Uncertainty analysis and variation reduction of three dimensional coordinate metrology. Part 3: variation reduction

In this paper, the study focuses on the coordinate variations for the case in which the deterministic error component of the sampled geometric errors is no longer negligible compared to the random error component. Two different approaches are proposed for the estimation of coordinate transformation. In the one-step approach, the best-fit method is applied to directly fit the measurement data to the nominal surface. In the two-step approach, a deterministic surface is first constructed from the measurement data and the fitted deterministic surface is then best-fitted with the nominal surface to estimate the coordinate transformation. The computation needed in the two-step coordinate estimation approach is more expensive than that required by the one-step approach. However, by estimating the deterministic error component of the surface geometric error, the two-step approach can effectively reduce the influence of the deterministic error component on the result of coordinate estimation. Therefore, with the same measurement data, the two-step approach gives a much more accurate coordinate estimation result than the one-step approach. In addition, the variation range of the obtained coordinate transformation parameters is much reduced.