Convergence of a finite difference approach for detailed deviation zone estimation in coordinate metrology

Abstract

In order to comprehend an entire surface's deviation zone, infinite measured points are required. Using the common measurement techniques through coordinate metrology, a limited number of surface actual points can be acquired. However, the obtained points would not provide sufficient information to examine the geometry thoroughly. A novel approach to predict surface behaviour via Distribution of Geometric Deviations (DGD) is examined in this paper. The methodology governs the mean value property of the harmonic functions to solve Laplace equation around each measured point. This DGD model can be used to reconstruct surface deviation values at any unmeasured point of the inspected surface based on a limited number of measured points. The convergence of the introduced approach is studied in this paper. A complete approach to implement the developed methodology is described, and the validation process is studied using actual case studies and mathematical functions. This methodology is practical in closed-loop inspection and manufacturing processes to form a scheme for compensating the surface errors during manufacturing process based on the DGD model.