A New Method of Distribution of Measurement Points on Curvilinear Surfaces of Products

The article presents the method of selecting scanning lines along which coordinate measurements, performed by using, e.g., a coordinate measuring machine working in the single point probing mode, of free-form surfaces of measured workpieces may be conducted. Additionally, the proposed method supports the user of a coordinate measuring system during defining the number of measurement points distributed along selected scanning lines, thus deciding on the final distribution of measurement points on a measured surface of a product. The proposed method enables distributing measurement points in the parts of a measured product characterized by the worst quality of manufacturing. Moreover, the new method is very automated, therefore it affects the increase in the efficiency of coordinate measurements. The effect of using the new method is the non-uniform distribution of measurement points located on free-form surfaces. The presented algorithm takes into account the lengths of selected cross-sections of a measured curvilinear surface of an object, its geometrical complexity and the accuracy of the probe radius correction process. The decision regarding the number of measurement points is made on the basis of the accuracy analysis of the calculations of the corrected measurement points obtained during the probe radius correction process and the accuracy of the substitute model representing a measured curvilinear surface. Two methods of the correction process were used. The accuracy of the applied methods of the probe radius compensation process was estimated on the basis of the deviations calculated between corrected measurement points and scanning lines. The selection of scanning lines and the number of measurement points was realized by using the expert system based on the fuzzy logic. The paper presents the results of both simulation and experimental investigations. The numerical calculations were performed for two selected free-form surfaces. The verification of the developed algorithm was carried out during experimental investigations based on a measurement of a selected free-form surface. The conducted research was aimed at verifying the correctness of the distribution of measurement points generated using the proposed method. In the case of real measurements, measurement points should be located in the places of surfaces of products characterized by the largest deviations of manufacturing. The results of the conducted investigations confirm the usefulness of the developed algorithm for defining the distribution of measurement points on curvilinear surfaces in the coordinate measuring technique. Moreover, the way of implementation of the developed method of the distribution of measurement points in selected commercial measurement software is presented, thus enabling the use of the new method in the industry.