Comprehensive Performance-Oriented Multi-Objective Optimization of Hemispherical Resonator Structural Parameters

The hemispherical resonant gyroscope is the highest-precision solid-state vibration gyroscope, widely applied in aviation, aerospace, marine, and other navigation fields. As the core component of the hemispherical resonant gyroscope, the design of its structural parameters directly influences the key performance parameters of the resonator—specifically, the thermoelastic damping quality factor and the minimum frequency difference from interference modes—affecting the operational accuracy and lifespan of the gyroscope. However, existing research, both domestic and international, has not clarified the effect of structural parameters on performance laws. Thus, studying the mapping relationship between the resonator’s performance and structural parameters is essential for optimization. In this study, a hemispherical resonator with a midplane radius of 10 mm serves as the research object. Based on a high-precision finite element simulation model of an ideal hemispherical resonator, the mechanism of thermoelastic damping and the influence of structural parameters on performance are analyzed. A PSO-BP neural network mapping model is then developed to relate the resonator’s structural and performance parameters. Subsequently, the NSGA-II algorithm is applied to perform multi-objective mapping of these parameters, achieving an optimized resonator with a 4.61% increase in the minimum frequency difference from interference modes and a substantial improvement in thermoelastic damping of approximately 70.41%. The comprehensive, performance-oriented multi-objective optimization method for the structural parameters of hemispherical resonators proposed in this paper offers a cost-effective approach to high-performance design and optimization, and it can also be applied to other manufacturing processes under specific conditions.