Defects identification and mass trimming in hemispherical resonators

Hemispherical resonator gyroscopes possess exceptional performance characteristics, yet their effectiveness is often hampered by mass defects resulting from manufacturing process. This study introduces a novel methodology for identifying and trimming mass defects, particularly focusing on the first three harmonics of density in the hemispherical resonator. Firstly, through dynamic analysis, the error mechanism of mass defects in the hemispherical shell affecting the support rod is elucidated. The hemispherical shell induces inertial forces and moments on the support rod, the effects of which can be characterized through harmonic analysis of the density. Specifically, the first and third harmonic components of the density excite transverse forced vibration in the support rod, while the second harmonic component induces longitudinal forced vibration. Then, an innovative identification strategy capitalizing on the steady-state velocity response of the support rod is proposed and validated through finite element simulations, showing good consistency between identified and predefined defect parameters. Finally, based on ion beam trimming technology, a systematic experiment is designed to eliminate mass defects by two equivalent rings. Multiple iterations of mass trimming led to a reduction of over 70 % in defect parameters for the first harmonic and approximately 70 % for the third harmonic. The velocity amplitudes of the support rod in the x and y directions are reduced by 69.41 % and 72.55 %, respectively. Furthermore, this process significantly enhances the quality factor and its circumferential uniformity of the hemispherical resonator. This study lays a foundation for the advancement of high-precision hemispherical resonator gyroscope manufacturing.