Multi-Damping Mechanism Analysis and Quality Factor Optimization of Micromachined Disk Resonator Gyroscopes

A high quality factor, denoted as the Q-factor, is crucial for micromachined disk resonator gyroscopes, commonly referred to as DRGs, to suppress thermomechanical noise and improve bias stability. However, the coupled energy dissipation mechanisms under low-pressure conditions impose significant limitations on further Q-factor enhancement. This paper establishes a rigorous multiphysics damping analysis framework for DRGs and quantitatively investigates the contributions of air damping, thermoelastic damping, and anchor loss. A free-molecular squeeze-film damping model is derived based on kinetic gas theory and molecular energy transfer mechanisms, avoiding the continuous fluid assumption of the classical Reynolds equation, which fails in low-pressure regimes. Due to the highly symmetric ring structure and central anchor design, finite element method simulations reveal an extremely high anchor-loss-limited quality factor, Q_anchor, of approximately 1.85 × 10¹², indicating negligible anchor-induced dissipation. Under an operating pressure of 0.1 Pa, air damping is validated as the absolute dominant energy dissipation mechanism with a gas quality factor, Q_air, of approximately 1.105 × 10⁵, which is significantly lower than the thermoelastic damping quality factor, Q_TED, evaluated at 8.98 × 10⁵. To break the classical trade-off between squeeze-film damping suppression and capacitive drive efficiency, a decoupled gap optimization strategy is proposed. By maintaining the drive electrode gap, gap_e, at 7.2 µm while increasing only the parasitic ring-to-suspended-mass gap, gap_m, to 12 µm, the squeeze-film-damping-limited Q-factor is improved by approximately 25% to 1.381 × 10⁵ without degrading electromechanical coupling efficiency. In addition, the optimal anchor radius is determined to be approximately 160 µm. The proposed framework provides practical design guidance for high-Q DRGs and other MEMS resonant inertial sensors.