Eng 2023 , 4
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Figure5. Perforation efficiency behavior as function of perforation line angle.
Figure6. Experimental and theoretical perforation efficiency results as function of perforation line angle.
The first case considered the optimization of the two parameters, the blank distance, d , and the angle of the perforation line, according to Figure 1, to minimize the tear force. The parameter boundaries used in the GA were 0 ◦ ≤ α ≤ 55 ◦ and 0.1 ≤ d ≤ 1.0mm. Regarding the upper boundary for the perforation line angle, α , the value of 55 ◦ was chosen to avoid the cut line cross of the upper or the lower edges of the paper model, where the displacement boundary conditions were applied. For the case regarding the optimization of the perforation line angle and the blank distance, the optimum configuration was achieved after 51 generations, with the tear force being in the region of 0.064 N. In the configuration for the minimum tear force, the optimum angle was 0.56 ◦ , which corresponds to a perforation efficiency of 96.8% and, as expected, d = 0.1 mm. In comparison to a perforation efficiency of 0 ◦ , in the case of the optimal angle, an increase of 29.3% was obtained. The GA’s best value and mean value over the generations is presented in Figure 7. In this figure, the best value is almost equal through all generations and the mean value converges to the best value after 17 generations. For the case where only the perforation line angle was the variable to be optimized (blank distance d was fixed and equal to 1 mm), the convergence occurred only after 66 generations, and the minimum tear force was 0.394 N. For this case, the angle for the minimum tear force was 0.67 ◦ , which corresponds to a perforation efficiency of 80.6%. Compared with a perforation efficiency at 0 ◦ , in the case of the optimal angle, an increase of 7.6% was obtained.
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