Interferometrical Measurement Technology For Geometrical Errors Of Hemispherical Resonator Shell Parts

Hemispherical Resonator Gyro(HRG)is a solid-state vibration gyro with the highest precision.It is regarded as a subversive technology in the field of high-precision navigation.The hemispherical resonator as the core component determines the performance of the HRG.It is a thin-wall hemispherical shell.Deformation of the shell under force excitation generates standing wave which causes precession under the Coriolis effect when rotating with the carrier.Angular velocity can then be obtained by detecting the vibration of the shell.An ideal resonator has perfectly uniform mass distribution in the circumferential direction.However limited by the accuracy of machine tools,the geometrical accuracy of traditionally machined resonators is not high enough.The mass distribution is then non-uniform and it results in frequency split and reduction of the quality factor.This thesis presents a method for interferometrically characterizing the geometrical error of hemispherical shells,which provides error feedback for deterministic corrective figuring and then enables effective improvement of machining accuracy.The major contents of this research include the following aspects:(1)For measurement of geometrical errors of the equal-thickness hemispherical resonator,the method combining the wavelength-tuning interferometry and subaperture stitching is proposed.Wavelength-tuning interferometry is able to obtain the surface error and the thickness variation of the inner and outer surfaces simultaneously.The measuring principle of wavelength-tuning interferometry as well as the measurable thickness limit is studied.Simulations show that this limit can be extended under certain conditions and the feasibility is verified through measuring the transmitted wavefront of a 0.7mm-thick plate.Different stitching algorithms are applied to subaperture measurements of the surface error and the thickness variation,in order to reconstruct the omnivision view of the error distribution.An hemispherical dome shell is used as an example to experimentally verify the accuracy of stitching measurement of the thickness variation.(2)For measurement of geometrical errors of the varying-thickness hemispherical resonator,the method combining the transmitted confocal interferometry and subaperture stitching is proposed.The physical meaning of the measured optical path difference(OPD)is interpreted as the inner and the outer surfaces are in focus,respectively.Mapping distortion is corrected for the inner surface as a result of refraction,and the measurements of the inner and the outer surfaces are then aligned to extract the thickness variation information.A stitching platform for hemispherical resonators is designed to realize subaperture scan.Stitching algorithm is applied to reconstruct the omnivision view of the error distribution.The annular Zernike polynomials are introduced for harmonic decomposition.Different harmonic orders are obtained to facilitate analysis the influence on the frequency split.An hemispherical resonator of 20 mm in diameter is used as an example to experimentally verify the accuracy of stitching measurement,compared with the full-aperture direct measurement and the roundness measuring results.(3)For ultra-precision figuring and tuning of the hemispherical resonator,methods for removal of unbalanced mass at given positions and for corrective figuring based on geometrical error feedback by using the ion beam are studied.The ion beam with small beam diameter is obtained by using the grid system and the aperture stop.According to the measured material removal function,unbalanced mass is removed by controlling the dwell time of the beam at given four edge positions of the resonator,which reduces the frequency split effectively.The omnivision distribution of geometrical errors is projected on the plane of longitude-Z coordinates to calculate the dwell time of the ion beam on the annular resonator.The NC codes are then generated for corrective machining.It is possible to produce high-profile resonators for subsequent mass tuning to achieve higher accuracy and efficiency.