Automatic design of a deep-drawn circumscribing preform

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