Frequency Splitting Analysis Of Hemispherical Harmonic Oscillator And Study On Vibration Energy Loss

Hemispherical Resonator Gyro（HRG）is the new type of high-precision gyroscope with the most development potential in the world at present.It has a simple structure,high accuracy,high reliability,long life and can continue to work for 15 minutes after power off.Such advantages have broad development prospects in many fields such as aerospace,military defense,and marine exploration.The hemispherical resonator is the core component of the hemispherical resonator gyroscope.The vibration state and energy loss of the hemispherical resonator have a decisive influence on the performance of the resonant gyroscope.In this paper,based on the multiphysics coupling simulation software COMSOL Multiphysics,the effects of structural parameters and processing errors on the frequency cracking and quality factor of the resonator are studied by simulation,which is laid for the preparation of high-precision,low energy loss hemispherical resonators.basis.The specific research contents are as follows:Based on the Kirchhoff hemispherical harmonic oscillator model and the hemispherical harmonic ring model,the working frequency and precession factor of the hemispherical harmonic oscillator are calculated,and the approximate relationship of frequency splitting caused by uneven radius and thickness of the hemispherical shell is analyzed and proposed;The precession ellipse equation of the hemispherical harmonic oscillator establishes the mapping relationship between the frequency splitting and the accuracy of the gyro,which provides a theoretical basis for the formulation of the processing error standard of the hemispherical harmonic oscillator.Based on the vibration simulation model of the hemispherical resonator,the influence of the structural parameters on the natural frequency of the resonator is studied and analyzed.Based on the actual processing error requirements of the hemispherical resonator,a simulation model of the hemispherical resonator hemispherical shell alignment error and the hemispherical shell surface machining error is established,and the degree and law of the influence of each processing error on the frequency cracking of the hemispherical resonator are analyzed;a metallized coating simulation model is established,comparative analysis of the influence of the coating on the vibration state of the resonator,and to explore the basis for the proposed precision requirements of ultra-precision machining of the hemispherical resonator.According to the type of energy loss during the vibration of the hemispherical harmonic oscillator,the loss mechanisms of thermoelastic damping,support loss,surface loss,air damping loss,phonon-electron,and phonon interaction are expounded.The simulation model of thermoelastic damping and supporting loss of the resonator is established,and the correctness of the model is verified based on the literature data.The limit value of the quality factor of a certain ideal hemispherical resonator is obtained by simulation.Furthermore,the single variable method is used to simulate the influence of each structural parameter of the hemispherical resonator on the Q_TED value of thermoelastic damping and the Q_anchor value of support loss.Simulation analysis of the influence of the processing errors of the hemispherical resonator on the quality factor of the resonator.It is found that the processing errors mainly affect the Q_anchor value of the resonator.Then,by analyzing the impact of the change of Q_anchor on the upper limit of the quality factor,the hemispherical resonator is guided.Error control requirements for precision machining.In addition,by simulating the effect of surface micro-cracks on the quality factor of the resonator,it is found that the presence of surface micro-cracks will greatly reduce the Q_TED value of the thermoelastic damping of the resonator,which provides a basis for reducing the necessity of subsurface damage of the resonator.