Motion equations of hemispherical resonator and analysis of frequency split caused by slight mass non-uniformity  

作　　者：Yan HUO Shunqing REN Guoxing YI Changhong WANG 

机构地区：[1]Space Control and Inertial Technology Research Centre,Harbin Institute of Technology,Harbin 150080,China

出　　处：《Chinese Journal of Aeronautics》2020年第10期2660-2669,共10页中国航空学报（英文版）

基　　金：the Pre-Research Fund during the“13th Five-Year Plan” (No. 41417060101)。

摘　　要：The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass non-uniformity and frequency split,which can provide a theoretical basis for mass balance of imperfect resonator.The starting point of error mechanism analysis for gyroscope is the motion equations of resonator.Firstly,based on the Kirchhoff-Love hypothesis in the elastic thin shell theory,the geometric deformation equations of resonator are deduced.Secondly,the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell.Thirdly,the kinetic energy equation of resonator is deduced by the Coriolis theorem.Finally,the motion equations of resonator are established by the Lagrange mechanics principle.The theoretical values of precession factor and natural frequency are calculated by the motion equations,which are substantially consistent with the ones by the finite element method and practical measurement,the errors are within a reasonable range.Simultaneously,the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis.The above conclusions prove the correctness and rationality of motion equations.Similarly,the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping,and the state equations with respect to the velocity and displacement of vibration system are derived,then twonatural frequencies are solved by the characteristic equation.It is concluded that one of reasons for frequency split is the 4 th harmonic of mass non-uniformity,and thus much attention should be paid to minimizing the 4 th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.

关 键 词：Hemispherical resonator Lagrange mechanics principle Theory of elastic thin shell Motion equations Mass non-uniformity Frequency split 

分 类 号：TN751.2[电子电信—电路与系统] V441[航空宇航科学与技术—飞行器设计]