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

1、<p><b>　　中文3387字</b></p><p><b>　　附錄A</b></p><p>　　沖壓中多工件的最佳排樣</p><p>　　摘要：在沖壓生產(chǎn)中，生產(chǎn)成本受材料利用率影響最大，材料支出占整個生產(chǎn)成本的75%。本文將介紹一種新的計算方法用于實(shí)現(xiàn)雙工件在沖壓排樣設(shè)計中的最佳規(guī)劃方法，以便提高

2、材料利用率。這種計算方法可以預(yù)示在帶料中結(jié)構(gòu)廢料的位置及形狀，以及工藝廢料的位置和最佳寬度。例如將兩個相同的工件中的其中一個旋轉(zhuǎn)180°,或是將兩個不同的工件嵌套在一起。這種計算方法適合與沖模設(shè)計CAE系統(tǒng)結(jié)合使用。</p><p>　　關(guān)鍵字：沖壓，模具設(shè)計，最佳化，材料利用率，明可夫斯基和，設(shè)計工具 </p><p><b>　　緒論</b></p

3、><p>　　在沖壓生產(chǎn)中，能夠快速生產(chǎn)不同復(fù)雜程度的薄片金屬零件，特別是在大產(chǎn)量的情況下，能夠高強(qiáng)度生產(chǎn)。生產(chǎn)過程效率高，其中材料成本占據(jù)整個沖壓生產(chǎn)成本的75% [1]。但材料不能被完全利用到零件上，因為零件不規(guī)則的外形必須被包含在帶料內(nèi)。沖壓生產(chǎn)的排樣設(shè)計直接決定廢料的大小。很明顯，使用最理想的排樣設(shè)計對于提高公司的競爭力是至關(guān)重要的。</p><p><b>　　前期工作&l

4、t;/b></p><p>　　曾經(jīng), 帶料排樣設(shè)計問題需要通過手工來解決。例如, 通過紙板模擬沖裁來獲取一個好的排樣方法。通過計算機(jī)介紹的設(shè)計過程所得出的步驟。也許首先要做出適合工件的矩形，然后將矩形順序排放在帶料上[2]。這種方法適合不相互重疊的矩形[3]、拉深多邊形[4, 5]、已知相互關(guān)聯(lián)的外形[6]。這種原理的方法具有一定局限性，盡管如此，在這種具有局限性下的設(shè)計中所產(chǎn)生較多的工藝廢料不能被避免，

5、這些額外損失的材料導(dǎo)致了設(shè)計方案無法達(dá)到最佳化。</p><p>　　增量旋轉(zhuǎn)法是一種流行的排樣設(shè)計方法[6-10, 16]。具體實(shí)現(xiàn)方法為，將零件旋轉(zhuǎn)一定的角度，例如2°，[7]，在設(shè)計中決定零件傾斜程度和帶料寬度以及合適的材料利用率。在不斷重復(fù)這些步驟以后工件旋轉(zhuǎn)量達(dá)到180º (由于對稱)，然后從中選出最佳排樣方法。這種方法的缺點(diǎn)是，在一般情況下，最佳材料定位將降低旋轉(zhuǎn)增量同時不能被找到

6、。盡管差別很小，但在大批量生產(chǎn)中每個零件所浪費(fèi)的材料會累計進(jìn)而導(dǎo)致較多材料損失。</p><p>　　梅塔-啟發(fā)式優(yōu)化方法適用于排樣設(shè)計，包括模擬退火[11, 12]和初步設(shè)計 [13]。當(dāng)解決較復(fù)雜設(shè)計問題時 (也就是在2D平面上將較多不同零件嵌套在一起)，它不能保證最佳排樣方法，但是可以根據(jù)獲得的計算結(jié)果進(jìn)而總結(jié)為一個較好的解決方法。</p><p>　　開發(fā)出一種在設(shè)計過程[15]中

7、確定單一零件在帶料上的布局以及帶料的寬度的確定[14]的精確的最佳的計算方法。這些計算方法基于建筑幾何學(xué)中一個外形從另外一個上‘發(fā)展’出來。相似的理論在這個學(xué)科中基于一個名叫‘無適合多邊形’，‘障礙空間’和‘明可夫斯基和’創(chuàng)建。從根本上來講， 它僅是一種解決位置關(guān)系的方法，這樣的外形有缺陷，但不會重疊。通過這種方法的應(yīng)用 (本文中，特殊的譯文是指明可夫斯基和)， 能夠創(chuàng)建一種全球化的最佳的具有高效率的排樣布局的計算方法。</p&g

