Identifying vibration characteristics of hemispherical resonators with mass defects

Abstract

The hemispherical resonant gyroscope (HRG) has become a key component of inertial navigation systems. Existing studies primarily focus on the effects of the first three harmonic components of non-uniform mass distribution defects in the hemispherical resonator. However, the mechanisms by which such defects alter the resonator’s vibration characteristics remain insufficiently characterized and lack robust experimental verification, undermining the accuracy and efficiency of repair and adjustment processes. This study presents a novel analytical framework, which derives multi-order coupled vibration equations for hemispherical resonators with mass defects and develops a comprehensive model to characterize their vibrational behavior. Additionally, a simple yet effective method for identifying mass defects is proposed. For the first time, triangulation consistency among the theoretical model, experimental results, and identification methodology is demonstrated. The proposed characterization model significantly enhances the accuracy of vibration analysis and reveals distinct variations in the quality factor and damping axis orientation due to mass non-uniformity. These findings provide new insights into the coupled vibration dynamics of hemispherical resonators and establish a validated theoretical basis for high-precision and efficient mass trimming techniques, offering valuable guidance for the performance optimization of next-generation navigation systems and other applications requiring precise vibration control.