Probabilistic method in form error evaluation: comparison of different approaches

The form error in manufactured parts needs to be assessed to verify the compliance of the parts with the specifications. Workpieces are usually measured by means of a coordinate measuring machine that extracts a set of three-dimensional points from the manufactured surface. It is obvious that the association method used to fit the nominal shape to the set of points plays an essential role in the error assessment process. Moreover, the uncertainty that arises during the measurement procedure must be estimated to provide a complete measurement result. Within this framework, the aim of this paper is to compare the performances of the so-called probabilistic method with those of the classical least squares methods in order to estimate different roundness errors together with the associated uncertainty. The latter has been estimated by means of two different approaches: the bootstrap and the so-called gradient-based method, and the differences between the two are discussed.