A Review of Theoretical Methods for Resonator Modeling of Hemispherical Resonator Gyro

JIANG Xin; ZHU Qiju; MEI Chunbo

doi:10.15892/j.cnki.djzdxb.2024.05.013

Abstract

The dynamic behavior of hemispherical resonator comprises the physical basis of hemispherical resonator gyros (HRG). This paper concerns the common problems that exists in the domestic researches of dynamic modeling of HRG to date, such as the lack of specific sources of reference, plenty of ambiguous deductions (some are even incorrect), hence the derivation process of dynamic modeling of resonator is carefully presented in detail. The paper summarizes the general background knowledge of relevant disciplines, and teases out two main types of modeling thoughts, in the sake of providing a theoretical support for the subsequent researches and engineering applications. Firstly, the elastic shell theory used as a general basis in dynamic modeling of hemispherical resonator is introduced, including the elastic geometric equations that describe the relationship between strain and displacement and the Hooke’s law that relates strain to stress; then the modeling method based on the d’Alembert principle commonly used in early theoretical researches is presented, and the second-order motion equations of resonator is obtained by establishing equilibrium equations and load analysis; finally, the modeling method based on Lagrangian mechanics which is inspired from aboard research is introduced, and the second-order motion equations are derived by calculating the kinetic and strain energy of the overall resonator with substitution of the Lagrangian equations. The latter method is increasingly popular by domestic researchers in recent years.

Key words： hemispherical resonator gyro; resonator; elasticity; D'Alembert principle; Lagrangian equations

Cite this article

JIANG Xin , ZHU Qiju , MEI Chunbo . A Review of Theoretical Methods for Resonator Modeling of Hemispherical Resonator Gyro[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2024 , 44(5) : 104 -114 . DOI: 10.15892/j.cnki.djzdxb.2024.05.013

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