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

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.

A Review of MEMS Vibrating Gyroscopes and Their Reliability Issues in Harsh Environments

“…Many other factors contribute to the mismatch between the driving and sensing resonant modes. The shortcomings in microfabrication technologies generally affect the material characteristics and geometry [ 18 , 19 ]. The various deposition and etching processes affect the thicknesses and widths of the MEMS structures.…”

Modeling and Analysis of a MEMS Vibrating Ring Gyroscope Subject to Imperfections

“…In [11], the frequency split and change in mode shapes' orientation were investigated for a VRG whose ring is subject to width variations. Ma et al [20] also investigated the same effects for a varying width profile with a uniform sidewall angle.…”

“…Applying the Ritz method, we then solve an optimization problem to find the coefficients of the basis functions and obtain the mode shapes of the whole structure. This step distinguishes our approach from the common method in the VRG literature where massless springs model the ring-suspension interaction [17], [20]; this approach provides more insight into the different components' contributions to the overall mass, Coriolis mass, and stiffness. 2) Using the calculated mode shapes, we parameterize the kinetic and potential energies of the VRG in terms of the generalized coordinates.…”