Variational techniques for assessing the technological signature of flat surfaces

The quality assessment of manufacturing operations performed to obtain given flat surfaces is always a problem of comparing the substitute model (approximating the features of the true manufactured part) to the nominal specifications, at any stage of the manufacturing cycle. A novel methodology, based on applications of classical tools of Calculus of Variations, is here presented with the aim of assessing the output quality of manufactured flat surfaces based on the information available on transformation imposed by technological processes. By assuming that any manufacturing process operates under equilibrium states, the proposed variational methodology allows to account for the traces left by different stages of manufacturing processes. A simple two-dimensional case is here discussed, to give the flavor of the methodology and its future potential developments.