Electromechanical Coupled Nonlinear Dynamics Of Electromagnetic Rail Launch System

Electromagnetic rail launch system is an advanced electromagnetic catapult device. It has many advantages such as high speed, high accuracy, long range, great power, small volume, light weight, low operating and maintenance costs, etc. However, there are nonlinear coupled vibrations under the combined effect of mechanical and electromagnetic forces during launching, which affect dynamic performance and launching precision of the railgun system. Therefore, The electromechanical coupled nonlinear dynamics of the electromagnetic rail launch system should be studied. In this paper, the dynamic model of the electromagnetic rail launch system is established. nonlinear free vibration, nonlinear forced vibration and parametric vibration of the electromechanical rail are researched. This thesis includes the following:The calculation formula of the electromagnetic force acting on rail is deduced. According to the change of the electromagnetic force along with the system parameters, the regression formula of electromagnetic force is obtained. Moreover, The coupled oscillation of electric system for electromagnetic railgun is analyzed. The results show that a small voltage fluctuation of the electric system in the railgun can cause a large dynamic magnetic force on the rails under some conditions.Electromechanical coupled dynamic model of the electromagnetic rail is established. Approximative analytic solutions and vibration frequency equations of nonlinear vibration for electromagnetic rail launching system are achieved by L-P method. Changes of the natural frequency of the nonlinear system along with the related parameters are analyzed. The results show that in order to meet the precision requirements, the dynamic electromagnetic force caused by displacement change should be taken to the third order nonlinear terms in Taylor expansion.The dynamic equations of the electromagnetic rail launch system under the current and speed excitations are established respectively. The differential equations for the forced responses of electromagnetic rail are solved by small parameter method. The dynamic responses of the system when excitation frequency is far from or near to natural frequency are studied. The influence of critical velocity is discussed. Forced vibration characteristics of electromagnetic rail launch system is analyzed. The results show that electromagnetic nonlinearity should be considered for a large rail current, a small distance between the two rails, small rail height, small rail width and a small stiffness of the elastic foundation.The differential equation for the parametric vibration of the electromagnetic rail launching system under the rail stiffness fluctuation is established. Based on stability diagram of the parametric vibration, the influence of the system parameters on the stability of electromagnetic rail launch system is discussed. Dynamic response characteristics of electromagnetic rail launch system under different steady states and excitation frequencies are studied.The dynamic response of the weak nonlinear vibration of electromagnetic rail launch system is simulated by R-K method. The proper range of the theory analysis is determined by comparing the numerical and analytical solutions. The validity of the theory analysis is proved.