Automatic design of a deep-drawn circumscribing preform

Abstract

The authors describe a procedure for the automatic design of a preform based on circumscription algorithms. The procedure is defined in general terms and applied to preforms realized by axisymmetric deep-drawing processes. The automatic design procedure is supervised by a 'generate, test, and rectify' tactic. The 'generate' stage hypothesizes a deep-drawn preform that either contains the finished workpiece or is 'close' to doing so. If the workpiece is not fully contained by the initial preform, the latter is 'rectified'. Rectification applies small changes to the radii of bending and to the wall thickness of the hypothesized preform cup. Either rectification continues recursively or a new hypothesis is generate. The cup is defined by its medial and a nominal uniform wall thickness. The design is accepted when a circumscribing cup is produced. The supervisory search mechanism is a combination of A*, hill-climbing, and depth-first.