套環(huán)的沖壓工藝與模具設計畢業(yè)論文-資料下載頁

　　

【正文】 or these two cases.Previous Work Originally, strip layout problems were 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。[7], the pitch and width of the layout determined and the material utilization calculated. After repeating these steps through a total rotation of 180186。 (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 pairs 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 Sum The 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 property is that if the Minkowski sum of a single part is calculated. With its negative, .,. (A plete explanation of these properties of the Minkowski sum is given in [15].) These observations were the basis for the algorithm for optimally nesting a single part on a strip.The situation when nesting pairs of parts is more plex, since not only do the optimal orientations of the blanks and the strip width need to be determined, but the optimal relative position of the two blanks needs to be determined as well. To solve this problem, an iterative algorithm is suggested:Given: Blanks A and B (where B=–A when a blank is paired with itself at 180186。)8. Select the relative position of B with respect to A. The Minkowski sum defines the set of feasible relative positions ().9. ‘Join’ A and B at this relative position. Call the bined blank C.10. Nest the bined blank C on a strip using the Minkowski sum with the algorithm given in [14] or [15].11. Repeat steps 13 to span a full range of potential relative positions of A and B. At each potential position, evaluate if a local optima may be present. If so, numerically optimize the relative positions to maximize material utilization.Layout Optimization of One Part Paired with ItselfThe first step in the above procedure is to select a feasible position of blank B relative to A. This position is defined by translation vector t from the origin to a point on, as shown in . During the optimization process, this translation vector traverses the perimeter of.Relative Part Translation Nodes on, showing Translation Vector t. Initially, a discrete number of nodes are placed on each edge of. The two p