Towards a Mathematical Definition of Skin Model for Geometrical Product Specification and Verification and its Physical Interpretation

Abstract

The concept of skin model is a foundation stone for ISO standards in Geometrical Product Specifications and Verification. At the conceptual level, it provides an abstraction of the physical part denoting the boundary which separates the part's physical shape from its environment. It conveys the designer's perception of potential defects and deviations from a nominal geometry, which can only be hypothesized. Considered as a surface on the boundary of a solid model of non-ideal geometry, which can only be imagined, the ‘skin’ can take an unrestricted variety of forms and representations at different scales. Despite its conceptual relevance, only a few research efforts have been devoted to a formal characterization of the skin model based on a sound mathematical definition supporting an appropriate and relevant physical interpretation. The work presented in this paper proposes new scientific foundations of the skin model based on the structure of solids as a compact packing of spheres characterized by Van der Waals radii. This physics-based description is extended and supported by mathematical models based on regular sets and morphological operations, which provide a set of conditions and properties that enable a physical interpretation in the context of mechanical parts and their measurements.