Optimization of strip-layout using graph-theoretic methodology for stamping operations on progressive die: a case study

Abstract

The design of the progressive die stamping process is optimized through minimizing the number of die stamping stations in the strip layout to reduce the die cost. In order to accomplish such end, in this study, a graph-theoretic based method is implemented to model and optimize the strip layout design. This method starts with mapping stamping features into stamping operations. This step is followed by constructing two graphs to model the precedence and adjacency constraints among stamping operations based on a set of manufacturing rules. These two graphs are called: operation precedence graph and operation adjacency graph. In the next step, a topological sorting algorithm clusters the operations into partially ordered sets. Then, a graph coloring algorithm clusters the partially ordered operations sets into final sequence of operations. The graph-theoretic technique has been implemented on a part currently manufactured by laser cutting process technology in some Egyptian factory in Cairo. This study indicated that the graph-theoretic technique offers several advantages including the ease of programming and transparency in understanding the obtained strip layout design. This is besides being a systematic and logically approach to obtain an optimized strip layout design. In general, the progressive die manufacturing can increase productivity of sheet metal works in Egypt, only in situations of mass production. The limitation is that it requires considerable skill level and training for labor to conduct die strip layout design.

Keywords

• progressive die stamping
• strip layout design
• graph theory
• graph coloring algorithm
• topological sorting algorithm