Anchor loss degradation in hemispherical resonators induced by manufacturing geometric errors

Manufacturing-induced geometric errors can break structural symmetry and intensify support-radiated dissipation in hemispherical resonators, thereby degrading the anchor-loss quality factor ( Q _anchor) of the second-order standing-wave mode. This study presents a unified framework for evaluating anchor-loss degradation caused by manufacturing geometric errors in hemispherical resonators. The framework combines geometric-error parameterization on a common nominal geometry, a multi-source measurement-to-model transformation, and a perfectly matched layer-enabled finite element model with coordinated swept meshing, enabling stable extraction of Q _anchor under weak dissipation and a unified assessment of figure, positional, and dimensional errors. The results reveal a clear sensitivity hierarchy. First- to third-order circumferential figure errors, radial concentricity deviation between the inner and outer spherical surfaces, and end-face perpendicularity deviation are identified as the dominant defect classes, whereas meridional figure errors, axial positional deviations, and dimensional deviations are much less influential. Among the circumferential harmonic defects, the isolated second-order harmonic produces the strongest deterioration in quality-factor uniformity, while the coupled first- and third-order harmonics form the most detrimental pair. The low-latitude rim and the fillet-adjacent region are further identified as the principal sensitive zones for anchor-loss degradation. An error-informed ion-beam directional trimming strategy is further established to suppress the dominant low-order defects. Vacuum ring-down tests provide trend-level experimental support: the total quality factors of the primary and secondary modes increase by 18.27% and 11.15%, respectively, and the circumferential non-uniformity decreases from 6.98% to 1.92%. This study provides quantitative guidance for identifying dominant manufacturing defects, evaluating anchor-loss sensitivity, and mitigating support-radiated dissipation in hemispherical resonators.