Modeling and approximate analytical solution of nonlinear behaviors for a self-excited electrostatic actuator

Analytical modeling and solution of nonlinear vibration behaviors are vitally important for the optimization of vibratory actuators. In this paper, the nonlinear vibration characteristics of a self-excited electrostatic actuator are investigated. The actuator consists of two plate electrodes and a metal cantilever, which is fixed on an isolated insulating base and placed in the middle of the electrodes. When a DC voltage is applied to the electrodes, the cantilever is excited into reciprocating vibration autonomously and collides with the electrodes with strongly nonlinear features. During modeling, the collision is considered as a transient process and only the velocities of the cantilever before and after the collisions are concerned. By using the phase plane method, the limit cycle and boundary conditions of the self-excited oscillation of the cantilever are obtained and the strongly nonlinear problem of the entire system is converted into a weakly nonlinear problem of the cantilever moving between the electrodes. The nonlinear equations are then solved by using the averaging method, and the approximate analytical results demonstrate good consistency with the numerical and experimental results. Besides, the approximate analytical results are also adopted in the optimization of the actuator for enhanced power density and efficiency. The modeling and solution methods provide a framework for further optimization of the electrostatic actuator in the application field of centimeter-scale robotics.