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Abstract In progressive dies, two or more stations are usedto produce sheet metal components. In each station, one ormore processes are applied. The progressive dies reduce thetime and cost of producing complex sheet metal com-ponents. However, the design and manufacture of these diesare difficult. CAD/CAM systems have been proved to bevery useful tools for this task. The main problem of CAD/CAM systems used in progressive die design is determiningthe bending operations sequence. In this paper, a newmethod for determining the sequence of the bendingoperations is described. In this method, sequencing is donein two stages. First, the bending operations, which can becarried out simultaneously, are defined by a classificationmethod. In this method, all the bends are initially pidedaccording to their bending directions (feed direction orperpendicular to it).61744
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Then for each direction, the bends arepided into operation groups according to classificationrules. Three rules are used to determine the bendingoperation groups in this paper. These rules are based onrelations between the bends in the component. Thesequence of the bending operation groups is then deter-mined using fuzzy set theory. Four components taken fromindustry and previous papers are used to show thecapabilities of the proposed method.Keywords Bending sequence . Progressive dies .Fuzzy set theory 1 IntroductionOne of the most common processes used for sheet metalforming is bending. The bending process has many appli-cations including electrical, automotive and in aircraftindustries.Bending dies are designed according to the sheet metalcomponent shape, its dimensions, and tolerances [1]. Thus,several types of dies are used in sheet metal bending. Whenthe number of parts is large and the shape is complex, thedesigners often use progressive dies to reduce lead time andproduction costs.Inpidual operations in a progressive die are oftenrelatively simple. But when the die contains several stationswhere in each station a few of these inpidual operationsare to be combined, it is often difficult to plan the mostpractical and economical strip design for optimum opera-tion of the die.The sequence of operations is the most importantproblem in progressive die design. In other words, thesequencing is the key to progressive die design.Most research in sheet metal working involves usinganalytical and experimental methods which address prob-lems of sheet metal behavior in forming process. Althoughmuch work has been carried out on sheet metal behavior,little work has been done on the automation of die designand the sequence of operations in progressive dies.In this paper, a new approach for sequencing bendingoperations in progressive dies is described. In this method,sequencing is done in two stages. First, the bendingoperations which can be carried out simultaneously aredefined by a classification method. The sequence of thebending classes is then determined by using fuzzy settheory. 2 Related workShaffer, Fogg, and S. Nakahara [2, 3] were the first peopleto work on computer-aided progressive die design systems.The early systems attempted to use basic computer graphicsfacilities and programs written in FORTAN to improve theproductivity of die design [2]. These systems were mostlyused for piercing and blanking operations.In recent years, some researchers have focused on thebending process in progressive dies.
De Vin et al. [4] havedescribed the use of a tolerance tree in sequencing pro-cedures for bending operations. This was used in anintegrated computer-aided process planning (CAPP) sys-tem. Ong et al. [5] used a fuzzy set system to determine thesequence of bending operations in press brake machines.Gupta et al. [6] have developed a process planning systemfor sheet metal components. They applied a greedy algo-rithm to determine the bending sequence. Prof. Duflou et al.[7] suggested a penalty function method and the travelingsalesman problem method to determine bending sequencesin press brake machines. Most researchers have worked onthe bending operations performed by press brake machinesor robot-assisted bending [8–10].A few researchers have used computer-aided systems forthe bending progressive dies. 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]. The 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.