Critical Parameters and Influence on Dynamic Behaviours of Nonlinear Electrostatic Force in a Micromechanical Vibrating Gyroscope

Abstract

The electrostatic force nonlinearity caused by fringe effects of the microscale comb will affect the dynamic performance of the micromechanical vibrating gyroscopes (MVGs). In order to reveal the influence mechanism, a class of four-degree-of-freedom (4-DOF) electrostatically driven MVG is considered. The influence of DC bias voltage and comb spacing on the nonlinearity of electrostatic force and the dynamic response of the MVG by using multiple time scales method and numerical simulation are discussed. The results indicate that the electrostatic force nonlinearity causes the system to show stiffness softening. The softening characteristics of the electrostatic force cause the offset of the resonance frequency and a decrease in sensitivity. Although the electrostatic nonlinearity has a great influence on the dynamic behaviour, its influence can be avoided by the reasonable design of the comb spacing and DC bias voltage. There exists a critical value for comb spacing and DC bias voltage. In this paper, determining the critical values is demonstrated by nonlinear dynamics analysis. The results can be supported by the finite element analysis and numerical simulation.