Mathematical Model for Evaluating Cylindricity Errors by Maximum Inscribed Cylinder

Abstract

An unconstrained optimization model applicable to radial deviation measurement is established for assessing cylindricity errors by the maximum inscribed cylinder evaluation. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory of 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. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function to get the wanted values of cylindricity errors by the maximum inscribed cylinder assessment. An example is given to verify the theoretical results presented.