Theoretical thermoelastic damping for micro ring gyroscopes by wave propagation

The microelectromechanical system (MEMS) vibrating ring gyroscope (VRG) holds significant promise for angle sensing applications, with its performance highly reliant on the thermoelastic damping (TED) of the resonating structure. However, the existing TED models struggle to accommodate the complex topology of VRGs. In this study, the wave propagation method is introduced to establish a theoretical TED model for in-plane motion VRGs. The modeling entails a comprehensive analysis of the thermoelastic coupling within the VRG structure, considering the displacement and the coupled temperature field. Treating VRG as a cyclic symmetric structure, the displacement and temperature fields within the minimum repetitive sector can be analyzed first and then extrapolated to the entire structure. The mode shape, natural frequency and temperature variation of the VRG are determined using the wave propagation method. Finally, The TED expression is obtained based on its energy definition. Comparisons with FEM and experimental results demonstrate the high accuracy, computational efficiency and versatility of the present TED model. Parametric analysis reveals that TED in VRGs is determined collectively by the TED of their substructures, with the influence weights depending on their respective strain energy proportions. Specifically, increasing the length and decreasing the width of the substructure, or scaling down the overall size can effectively reduce TED in most cases. VRGs with a larger width are not recommended due to their high TED value and complex TED behavior. Additionally, VRG's TED is predicted to increase rapidly with rising ambient temperature due to the temperature dependence of material properties. This study presents an efficient TED modeling method for complex ring-beam combined structures and offers practical guidelines for designing high Q-factor VRGs.