The minimum zone evaluation for elliptical profile error based on the geometry optimal approximation algorithm

• A new method for elliptical profile error evaluation using Geometry Optimal Approximation Algorithm (GOAA) has been presented.
• The algorithm is no requirement to the distribution of the measure points, and can realize error evaluation to the elliptical profile.
• The minimum zone evaluation for elliptical profile error is realized by using the iterative approximation method.
• The algorithm is simple, intuitive and easy to program, and it has the commonality and better practicability.

To realize a more accurate evaluation for elliptical profile error, based on the minimum zone geometry optimization approach method, an algorithm for evaluating elliptical profile error is presented. Firstly, based on the least squares method, a reference ellipse and a pair of initial reference points are determined, taking the pair of reference points as reference points, auxiliary focuses is established and auxiliary ellipses are constructed by using the auxiliary focuses. Secondly, the elliptical profile errors are calculated, when the reference ellipse and the auxiliary ellipses as supposed ideal ellipses. Through comparing, judging and changing the reference points, constructing new auxiliary points and auxiliary ellipses, forming new assumed ideal ellipses, the minimum zone evaluation for elliptical profile error is realized finally by using the iterative approximation method. The process and the steps of solving elliptical profile error are described in detail, the mathematical formulas are given. Which shows this algorithm can not only get the results accurately but also stably.