8、t;<p>　　對于排樣設(shè)計中零件間布局的特殊問題則根據(jù)問題報告采用增加旋轉(zhuǎn)計算方法 [7, 16]和模擬退火 [11]， 但是迄今為止并沒有能夠被實(shí)際應(yīng)用的精確的計算方法。在下文中，將簡要介紹明可夫斯基和，以及它在帶料排樣設(shè)計中的應(yīng)用，和它在成對零件間嵌套問題的延伸的描述。 </p><p><b>　　明可夫斯基和 </b></p><p>　　零件

9、的外形被近似嵌套在每個多邊形的n 個頂點(diǎn)上，在CCW方向上有限連續(xù)。隨著頂點(diǎn)數(shù)量的增加零件邊上的彎曲刃口能夠近似的得到任意想要達(dá)到的精確度。例如兩個多邊形，A 和 B， 明可夫斯基和詳細(xì)說明了A和B上每一個頂點(diǎn)的總和。</p><p><b>　　(1)</b></p><p>　　表面上看, 令人聯(lián)想到這種方法中的零件A‘成長于’零件B，或是變化后的零件–B (也就

10、是零件B旋轉(zhuǎn)180°) ，零件A周圍和接著零件B周圍參考點(diǎn)所連接而成的軌跡。例如，圖1所示零件A。如果基于其中一個參考頂點(diǎn) (0，0)，將旋轉(zhuǎn)180°后的零件A (也就是–A)圍繞著零件A，–A上的參考點(diǎn)以粗線描述出圖2中所示輪廓。 這個輪廓即是麥克馬斯特和 。麥克馬斯特和計算所用的方法能夠被創(chuàng)建在計算出的幾何圖形中如[17，18]。 </p><p>　?。▓D1） 示例零件A被嵌套</

11、p><p>　?。▓D2） 示例零件（虛線）在麥克馬斯特和 (粗線)中。</p><p>　　這個方法的意義在于如果–A的參考頂點(diǎn)是在 的周界上，A和–A將會相接觸但不會產(chǎn)生重疊。兩個零件將會盡可能的緊密貼合在一起，因而在設(shè)計時將一對零件其中的一個旋轉(zhuǎn)180°。 定義了一對零件間所有可行的位置關(guān)系。</p><p>　　這個性質(zhì)的一個推論是如果單一零件的麥克馬斯

12、特和是合適的。那么該零件將被否定，也就是 。(麥克馬斯特和推出的一個完整的說明[15]。)這些報告是根據(jù)帶料上單一零件間的最佳嵌套計算方法得出。</p><p>　　嵌套的成對零件太過復(fù)雜的情況時，不僅要作出零件的最佳定位和選定帶料寬度還要設(shè)計成對零件間最佳的位置關(guān)系。為了解決這一問題，故提出一種重復(fù)運(yùn)算方法：</p><p>　　假設(shè)：零件A和B(B=–A，–A即將A旋轉(zhuǎn)180°

13、;)</p><p>　　5. 在不干涉A的情況下選擇B的位置關(guān)系麥克馬斯特和 定義了可行的位置關(guān)系 (圖2)。</p><p>　　6. 在這個位置關(guān)系中‘加入’A和B. 創(chuàng)建出新的組合零件外形C。</p><p>　　7. 在帶料上使用麥克馬斯特 和套入組合零件C以及[14]或[15]給出的運(yùn)算法則。</p><p>　　8. 重復(fù)步驟1

14、-3直到排列出所有A和B可能的位置關(guān)系。在每個位置關(guān)系中找出最好的位置關(guān)系，如果這樣，數(shù)字上最佳的位置關(guān)系即是最高的材料利用率。</p><p>　　兩相同零件間最佳設(shè)計方法</p><p>　　上述方法的第一步是選擇一個可行的B和A的位置關(guān)系。 上的一個平移矢量t定義了這個位置，如（圖3）所示。當(dāng)這個平移矢量t穿過 的輪廓時為最佳的方法。</p><p>　?。▓D

15、3） 上關(guān)系零件的平移節(jié)點(diǎn)，顯示出平移矢量 t。</p><p>　　最初，節(jié)點(diǎn)上不連續(xù)的數(shù)被放置在 中的每個邊界上。每個平移節(jié)點(diǎn)描述了兩個零件臨時‘加入’位置關(guān)系，然后組合零件帶料寬度中的最佳位置上使用單件生產(chǎn)設(shè)計程序(例如在 [14]或[15]中)。在此例中, 由12條邊組成，每條邊包含10個節(jié)點(diǎn)，總共多達(dá)120個平移節(jié)點(diǎn)。每個節(jié)點(diǎn)的位置是通過每條邊 直線的插補(bǔ)創(chuàng)建，在麥克馬斯特和上 即頂點(diǎn)I的坐標(biāo)是( ,

