Fused-Silica Micro Birdbath Resonator Gyroscope ( $\mu$ -BRG)

We present a 3-D fused-silica micro-scale shell gyroscope, called the birdbath resonator gyroscope (BRG). The BRGs axisymmetric geometry leads to a good frequency and Q symmetry. The birdbath resonator can be fabricated with a good structural symmetry because its anchor is self-aligned to the rest of the structure. The BRG has n=2 wine-glass modes at 10.5 kHz and has a large frequency separation between the n=2 wine-glass modes and the closest parasitic mode (|fparasitic-fn=2|/fn=2=0.3), which will potentially lead to a low vibration sensitivity. The equations of motion for 3-D shell gyroscopes are derived and the effective mass and angular gain of the BRG is estimated using finite element method (FEM). The BRG is fabricated using a 3-D micrometer-blow-torching process and assembly on an electrode substrate made with the silicon-on-glass process. The BRG is operated in the force-rebalance mode at vacuum at room temperature and has a scale factor of 27.9 mV/(deg/s), a full-scale range , an angle random walk of 0.106 deg/√h, and a bias stability of 1 deg/h. A large angular gain (0.317) is measured, which is close to the estimated value of 0.25 obtained via FEM.