Modelling and experimental investigation of frequency splitting of hemispherical resonator with machining errors

Hemispherical Resonator (HSR) is a typical high-performance component due to the complex coupling relationship between the machining errors and performance parameters. To understand the impact of machining errors on frequency splitting, the frequency splitting model that couples the multiple machining errors was developed to elucidate the mechanism of frequency splitting and reveal the effect of geometric error parameters on frequency splitting innovatively. In addition, a method for characterizing machining errors is established to describe the circumferential mass uniformity of the hemispherical shell. Furthermore, measurement experiments of HSRs were performed to verify the accuracy of the model, and the results showed that the predicted errors of the model were within 15%. Both theoretical and experimental results demonstrated that the direct cause of frequency splitting is the uneven circumferential mass of HSR. In particular, the radial concentricity has the most significant influence on frequency splitting, followed by the coaxiality and roundness. Within the error range of 0–0.5 μm, frequency splitting values change by 0.945 Hz, 0.098 Hz, and 0.039 Hz, respectively. Furthermore, the coupling effect of machining errors and surface quality on frequency splitting was discussed, which showed machining errors is the predominant factor contributing to frequency splitting. This work not only enhance the understanding of the mechanism of frequency splitting, but also provide theoretical guidance for the parameter optimization involved in high-performance manufacturing of HSR.