Simulation Analysis of How Scratches Influence Frequency Splitting and Energy Dissipation of Hemispherical Resonator

Abstract The fused quartz hemispherical resonator is the core component of the hemispherical resonator gyroscope. It features a complex shape and is Made from a Material that is difficult to process. Scratches are easily introduced during grinding, potentially degrading the mass-stiffness-damping symmetry; however, the underlying mechanisms of this influence have not been fully understood. This paper aims to investigate the effects of scratch defects on the frequency splitting and quality factor of the hemispherical resonator. First, finite element models of the hemispherical resonator with scratches are established. Then, the effects of the mass-stiffness factor, as well as the latitude and length of the scratches, on frequency splitting are analyzed. Furthermore, the impacts of latitude, length, and the first four harmonics of the unbalanced mass caused by scratches on thermoelastic damping and anchor loss are examined. Simulation results indicate that scratches above 55° latitude cause frequency splitting solely due to stiffness changes. Frequency splitting caused by scratches of the same size on the inherent rigidity shaft at the rim is approximately 50% of that near the transition fillet. Frequency splitting varies linearly with the volume of material removed by scratches. Scratches have little effect on thermoelastic damping. The first three harmonics of the unbalanced mass due to scratches at the rim are the primary contributors to anchor loss. Finally, focused ion beam trimming experiments are conducted at different locations on the hemispherical resonator. The trends observed in the experimental results are consistent with the simulation results. This work provides guidance for evaluating the impact of scratches on the performance of hemispherical resonators and for developing appropriate trimming processes.