Fundamental Development of Mathematical Techniques and Computational Metrology for Coordinate Metrology

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

The goal of this research project is to advance mathematical and computational geometry tools to effectively and efficiently determine if the geometry of an artifact meets the target geometry that is specified. To achieve this task two primary objectives will be pursued. The first is the development of point-to-surface assignment based on a linearly faceted geometric model using a modified Voronoi diagram technique. A mathematical proof demonstrating that the faceted model in conjunction with the computational metrology techniques developed in this research will be developed to prove that the point-to-surface assignment is correct for the true (non-faceted) model. The second major objective is to derive the analytic partial derivatives for spline surfaces of any order. These partial derivatives will be tested against both numerical derivatives as well as currently used approximation techniques for both speed and accuracy. Finally, to demonstrate that the fundamental developments in mathematics and computational metrology are realistic and of use, they will be implemented and tested on a variety of industrial applications. If successful, the results of this research will provide faster and more accurate analyses of manufactured parts. The mathematics developed in this research to precisely align points to complex geometric surface models will permit improved analysis of parts such as complex injection molds and airfoil geometries. Furthermore, the techniques to be developed will also substantially reduce the computational time necessary to inspect complex geometries that have been made feasible via new manufacturing techniques, such as rapid prototyping. It is anticipated that the accuracy and speed results of this research will provide the enabling technology to directly and economically integrate optical and tactile scanning technology into production facilities such as automotive and aerospace facilities for use in real-time feedback for quality control.