An Approach to Estimate the Detailed Deviation Zone in Coordinate Metrology Using Harmonic Function Properties

Understanding the exact details of deviation zone related to a manufactured surface needs measurement of infinite number of points. Coordinate metrology provides deviation of the limited number of discrete points on a measured surface, but typically it is not capable to explore any information of the surface regions between these measured points. An approach to estimate the Distribution of Geometric Deviations (DGD) on the entire inspected surface is presented in this paper. The methodology is developed based on estimation of mean value property of the harmonic functions and Laplace equation. The resulting DGD model can be employed to estimate the deviation values at any unmeasured point of the inspected surface when a detailed understanding of the surface geometric deviations is required. Implementation of the developed methodology is described and case studies for typical industrial parts are presented. This methodology can be used for closed-loop of inspection and manufacturing processes when a compensation scheme is available to compensate the manufacturing errors based on the DGD model.