Construction heuristics for generating tool paths for laser cutters

Abstract

This paper deals with generating paths for cutting irregular parts nested on thin or thick metal sheets. The objective is to minimise the total time required to cut all parts from the metal sheet explicitly taking the cost of piercing and pre-cutting into account. The problem is modelled as a generalised travelling salesperson problem with special precedence constraints. A set of construction heuristics is presented that incorporates the constraints originating from inner–outer contours, common cuts, piercing points and pre-cuts. Computational tests on a set of real-life cutting problems show that our solution approach is able to generate tool paths that for thick plates spend on average 33.4% less time than those generated by a commercial package for air movements, pre-cuts and sharp angle macros with cutting and piercing times being equal.

Keywords:

• laser cutting
• cutting path
• tool path
• heuristics
• precedence constraints

Acknowledgement

The authors acknowledge the financial support from IWT-Vlaanderen (Instituut voor de Aanmoediging van Innovatie door Wetenschap en Technologie Vlaanderen).

Notes

1 The exact definition of thin, thick or very thick plates depends on the material and laser cutting machine combination.

2 If multiple contours are nested in common cut with one another, composite contours consisting of more than two contours can be identified and also here exists the constraint that all common cuts within such a composite contour have to be cut before the last element of the composite contour is cut. This quickly leads to a very large number of constraints. However, if none of the common cuts within such a composite contour is the last element of both its contours to be cut, then the composite contour will not be closed before the common cuts within are all cut. Since, if it would contain uncut common cuts, it would imply that when the last common cut within this area is cut, that cut would close both its contours, violating the initial assumption that no element closes both its contours.

3 Since piercings are so costly, the optimal solution of most practical instances will have exactly one piercing per pierce group.