An accurate thermoelastic model and thermal output error analysis of a hemispherical resonator gyroscope under varying temperatures

This paper proposes an accurate thermoelastic model of a hemispherical shell resonator (TM-HSR) taking into consideration thermal stress and reveals the effect of its thermal deformation on the hemispherical resonator gyroscope (HRG) output error for the first time. First, a set of thermoelastic dynamic equations of the TM-HSR are derived by leveraging the thermoelastic shell theory, and the relationship between temperature and the equivalent thermal load is determined. Next, an approximate analytical solution of thermal deformation of HSRs is derived using Bubnov-Galerkin method and its accuracy is evaluated by comparing its result with ANSYS simulation results of HSRs with different structures. The approximate analytical solution is found to be very accurate, which is important for temperature testing of HRGs and application to various vibratory sensors with hemispherical shell structures. Subsequently, the effects of thermal deformations under uniform and nonuniform temperature distributions on the HRG output error are revealed by using a thermal output error model. Comparative simulation and experimental results demonstrate the effectiveness and practicability of the proposed model. The proposed model can be used for accurate error analysis and developing a compensation scheme for the thermal output error of HRGs.