Dynamic modeling and output error analysis of an imperfect hemispherical shell resonator

Abstract

A hemispherical resonator gyroscope (HRG) is very useful for inertial sensors in the 21st century. This paper proposes a novel dynamic model of an imperfect hemispherical shell resonator (DM-IHSR) with thickness nonuniformity and an output error model of the HRG (OEM-HRG) associated with frequency split. First, the DM-IHSR is established based on the thin shell theory of elasticity, and the thickness nonuniformity is described. The differential equations of vibratory motion of the IHSR are derived by leveraging Bubnov-Galerkin method, which reveals that frequency split is mainly dominated by the fourth harmonic of thickness nonuniformity. Then, by considering the characteristics of standing waves, the OEM-HRG is proposed, which discovers the effects of frequency split and the initial orientation angle on the HRG output error. Finally, the effect of thickness nonuniformity on the HRG output error is clarified. The quantitative relationship among the HRG output error, the fourth harmonic of thickness nonuniformity, and the initial orientation angle is determined, which gives machining accuracy ranges of these variables. The above dynamic models and machining accuracy ranges are of great significance for producing and processing high-precision HSRs and HRGs.