Sphericity error evaluation: theoretical derivation and algorithm development

Several methods for the evaluation of sphericity error exist. The Minimum R adial Separation (MRS) spheres method is a method that has been studied by several researchers. In the MRS criterion, two concentric spheres at minimu m radial separation must be found such that they contain all points on the actual spherical surface. The existing procedures for finding MRS spheres a re either too complex and time consuming or do not provide an optimal solut ion to the sphericity error evaluation problem. In this paper, mathematical optimization concepts are utilized to develop a theory and an algorithm fo r the evaluation of sphericity error based on MRS criterion. Results indica te that the algorithm is fast and accurate in providing optimal solution to the sphericity error evaluation problem.