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Theescape space should be at a minimum considering the diestrength, the part to be fixed, the loss of die material, andthe manufacturing time.Bending processes requiring a large escape space shouldbe performed later to minimize the escape space. Because a bend perpendicular to the feeding direction requires asmaller escape space than a bend in the feeding direction,the former precedes the latter. The membership value forthe perpendicular feeding direction is unity, and zerootherwise. The fuzzy membership function for this rule isshown in Fig. 6d.Note: To determine the grade of the membership foreach group, the maximum grade of its bends is chosen andlater used in the fuzzy matrix.3.3.2 Fuzzy matrixLet C={ci | i=1, 2,…….., n} represent the set consisting ofall the remaining bend classes that are being considered forbending, where ci is one of the bend classes.Let R={rj | j=1, 2, 3, 4} represent the set of four criteriain the handling rules, where rj represents one of the criteria.A fuzzy relation is a mapping from C×R into [0, 1],such that (Vij)c, is expressed as follows:Vij cfci ; rj 1Since related sets C and R are finite, a fuzzy relation f onC×R can be represented as a fuzzy matrix [M], the entriesof which are (Vij)c.The determination of the grade, which may varyanywhere between zero and unity, is based on thesequencing rules. The fuzzy matrix [M] is shown in Table 1.3.3.3 Determination of final value matrix (FVM) setFVM is a matrix consisting of fuzzy values for eachbend groups that are being considered. The fuzzy valuesare determined by implementing rules described inSection 3-3-1. These rules have been found to givesuitable results in bending operations. The higher value abend group has, the sooner it should be formed. The relative importance of the rules is represented as a fuzzysetW[R],asshowninEq.(2).WR r1 * 1:2; r2 * 0:8; r3 * 0:6; r4 * 0:2 2Thus, the FVM set can be presented by Table 2 andexpressed as follows:FVM C V :W R 34 ExamplesTo evaluate the described method, four components areselected (Figs. 7, 11, 14, and 16) and will be presented asfollows:Example 1 Figure 7 presents a part which is used inelectrical components. To produce this part, five bending andseveral cutting operations are carried out. However, in thepresent paper, only bending operations will be investigated.According to the rules regarding the mother plane,described in Section 3-1, the central plane of the part isdetermined as the mother plane.The unfolded shape of the part is shown in Fig.
8.Amongst the bending operations, four are in perpendicularand one in feed direction. According to the classificationrules, the classes of this part are determined as follows:1. Bends b1and b5 are in one class (class one), accordingto rule 2. 2. Bends b2 and b4 are in one class (class two), accordingto rule 2.3. Bend b3 is in one class (class three) since this bend isthe only one perpendicular to the feed direction.After the classification of the bending operations isdetermined, the sequence of the operations can now bedetermined according to the fuzzy matrix [M] as shown inTable 3.The membership grades for class one are described asfollows:– From rule 1 (R1)—The bends in this class are each atmaximum distance from the mother plane, so eachhas a grade 1 and hence the resulting grade of theclass one is 1.– From rule 2 (R2)—The number of bends in this class istwo, thus its grade is zero.– From rule 3 (R3)—The bends angles are 90°, thus itsgrade is zero.– From rule 4 (R4)—The bends of this class areperpendicular to the feed direction, thus its grade is 1.Hence, the final value matrix (FVM) is determined asTable 4.According to Table 4, the final grade for class one is 1.4,class two is 0.2, and class three is 0.8 (Fig. 9). Thus, thesequence of the bending processes is as follows:Bends b1 and b5 are performed in the first station. Bendb3 is performed in the second station. Bends b2 and b4 areperformed in the third station.
摘 要：在级进模中，有两个或两个以上的工位被用来生产金属板材。在每一道工位上，一个或多个工序被应用。级进模降低了金属复合板的制造时间和成本。然而，这些模具的设计和制造是困难的。计算机辅助系统CAD/CAM已被证明对模具加工任务是非常有用的工具。用于进行级进模设计的计算机辅助系统CAD/CAM的主要问题是确定弯曲的操作顺序。在本文中，描述的是一种确定弯曲操作序列的新方法。在这个方法中，测序是在两个阶段完成的。首先，被定义的分类方法是弯曲操作可以同时进行。在这种方法中，根据它们的弯曲方向（进给方向或垂直于进给方向），所有的弯曲被初步划分。然后在每个方向上，根据分类规则，弯曲分为操作组。本文中采用三个规则来确定弯曲操作组。这些规则是基于组件的弯曲之间的关系。弯曲操作组的顺序是使用模糊集理论来确定的。取自工业和以前文件的四个构成要素是用来显示所提出的方法的能力。