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Two-dimensional minkowski-sum optimization of ganged stamping blank layouts for use on precut sheet metal for convex and concave parts
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|Title: ||Two-dimensional minkowski-sum optimization of ganged stamping blank layouts for use on precut sheet metal for convex and concave parts|
|Authors: ||Mulero, Rafael|
Layton, Bradley E.
|Keywords: ||Stamping Die;Sheet Metal;Optimization;Material Utilization;Two-Dimensional Minkowski Sum|
|Issue Date: ||2007|
|Citation: ||Journal Unknown|
|Abstract: ||As the number of parts that manufacturers need to place on a piece of material such as sheet metal increases, the need for more sophisticated algorithms for part orientation and spacing also increases. With greater part shape complexity, the ability of a skilled craftsman becomes challenged to minimize waste. Building upon the previous work of Nye, we present 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. We also provide results for laying out a more complex part in ganged sections, demonstrating a result that would be difficult for a human to reproduce. Our 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 we add 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 (2000) and Choi et al. (1998) are provided demonstrating the existence of a local maximum number of parts that may be stamped within a single ganged blank. Our 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.|
|Appears in Collections:||Faculty Research and Publications (MEM)|
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