High-Precision Identification and Balance Method for the First-to-Third Harmonics of Mass Defects of Fused Quartz Hemispherical Resonator

In the article, the ultrahigh-precision identification and balance method for the first-to-third harmonics of mass defects of the hemispherical resonator are proposed. First, the mechanical analysis model of the hemispherical shell acting on the supporting stem is established, and the energy transfer mechanism from the hemispherical shell to the supporting stem is revealed. According to the theoretical analysis, the identification model and test method for the amplitude and azimuth of the first-to-third harmonics of mass defects based on the coupled vibration of the supporting stem are proposed, respectively. Second, the optical testing system is implemented for measuring the mass imperfection and damping anisotropy, which includes the amplitude-phase control system of the hemispherical shell with PXI platform as the core and the weak vibration signal extraction system of the supporting stem with the lock-in amplifier as a core. After that, the important etching process parameters are optimized based on the vibration energy function of the resonator and mass removal function of the ion beam for improving the efficiency and accuracy of the mass balance, and the etching path and time series of the ion beam are planned by the identification result of mass defects and calibration result of the etching efficiency. Finally, the mass balancing results indicate that the first-to-third harmonics of mass defects are reduced by 95.85%, 89.52%, and 81.69%. Correspondingly, the average of the quality factor is increased from 1.6616 × 10⁷ to 1.8364 × 10⁷ , the split of the quality factor is reduced from 3.9152 × 10⁶ to 9.7717 × 10⁴ , and the nonuniformity of the quality factor is decreased from 23.56% to 0.53%, which can significantly improve the vibration performance of the resonator.