Investigation of cylindrical resonators’ damping asymmetry via analyzing Q factor circumferential distribution

Abstract

High quality cylindrical resonators are extremely important to guarantee the performance of cylindrical vibratory gyroscope. Cylindrical resonators’ damping asymmetry is one of the major sources which result in the gyroscope's drift. In this paper, the method of evaluating damping asymmetry based on the Q factors of the damping axes is proposed. The dynamic model of cylindrical resonators is established to analyze the Q factor's variation under the effect of mode superposition. The weakness of measuring Q factors by amplitude-frequency response analysis is figured out. Theoretical calculation analysis based on amplitude-frequency response is also carried out to investigate the laws of Q factor circumferential distribution in detail. Theoretical results show that the Q factor circumferential distribution is influenced by the frequency difference, Q factor difference and the angle difference between damping axes and frequency axes. Furthermore, the Q factors of the damping axes can be obtained from the Q factor circumferential distribution under certain conditions when the frequency difference is relatively large. The Q factor circumferential distribution will be almost the same to the real Q factor distribution of the cylindrical resonator when the frequency difference is small enough. Furthermore, the Q factors and locations of the damping axes are able to be acquired more easily. Experiments of amplitude-frequency response analysis are also set up to validate the theoretical analysis results, from which damping asymmetry and damping axes of the cylindrical resonator can be identified.