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

Abstract

Dimensional inspection of a manufactured surface by means of a coordinate measuring machine (CMM) produces a set of Cartesian coordinates. The coordinates are processed to yield the geometric tolerance of the 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, through homogeneous transformation matrices, the coordinates measured to best fit the reference element of the surface class from which the actual measurements were sampled. The transformation matrix is simplified taking into account the invariance of the sum of the squared normal distances of the measured points from the nominal surface as regards some rigid motions. This invariance is a consequence of the invariance as regards some displacements of the nominal surface from which the data points were sampled. In this way, the number of parameters to be optimised is reduced in comparison with the six parameters characterizing the general homogeneous transform matrix. The methodology was computer implemented and numerical simulations were performed for planes, cylinders, and spheres in order to validate the effectiveness of the approach. The results indicate that the proposed algorithm provides accurate and quick assessments.

Influence of welding parameters and post-weld aging on tensile properties and fracture location of AA2139-T351 friction-stir-welded joints

“…Then, as-welded joints are still capable of heat treatment hardening. Of course, post-weld aged joints do not reach the hardness of the 2139-T851, because the heat input of the FSW process lowered the age hardenability of the 2139-T351, due to nugget recrystallization, grain coarsening and diffusion of alloy elements in the HAZ; this partially prevents Mg-Al co-clustering which promotes the precipitation of the W phase during the subsequent heat treatment 13 . Finally, it is to be notice that, in the studied RP range, HAZ hardness of as-welded joints increases of about 20%, while that of the post-weld aged joints of about 10%, meaning that the post-weld treatment has also the effect of reducing and redistributing residual stresses, with consequent levelling of the mechanical properties of the joints.…”

Minimum centroid neighborhood for minimum zone sphericity

“…All the (five) datasets available from the literature, which have been tested with center-based methods and where the minimum zone center C MZ is declared, are listed in Table 1 with the reference to the original works and with the results achieved by other authors by their respective methods. Minimum zone centers are not available from [7], [30] and [31], and from the authors of dataset 1 [14].…”

Soft-Sensing Model of Flatness Error on the Surface of Machining Workpiece and its Application

“…The common methods of assessing flatness error [1] are the minimum area method, the diagonal method, the three-point method and the least squares method. The traditional evaluation algorithms on shape error tend to occur problems such as not converging and slow computation during the calculation [2][3], it is difficult to adapt to the requirements of product testing development, so the study on high accuracy, reliability and efficiency of modern evaluation method has an important practical significance. The SVM (Support Vector Machine, SVM) [4][5][6] can use small samples for training and obtain a better effect of soft measurement, providing an effective new idea for solving the problem that the soft sensing accuracy of flatness error on the surface of mechanical workpiece is low.…”