High Precision Mass Balancing Method for the Fourth Harmonic of Mass Defect of Fused Quartz Hemispherical Resonator Based on Ion Beam Etching Process

In this article, a novel ultrahigh precision mass balancing method for fused quartz hemispherical resonator based on the ion beam etching process is proposed from the perspective of vibration mechanics. First, the motion equations of resonator with mass defect are established to reveal the quantitative relationship between the amplitude of defective mass and frequency split, and the geometrical relationship between the distribution of defective mass and eigenfrequency axis, which is the equivalent morphology of mass defect. Second, according to the motion equations, the radial vibration model of resonator lip edge is deduced, then a new identification model for the vibration parameters composed of the frequency split, mechanical time constant, and azimuth of eigenfrequency axis based on the vibration envelope and spectral analysis is established. The vibration parameters are identified by nonlinear optimization method. After that, the mass removal function and etching efficiency function of ion beam acting on the resonator are calibrated by experimental data, then the etching trajectory is planned and the etching time is calculated. Finally, the experimental result of mass balancing indicates that the frequency split is reduced from 0.2354 to 0.0006 Hz, and the quality factor is greater than 2.2 × 10 ⁷ , which can significantly improve the vibration performance of resonator.