16、)。定義一個位置參數(shù) 中s = 0和 中s = 1，每個平移節(jié)點(diǎn)的坐標(biāo)創(chuàng)建方式如下:</p><p><b>　　(2)</b></p><p><b>　　(3)</b></p><p>　　如果點(diǎn)m放置在每條邊上， ， 位置參數(shù)的值 ,按如下公式創(chuàng)建：</p><p><b>　　(4

17、)</b></p><p>　　利用圖3所示120個節(jié)點(diǎn)計算出的結(jié)果如圖4所示。在此圖中，當(dāng)每條邊移動時 顯示了如何利用截線改變每條邊后平移矢量的線被打斷。當(dāng)一些邊的截線上述單一的變化，其他截線的則顯示了2到3個局部截線。 從中找最合適的位置，這就是需要許多節(jié)點(diǎn)的原因。</p><p>　　（圖4）零件 A 和–A的最佳材料利用率</p><p>　　根

18、據(jù) 創(chuàng)建出的級數(shù)，當(dāng)局部最大利用率被顯示出時即可調(diào)用一個理論上最佳的方法。在引出工作利用率之前不可用(無附加計算結(jié)果)，可以使用區(qū)間分半法 [19]。節(jié)點(diǎn)最初組成的間距能夠顯示出局部最大的點(diǎn)。三個相同間距的點(diǎn)放置在上述間距間 (也就是在 1/4, 1/2和3/4 的位置)，然后計算出每個點(diǎn)上的利用率。比較每個點(diǎn)上的利用率之值，能夠根據(jù)反復(fù)降低所得間隔的一半得出結(jié)果。上述步驟直到得到想要的精度為止。 </p><p&g

19、t;　　應(yīng)用這種方法推導(dǎo)出最佳平移矢量點(diǎn) (747.894，250.884)，如（圖5）所示排樣圖材料利用率達(dá)92.02%。</p><p>　　有趣的是，較好的設(shè)計看起來成對零件能夠更加的貼近，以便提高材料利用率。</p><p>　?。▓D5）單一零件A的最佳排樣方法</p><p>　　不同零件同一帶料上的最佳排樣方法生產(chǎn)中常遇到相同材料和相同產(chǎn)量的各類零件，

20、例如，需要裝配在一起的左右兩部分零件。將類似的零件組合在一起生產(chǎn)可以獲得更高的效率，還能提高材料的利用率。這種運(yùn)算法則的排樣設(shè)計同樣適合相同零件的排樣設(shè)計。例如（圖6）所示的零件B。決定平面位置關(guān)系的相應(yīng)的麥克馬斯特和 ，如（圖7）所示。在此例中, 包含15條邊，材料利用率的值如（圖8）所示。重復(fù)一次，通過 的邊精確顯示出多種局部最大利用率。（圖9）所示即為最佳排樣平移矢量點(diǎn)坐標(biāo)(901.214, 130.314)。材料利用率為85.3

21、2%。此例中帶料寬度為1229.74、步距為1390.00。</p><p>　?。▓D6）被嵌套的示例零件B的麥克馬斯特和 (粗線)</p><p>　　（圖7）示例零件(細(xì)線和虛線)</p><p>　?。▓D8）示例零件A和B不同排樣方法的材料利用率</p><p>　?。▓D9）示例零件A和B的最佳排樣方法</p><

22、p><b>　　結(jié)論</b></p><p>　　在沖壓工作中，材料成本占產(chǎn)品成本很大比重，所以即使每個零件上微小的節(jié)約，也能累計成可觀的價值。本文介紹了一種新的創(chuàng)建零件間嵌套的最佳排樣計算方法。這種計算方法利用了麥克馬斯特和計算出成對零件間所有可行的位置關(guān)系，和選取零件最佳位置以及帶料的寬度。</p><p>　　做排樣設(shè)計時應(yīng)注意：所有的排列方式都應(yīng)該被考慮

23、。例如，本文中示例零件的排樣方法應(yīng)該考慮：零件A單獨(dú)排樣成對生產(chǎn)，零件B單獨(dú)排樣成對生產(chǎn) 以及A和B成對一起生產(chǎn)。設(shè)計者應(yīng)該考慮原料成本，模具加工成本和操作成本以及沖出零件需要的工具盡量降低生產(chǎn)成本。</p><p>　　這種計算方法的應(yīng)用還可以拓展，其中一個顯而易見的拓展應(yīng)用即是零件間旋轉(zhuǎn)后的最佳位置關(guān)系，即改變零件B在帶料上相對于零件A的位置。另一個拓展是可以更深入的學(xué)習(xí)函數(shù)的運(yùn)用。</p>&

