Nonlinear dynamics of MEMS turning fork gyroscope

Abstract

Accuracy improvement of MEMS gyros requires not only microelectronic development but also the investigations of the mathematical model of sensitive element dynamics. In the present paper, we study the errors of the vibrating microgyroscope which arise because of nonlinear dynamics of a sensitive element. A MEMS tuning fork gyroscope with elastic rods is considered. Nonlinear differential equations of bending vibrations of sensitive element on the moving basis are derived. Free nonlinear vibrations of gyroscopes as the flexible rod are studied. Nonlinear dynamics of gyroscope on the moving basis are investigated by asymptotic two scales method. Sensitive element frequencies split on two frequencies resulted from slowly changing angular velocity are taken into account in the equations of zero approximation. The differential equations for slowly changing amplitudes and phases of two normal waves of the oscillations measured by capacitor gauges and an electronic contour of the device are obtained from the equations of the first approximation.