An iterative neighborhood search approach for minimum zone circularity evaluation from coordinate measuring machine data

Abstract

An iterative neighborhood search approach (INSA) was proposed to precisely evaluate the circularity error under minimum zone conditions without directly solving nonlinear equations from coordinate measurement machine (CMM) data. The method starts with calculating the initial location and radius of an initial circular search scope. The location is the center of the circle based on an approximate least-squares method of all measurement data points uniformly sampled around the circle, and the radius is the circularity error value by using the approximate center as the datum center of two concentric circles enclosing all measurement data points. Then the circular search scope was divided according to some concentric circles and radials with some radius and angle step lengths. Intersections of the circles and radials were candidate centers for circularity evaluation under the minimum zone criteria. An optimal center with minimum circularity error value was picked out as a new location of the search scope. The distance from the old location was the radius of the new search scope. Further it was divided and the intersections were evaluated until the optimal solution was met. Some examples in the literature were used to verify the validity of this method. The results are the same as or better than those minimum zone solutions adopted from previous work, and computation time is no more than 0.07 s implementing on an IBM ThinkPad R40 laptop for all examples. The computation and comparison show that the proposed INSA is a precise, fast, convergent and simple approach which solved circularity evaluation problems effectively.

A Novel Approach for High-Precision Evaluation of Sphericity Errors Using Computational Geometric Method and Differential Evolution Algorithm

“…Sphericity Error Least squares (−0.2545316, −0.6600826, 0.0380931) 3.735706 [27] (−0.388729, −0.355488, −0.299887) 3.332518 [37] (−0.38873, −0.355488, 0.299888) 3.33252 [26] (−0.412356, −0.335014, −0.326140) 3.351375 [36] (−0.38872967, −0.35548811, −0.29988752) 3.33251813257 [35] (−0.3887296, −0.3554883, −0.2998876)…”

A simple unified branch-and-bound algorithm for minimum zone circularity and sphericity errors

“…Noticing that the circularity error can be determined from a small number of critical data points, Huang [10] proposed a new strategy for improving computational efficiency by collecting the farthest and nearest data points from the current minimum radial separation center until all collected data points meet an optimal condition. In addition, the evaluation of the MZC error was often treated algebraically as an optimization problem and solved using various techniques, such as iterative search approaches [11][12][13][14][15][16][17], evolutionary algorithms [18,19], a particle swarm optimization algorithm [20] and a linear programming method [21]. Recently, Rhinithaa et al [22] conducted a comparative study of several selected algorithms and a new geometric algorithm using the reflection mapping technique.…”

Improved evaluation of minimum zone roundness using an optimal solution guidance algorithm

“…However, in the last decade, a number of new methods have been proposed. The iterative neighborhood search algorithm achieved precise and rapid convergence by dividing the new searching zone [3]. A new method for circularity evaluation using a polar coordinate transform algorithm (PCTA) utilized polar radius optimization [4].…”