24、lt;p><b>　　附錄B</b></p><p>　　Stamping Die Strip Optimization for Paired Parts</p><p><b>　　Abstract</b></p><p>　　In stamping, operating cost are dominated by

25、 raw material costs, which can typically reach 75% of total costs in a stamping facility. In this paper, a new algorithm is described that determines stamping strip layouts for pairs of parts such that the layout optimiz

26、es material utilization efficiency. This algorithm predicts the jointly-optimal blank orientation on the strip, relative positions of the paired blanks and the optimum width for the strip. Examples are given for pairing

27、the same parts t</p><p>　　Keywords: Stamping, Die Design, Optimization, Material Utilization, Minkowski Sum, Design Tools</p><p>　　Introduction</p><p>　　In stamping, sheet metal par

28、ts of various levels of complexity are produced rapidly, often in very high volumes, using hard tooling. The production process operates efficiently, and material costs can typically represent 75% of total operating cost

29、s in a stamping facility [1]. Not all of this material is used in the parts, however, due to the need to trim scrap material from around irregularly-shaped parts. The amount of scrap produced is directly related to the e

30、fficiency of the stamping strip </p><p>　　Previous Work</p><p>　　Originally, strip layout problems were solved manually, for example, by cutting blanks from cardboard and manipulating them to ob

31、tain a good layout. The introduction of computers 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

32、 approach have involved fitting blanks into non-overlapping composites of rectangles [3], convex polygons [4,5] and known interlocking shapes[6]. A fun</p><p>　　A popular approach to performing strip layout

33、is the incremental rotation algorithm [6-10, 16]. In it, the blank, or blanks, are rotated by a fixed amount, such as 2º[7], the pitch and width of the layout determined and the material utilization calculated. Afte

34、r repeating these steps through a total rotation of 180º (due to symmetry), the orientation giving the best utilization is selected. The disadvantage of this method is that, in general, the optimal blank orientation

35、 will fall between the r</p><p>　　Meta-heuristic optimization methods have also been applied to the strip layout problem, both simulated annealing [11, 12] and genetic programming [13]. While capable of solv

36、ing layout problems of great complexity (i.e. many different parts nested together, general 2-D nesting of sheets), they are not guaranteed to reach optimal solutions, and may take significant computational effort to con

37、verge to a good solution.</p><p>　　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 lay

38、out 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 ‘no-fit polygon’, ‘obstacle space’

39、and ‘Minkowski sum’. Fundamentally, they simplify the process of determining relative positions of shapes su</p><p>　　For the particular problem of strip layout for pair s of parts, results have been reporte

40、d 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 introdu

41、ced, and its extension to nesting pairs of parts is described. </p><p>　　The Minkowski Sum</p><p>　　The shape of blanks to be nested is approximated as a polygon with n vertices, numbered consec

42、utively 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

43、 point in A with each point in B,</p><p><b>　　(1)</b></p><p>　　Intuitively, one can think of this process as ‘growing’ shape A by shape B, or by sliding shape –B (i.e., B rotated 180

44、º) around A and following the trace of some reference point on B. For example, Fig.1 shows an example blank A. If a reference vertex is chosen at (0, 0), and a copy of the blank rotated 180º (i.e., –A) is slid

45、around A, the reference vertex on –A will trace out the path shown as the heavy line in Fig.2. This path is the Minkowski sum . Methods for calculating the Minkowski sum c</p><p>　　Sample Part A to be Nested

46、.</p><p>　　Minkowski Sum (heavy line) of sample Part (light line).</p><p>　　The significance of this is that if the reference vertex on –A is on the perimeter of , A and –A will touch but not ov

47、erlap. The two blanks are as close as they can be. Thus, for a layout of a pair of blanks with one rotated 180º relative to the other, defines all feasible relative positions between the pair of blanks. </p>

48、<p>　　A corollary of this property is that if the Minkowski sum of a single part is calculated. With its negative, i.e., . (A complete explanation of these properties of the Minkowski sum is given in [15].) These ob

49、servations were the basis for the algorithm for optimally nesting a single part on a strip.</p><p>　　The situation when nesting pairs of parts is more complex, since not only do the optimal orientations of t

50、he 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:</p><p>　　G

51、iven: Blanks A and B (where B=–A when a blank is paired with itself at 180º)</p><p>　　1. Select the relative position of B with respect to A. The Minkowski sum defines the set of feasible relative posit

