Computation of Sphericity from Minimum Circumscribing and Maximum Inscribing Centers by Means of Simulation Data and Downhill Simplex Method

This article deals with calculation of three-dimensional sphericity values from minimum circumscribing and maximum inscribing centres, although ISO and JIS define two-dimensional sphericity by means of two or three roundness measurements from minimum circumscribing centre. One of the reasons is the difficulties of measuring technique for the whole spherical surface. In this article, the data to be referred is simulated by applying surface harmonics (Laplace's spherical function). Downhill simplex method, one of nonlinear optimization techniques, is applied for search of minimum circumscribing and maximum inscribing centres. Then, their application conditions are investigated. Furthermore, two- and three-dimensional values of the spherical form errors are compared. In the future, further evaluation methods should be studied for actual three-dimensionally measured spherical form errors.