Geometric Conformity-Analysis for Automated Fabrication Processes Generating Ruled Surfaces (2009-09)¶

The purpose of this paper is to present an introduction to geometric conformity principles for examining the geometric deviation between the desired (designed) and the fabricated surfaces which may be generated by a class of surface ruling fabrication processes such as flank milling, wire electrical discharge machining (WEDM), and contour crafting (CC). In general, it is computationally challenging to calculate error approximation based on points. This paper proposes methods that efficiently calculate error approximation based on curve, surface area, and volume. This paper derives the equations for calculating the ruled surface areas and the volume of 3D slices in 3D object models. One may use the difference of surface areas or volumes to determine the extent of the global conformity of the ruled surfaces. Additionally, local conformity analysis through calculating curve deviation has been introduced to improve the reliability of the global conformity analysis. The research results apply only to fabrication processes that generate ruled surfaces. There are, however, numerous applications in which ruled surfaces are generated, such as WEDM, any numerical control machining which uses cylindrical or conical cutting bits, and CC. The research results presented will be applicable to fabrication processes such as flank milling, WEDM, and CC. Originality/value – All developments presented are original. Also, CC, which is a candidate process for the developments presented in the paper, has been invented and developed by the authors.