谐振子支柱偏心误差对谐振子振动特性影响分析(英文)

Influence analysis of the pole's eccentricity error on vibration characteristics of resonator

半球壳谐振子是半球谐振陀螺的核心部件。基于弹性力学的有限单元法建立了谐振子的弹性动力学有限元方程,得到谐振子自由谐振方程。为分析谐振子支柱偏心误差对谐振子振动特性的影响,利用有限元分析软件(ANSYS)建立了半球壳谐振子有限元模型,分析了理想谐振子和存在支柱偏心误差谐振子的二阶谐振状态振动特性。深入分析了支柱偏心误差对谐振子谐振频率和变形特性等振动特性的影响规律。通过对两种影响规律的比较分析得到,支柱偏心误差导致的频率差将会引起陀螺的随机漂移;而支柱偏心误差引起的变形将会影响陀螺的零偏,可以通过标定补偿。为减小支柱偏心误差对陀螺精度和性能的影响,偏心误差的加工误差范围应小于1.2μm,分析结果为谐振子的加工设计和结构误差分析提供了理论基础。

Hemispherical shell resonator is the key component of hemispherical resonator gyro(HRG). Based on the finite element method of elasticity, the elastodynamic finite element equation of resonator is established, which obtains the free resonant equation of resonator. In order to analyze the influence of the pole’s eccentricity error on vibration characteristics of resonator, a finite element model of hemispherical shell resonator is established by the finite element analysis software ANSYS. The vibration characteristics of the second resonant state for the ideal resonator and the resonator with eccentricity error are investigated. The comparison on the two kinds of influence laws shows that the influence of eccentricity error on resonant frequency causes the frequency difference which can cause the random drift of HRG. The deformation caused by the pole’s eccentricity error will affect the zero bias of the HRG, which can be compensated by calibration.The analysis results show that in order to reduce the influence of the pole’s eccentricity error on the precision and performance of HRG, the machining error range of eccentricity error should be less than 1.2 μm, which provides a theoretical basis for the processing design and structural error analysis of resonator.