Anchor loss improvement in hemispherical resonators with ion beams

This paper presents a high-precision method for identifying the unbalanced mass of a fused silica hemispherical resonator and an ion-beam trimming process for removing defective masses on the resonator's surface. This method effectively reduces the coupling effect of beam and shell vibrations and significantly improves the anchor loss and damping asymmetry errors. This study effectively addresses the lack of identification methods and trimming processes for the first three harmonics of the unbalanced mass of high-precision hemispherical resonators in current engineering applications. Firstly, the dynamical models of imperfect hemispherical resonators were developed, revealing that the additional inertial force generated by the unbalanced mass in the operating mode is the main reason for the mutual coupling of the shell and the support beams, which further results in the anchor loss and damping asymmetry error. Then, based on the mechanism of the effect of unbalanced mass on the coupling between the shell and the support beam, a simple harmonic excitation signal input along the support beam leads to the distribution of the precession rate of the standing wave in the form of harmonics at different azimuthal angles. This rule of standing wave evolution was employed to develop a method and system for identifying the magnitude and location of unbalanced masses. Finally, based on the identification results, an ion beam trimming process was designed to remove the equivalent defective mass in harmonic form. The experimental results indicate that by trimming the first three harmonic components of the unbalanced mass, the defective mass was reduced by more than 60%, the damping asymmetry error was reduced from 18.48% to 5.46%, and the maximum amplitude of the gyroscope's systematic angular rate drift error has been reduced from 25.02°/h to 6.3°/h, which radically and significantly improves the performance of the resonator.