Sphericity error evaluation based on conical search algorithm

Yueping Chen

doi:10.1088/1361-6501/ae26a3

2026-01-09

PRE

DOI：10.1088/1361-6501/ae26a3

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摘要

En 中文

To improve the evaluation accuracy and calculation efficiency of sphericity error, a high-accuracy and high-efficiency sphericity error evaluation method based on the conical search algorithm is proposed. Firstly, an auxiliary sphere is constructed with the least squares sphere center as a reference, and seven auxiliary search points are selected for coarse search to identify the optimal and suboptimal auxiliary search points. Secondly, fine search is performed: taking the optimal solution of the coarse search as the vertex and the line connecting the optimal and suboptimal solutions as the axis, a conical search space is constructed. Conical search points are generated by layered equal-angle sampling on the conical surface. By utilizing the feature that the radius of the conical cross-section decreases as height increases, high-density sampling is achieved in the region close to the optimal solution, and a global optimal sphere center is obtained through iterative convergence. Finally, based on the '3 + 2' and '2 + 3' geometric configurations of the minimum zone theory, the accurate solution of sphericity error is completed. Experimental results show that in the four groups of simulated datasets, the evaluation results of the proposed algorithm are consistent with the ideal values. Compared with the genetic algorithm, the average running time is shortened by approximately 98.6%; compared with the particle swarm optimization algorithm, it is reduced by about 93.9%, showing a significant improvement in computational efficiency. The standard deviation of 20 repeated experiments is 0, indicating high stability. In the comparison of three groups of reference datasets, the sphericity error evaluation results are more accurate than those of existing mainstream algorithms, verifying the effectiveness of this algorithm in sphericity error evaluation.

Keyword:

conical search algorithm

minimum zone

geometric configuration

sphericity error