Graph Theoretic Algorithm for Automatic Operation Sequencing for Progressive Die Design

The paper presents a formal graph representation scheme for stamping operation sequencing for sheetmetal progressive dies and a graph theoretic method for automatic determination of the stamping operation sequence. Operation relations are represented by two graphs: an operation precedence graph and an adjacency graph. The first represents precedence constraints defined by best manufacturing practices. The second represents geometric infeasibility relations between operations. Each operation is a member of both graphs. The graphs are automatically generated from a set of stamping operations, which in turn are associated with stamping features of a part. The operation precedence graph is then verified to be acyclic using a coloured Depth First Search. Based on the operation precedence graph, a modified topological sort algorithm is applied to cluster the operations into partially ordered sets. Finally, a graph-colouring algorithm is applied to the operation adjacency graph on the partially ordered operation sets. The algorithm is implemented in C++ and is fully integrated with SolidWorks computer-aided design system. A case study is presented to illustrate the algorithm.