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.

微机电系统（MEMS）陀螺仪是一种重要的惯性传感器，用于基于科里奥利效应来识别纺纱结构的参数，例如纺纱速度和角度偏差。本文通过应用完全耦合的非线性模型分析了MEMS振动环陀螺仪的非线性机制，其中考虑了陀螺耦合以及几何和结构上的非线性耦合。通过拉格朗日方程建立了控制驱动运动和感应运动的耦合微分方程。进行了数值仿真，并阐明了驱动模式和传感模式之间的关键非线性成分和能量传递行为。揭示了三次刚度非线性是导致陀螺耦合之外的驱动模式和感测模式之间耦合的另一个重要因素。扰动分析也可以使用多尺度方法进行。获得了驱动器和感应振动的非线性频率-振幅响应，并进行了全面的参数研究。讨论了系统阻尼，激励幅度，驱动幅度和旋转速度对响应的显着影响，这将有助于改善陀螺仪的非线性性能和灵敏度。并进行全面的参数研究。讨论了系统阻尼，激励幅度，驱动幅度和旋转速度对响应的重大影响，这将有助于改善陀螺仪的非线性性能和灵敏度。并进行全面的参数研究。讨论了系统阻尼，激励幅度，驱动幅度和旋转速度对响应的重大影响，这将有助于改善陀螺仪的非线性性能和灵敏度。