沖壓模具畢業(yè)設(shè)計外文翻譯---沖壓中多工件的最佳排樣-在線瀏覽
2024-09-16 07:19本頁面
【正文】 solved manually, for example, by cutting blanks from cardboard and manipulating them to obtain a good layout. The introduction of puters into the design process led to algorithmic approaches. Perhaps the first was to fit blanks into rectangles, then fit the rectangles along the strip[2]. Variations of this approach have involved fitting blanks into nonoverlapping posites of rectangles [3], convex polygons [4,5] and known interlocking shapes[6]. A fundamental limitation exists with this approach, however, in that the enclosing shape adds material to the blank that cannot be removed later during the layout process. This added material may prevent optimal layouts from being found.A popular approach to performing strip layout is the incremental rotation algorithm [610, 16]. In it, the blank, or blanks, are rotated by a fixed amount, such as 2186。 (due to symmetry), the orientation giving the best utilization is selected. The disadvantage of this method is that, in general, the optimal blank orientation will fall between the rotation increments, and will not be found. Although small, this inefficiency per part can accumulate into significant material losses in volume production.Metaheuristic optimization methods have also been applied to the strip layout problem, both simulated annealing [11, 12] and genetic programming [13]. While capable of solving layout problems of great plexity (. many different parts nested together, general 2D nesting of sheets), they are not guaranteed to reach optimal solutions, and may take significant putational effort to converge to a good solution.Exact optimization algorithms have been developed for fitting a single part on a strip where the strip width is predetermined [14] and where it is determined during the layout process [15]. These algorithms are based on a geometric construction in which one shape is ‘grown’ by another shape. Similar versions of this construction are found under the names ‘nofit polygon’, ‘obstacle space’ and ‘Minkowski sum’. Fundamentally, they simplify the process of determining relative positions of shapes such that the shapes touch but do not overlap. Through the use of this construction (in this paper, the particular version used is the Minkowski sum), efficient algorithms can be created that find the globally optimal strip layout.For the particular problem of strip layout for pair s of parts, results have been reported using the incremental rotation algorithm [7, 16] and simulated annealing [11], but so far no exact algorithm has been available. In what follows, the Minkowski sum and its application to strip layout is briefly introduced, and its extension to nesting pairs of parts is described. The Minkowski SumThe shape of blanks to be nested is approximated as a polygon with n vertices, numbered consecutively in the CCW direction. As the number of vertices increases, curved edges on the blank can be approximated to any desired accuracy. Given two polygons, A and B, the Minkowski sum is defined as the summation of each point in A with each point in B,(1)Intuitively, one can think of this process as ‘growing’ shape A
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