Improved sphericity error evaluation combining a heuristic search algorithm with the feature points model

This paper describes a high-speed method of evaluating sphericity errors using a heuristic search algorithm combined with a feature points model (HSA-FPM). First, the sphere center and sphericity of the least-squares sphere are calculated to establish the initial candidate points of the sphere center. An iterative search procedure is then conducted based on the specified heuristic search algorithm and sphericity evaluation criterion, and the current globally optimal sphere center O is obtained under certain termination conditions. To determine the decisive feature points and construct a sphericity evaluation model, the distances d_i between the sphere center O and all sampling points are calculated and sorted. The modified sphere centers are then determined using the corresponding feature points model. As an application example, the Nelder-Mead algorithm is combined with the feature points model. Experimental results demonstrate that the proposed method achieves the exact sphericity solution with relatively few iterations, requiring only ∼0.01 s for the whole evaluation procedure. This corresponds to an improvement in evaluation efficiency of ∼26%-61% over previous methods. The proposed HSA-FPM method is in complete agreement with several well-known evaluation criteria and is quite suitable for real-time measurements and evaluations of sphericity errors.