Vibration modeling of disk resonator gyroscope by wave propagation

Abstract

This paper proposes an analytical vibration model of a disk resonator gyroscope (DRG) based on the wave propagation theory, which can predict the key specifications of a DRG rapidly and accurately before fabrication, and can be employed in design optimization. This wave propagation analysis is based on the ray tracing method (RTM) which considers wave propagation and scattering in the formulation. In the RTM, wave transmission and reflection coefficients are the key issues that must be accurately predicted. A novel C-joint is proposed to predict these key coefficients between the rings and spoke with high precision and short estimated time. To verify the soundness of the proposed model, a tentative vibration model for a double-ring (the basic element of a DRG) is established by the RTM and compared with the 3D finite element (FE) model. The two models show excellent agreements in natural frequencies, trend predictions and harmonic displacements. Then, the proposed model is expanded to a multi-ring practical DRG. In addition, taking the advantage of the symmetry in the DRG, the substructuring and recursive methods are employed to reduce the computational overhead. The numerical experiments show that the proposed analytical vibration model for a DRG meets well with the 3D FE model. For instance, the differences between the calculated resonant frequencies from the 3D FE model and the analytical model are less than 3%. After fabrication, the measured average resonant frequency of the prototypes deviates 6.7% from that of the theoretical prediction.