In computing geometric tolerances using point data from a coordinate measuring machine (CMM), a best fit process needs to be carried out to bring the measurement data to the coordinate system of the substitute geometry. The measurement data does not precisely conform to the substitute geometry. It involves errors from machining as well as measurement itself. With this error-carrying measurement data, the best fit result contains uncertainties which in turn reduce the accuracy of the evaluated tolerances. In this paper, a model is proposed to estimate the best fit uncertainties caused by surface deviation, point location, and CMM sample size. The model was verified by simulation and experiment. To explore factors that affect the uncertainty variations, geometric variables that influence the uncertainties were first studied. Then, to understand the effect of point location on the uncertainty, optimization using the conjugate gradient method was developed to find the best measurement locations by minimizing the total uncertainties. In addition, simulations showed that the uncertainty is inversely proportional to the squared root of the number of points. This result can be used to predict the CMM sample size that will control the best fit uncertainty under certain tolerances.

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