Analysis of the influence of mass defects in hemispherical resonators on quality factors

The hemispherical resonator is the core component of the currently most promising gyroscope - the hemispherical resonator gyroscope (HRG). The mass defects introduced in its processing are a major challenge for ultra-precision optical manufacturing technology. This paper systematically analyzes the influence of the first three harmonic errors of mass defects on the vibration characteristics of hemispherical resonators. Firstly, the vibration model of the support beam of the resonator was established. Then, based on this model, the influence formula of the errors of the first three harmonics on the support loss was derived, revealing that the first three harmonics of the mass defect would lead to significant reduction and non-uniformity in the quality factor (Q-factor) of the resonator. Meanwhile, the correctness of the theoretical formula was verified through finite element simulation. The research provides a theoretical basis for optimizing the manufacturing process of ultra-precision optics and improving the processing quality of resonators, and has important engineering guiding value for breaking through the manufacturing bottleneck of high-precision HRG.