。

Abstract

Numerical simulation of transient electromagnetic fields is a hot issue in the study of launch dynamics of electromagnetic rail guns. In order to improve the simulation speed of electromagnetic rail gun launching dynamics, for the problem of fast calculation of transient electromagnetic field during the launching process of electromagnetic rail gun, the coupled method of finite element and boundary element was adopted to establish the three-dimensional transient electromagnetic field differential-equation. The higher-order differential product time integration method was used to discretise the differential equation in the time domain, and the variable step-size strategy of the circular-frequency-based differential product was put forward, forming the method of finite-element-boundary-element-variable step-size differential product time integration transient electromagnetic field analysis. For the classical three-dimensional transient electromagnetic field spatio-temporal evolution problem, comparisons of the calculation results among fixed-step-length, variable-step-length differential product discrete-time method and Euler backward-difference method reveal that the variable-step-length differential product discrete-time method has a higher computational efficiency and computational accuracy. The proposed method and the formed computational model were used for the transient electromagnetic field analysis of the launching process of the electromagnetic rail gun. The velocity and displacement of the rail gun armature, as well as the current density distribution of the track and armature, and the magnetic field strength distribution were obtained. The validity of the computational model was verified by comparing the results with that obtained from LS-DYNA. The finite element boundary element-variable step size differential product time-integrated transient electromagnetic field analysis method provides an efficient solution strategy for the analysis of electromagnetic rail gun launch dynamics.

关键词

电磁轨道炮 / 瞬态电磁场 / 发射动力学 / 变步长微分求积法

Key words

electromagnetic rail gun / transient electromagnetic field / launch dynamics / variable step-size differential quadrature method

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基金资助

国家自然科学基金(92266201)