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(編輯修改稿)
2024-09-02 07:19 本頁面
【文章內(nèi)容簡介】 s 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 by shape B, or by sliding shape –B (., B rotated 180186。) around A and following the trace of some reference point on B. For example, shows an example blank A. If a reference vertex is chosen at (0, 0), and a copy of the blank rotated 180186。 (., –A) is slid around A, the reference vertex on –A will trace out the path shown as the heavy line in . This path is the Minkowski sum . Methods for calculating the Minkowski sum can be found in putational geometry texts such as [17, 18]. Sample Part A to be Nested.Minkowski Sum (heavy line) of sample Part (light line).The significance of this is that if the reference vertex on –A is on the perimeter of , A and –A will touch but not overlap. The two blanks are as close as they can be. Thus, for a layout of a pair of blanks with one rotated 180186。 relative to the other, defines all feasible relative positions between the pair of blanks. A corollary of this p
范文總結(jié)相關(guān)推薦
鄂ICP備17016276號-1