Optical Method for Material Imperfections Identification in the Resonator Workpiece of Hemispherical Vibratory Gyroscope

Introduction. The implementation of high-precision attitude control systems of a new generation with improved technical characteristics remains a key task in precision instrumentation — this is required for the reliable operation of moving objects with a long service life. One of the promising ways is the use of sensors based on the Bryan effect (hemispherical resonator gyroscopes, HRG),), which show significant advantages in stability of characteristics under external factors. Over the past 10 years, foreign and domestic research has reached noticeable success in increasing the target parameters of HRG, however, certain improvement problems remain open. Thus, in the literature, attention is paid to reducing the errors in measuring the HRG through compensating for the impact of imperfections of the resonator, but more often these methods are applicable at stages after geometry generation. Methods for early identification of material inhomogeneities (density variation) during workpiece inspection are insufficiently developed, creating a gap in the process chain and reducing the efficiency of subsequent balancing and calibration. The objective of this study is to develop a method for identifying resonator density variations at an early stage of the process — during workpiece inspection.

Materials and Methods. An optically transparent material is considered – fused quartz glass, which is the most common material for making a HRG resonator, in particular, the KU-1 brand (foreign analogs — Corning HPFS 7980, JGS1). The identification method is based on the relationship of the optical properties of quartz glass (absorption coefficient) with the desired density distribution over the volume of the workpiece. A virtual experiment was conducted, which consisted in the formation and resolution of a system of linear algebraic equations (SLAE) based on the measurements series results of a light beam intensity passing through a workpiece. A polynomial approximation was used to describe the density distribution in order to increase the robustness of the method. The SLAE roots were obtained through finding a pseudosolution by the least square method based on the singular value decomposition.

Results. A method for identifying the density variation of quartz glass at the stage of quality control of the technological workpiece of the HRG resonator was developed. The desired density distribution of quartz glass over the volume of the workpiece was obtained, coinciding with the “true” one — the difference was no more than 5%. The sensitivity of the method to the presence of macrodefects in the volume of the workpiece (pores, bubbles, etc.) was assessed.

Discussion. The results show that the proposed method can effectively control the density variation of the workpieces and optimize the resonator production, thereby improving the efficiency of the processes and minimizing the impact of imperfections on their characteristics. Virtual experiments have demonstrated that measuring the light beam intensity passing through the workpiece allows for the accurate reconstruction of the absorption coefficient and density distribution with an accuracy of at least 0.005%. The developed system of linear algebraic equations (SLAE) makes it possible to determine these parameters by volume. The paper highlights some features related to solving uncertain SLAE. Particular attention is paid to the need to control the ratio between the number of roots and unknowns to obtain a stable solution.

Conclusion. The proposed method for identifying the density variation of quartz glass at the stage of workpiece quality control in the production of HRG resonators demonstrates high efficiency and accuracy. The presented method has high accuracy for describing the distribution function, and is also flexible in terms of obtaining the optimal dimension of the SLAE, which is directly related to the number of experiments performed. The obtained results confirm the applicability of the material optical properties for controlling the density distribution over the volume, which allows for improved control of workpieces and optimization of production processes. The required measurement accuracy, determined by the level of density variation that affects the HRG characteristics, is practically achievable, which indicates that the method can be used in the manufacturing process. This approach can be applied in future research and development of highprecision systems, which will contribute to progress in the precision instrumentation industry and improve the quality of manufactured products.

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