A Method for Extracting and Thickening a Mid-Surface of a 3D Thin Object Represented in NURBS

Abstract

In analyses of manufacturing processes such as injection molding of plastics or die casting of metals, the geometry of a typical 3D thin-walled structure is usually represented by an aggregation of mid-surfaces. This geometric simplification associated with assigned part thicknesses significantly reduces the computational complexity in engineering analysis (e.g., flow and solidification simulations). On the other hand, it complicates data transfer from and back to any CAD/CAM system in which objects are not represented by their mid-surfaces. As a part of an overall effort to develop a feature-based system for concurrent design and manufacturing of complex thin parts, a new algorithm has been developed for representing both the objects and their mid-surfaces. This algorithm can extract a mid-surface representation from a complex 3D thin object and then reconstruct the object from the modified mid-surface according to the analysis results. The objects consist of sculptured features with tubular topology and are represented by NURBS. The proposed method is based on offsetting techniques and deals directly with the control polygons of the object boundaries and of the mid-surfaces. The algorithms are based on offsetting techniques since there is a high correlation between medial surfaces and offset surfaces. In the case of swept features, simplification is achieved by using 2D rather than 3D techniques.