Optimization approach for the evaluation of geometric errors in computer-aided inspection

Geometric dimensioning and tolerancing (GD&T) is a set of standards that defines a clear and concise mathematical language for communicating product definition. A design based on GD&T clearly reflects the functional requirements of a product, provides unique definition of a drawing among design, manufacturing and inspection engineers and conveys the design intention clearly without any ambiguity. The latest version of this standard is ASME Y14.5M-1994.; Traditional methods for the inspection of geometric tolerances have been mostly with the use of functional gages and Coordinate Measuring Machines (CMM). Function gages are very expensive and only provide a yes/no result. CMMs have embedded algorithms to verify geometric tolerances according to the design specification. However, it has been shown that these embedded algorithms neither provide accurate evaluation of geometric errors nor do they conform to the ASME standards.; High accuracy requirements in the manufacture of precision parts with complex geometries have made accurate evaluation and verification of geometric tolerances very critical. Over the years, researchers have developed many algorithms to evaluate some of the geometric errors. However, there is still a significant lack of evaluation procedures for complex geometric errors.; In this dissertation, mathematical models have been built for the evaluation of a certain set of complex geometric characteristics. The concentration has been on the evaluation of 3D feature relating positional error, cylindricity error and straightness error of spatial line. Research has been carried out to understand the mathematical natures of these problems. Based on the research results, efficient solution methodologies have been developed according to the ASME standards. A robust and efficient procedure has also been developed for the identification of candidate datum sets. The proposed procedures have been implemented using the C++ or C programming language. Experimental results and comparison with the results from the literature demonstrate the validity and efficiency of the developed algorithms.