A Novel Approach for High-Precision Evaluation of Sphericity Errors Using Computational Geometric Method and Differential Evolution Algorithm

Abstract

The sphericity error is a critical form and position tolerance for spheres. We explored the distribution of sphericity errors within the solution space to achieve a high-precision evaluation using the minimum zone criteria. Within local solution spaces, we propose treating the evaluation of sphericity errors as a unimodal function optimization task. And computational geometric methods are employed to achieve highly accurate solutions within the local solution spaces. Subsequently, we integrated the computational geometric method with the differential evolution algorithm (DE algorithm). By centering on individual population members of the DE algorithm, we partitioned the local solution spaces and utilized the best solutions within them to optimize the population. With the gradual convergence of the DE algorithm, we successfully achieved the high-precision resolution of sphericity errors. The experimental results demonstrate a significant order-of-magnitude improvement in precision compared to traditional algorithms in the field of sphericity error evaluation, with uncertainty levels reaching magnitudes of 10−14 mm. Moreover, this method enhances the accuracy of sphericity error evaluation by approximately 10% for three-coordinate measuring machines. Additionally, we conducted ablation experiments to validate the effectiveness of the proposed computational geometric method. In summary, this approach enables the high-precision evaluation of sphericity errors and provides a practical methodology for applying ultra-precision spheres in precision engineering.

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

“…It is widely acknowledged that the sphericity error varies at different rates depending on the position [ 42 , 43 ]. To demonstrate this, we use the spherical contour sampling dataset from reference [ 29 ] and apply the least squares method to obtain the initial spherical center.…”