### 一种半球谐振陀螺谐振子动力学建模方法

1. 1. 哈尔滨工业大学 航天学院, 哈尔滨 150001;
2. 上海航天控制技术研究所, 上海 201109
• 收稿日期:2017-07-24 修回日期:2017-11-17 出版日期:2018-03-15 发布日期:2017-11-17
• 通讯作者: 伊国兴,E-mail:ygx@hit.edu.cn E-mail:ygx@hit.edu.cn
• 基金资助:
总装预研重点基金（9140A09012015HT01026）；"十三五"预研基金（41417060101）

### A dynamic modeling method for resonator of hemispherical resonator gyro

XU Zeyuan1, YI Guoxing1, WEI Zhennan1, ZHAO Wanliang2

1. 1. School of Astronautics, Harbin Institute of Technology, Harbin 150001, China;
2. Shanghai Aerospace Control Technology Research Institute, Shanghai 201109, China
• Received:2017-07-24 Revised:2017-11-17 Online:2018-03-15 Published:2017-11-17
• Supported by:
National Defense Pre-research Key Foundation (9140A09012015HT01026); The 13th Five-year Pre-research Foundation (41417060101)

Abstract: The accurate and complete dynamic model for the hemispherical shell resonator is the basis of error analysis of the Hemispherical Resonator Gyro (HRG). A dynamic modeling method for the hemispherical shell resonator is proposed based on the thin shell theory of elasticity. First, the deformation geometry equation for the hemispherical shell resonator is derived based on the elasticity geometry equation for the thin shell. Second, based on the improvement of calculation accuracy of force analysis, the physical equation for the hemispherical shell resonator is developed. After an analysis of the force equilibrium relationship for the middle surface of the resonator, the equilibrium differential equation for the resonator is obtained. Finally, based on the above dynamic analysis of the whole resonator, the dynamic equation for the resonator is established. After an analysis of the external load forms of the resonator, the second-order resonant dynamic model for the resonator is obtained by using the Bubnov-Galerkin method, and the expressions for the proportion coefficients and second-order resonant frequency of the resonator are also obtained. Comparison shows that the calculation results are consistent with the measured data, proving the accuracy of the dynamic model proposed.