## 3 Results
### Experimental Cups Analysis  
Figure 5 and Table 3 present qualitative and quantitative results of LP analysis.  
Comparing the above results, it is clear that RG is more accurate than PG. Figure 4(a) shows how the RG geometry profile fits that of CAD. Figure 4(b) shows the main difference between the two, with respect to the fillet radius, where a difference of 1.09 mm was recorded. However, considering the 10 mm value of the ideal fillet radius, this is equivalent to a percentage deviation of 89%. In terms of drawing depth, the results shown in Table 3 reveal that RG produced cups with a drawing depth which was 99% of the expected value. In the PG test, the percentage deviations from the ideal fillet radius of 6 mm, and from the expected drawing depth of 15 mm, were 75% and 92%, respectively. It can therefore be asserted that the linear profile obtained with RG is more accurate than that obtained with PG.  
CP analysis confirmed the LP results. The cups were produced with an average radius R\({}_{\text{med}}\) that diverged from the punches' radius by just hundreds of microns, and with near-negligible standard deviation, as Figure 6 illustrates visually, and Table 4 describes quantitatively. Table 4 also shows that absolute values of roundness tolerances were higher in RG but were lower in percentage terms when related to the R\({}_{\text{med}}\) (0.53%).  
and PG punch fillet radii are compared with those of CAD. Table 5 presents the punch heights measured at the end of cup deformation. The analysis demonstrates that neither punch suffered permanent deformation.  
The CP analysis highlighted the behaviour of punches, as follows: the two circumferences obtained at different distances from the punch top (Figure 8) are perfectly overlapped for PG; in RG the circumference acquired at 15 mm (the black line in Figure 8) is slightly inferior to the circumference acquired at 30 mm (the red dotted line). However, an analysis of the roundness tolerances shown in Table 6 and the r\({}_{\text{t}}\) percentage on radii revealed that all values of the latter were below 1.5%, with a minimum value of 0.4% in the case of RG_H30.  
The results of the roughness profile (RP) analysis are presented in Figures 9 and 10. A qualitative and comparative observation of Figure 9 shows that RG has a smoother morphology than PG. To confirm this finding, Figure 10 presents the results of an analysis  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **RG\_H15** & **RG\_H30** & **PG\_07** & **PG\_H15** \\ \hline R\({}_{\text{med}}\) [mm] & 56.9 \(\pm\) 0.1 & 58.8 \(\pm\) 0.05 & 19.5 \(\pm\) 0.08 & 19.5 \(\pm\) 0.07 \\ \hline r\({}_{\text{t}}\) [mm] & 0.384 & 0.236 & 0.274 & 0.270 \\ \hline \% r\({}_{\text{t}}\)/R\({}_{\text{med}}\) & 0.65\% & 0.40\% & 1.40\% & 1.38\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Main results of punch CP analysis.  
Figure 8: Main results of punch CP analysis.  
Figure 7: Main results of cup LP analysis.  
of variance (ANOVA) test of the average surface roughness \(\rm S_{a}\). These results (\(p\)-value \(<0.05\)) confirm that the choice of punch geometry is significant. In addition, the interval plot depicted in Figure 9(b) shows that the filled radius of RG has a lower \(\rm S_{a}\) value (16.6 \(\rm\upmu m\)).