An integrated approach for the estimation of spherical form tolerance

Abstract

The functionality and interchangeability of a product are key concerns during quality inspection, necessitating research to improve accuracy of inspection while reducing time and costs. The computation of form tolerance invariably involves a discretization of the surface (form) and a subsequent comparison of deviations from an evaluated “best” fit. In this paper, the effects of and interactions between various factors involved in spherical form verification—fitting algorithms, sample sizes, and sampling strategies—are analyzed. The principal objective is to consider sampling and fitting in an integrated manner and make pilot conclusions that would serve as the basis for developing decision support for part inspection. Sample sizes of 16, 64, and 256 are chosen to include a low, medium, and large sample size, respectively. Sampling strategies investigated include a randomly generated sequence, a Hammersley sampling strategy, and the aligned systematic sampling scheme. The linear least-squares fitting algorithm and a linear and nonlinear optimization approach are considered. In addition, minimum zone sphericity is computed by taking advantage of the robust properties of support vector regression, and the method is evaluated against traditional algorithms. Subsequently, these various factors are incorporated into an experimental design model, and interactions and main effects are analyzed.