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FVM is a matrix consisting of fuzzy values for each bend groups that are being considered. The fuzzy values are determined by implementing rules described in Section 3-3-1. These rules have been found to give suitable results in bending operations. The higher value a bend group has, the sooner it should be formed. The relative importance of the rules is represented as a fuzzy set W[R], as shown in Eq. (2).
W[ R] ={r1 * 1.2、r2 * 0.8、r3 * 0.6、 r4 * 0.2 }
Thus, the FVM set can be presented by Table 2 and expressed as follows:
FVM（C）=[V]*W[R]
4 Examples
To evaluate the described method, four components are selected (Figs. 7, 11, 14, and 16) and will be presented as follows:
Example 1 Figure 7 presents a part which is used in electrical components. To produce this part, five bending and several cutting operations are carried out. However, in the present 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 is determined as the mother plane.
The unfolded shape of the part is shown in Fig. 8. Amongst the bending operations, four are in perpendicular and one in feed direction. According to the classification rules, the classes of this part are determined as follows:
1. Bends b1and b5 are in one class (class one), according to rule
2. Bends b2 and b4 are in one class (class two), according to rule 2.
3. Bend b3 is in one class (class three) since this bend is the only one perpendicular to the feed direction.
After the classification of the bending operations is determined, the sequence of the operations can now be determined according to the fuzzy matrix [M] as shown in Table 3.
The membership grades for class one are described as follows:
– From rule 1 (R1)—The bends in this class are each at maximum distance from the mother plane, so each has a grade 1 and hence the resulting grade of the class one is 1.
– From rule 2 (R2)—The number of bends in this class is two, thus its grade is zero.
– From rule 3 (R3)—The bends angles are 90°, thus its
grade is zero.
– From rule 4 (R4)—The bends of this class are perpendicular to the feed direction, thus its grade is 1.
Hence, the final value matrix (FVM) is determined as Table 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, the sequence of the bending processes is as follows:
Bends b1 and b5 are performed in the first station. Bend b3 is performed in the second station. Bends b2 and b4 are performed in the third station.
In Fig. 10, the bending operations in the three stations are shown. These results are the same as the results in Refs. [13–14].
Example 2 A part of the Samand automobile (Iran Khodro Company) (Fig. 11) is the second example which is studied in this paper. This part has seven bends. Figure 12 shows the unfolded shape of the part.
According to the classification rules, the classes of this part are determined as follows:
– Class 1: bends B1 and B7
– Class 2: bends B3 and B5
– Class 3: bend B2
– Class 4: bend B4
– Class 5: bend B6
Final value matrix for the classes of this part is presented in Fig. 13.
Since the grades of class 3 and class 5 are similar, they are performed in one station. So the total number of the bending stations is four. The sequencing that is suggested for this part as follows:
– Station 1: bends B2 and B6
– Station 2: bends B1 and B7
– Station 3: bend B4
– Station 4: bends B3 and B5
Example 3 The component which is studied as the third example (Fig. 14a) is a part of GPI Company. This part has 12 bends. The unfolded shape of the part is shown in Fig. 14b.