Mathematical Model for Evaluating Cylindricity Errors by Minimum Zone Method

Abstract

An unconstrained optimization model is established for assessing cylindricity errors by the minimum zone method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on a subset of the four-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, so long as it is convergent, can be applied to solve the objective function in order to get the wanted cylindricity errors by the minimun zone assessment. An example is given to verify the theoretical results presented.