Evaluation of form tolerance using a linear approximation technique
Weber, Timothy P.
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Evaluation of form tolerance is a critical aspect of many manufacturing processes. Machines such as the coordinate measuring machine often employ the technique of the least squares form-fitting algorithms. While based on sound mathematical principles, it is well known that the method of least squares often overestimates the tolerance zone, causing good parts to be rejected. Many methods have been proposed in efforts to improve upon results obtained via least squares, including those which result in the minimum zone tolerance value. However, these methods are typically complex and computationally slow, making them impractical for implementation in measuring equipment. In this thesis a new method, the linear approximation technique, is introduced for use in evaluating the forms of straightness, flatness, circularity, and cylindricity. It is a general technique that can be applied to most any form type. Nonlinear equations are derived for each form and linearized using Taylor expansion, then solved as linear programs using software written in C++ language. Examples are taken from the literature as well as from data collected on a coordinate measuring machine for comparison with least squares and minimum zone results. For all examples, the new formulations are found to equal or best the least squares results and provide a good approximation to the minimum zone tolerance.