Study on the properties of flatness error objective function

Abstract

Optimization algorithms are generally used to seek the minimal values of form error objective functions by iteration when a microcomputer is used to evaluate form errors of machine components by the minimum zone evaluation methods. The properties of such objective functions are very important for seeking the minimum zone values of error quickly and reliably. In this article, the unconstrained optimization model is established for assessing flatness errors by the minimum zone assessment method. The properties of the corresponding objective function are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the established flatness objective function by the minimum zone assessment method is a continuous, non-differentiable and convex function defined on the two-dimensional Euclidean space R 2 . Therefore, the global 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, as long as it is convergent, can be used to solve the objective function to get the reliable minimum zone flatness errors, without the possibility of seeking a value which is not in accord with the minimum zone for flatness. Two examples are given to verify the theoretical results presented.