Modeling, Identifying, and Ultrahigh-Precision Trimming of Mass Imperfection in Hemispherical Resonator

The measurement performance of the hemispherical resonator gyroscope (HRG) is fundamentally determined by the structural symmetry of its hemispherical resonator. However, mass imperfection inevitably introduced during fabrication degrades this symmetry, which breaks the frequency degeneracy and leads to standing wave drift, thereby degrading the HRG measurement accuracy. This article presents the modeling of the resonator with mass imperfection, identifies this imperfection, and proposes a novel ultrahigh-precision trimming method for its elimination. First, a dynamic model of the resonator is established using the variable density method and the thin shell theory. Based on this model, the polar decomposition method is employed to derive the frequency split and the stiffness axis angle, thereby elucidating the influence mechanism of the mass imperfection. Then, a noncontact measurement system based on a laser vibrometer is developed. It identifies mass imperfection through envelope analysis of the measured vibration signals. Finally, a mass trimming system is designed using ion beam etching technology and the innovative “harmonic-then-point” trimming method is proposed to eliminate this imperfection. It achieves ultrahigh-precision mass trimming, suppressing the frequency split of the resonator to the submillihertz level while optimally balancing efficiency and precision. Experimental results show that after six iterative trimming cycles, the frequency split is reduced from an initial 0.09857–0.00023 Hz and a reduction of 99.76 %. This achievement validates the accuracy and effectiveness of the proposed theoretical model and trimming method.