The nonlinear electromagnetic force can change the critical velocity of the projectile for a railgun. It corresponds to the resonance state in railgun. Here, the nonlinear electromechanical coupled dynamics equations for the railgun are proposed. Based on it, the equation of the nonlinear critical velocity of the projectile is given and the effects of the electromagnetic nonlinearity on the critical velocity of the projectile are investigated. Besides it, the effects of the fire velocity on the nonlinear critical velocity are studied as well. Results show that the critical velocity of the railgun system increases when the electromagnetic nonlinearity is considered, and the nonlinear critical velocity is influenced by the system parameters such as rail current, rail thickness, rail distance, etc. A FEM analysis package, ANSYS, is used to simulate dynamics performance of the railgun system and illustrate the analytical results about critical velocities of the railgun system. The results can be used to design dynamics performance of the railgun system
