Nonlinear electrostatic effects in MEMS ring-based rate sensors under shock excitation

The vibration response of a capacitive ring-based Coriolis Vibrating Gyroscope (CVG) subjected to in-plane shock is modelled and analysed to quantify the effect of shock on angular velocity measurement. The model developed considers a ring resonator with 8 uniformly spaced support legs and describes the in-plane ring response as the sum of the first 3 modes of a perfect ring and the nonlinear electrostatic force as a Taylor series. When a severe in-plane shock is applied, the rigid body response of the ring reduces the electrode gap significantly and a high order expansion is needed to represent the electrostatic force. These nonlinear forces are shown to cause direct and mixed mode coupling to occur, which can significantly modify the response characteristics. Numerical results are presented and interpreted for a range of shock cases to demonstrate the importance of mode coupling, and estimates are made to quantify the angular rate measurement error caused by shock for devices based on 2 theta- and 3 theta-modes of operation. To aid the design of devices that are more resilient to shock, a parameter study is performed to identify the modal frequency ratios that minimise this coupling.