An Algorithm of Form Deviation Calculation in Coordinate Measurements of Free-Form Surfaces of Products

Abstract

The article presents the new method of form deviation calculation in the case of coordinate measurements of free-form surfaces of workpieces. The proposed algorithm of form deviation evaluation is based on the interpolation process of corrected measured points. Corrected measured points are the results of probe radius correction process applied in the coordinate measuring technique. The interpolation is conducted by using of the Lagrange and Chebyshev methods. The developed algorithm of deviation calculation can be implemented in most commercial software cooperating with a coordinate measuring machine. In the article the results of numerical and experimental investigations connected with the proposed algorithm are presented. The numerical investigations concern the simulation of contact coordinate measurements of products, which can be conducted on a coordinate measuring machine. The measured products are composed of free-form surfaces characterized by various curvature and consequently various degree of geometric complexity. The experimental investigations were conducted in order to verify the results of simulation studies. The presented method improves the accuracy of measurements of free-form surfaces of products.

A Comparison of Selected Algorithms of Form Deviation Calculation

“…Therefore, this method enables calculation of form deviations based on measured points (the method denoted as R) [11]. On the basis of the results of numerical investigations, which were presented by Magdziak [10], the method R can be treated as the reference one. It means that the method R is the most accurate.…”

“…The research was performed with the application of different measurement strategies. The need of conducting detailed real investigations arose from the results of preliminary investigations which were presented by Magdziak [10]. The preliminary research concerns coordinate measurements of only one free-form surface of a measured object.…”

The accuracy of calculating form deviations of selected free-form surfaces

“…Analogous results of research were obtained in the case of measurements' simulations of other objects. The results are presented in paper [4]. It may be associated with incorrect calculation of curves representing the shape of measured object.…”

“…The selection of interpolation method was the effect of performed statistical analysis of the results of coordinate measurements' simulations. The results of the analysis are presented in paper [4]. Moreover, investigations were made for various values of dispersion of measured points (±0.05 mm and ±0.1 mm) with regard to nominal profiles and for various distances between the measured points (0.1 mm; 0.25 mm; 0.5 mm; 0.75 mm and 1 mm).…”

“…Moreover, in paper [4] there was proposed a method for computing the form deviations of curvilinear surfaces of products which considers the Lagrange and Tschebyschev interpolation of corrected measured points. That method is denoted in the following sections of the paper with symbol L-C.…”