Thermo-elastic damping and anchor loss in the operational modes of a hemispherical shell resonator

The hemispherical resonator gyro (HRG) is a type of precision inertial sensor that has the advantages of direct angle measurement and unlimited dynamic range. The overall accuracy of the HRG is due to the quality of its resonator shell, and improving the performance of resonators requires a proper understanding of the processes of energy damping in each resonance cycle, which has a significant impact on sensor performance. In this paper, in order to investigate the losses in the hemisphere shell resonator, first, the equations governing the shell are studied, and three-dimensional modeling is performed in COMSOL software. By performing mechanical simulations, the resonance modes and the natural frequency of the shell are investigated, and finally, the second and third resonance modes are selected as the optimal operating mode of the gyroscope. Also, by performing thermal simulations, the dominant energy damping processes, such as thermo-elastic damping and anchor loss were analyzed and simulated, and the effect of shell material on damping was investigated. Then the quality factor of the resonator was evaluated based on its geometry and material. In this way, according to the scope of work of the gyroscope, this process can be used to design the specifications of the shell to achieve a resonator with the desired quality factor.