Quality factor variation measured in a monolithic fused silica cylindrical resonator

Cylindrical resonators are commonly used in Coriolis vibratory gyroscopes, which measure angular velocity through the precession of solid wave. Quality factor and its homogeneity are critical indicators of the resonator characteristics. In this paper, we report that the Q factor varies regularly around the resonator's axis of symmetry. We measured the resonator Q factor by the amplitude frequency response (AFR) using a non-contact method with an acoustic source for excitation and a laser Doppler vibrometer (LDV) for detection. By analyzing experimental results, we concluded that measuring Q factor at antinode can be a convenient and relatively accurate method for Q factor studies. However, one needs to be careful that the measurement point should be near the vibration antinode, otherwise the results may contain huge errors. We then built a theoretical model based on the two degree-of-freedom mass-spring system to analyze the Q variation behavior. The experimental results were consistent with the theoretical calculation. By comparing experimental results with numerical calculations, we showed that the circumferentially Q variation is due to the complex combined effect of frequency mismatch, Q factor mismatch, and the angle between excitation direction and the principle frequency axes (Qk) and the principle damping axes (Qc). We believed it is possible to combine the scan measurement of LDV with proposed model to determine the Q mismatch and direction of the damping axes without labor-consuming procedures, and therefore the proposed method can be developed for pre-screening of resonators for high-performance cylindrical resonator gyroscopes.