Flatness, Cylindricity and Sphericity Assessment Based on the Seven Classes of Symmetry of the Surfaces

Dimensional inspection of a mechanical part produces a set of Cartesian coordinates of points measured by a coordinate measuring machine (CMM) from a manufactured surface of the part. The coordinates are elaborated to yield the geometric deviations of the manufactured surface from the nominal one. Many best fitting techniques, that calculate the substitute feature, and many algorithms, that evaluate the minimum zone deviation of a surface, may be currently employed to assess the form tolerance of a measured surface. This paper presents a new approach to the evaluation of flatness, cylindricity and sphericity tolerance based on surface invariance with regard to the rigid motions. The proposed algorithm transforms the coordinates measured, through homogeneous transformation matrices, in order to best fit the reference element (datum) of the class of the surface from which the actual measurements were sampled. The best fitting transformation matrix is found by means of the minimization of the sum of the squared normal distances of the measured points from the reference element of the nominal feature. The methodology was computer implemented, and numerical simulations were performed for planes, cylinders and spheres in order to validate the effectiveness and the robustness of the approach. The values obtained by this approach are compared with the form tolerance a priori known of the used datasets. The results indicate that the proposed algorithm provides accurate and quick assessments. The implementation of these inspection algorithms in a manufacturing environment can reduce the rejection of good parts, thereby reducing costs.