Two-dimensional Minkowski sum optimization of ganged stamping blank layouts for use on pre-cut sheet metal for convex and concave parts

With the increasing number of parts that manufacturers need to place on a piece of material such as sheet metal, the need increases for more sophisticated algorithms for part orientation and spacing. With greater part shape complexity, the ability of a skilled worker is challenged to minimize waste. Building on the previous work of Nye, this paper presents a Minkowski sum method for maximizing the number of parts within gangs on a rectangular sheet of material. The example provided uses a simply shaped part to illustrate the presented method, yielding a packing efficiency of 62% that is identical to the efficiency that a skilled worker would produce without the algorithm. The paper also provides results for laying out a more complex part in ganged sections, demonstrating a result that would be difficult for a human to reproduce. This work extends that of Nye by adding practical constraints such as the number of parts that can be blanked at once as well as the amount of horizontal and vertical spacing between ganged blanking sets. Additionally, the paper adds an algorithm for laying out polygons with concave geometries by separating the part into a set of convex polygons. Two examples for optimization, one of a chevron-shaped part and one of a complex shape previously used by Nye [Nye TJ. Stamping strip layout for optimal raw material utilization. journal of Manufacturing Systems 2000:19(4):239-46] and Choi et al. [Choi JC, Kim BM, Cho HY, Kim C. A compact and practical CAD system for blanking or piercing of irregular-shaped sheet metal products and stator and rotor parts. International journal of Machine Tools & Manufacture 1998:38:931-63], are provided, demonstrating the existence of a local maximum number of parts that may be stamped within a single ganged blank. The algorithm is extendable to a program that may provide stamping manufacturers with a tool that can maximize the total number of parts stamped on stock sheet metal, or for other tiling problems. (C) 2008 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.