Nonlinear Performance of MEMS Vibratory Ring Gyroscope
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ISSN 1860-2134
Nonlinear Performance of MEMS Vibratory Ring Gyroscope Feng Liang1
Dong-Dong Liang2
Ying-Jing Qian2
1
( College of Mechanical Engineering, Yangzhou University, Yangzhou 225127, China) (2 Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering, College of Mechanical Engineering and Applied Electronics, Beijing University of Technology, Beijing 100124, China)
Received 25 May 2020; revision received 16 September 2020; Accepted 18 September 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020
ABSTRACT 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.
KEY WORDS MEMS vibratory ring gyroscope, Nonlinear performance, Drive mode, Sense mode, Method of multiple scales
1. Introduction Gyroscopes, also called angular-rate sensors, are a sort of devices for measuring the spinning speed and angular deviation of spinning structures. As an indispensable component for modern guidance, location and motion control, gyroscopes have been extensively applied in the fields of aerospace, navigation, national defense and civil electronics. In terms of different measuring mechanisms, gyroscopes can be classified as conventional mechanical gyroscopes, vibratory gyroscopes and optical gyroscopes. Conventional mechanical gyroscopes utilize conservation of angular momentum and take momentum wheels to sense the spinning motion, which often leads to a complex structure and susceptible precision of measurement. Based on the Coriolis effect, vibratory gyroscopes adopt vibrating masses instead of momentum wheels as the sense components, which dramatically simplifies the internal structure, and in the meantime enhances the stability and reliability of the gyroscope. Optical gyroscopes, such as the
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