Thermoelastic Damping in Micro-Electro-Mechanical Systems Gyroscopes with a Double-Ring Structure

The Quality factor (Q) represents energy losses in a resonant system and is a key parameter that determines the ultimate resolution of micro-electro-mechanical systems (MEMS) gyroscopes. Since Q is inversely proportional to damping, lower damping yields higher Q. Among various damping types, thermoelastic damping (TED) is the dominant energy-loss mechanism in vacuum-packaged MEMS gyroscopes. Accurate prediction of thermoelastic Q requires solving coupled thermal and mechanical equations. While analytical TED models have been developed for simple beams and rings, no analytical solution currently exists for rings incorporating a complex internal suspension. This work proposes an energy-based analytical TED modeling approach that accurately predicts the Q of a silicon capacitive MEMS ring gyroscope over temperature. The method determines the overall Q by first calculating the thermoelastic losses of individual components and then combining these losses based on their respective stiffness contributions. The analytical calculations closely match the experimental measurements with errors <4%, validating the model's efficiency. Furthermore, the model quantifies the contribution of each structural element to the overall Q and provides physical insight into the observed temperature dependence across different operating regimes.