| Hemispherical Resonator Gyro(HRG)is originated in the 1960 s,and has a promising application in aerospace,tactical weapons and other fields due to its outstanding advantages such as high precision,simple structure and long service life.As the core part of HRG,the hemispherical resonator is a hard,brittle,thin part with high gradient surface.However limited by the current machining level,it is difficult to obtain good geometrical accuracy,which leads to the distribution non-uniform of mass then results in frequency split and affects the precision of HRG.With precision machining of resonators as background,this thesis studied the influence of geometrical errors on the vibration characteristics of hemispherical resonators to find out the main factors affecting frequency split.It can be taken as the basis for controlling geometrical errors during machining of resonators,and also be of great significance to improve the machining quality of resonators.This thesis analyzes the influence of geometrical errors on frequency split for resonators by combining dynamics modeling,finite element analysis with the measurement of geometrical errors,then the results of vibration test is used to verify the conclusions.The research contents of this thesis are as follows.(1)Dynamics Modeling of hemispherical resonators with thickness errors.Based on the theory of elasticity and vibration,the dynamics models of ideal hemispherical resonator are derived.Then the geometrical errors of the inner and outer hemispherical surface are transformed into thickness non-uniform errors.And the dynamics equations with thickness errors are established under free vibration and external force respectively.Thus the mathematical expressions of frequency split are calculated,which reveals the mechanism of frequency split.(2)Finite element analysis of the 3-D models with geometrical errors.By building resonator’s 3-D models with errors of thickness and diameter non-uniform for hemispherical shell,surface errors of end surface and non-coincidence of axis,the influence of the above geometrical errors and density non-uniform on frequency split is analyzed,and the main factors are summarized.The convergence effect of the equivalent mass block removal method with different parameters on modification of frequency split for the 3-D models with thickness errors is analyzed,which is used to guide precision grinding and ion beam machining of resonators.(3)Measurement of geometrical errors and test of frequency split for hemispherical resonators.Talyrond 565 H is used to measure the inner and outer roundness errors of resonator’s hemispherical shell,so the thickness errors of the hemispherical shell is calculated based on the data of roundness errors.Then the harmonic information of the thickness errors are extracted by Fast Fourier Transform(FFT).The measurement of the full-aperture surface errors of the hemispherical shell’s end face is achieved by SWLI and sub-aperture stitching method.By carrying out the harmonic decomposition of the errors based on Zernike polynomial,the harmonic information of the end face shape errors is obtained.The vibration testing system for resonators based on LDVS is built to accomplish the measurement of frequency split and the position of rigid shaft for resonators.The results of the geometrical errors measurement and vibration test verify the conclusions of theoretical calculations and finite element analysis. |
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