# Improvement of the Method for Fixing a Punch in the Punch Holder
## 4 Discussion
### Second Improvement of the Tool  
The second issue discussed was the fixture position. In fact, most of the previous studies focused on the cutting part of the tool and the upper part is not described [8; 9; 12]. In many cases, the studies exploit a cylindrical punch with an external shoulder [2; 7; 18; 19], but this geometry is not applicable in our case. The study from [PERSON] et al. [14] utilizes a flat punch without defining precisely how it is fixed to the system. Considering this context, we decided to perform a dedicated study to improve the design of the initial fixing. The improvements in the test consisted of replacing the pins with a single pin in the center of the punch to reduce the maximum stress (illustrated in Figure 15). This modification generated a larger contact surface between the pin and the tool, thus a smaller stress in tension.  
Figure 14: Maximum stress after shape change.  
Figure 15: Punch with a round centered fixation.  
To find the maximum permissible diameter \(d_{max}\) without exceeding the elastic limit in compression, the following Formula (3) was used:  
\[R_{e\_{\text{punch}}}=\text{F}_{\text{cutting}}/A_{min}, \tag{3}\]  
where:  
\(A_{min}=e\left(w-d_{max}\right)\) is the minimum area of the punch;  
\(\text{F}_{\text{cutting}}=\) 20,000 is the cutting force calculated previously in N;  
\(R_{e\_{\text{punch}}}=\) 2500 is the elastic limit of the punch in MPa;  
\(w=\) 15.75 is the width of the punch in mm;  
\(e=\) 0.9 is the thickness of the punch in mm.  
The maximum value of the diameter was therefore \(d_{max}=\) 7.03 mm.  
To find the optimal value of the diameter, numerical analyses were conducted on diameters of 2, 3, 4, 5, 6 and 7 mm for compression and tension.  
The results of Table 4 show that, as the diameter of the pinhole increased, there was a decrease in tensile stress and an increase in compressive stress. The goal was to find a compromise between the two constraints. First, and to ensure that our compressive stress did not reach 2500 MPa, we studied the diameters giving a compressive stress less than 2000 MPa, i.e., diameters ranging from 2 to 4 mm. Subsequently, since at this level the compressive stress varies little with respect to the tensile stress, the diameter with the minimum tensile stress, i.e., 4 mm, was chosen (see Figures 16 and 17).  
Figure 19: Maximum stress for the square pinhole, (**a**) in compression, (**b**) in tension.  
Figure 20: Oblong hole dimensions and partitions.  
Figure 21: Maximum stress for the oblong pinhole, (**a**) in compression, (**b**) in tension.  
The results in Table 5 show that the round configuration is optimal in terms of compression and traction. The round pinhole has a compressive stress slightly greater than that present in the oblong case, but its tensile stress is much lower than that of the oblong configuration, whereas the square configuration has a much higher stress in both compression and tension.  
As a result of this study, the round shape has been selected as a new design for the punch and the punch holder, with satisfactory results in the production process. The first tests show a significant improvement, as the fatigue life of the punch is approximately ten times greater compared to the initial configuration.