半球谐振子装配倾角误差对频率裂解的影响分析

The influence of assembly inclination error in hemispherical resonator on frequency splitting

精密的装配工艺是保证半球谐振陀螺仪高精度性能的关键技术,研究装配误差对陀螺性能的影响可以为完善和优化工艺参数提供理论指导和依据。围绕装配过程中产生的偏心、倾斜误差对谐振子频率裂解的影响开展研究,建立了倾斜装配误差对谐振子频率裂解的影响数学模型。首先将谐振子唇沿与极板作为等效电容,建立装配倾角误差与等效电容之间的关系模型;然后基于等效电容两端电压与半球谐振子的静电力之间的数学模型,分析静电力不均匀对谐振子刚度的影响;最后建立数学模型分析了刚度扰动对频率裂解的影响。研究结果表明,对于直径30 mm的熔融石英半球谐振子,与基座的装配倾角误差为1角分时,由倾角误差引入的频率裂解为10^(-4) Hz量级。关于倾角误差对谐振子频率裂解的影响分析,为高精度半球谐振陀螺的精密装配工艺以及工艺参数配置奠定理论分析基础。

The precise assembly process is the key technology to ensure the high-precision performance of the hemispherical resonant gyroscope.The study of the influence of assembly errors on gyroscope performance can provide theoretical guidance and basis for perfecting and optimizing process parameters.The effect of eccentricity,tilt errors in the assembly process on the frequency cracking of the harmonic oscillator is studied,and a mathematical model of the effect of tilt assembly errors on frequency cracking of harmonic oscillator is established.Firstly,the lip and the polar plate of the harmonic oscillator are used as the equivalent capacitance,and the relationship model between the assembly tilt error and the equivalent capacitance is established.Then,based on the mathematical model between the voltage across the equivalent capacitance and the electrostatic force of the hemispherical harmonic oscillator,the influence of the uneven electrostatic force on the stiffness of the harmonic oscillator is analyzed.Finally,a mathematical model is established to analyze the influence of the stiffness disturbance on the frequency splitting.The research results show that for a fused silica hemispherical resonator with a diameter of 30 mm,when the inclination error of the assembly with the base is 1 arc minute,the frequency splitting introduced by the inclination error is on the order of 10^(-4) Hz.The analysis of the influence of the tilt error on the frequency splitting of the harmonic oscillator provides theoretical guidance and basis for the precision assembly process and process parameter configuration of the high-precision hemispherical resonator gyroscope.