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

Conference Name: 2021 21st International Conference on Solid-State Sensors, Actuators and Microsystems (Transducers) Date of Conference: 20-24 June 2021 Structural imperfections affect the performance of MEMS vibrating ring gyroscopes (VRGs), dominantly in terms of quadrature error and frequency split. We consider a VRG with a ring subjected to width nonuniformity and supported by an imperfect suspension. This reflects the scenario of nonuniform etching, common in microfabrication processes. We show that the ring's width nonuniformity mainly results in a rotation of the mode-shapes with respect to those of a perfect ring while an imperfect suspension induces frequency split between the modes. On this basis, we calculate the quadrature error in the gyroscope's output. As an example, a 4° mode-shape rotation and 15Hz frequency split in a 60kHz VRG generate an approximate quadrature error of 1000°/s.