基于加工误差仿真的半球谐振子优化设计

针对半球谐振陀螺谐振子制造过程中存在的加工误差，采用有限元仿真，分析了半球谐振子结构参数、尺寸公差和形位公差变化对其工作模态频率和临近模态频率的影响，研究了半球谐振子形位公差变化对频率裂解和品质因数的影响。通过仿真分析可知，半球谐振子结构参数壁厚、半球中心半径及内倒角半径都会影响模态频率；半球谐振子形位公差中的内外球心距离误差对其工作模态影响较大，中心轴平行误差对频率裂解和品质因数影响较大；半球谐振子壁厚、内倒角半径、小柱半径及内外球心距离误差变化会使工作模态频率与相邻模态间存在干扰。在此基础上，提出了半球谐振子结构参数及形位公差优化设计建议，并通过半球谐振子品质因数Q值和频率裂解测量对该建议进行了验证。

Optimization design of hemispherical harmonic oscillator based on machining error simulation

In response to the machining errors in the manufacturing process of hemispherical resonator gyroscopes, finite element simulation is used to analyze the effects of structural parameters, dimensional tolerances, and geometric tolerances on the working mode frequency and adjacent mode frequency of the hemispherical resonator. The effects of positional tolerances on frequency splitting and quality factor are studied. Through simulation analysis, it can be concluded that the structural parameters of the hemispherical resonator, such as wall thickness, hemispherical center radius, and internal chamfer radius, all affect the mode frequency; the distance error between the inner and outer spherical centers in geometric tolerance of the hemispherical resonator has a significant impact on the working mode of the hemispherical resonator, and the parallel error of the central axis of the hemispherical resonator has a significant impact on frequency splitting and quality factor; the variation in wall thickness, inner chamfer radius, small column radius, and distance between inner and outer spherical centers of the hemispherical resonator results in interference between the working mode frequency and adjacent modes. On this basis, optimization design suggestions for the structural parameters and geometric tolerances of the hemispherical resonator are proposed, and these suggestions are verified through quality factor Q values and frequency splitting measurements of the hemispherical resonator.