Nonlinear Performance of MEMS Vibratory Ring Gyroscope

Micro-electro-mechanical system (MEMS) gyroscopes are an important sort of inertial sensor for identifying parameters of spinning structures, such as the spinning speed and angular deviation, based on the Coriolis effect. In this paper, the nonlinear mechanism of MEMS vibratory ring gyroscopes is analyzed by applying a fully coupled nonlinear model, in which the gyroscopic coupling and geometrically and structurally nonlinear couplings are all taken into account. The coupled differential equations governing the drive and sense motions are established via the Lagrangian equations. Numerical simulation is conducted, and the key nonlinear components and energy transfer behaviors between the drive and sense modes are elucidated. It is revealed that the cubic rigidity nonlinearity is another significant factor leading to the coupling between the drive and sense modes other than the gyroscopic coupling. Perturbation analysis is also carried out by using the method of multiple scales. The nonlinear frequency-amplitude responses of the drive and sense vibrations are obtained, and comprehensive parametric studies are performed. The significant effects of system damping, excitation amplitude, drive amplitude and spinning speed on the responses are discussed, which will facilitate to improve the nonlinear performance and sensitivity of the gyroscope.