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According to the classification rules, the classes of this part are determined as follows:
– Class 1: bends B1 and B7
– Class 2: bends B2 and B8
– Class 3: bends B3 and B9
– Class 4: bends B4 and B10
– Class 5: bends B5 and B11
– Class 6: bends B6 and B12
According to fuzzy membership functions, the final value matrix of these classes is presented in Fig. 15.
Thus, this part can be finished in four stations: The first station includes bends B1, B2, B7, and B8. In the second station, bends B4 and B10 are performed. In the third station, bends B3, B5, B9, and B11 are performed and in the fourth station bends B6 and B12 are performed.
Example 4 The fourth sample which is used in this paper is an electrical product. This part is shown in Fig. 16. It has 17 bends (unfolded shape is shown in Fig. 17). This part is used by Kim et al. [14] and here a comparison test is carried out as follows:
According to the classification rules used in the present work, the classes of this part are determined as follows:
– Class 1: bends B8, B3, B12, and B15 (according to rule 1)
– Class 2: bends B17, B5, B2, B7, B11, and B14(according to rule 1)
– Class 3: bend B16 (this bend is the only one where none of the rules address it)
– Class 4: bends B13 and B6 (according to rule 2)
– Class 5: bends B4 and B10 (according to rule 2)
– Class 6: bends B1 and B9 (according to rule 2)
The final value matrix for this part is presented in
According to FVM, the total number of the bending stations is six. The sequencing that is suggested for this part is as follows:
– Station 1: bends B8, B3, B12, and B15
– Station 2: bends B17, B5, B2, B7, B11, and B14
– Station 3: bends B13 and B6
– Station 4: bends B4 and B10
– Station 5: bend B16
– Station 6: bends B1 and B9
The number of stations suggested by the fuzzy set matrix in Kim et al. [14] is nine. The number of stations suggested with the present method is six which shows a clear reduction in the number of stations.
5 Conclusion
In this paper, a new method for the determination of bending sequences for progressive dies is presented. In this method, a classification system and fuzzy set theory are used for the sequencing. In the first step, the bends which can be performed in one station are determined by the classification system. The sequencing of the bends is then determined by using fuzzy rules and fuzzy sets. To the best of the authors’ knowledge, the classification algorithm used in the present work is the first of its type. Four examples have been used to demonstrate the capability of the method. The results show that, compared with the existing automated systems, this method successfully determines the bending sequences for the parts and further reduces the number of the stations.
The drawbacks of this classification system are that it cannot completely determine the existence of simultaneous
bends. This is due to the fact that the classification rules are not yet enough to cater for all possible situations in sheet metal components. This problem, along with the considerations for the existence of idle stations and their positions in the progressive dies, will be studied in future works by the authors.
级进模中决定弯曲工艺的一种新方法的发展
摘要：在级进模中，需要两个或两个以上的工位来生产金属件。在每个工位上有一道或两道以上的工序。级进模可以减少生产复杂金属件的时间和费用。然而，设计和制造这些模具是十分困难的，对于这项任务，计算机辅助设计和计算机辅助制造被证明用在级进模中是十分有效的，在计算机辅助制造和计算机辅助设计被用在级进模设计中的主要问题是弯曲这一操作工序。在本论文中，阐述了一个新的方法来完成弯曲这道操作工序。在这一方法中，分为两个步骤。首先，弯曲将用一种方法来定义，弯曲操作可以同时进行，在这一方法中，所有的弯曲操作将根据他们最初的弯曲方向来划分（回弹方向或垂直于弯曲方向），然后在每个方向上的弯曲根据分类法则划分为几组不同的弯曲，在这篇论文中，有三条规则决定弯曲操作组。这三条规则是基于弯曲在金属件中关系。然后弯曲操作组的工序决定如何使用模糊集合论。从工业中的四种金属件和先前的论文可以用来证明被提议的方法的可行性。