Investigation on Influence of Geometric Error and Structure on Vibrational Characteristics of Hemispherical Resonator

The fused silica hemispherical resonator is the core component of hemispherical resonator gyroscopes. The vibrational characteristic of hemispherical resonator is a critical parameter, which affects the performance of hemispherical resonator gyroscopes. Recently, the quality factor of fused silica hemispherical resonator has exceeded 25 million due to optimizing the resonant structure, manufacturing processes and post-processing technology. At present, the quality factors of most fused silica hemispherical resonator have met the application requirements of high precision gyroscopes. It is urgent to study the frequency splitting, quality factor nonuniformity and anti-vibration performance of hemispherical resonator. In this paper, the influence of geometric error and structure on vibrational characteristics of hemispherical resonator is investigated. The vibrational characteristics of three hemispherical resonators with different structures are simulated. The influence of the first eight harmonic errors on the frequency splitting and quality factor nonuniformity of the resonator is investigated. Anchor loss and thermoelastic dissipation models are used to study the quality factor nonuniformity. The simulation results illustrate that the quality factor nonuniformity is primarily affected by the fourth and the second harmonic errors, and the frequency splitting is affected by the fourth harmonic error. Besides, the anti-vibration performance and thermal equilibrium time of resonators with different structures is studied by simulation. The simulation results illustrate that the resonator with thicker bottom brings a longer thermal equilibrium time after starting vibration and better anti-vibration performance.