The influence mechanism and identification of mass defects in hemispherical resonators are currently highly challenging and significant research directions. This paper first establishes a shell–rod coupling vibration model under the influence of mass error, and, based on this model, constructs a characterization system for the vibration characteristics (quality factor and frequency split) of the resonator. The influence of the first four harmonic components of the mass defect on the quality factor and frequency split of the resonator was systematically studied, and the analytical expression of its quantitative representation was derived, which reveals the internal physical relationship between the mass defect and the vibration characteristics. Subsequently, the theoretical model was verified by using finite element simulation. Finally, an efficient and high-precision method for identifying the first four harmonics of hemispherical resonator mass defects was proposed, and an experimental device was set up to successfully achieve the synchronous identification of the first four harmonic components. An innovative beam-split optical system that streamlines displacement metrology reduced test complexity by >60%.

As a high-precision inertial device, the hemispherical resonant gyroscope (HRG) has found widespread application in critical domains including aerospace and tactical weapons, owing to its advantages of high precision, simple structure, and long service life. However, the machining form and position errors of the hemispherical resonator—the core component of an HRG—are primary bottlenecks that restrict gyroscopic accuracy. To address the limitations of existing research, which include inadequate simulation accuracy, an incomplete consideration of form and position errors, and an unclear mechanism of the quality factor’s influence, this study employs a methodology comprising theoretical modeling, high-precision finite element simulation, and multi-parameter coupling analysis to undertake an in-depth investigation of the modal characteristics of hemispherical resonators. This work establishes a quantitative correlation linking machining errors to modal characteristics and subsequently to gyroscopic accuracy. This correlation provides critical guidance for controlling machining precision and achieving high-Q (quality factor) designs of hemispherical resonators, thereby offering significant engineering implications for enhancing the overall performance of HRGs.

The characteristic parameters of fixed joint surfaces, such as stiffness and damping, play a dominant role in determining the overall performance of various mechanical structures, especially in high-performance machine tools. However, accurate characterization of these joint parameters remains challenging, due to a lack of direct validation methods. In this study, we consider the deformation of the base caused by the interaction of micro-convex bodies based on the 3D Kogut and Etsion (KE) model, and modify the characteristic parameter model of joint surfaces. Interfacial fractal parameters were determined using the structural function method, which enabled direct experimental validation of the characteristic parameter model. Finally, a comprehensive dynamic performance analysis of the GP300 grinding machine was conducted, and the results revealed that the joint surface changed the various modes of vibration and the corresponding natural frequencies of the machine tool. These findings deepen our understanding of the characteristic parameters of the binding surface and their effects, and have important guiding significance for the performance analysis and design of machine tools.