Approximation method for frequency split calculation of coriolis vibrating gyroscope resonator

Abstract

One of the main characteristics influencing the accuracy of Coriolis Vibrating Gyroscopes (CVG) is the frequency split caused by various manufacturing defects. It is well known that in most cases, the largest part of the frequency split is determined by the circumferential harmonic of a defect with the number k=2n (where n is a circumferential wave number). Also, frequency split is strongly influenced by the meridional distribution of the kth defect harmonic because the resonator shell has both the circumferential and meridional directions. Meridional defects of different distribution can appear because of manufacturing inaccuracies and because of different balancing methods. This paper presents a new simple, fast and accurate frequency split calculation technique for various meridional defect functions. The frequency split can be calculated as a linear function of a defect’s meridional ordinates (as a simple dot product of two vectors). The proposed approach is based on the linearity of the relationship between the frequency split and a defect’s kth harmonic. The proposed approach also allows estimating the sensitivity of frequency split to the location of a defect on the meridian of the resonator shell. Besides, the calculation simplicity, accuracy, and speed enable the optimization of frequency split balancing parameters. The paper considers cylinder and bell-shaped resonators, and the proposed calculation approach was validated for meridional defect distributions. The results obtained using the proposed method are in good agreement with the results obtained using FEM.