半球谐振陀螺凭借结构简单、高精度、长寿命、高可靠、抗辐射等突出优点，成为近年来国内外关注的研究热点。半球谐振陀螺的性能，很大程度上取决于谐振子的振动不对称误差（频差和阻尼差）。尽可能地降低频差和阻尼差，是半球谐振子加工的核心问题。 本文围绕振动不对称误差的高精度修调问题，开展了以下3个方面研究： （1）半球谐振子振动不对称误差机理分析推导了频差、阻尼差与密度1-4次谐波之间的关系式，并进行了仿真验证。理论分析得出了杨氏模量、各向同性阻尼不均匀对频差和阻尼差影响很小的结论。在此基础上，得到了厚度不均匀近似与相同幅度密度不均匀等效的结论，并进行了仿真和实验验证。同时，理论分析了0阶和1阶模态振动特性对频差和阻尼差的影响，并进行了仿真验证。 （2）半球谐振子振动不对称误差高精度辨识方法针对微小频差和阻尼差的高精度辨识问题，研究了基于解调量动力学方程的线性和非线性最小二乘辨识算法，实现了频差、频率主轴、阻尼差、阻尼主轴和Q值多个参数同时辨识。分析发现由于解调量动力学方程参数与谐振固有频率有关，算法辨识精度容易受环境温度变化影响。针对性地改进提出了基于EHRS动力学方程的辨识算法，仿真结果表明算法的辨识精度比“耦合振动法”提高了一个数量级。 （3）半球谐振子不对称误差测试及修调系统设计针对半球谐振子微小频差的高精度修调问题，提出了一种振动不对称误差测试和修调系统的设计方案。通过2通道平面叉指电极优化设计，实现了任意角度大振幅激励；采用多通道光纤干涉仪，实现了多通道高精度振动检测；优化设计了小尺寸短焦距光纤探头，有效降低了光路调试的难度；设计了外设控制、测试逻辑、辨识算法和数据可视化算法库，实现了扫频、多位置自由振动和参数辨识等多种功能。实测结果表明，系统可以将半球谐振子频差修调至0.2mHz以下。
Hemispherical resonant gyroscope has become a research hotspot in recent years due to its outstanding advantages such as simple structure, high accuracy, long lifespan, high reliability, and radiation resistance. The performance of hemispherical resonator gyroscope (HRG) depends largely on the vibration asymmetry (frequency split and damping asymmetry) of hemispherical shell resonator (HSR). Reducing the frequency split and damping asymmetry as far as possible is the core problem of HSR machining. The main works of this thesis are as follows: (1) Vibration Asymmetry Mechanism of HSRThe relationship between frequency split, damping asymmetry, and density 1-4th harmonics was derived and verified through simulation. Through theoretical analysis, it was found that the Young‘s modulus and isotropic damping non-uniformity have little effect on frequency split and damping asymmetry. The effect of thickness non-uniformity was found to be approximately equivalent to density non-uniformity with the same amplitude. The impact of the vibration characteristics of the 0th and 1st order modes on frequency split and damping asymmetry was studied theoretically and verified through simulation. (2) High Precision Identification Method of Vibration Asymmetry of HSRAiming at the high-precision identification problem of small frequency split and damping asymmetry, linear and nonlinear least squares identification algorithms based on demodulated quantity’s dynamic equations were studied, achieving simultaneous identification of multiple parameters such as frequency split, frequency principal axis, damping asymmetry, damping principal axis, and Q-value. Analysis found that due to the correlation between the parameters of the demodulated dynamic equation and the resonant natural frequency, the algorithm identification accuracy is easily affected by changes in environmental temperature. An improved identification algorithm based on the EHRS dynamic equations was proposed, and simulation results showed that the identification accuracy of the algorithm was improved by one order of magnitude compared to the "coupled vibration method". (3) Design of Vibration Asymmetry Test and Balancing System for HSRAiming at the problem of high-precision balancing of small frequency split of HSR, a design scheme of test and balancing system for vibration asymmetry is proposed. By optimizing the design of a 2-channel planar interdigital electrode, large amplitude excitation at any angle was achieved; By adopting a multi-channel fiber optic interferometer, multi-channel high-precision vibration detection was achieved; By optimizing the design of small-sized short focal length fiber optic probes, the difficulty of optical path adjusting was effectively reduced; An algorithm library that includes peripheral control, test logic, identification algorithm and data visualization was designed to realize various functions such as frequency sweeping, multi position free vibration and parameter identification. Test results show that the system can decrease the frequency split of HSR to less than 0.2 mHz.
