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Abstract：
The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks with large angular velocities and angular accelerations, this paper investigates the standing wave precession of a non-ideal hemispherical resonator under nonlinear high-intensity dynamic conditions. Based on the thin shell theory of elasticity, a dynamic model of a hemispherical resonator is established by using Lagrange\'s second kind equation. Then, the dynamic model is equivalently transformed into a simple harmonic vibration model of a point mass in two-dimensional space, which is analyzed using a method of averaging that separates the slow variables from the fast variables. The results reveal that taking the nonlinear terms about the square of the angular velocity and the angular acceleration in the dynamic equation into account can weaken the influence of the 4th harmonic component of a mass defect on standing wave drift, and the extent of this weakening effect varies with the dimensions of the mass defects, which is very important for steering the development of the high-precision hemispherical resonator gyroscope.
摘要：
小尺寸的属性，低噪音,高性能和无磨损使半球形谐振陀螺仪成为高价值太空任务的好选择。为了提高半球形谐振陀螺仪在具有大角速度和角加速度的任务中使用的精度，本文研究了非线性高强度动态条件下非理想半球形谐振器的驻波进动。基于薄壳弹性理论,利用拉格朗日第二类方程建立了半球形谐振器的动力学模型。然后，将动力学模型等效转换为二维空间中的点质量的简谐振动模型，这是使用一种将慢速变量与快速变量分开的平均方法进行分析的。结果表明，考虑到动力学方程中关于角速度平方和角加速度的非线性项，可以减弱质量缺陷的4次谐波分量对驻波漂移的影响。这种弱化效应的程度随质量缺陷的大小而变化，这对于指导高精度半球形谐振陀螺的发展具有十分重要的意义。
