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

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 differen-tial 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 ori-entation 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 er -ror, 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 process -ing high-precision HSRs and HRGs. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes a dynamic model and machining accuracy ranges for hemispherical resonator gyroscopes, investigates the effect of thickness nonuniformity on HRG output error, and discusses the impact of frequency split and initial orientation angle.