Research on the properties of axis straightness objective function

Abstract

An unconstrained optimization model applicable to radial deviation measurement is established for assessing axis straightness errors by the minimum zone method. 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 the four-dimensional Euclidean space R4. 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 axis straightness errors by the minimum zone assessment. An example is given to verify the theoretical results presented. © 2011 Springer-Verlag.