Trimming of the unbalanced mass in resonators with ion beams

The eccentric mass defects generated during the machining process of the fused quartz hemispherical shell resonator are the primary factors that degrade the performance of the hemispherical resonator gyroscope. Accurate identification and trimming of the eccentric mass in the resonator are key processes for improving the performance of high-precision gyroscopes. This paper proposed an innovative approach for identifying and trimming the first three harmonics of eccentric mass in resonators. The proposed technique demonstrates high precision in detection, identification efficiency, straightforward implementation, and strong applicability in practical engineering scenarios. Firstly, a model was developed to elucidate that the additional inertial forces and torques generated by the eccentric mass in the operating mode of the resonator lead to parasitic vibration modes and anchor loss, which in turn affect the performance of the gyroscope. Then, based on the mechanism by which the eccentric mass in the resonator causes standing waves to generate additional angular rates under parametric excitation of harmonic forms, an innovative identification approach was proposed. This approach identifies the magnitude and location of the equivalent eccentric mass by demodulating and analyzing the angular rates of standing wave at different azimuth angles. Finally, based on the identification results, a 6-DOF identification system and an ion beam trimming process were developed to remove the first three harmonics of the equivalent unbalanced mass from two pre-selected circular rings. After several iterations, the magnitudes of the 1st, 2nd, and 3rd harmonics of the unbalanced mass decreased by more than 70%, 10%, and 36%, respectively. Additionally, the damping asymmetry error of the gyroscope improved by about 8.6 times. The experimental results demonstrate the effectiveness of the unbalanced mass identification method and the ion beam balancing technique proposed in this paper.