A NONLINEAR DYNAMICS MODEL OF A MICROELECTROMECHANICAL GYROSCOPE

摘要

Microelectromechanical gyroscopes (micro gyros) sense the rotational input to the device by measuring the mechanical deformation on a vibrating structure caused by Coriolis forces. To utilize the magnification factor at mechanical resonances, the frequency of the electrostatic excitation and the natural frequencies of the structure are closely matched. Recently, it has been reported that as the mismatch decreases, the device operation becomes more and more unstable. This paper presents a nonlinear dynamics model of a microelectromechanical vibrating wheel gyroscope to obtain quantitative prediction on the instability related to the mismatch. Under the assumption of small motions, weakly nonlinearity is incorporated into the model. The nonlinear terms introduce coupling between two linearly independent modes, namely the drive mode and the sense mode. The method of averaging is applied to further reduce the coupled equations of motion. In the averaged equations, the periodic motions become fixed points in the amplitude and phase variables. Stability analysis of the fixed points leads to the criterion for the mismatch in terms of the gyro geometric design. Since current micro gyros are designed to maximize the sensitivity by utilizing the mechanical magnification effect at the resonances, the occurence of modal coupling is a very likely event. Our analysis indicates that such occurences can lead to the energy transfer from the drive mode to the sense mode. Consequently, the sensor will give non-zero output even when there is no rotational input to the sensor.