Harmonic fitting approach for plane geometry measurements

The dimensional control of a plane geometry is performed by measuring a limited number of points on the manufactured part and by fitting a substitute geometry to the measured points. The accuracy of the dimensional control depends on several factors among which the number of sampled points plays a significant role. the optimal number derives from a compromise between cost and accuracy of inspection. To date, no analytical relationship has been established between the number of points and the accuracy of dimensional control, and the selection of the number of sampled points is still performed using experience-based rules. The paper proposes the harmonic fitting (HF) approach for the selection of the number of sampled points when measuring a plane geometry. Hf is the spatial frequency correspondent of the least squares method (LSM) and it will be demonstrated that following HF, the estimated errors can be evaluated as a function of the number of sampled points with closed analytical formulae. This is the basis for the development of a parsimonious sampling for coordinate measuring machines (CMMs).