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

We present a new mathematical model for vibrating ring gyroscope (VRG) in the presence of imperfections, namely, structural defects and material anisotropy. As novelty, we calculate mode shapes internal suspension structure to enable more accurate modular analysis VRG’s mass stiffness distributions. Solving associated eigenvalue problem shows that imperfections result frequency split between gyroscope’s operating shapes, rotating their orientation with respect nominal drive sense axes. then use perturbation solve equations motion analyze quadrature error arises from frequency/damping mismatch shapes. our detail various effects etching-related undercuts, uncertainties, Young’s modulus anisotropy–in form suitable space-dependent functions–on first time. The results reveal rings are robust against imperfection, while straight beams used system most likely responsible error. For example, 50 nm (0.5%) width variation beam connects an anchored leads 4700°/s To validate modeling, using experimental data fabricated 59 kHz VRG, provide rigorous, comparative simulations finite element method (FEM). [2022-0035]