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As the core component of the all-metal micro resonant gyroscope, the structural parameters and form and position errors of the resonator significantly influence its vibration characteristics, and consequently, the accuracy of the gyroscope. By establishing the finite element model of an ideal hemispherical resonator and optimizing the meshing method, we refined the frequency difference to 0.1 Hz, enhancing the accuracy of the simulation model. Through finite element simulation, we examined the impact of various structural parameters and processing errors on the natural frequencies of each mode. We analyzed how form and position errors, including shell thickness error, central axis error, equatorial plane error, and edge rectangular tooth position error, affect the frequency splitting of the resonator. We provided optimization suggestions for the structural parameters, ensuring frequency splitting variations of less than 1 Hz. Theoretical modeling and simulation analysis indicated that the primary factors influencing the vibration modes and frequency splitting are the rectangular tooth structure and shell thickness. Following the optimized parameters, the frequency splitting of the All-Metal Micro Resonant Hemisphere was reduced by an order of magnitude to 14 Hz, demonstrating that these optimized conditions can significantly enhance the resonator's performance. [ABSTRACT FROM AUTHOR]

Metal- μ hemispherical resonant gyros (M- μ HRGs) are widely used in highly dynamic navigation systems in extreme environments due to their high accuracy and structural stability. However, the effect of temperature variations on the capacitance characteristics of M- μ HRGs has not been fully investigated, which is crucial for optimizing the performance of the gyro. This study aims to systematically analyze the effect of temperature on the static and dynamic capacitances of M- μ HRGs. In this study, an M- μ HRG structure based on a 16-tooth metal oscillator is designed, and conducted simulation experiments using non-contact capacitance measurement method and COMSOL Multiphysics 6.2 finite element simulation software in the temperature range of 233.15 K to 343.15 K. The modeling analysis of the static capacitance takes into account the thermal expansion effect, and the results show that static capacitance remains stable across the measured temperature range, with minimal effect from temperature. The dynamic capacitance exhibits significant nonlinear variations under different temperature conditions, especially in the two end temperature intervals (below 273.15 K and above 313.15 K), where the capacitance values show local extremes and fluctuations. In order to capture this nonlinear behavior, the experimental data were smoothed and fitted using the LOESS method, revealing a complex trend of the capacitance variation with temperature. The results show that the M- μ HRG has good capacitance stability in the mid-temperature range, but its dynamic performance is significantly affected at extreme temperatures. This study provides a theoretical reference for the optimal design of M- μ HRGs in high- and low-temperature environments. [ABSTRACT FROM AUTHOR]