An Adaptive Multi-Population Approach for Sphericity Error Evaluation in the Manufacture of Hemispherical Shell Resonators.

The performance of a hemispherical resonant gyroscope (HRG) is directly affected by the sphericity error of the thin-walled spherical shell of the hemispherical shell resonator (HSR). In the production process of the HSRs, high-speed, high-accuracy, and high-robustness requirements are necessary for evaluating sphericity errors. We designed a sphericity error evaluation method based on the minimum zone criterion with an adaptive number of subpopulations. The method utilizes the global optimal solution and the subpopulations' optimal solution to guide the search, initializes the subpopulations through clustering, and dynamically eliminates inferior subpopulations. Simulation experiments demonstrate that the algorithm exhibits excellent evaluation accuracy when processing simulation datasets with different sphericity errors, radii, and numbers of sampling points. The uncertainty of the results reached the order of 10-9 mm. When processing up to 6000 simulation datasets, the algorithm's solution deviation from the ideal sphericity error remained around -3 × 10-9 mm. And the sphericity error evaluation was completed within 1 s on average. Additionally, comparison experiments further confirmed the evaluation accuracy of the algorithm. In the HSR sample measurement experiments, our algorithm improved the sphericity error assessment accuracy of the HSR's inner and outer contour sampling datasets by 17% and 4%, compared with the results given by the coordinate measuring machine. The experiment results demonstrated that the algorithm meets the requirements of sphericity error assessment in the manufacturing process of the HSRs and has the potential to be widely used in the future.