Advances in Modeling and Optimization of Manufacturing Processes
Open Access

Table 1

A methodology for graph-theoretic sheet metal die stamping.

Step No. Step label Step input Step description Step output
A Stamping FEATURES GENERATIONS Feature-based CAD model The stamping features are extracted from the sheet metal CAD part model. Auxiliary stamping features (pilot and scrap features) are specified by the process planner. Stamping features set
B Features operations mapping Stamping features set Stamping features are mapped to stamping operations through direct (one-to-one) and compositional (many-to-one) mapping. Stamping operations tree
C Generate operations precedence & adjacency graphs/matrices Stamping operations tree Generate the operation precedence and adjacency matrices. Verify the operation precedence graph is acyclic using a colored DFS. Cyclic graphs must be corrected manually by the process planner by modifying the rule database and/or the design-to-operation feature assignment. Precedence & adjaceny graphs/matrices
D Applying topological sort algorithm Precedence & adjacency graphs/matrices Cluster the operations into partially ordered sets using a modified topological sorting algorithm Partially ordered operations clusters
graph coloring algorithm [23]
Partially ordered operations clusters For each cluster use the graph coloring algorithm to sub-color the clusters − this will carry out additional sorting to take into account the closeness relationships Fully ordered operations clusters
F Verify stamping sequence using Index of priority (IOP) matrix [25] Fully ordered operations clusters and use joint operation matrix and calculate IOP Optimal stamping operations sequence