Nonlinear Dynamics of an Oscillating Electromechanical System Based on Coil Gun Principle: Theory and Experiment

Abstract

The nonlinear dynamics of a modified coil gun system are studied theoretically and experimentally in this work. The system is modified through the addition of a spring holding the moving mass. The mathematical equations of the system are derived using the Hopkinson, Kirchhoff, and Newton laws leading to nonlinear terms due to the variation of the electrical inductance. The analytical calculations using the harmonic balance method are carried out when the system is supplied with a sinusoidal voltage source. The obtained coupled electromechanical equations of motion are integrated numerically, and the comparisons between numerical results and analytical predictions are presented. Considering the equilibrium distance between the movable metal and the stator, the frequency and the magnitude of the excitation voltage (sinusoidal or square) as the control parameters, the two-parameter bifurcation diagrams are plotted showing the different dynamical states of the system. Amplitude jumps, hysteresis, and multistability are also observed. In the experimental part, both the sinusoidal and square voltage generators are used to provide the required current in the solenoid. Good agreements are found between the theoretical and experimental results.