Pierce point minimization and optimal torch path determination in flame cutting

This paper addresses the problem of sequencing a torch for the cutting of a stock sheet nested with regular or irregular parts. The image of the nesting is reduced to an equivalent graph, and the objective is to traverse this graph with a minimum number of pierce points, or blowthroughs. If the graph has $\text{2k}$ vertices of odd degree, then $\text{k}$ pierce points are necessary and sufficient to traverse the graph. The torch path problem formulation includes manufacturing cost, efficiency, and distortion considerations. We present three algorithms for the problem. The first algorithm shows how to determine the $\text{k}$ torch paths, and is optimal in run time complexity. The second algorithm uses trim margin edges to investigate further reduction in the number of pierce points. The third algorithm guarantees that for the special case where a torch path has no vertices of odd degree, no piece will be dropped that needs further interior cuts. Some possible extensions to this work are also addressed.