Effects of Structural Dimension Variation on the Vibration of MEMS Ring-Based Gyroscopes.

Zhipeng Ma,Zhonghe Jin,Xiaojun Jin,Xiaoli Chen,Xudong Zheng,Yiming Jin

doi:10.3390/mi12121483

Abstract

This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of Young’s modulus was developed via Lagrange’s equations for simulating the dynamical behavior of an imperfect ring-based gyroscope. The dynamical analyses are focused on the effects on the frequency split between two vibration modes of interest as well as the rotation of the principal axis of the 2θ mode pair, leading to modal coupling and the degradation of gyroscopic sensitivity. While both anisotropic Young’s modulus and nonideal deep trench verticality affect the frequency difference between two vibration modes, they have little contribution to deflecting the principal axis of the 2θ mode pair. However, the 4θ variations in the width of both the ring and the supporting beams cause modal coupling to occur and the degenerate 2θ mode pair to split in frequency. To aid the optimal design of MEMS ring-based gyroscopic sensors that has relatively high robustness to fabrication tolerance, a geometrical compensation based on the developed model is demonstrated to identify the geometries of the ring and the suspension.

Highlights

IntroductionDegenerate modes of vibratory axisymmetric ring-based structures are exploited to measure the angular rate through Coriolis coupling
Ring-based gyroscopic sensors based on micro-electro-mechanical-system (MEMS)technology become increasingly attractive because of their high-quality factor (Q factor) and insensitivity to environmental excitation as a result of inherently symmetric structures [1,2,3].Degenerate modes of vibratory axisymmetric ring-based structures are exploited to measure the angular rate through Coriolis coupling
The estimated frequency split between two vibration modes is around 593 Hz for the ring-based gyroscope, which is in good agreement with the measured frequency split of about 625 Hz (σ = 18 Hz)

Summary

Introduction

Degenerate modes of vibratory axisymmetric ring-based structures are exploited to measure the angular rate through Coriolis coupling. For a ring-based angular-rate gyroscope, one of the degenerate modes is excited with controlled amplitude and frequency, while the Coriolis force-induced vibration of the other mode is utilized to measure the angular-rate input through capacitive sensing. The ring-based gyroscopes fabricated with isotropic materials, such as polysilicon, (111) SCS, and fused silica, are advantageous to realize mode-matching between two degenerate modes. The ring-based gyroscopes of isotropic materials require a more complicated and precise fabrication process than those fabricated with (100) SCS. The ring-based gyroscopes fabricated with (100) SCS frequently suffer from a large initial frequency split and modal coupling arising from the anisotropic Young’s modulus and the fabrication imperfections. In order to improve the dynamic performance of the imperfect ring-based

Methods

Results

Conclusion