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Li et al. [11] and Prof. Choi etal. [12] were probably among the first to develop suchsystems for bending progressive dies. J H Kim et al. [13,14] developed a fuzzy set theory method for determiningthe sequence of the bending operations. They modifiedfuzzy rules and weight factors for the rules. These systems are mostly used as an assistant for theprogressive die designer. Simultaneous bends determinationis a major problem in these systems. Thus, the number ofthe bending stations suggested by these systems is oftenmore than the actual industrial parts. So the die layoutsuggested by these systems is usually modified manuallyby the designer.3 Process planningIn a CAPP system for sheet metal components, thedetermination of the bending sequence is one of the mainproblems. If N is the number of bends in a given part, thenthe domain of possible sequences in principle is N! [7].However, this number is usually limited due to geometricaland technical constraints. In other words, the number ofpossible sequences depends on the shape of the component.A flow chart of the operations which are used for computer-aided bending sequence determination is shown in Fig. 1.3.1 Mother planeMother plane has a very important role in bendingprogressive die design. The mother plane is a fixed planewhich stays without any rotations throughout the bendingoperations. All the rotating planes are called childrenplanes. The rules for the determination of mother planesare as follows:– A plane surrounded by other planes– A plane located in the center of the part– The largest plane in the componentFigure 2 shows the mother plane for part 1; the motherplane is colored in this figure. When the determination of amother plane is not clear from the conditions as statedabove, it is determined by the minimum number of bendsbetween a plane and the plane in the central plane [14]. 3.2 Bending classification methodThe classification technique is applied to the determinationof simultaneous bends which can be performed in onestation. The die designers use different rules to definesimultaneous bends, because several parameters affect thisprocedure. According to experimental studies, many factorsaffect the determination of the simultaneous bends. How-ever, the following rules can be summarized [15].Rule 1 The bends that have bend lines along one line andwhose bending directions are the same (up or downbending) can be performed in one station. Thus, they aresaid to be in one group. In Fig. 3, according to rule 1, bendsB1and B2 are in one class. But bends B3 and B4 are not inone group, since their bending directions are not similar(B3 is down and B4 is up).Rule 2 The bends that have parallel bending lines and theirbending directions are the same (up or down bending) andare placed on opposite sides of the mother plane can beperformed in one station and are said to be in one group ifthe number of the planes between them and the motherplane are equal.
In Fig. 4, the directions of bends B1 andB2 are the same and they satisfy the rest of the conditionsof rule 2, hence, they are said to be in one group. Rule 3 Related bends. In some sheet metal components,two planes can be related through geometric or dimensionaltolerances. To obtain the tolerance and to comply with thepositioning errors, these bends should be (or better be)performed together. For example, in the part that ispresented in Fig. 5, planes A and B have parallel tolerances.Thus, they should be performed together.In the classification procedure, first, all the bends arepided according to their bending directions (feed directionor perpendicular to it). Then in each direction, the bends areclassified. In other words, the bends which are parallel andperpendicular to the feed direction cannot be formed insimilar groups.3.3 Fuzzy set theoryThe handling rules and criteria needed for determining thebending sequence is discussed in this section. These rulesdeal with the selection of the next best bend for the bendingoperation. Each of these rules establishes relationshipsbetween pairs of bending operation groups. A highmembership grade indicated for a particular rule meansthat the bend group is a good selection for the nextoperation according to this rule. These relationshipsbetween the bending and criteria are represented as fuzzyrelations, and the membership grades of these fuzzy relations are determined through fuzzy membership func-tion, as shown in Fig. 6.3.3.1 Sequencing rulesFuzzy relations or sequencing rules describe the priority ofeach group. Thus, definition of these rules for a computer-aided system is important. According to previous studiesand experience of the authors [15], the following rules aresuggested:Rule 1: Distance rule This rule describes the influence ofthe shape of a bend on the sequencing strategy. The furthera bend is away from the mother plane, the higher its gradewill be and thus should be bent earlier. The fuzzy functionspresented in Fig. 6a are used to determine the grade ofmembership by this rule.Rule 2: Number of bends in a group The higher the numberof bends in a group, the more impact it will have on theoverall shape of the part and vice versa. The more impact agroup will have, the later it should be addressed in theFig. 6 Fuzzy membership function. a Distance rule. b Number ofbends in a group. c Bending angle. d Feeding direction operation. So the fuzzy relationship value of this rule can berepresented as in Fig. 6b.Rule 3: Bending angle This rule is to determine the fuzzyrelationship value according to the angle of each plane.This is the angle between the mother plane and each rotatedplane. If this angle is greater than 90°, the bending processis pided into one or more processes. The fuzzy relation-ship value is unity in the case of a bend angle less than 90°and zero in other cases. These relationships according tobend angles are represented as fuzzy functions as shown inFig. 6c.Rule 4: Feeding direction [14] This rule is to determine thefuzzy relationship value of a fuzzy function according towhether or not the bend is in the feeding direction. Afterbending, an escape space is necessary in either the stripperplate of the upper die or the die plate of the lower die.