52、ions (Fig.2).</p><p>　　2. ‘Join’ A and B at this relative position. Call the combined blank C.</p><p>　　3. Nest the combined blank C on a strip using the Minkowski sum with the algorithm given i

53、n [14] or [15].</p><p>　　4. Repeat steps 1-3 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 optimiz

54、e the relative positions to maximize material uti lization. </p><p>　　Layout Optimization of One Part Paired with Itself</p><p>　　The first step in the above procedure is to select a feasible po

55、sition of blank B relative to A. This position is defined by translation vector t from the origin to a point on , as shown in Fig.3. During the optimization process, this translation vector traverses the perimeter of .&l

56、t;/p><p>　　Relative Part Translation Nodes on , showing Translation Vector t.</p><p>　　Initially, a discrete number of nodes are placed on each edge of . The two parts are temporarily ‘joined’ at a

57、 relative position described by each of the translation nodes, then the combined blank is evaluated for optimal orientation and strip width using a single-part layout procedure (e.g., as in [14] or [15]). In this example

58、, consists of 12 edges, each containing 10 nodes, for a total of 120 translation nodes. The position of each node is found via linear interpolation along each edge , wher</p><p><b>　　(2)</b></

59、p><p><b>　　(3)</b></p><p>　　If m nodes are placed on each edge, ,the position parameter values for the node, , are found as:</p><p><b>　　(4)</b></p><

60、p>　　Calculating the utilization at each of the 120 nodes on Fig.3 gives the results shown in Fig.4. In this figure, the curve is broken as the translation vector passes the end of each edge of to show how utilization

61、can change during the traversal of each edge. While some edge traversals show monotonic changes in utilization, others show two or even three local maxima. Discovering these local optima is the reason why a number of tra

62、nslation nodes are needed.</p><p>　　Optimal Material Utilization for Various Translations Between Polygons A and –A.</p><p>　　As a progression is made around , when local maxima are indicated, a

63、 numerical optimization technique is invoked. Since derivatives of the utilization function are not available(without additional computational effort),an interval-halving</p><p>　　Approach was taken [19]. Th

64、e initial interval consists of the nodes bordering the indicated local maximal point. Three equally-spaced points are placed across this interval (i.e. at 1/4, 1/2 and 3/4 positions), and the utilization at each is calcu

65、lated. By comparing the utilization values at each point, a decision can be made as to which half of the interval is dropped from consideration and the process is repeated. This continues until the desired accuracy is ob

66、tained.</p><p>　　Applying this method to the example leads to the optimal translation vector of (747.894, 250.884), giving the strip layout shown in Fig.5, with a material utilization of 92.02%.</p>&

67、lt;p>　　Interestingly, while it appears that the pairs of parts could be pushed closer together for a better layout, doing so decreases utilization.</p><p>　　Optimal Strip Layout for Part A Paired with Its

68、elf. </p><p>　　Layout Optimization of Different Parts Paired Together</p><p>　　Very often parts made from the same material are needed in equal quantities, for example, when left-and right-hand

69、parts are needed for an assembly. Blanking such parts together can speed production, and can often reduce total material use. This strip layout algorithm can be applied to such a case with equal ease. Consider a second s

70、ample part, B, shown in Fig.6. The relevant Minkowski sum for determining relative position translations, , is shown in Fig.7. In this case, contains 15 edges, whose</p><p>　　Sample Part B to be Nested.</

71、p><p>　　Minkowski Sum (heavy line) of Sample Parts (light and dashed lines).</p><p>　　Optimal Material Utilization for </p><p>　　Various Translations Between Polygons A and B.</p>

72、;<p>　　Conclusions</p><p>　　In the stamping operation, production costs are dominated by material costs, so even tiny per-part gains in material utilization are worth pursing. This paper has presented

73、 a new algorithm for creating optimal strip layouts for pairs of parts nested together. This algorithm takes advantage of the Minkowski sum calculation to both find feasible relative positions between the pairs of parts,

74、 and to determine the optimal orientation and strip width for the strip layout.</p><p>　　When evaluating combinations of layouts, it should be kept in mind that all permutations should be considered. For exa

75、mple, the strip layout process for the sample parts in this paper would consider strip layouts for A alone, A paired with itself, B alone, B paired with itself, and A and B paired together. The designer would then consid

76、er total raw material costs, tooling construction costs and press operating costs since blanking parts together requires larger tools and presses and changes prod</p><p>　　There are opportunities to extend t

77、his algorithm, as well. One obvious extension is to include optimization over relative rotations between the pairs of parts, i.e., changing the orientation of part B relative to A on the strip. A second opportunity is to