## 3 Results  
### Determination of Most Influential Parameters in the Extrusion Force  
After performing the simulations according to the DOE defined in the previous section, the values obtained for the extrusion force are placed in a perturbation chart (Figure 8) in order to check which parameters produce a bigger deviation between the lowest and the highest extrusion force values. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Simulation** & \begin{tabular}{c} **X1** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **X2** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **X3** \\ **(mm/s)** \\ \end{tabular} & \begin{tabular}{c} **X4** \\ **(°C)** \\ \end{tabular} & \begin{tabular}{c} **X5** \\ **(°)** \\ \end{tabular} & \
\begin{tabular}{c} **X6** \\ **(kN)** \\ \end{tabular} &
\begin{tabular}{c} **Extrusion Force** \\ **(kN)** \\ \end{tabular} \\ \hline
1 & 6 & 20 & 2 & 200 & **0.030** & 45 & 136.63 \\
2 & 6 & 20 & 2 & 200 & **0.065** & 45 & 198.06 \\
3 & 6 & 20 & 2 & 200 & **0.100** & 45 & 207.46 \\
4 & 6 & 20 & 2 & 200 & **0.135** & 45 & 243.50 \\
5 & 6 & 20 & 2 & 200 & **0.170** & 45 & 276.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Variables combination by varying X\({}_{5}\) (friction coefficient). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Simulation** & \begin{tabular}{c} **X1** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **X2** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **X3** \\ **(mm/s)** \\ \end{tabular} & \begin{tabular}{c} **X4** \\ **(°C)** \\ \end{tabular} & \begin{tabular}{c} **X5** \\ **(°)** \\ \end{tabular} & \
\begin{tabular}{c} **X6** \\ **(kN)** \\ \end{tabular} &
\begin{tabular}{c} **Extrusion Force** \\ **(kN)** \\ \end{tabular} \\ \hline
1 & 6 & 20 & **1.5** & 200 & 0.1 & 45 & 215.94 \\
3 & 6 & 20 & **2.5** & 200 & 0.1 & 45 & 211.10 \\
5 & 6 & 20 & **3** & 200 & 0.1 & 45 & 208.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Variables combination by varying X\({}_{3}\) (ram speed). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Simulation** & \begin{tabular}{c} **X1** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **X2** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **X3** \\ **(mm/s)** \\ \end{tabular} & \begin{tabular}{c} **X4** \\ **(°C)** \\ \end{tabular} & \begin{tabular}{c} **X5** \\ **(°)** \\ \end{tabular} & \
\begin{tabular}{c} **X6** \\ **(kN)** \\ \end{tabular} &
\begin{tabular}{c} **Extrusion Force** \\ **(kN)** \\ \end{tabular} \\ \hline
1 & 6 & 20 & **1.5** & 200 & 0.1 & 45 & 215.94 \\
3 & 6 & 20 & **2** & 200 & 0.1 & 45 & 207.46 \\
4 & 6 & 20 & **2.5** & 200 & 0.1 & 45 & 211.10 \\
5 & 6 & 20 & **3** & 200 & 0.1 & 45 & 208.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Variables combination by varying X\({}_{4}\) (temperature). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Simulation** & \begin{tabular}{c} **X1** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **X2** \\ **(mm/s)** \\ \end{tabular} & \begin{tabular}{c} **X3** \\ **(mm/s)** \\ \end{tabular} & \begin{tabular}{c} **X4** \\ **(°C)** \\ \end{tabular} & \begin{tabular}{c} **X5** \\ **(°)** \\ \end{tabular} & \
\begin{tabular}{c} **X6** \\ **(kN)** \\ \end{tabular} &
\begin{tabular}{c} **Extrusion Force** \\ **(°)** \\ \end{tabular} \\ \hline
1 & 6 & 20 & 2 & **100** & 0.1 & 45 & 241.82 \\
2 & 6 & 20 & 2 & **150** & 0.1 & 45 & 222.75 \\
3 & 6 & 20 & 2 & **200** & 0.1 & 45 & 207.46 \\
4 & 6 & 20 & 2 & **200** & 0.1 & 45 & 185.97 \\
5 & 6 & 20 & 2 & **300** & 0.1 & 45 & 170.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Variables combination by varying X\({}_{5}\) (friction coefficient). In the perturbation chart shown in Figure 8, it can be verified that the most influential parameters in the extrusion force are billet height, friction, and die semi-angle. However, in the case of the temperature and the core diameter, the difference is not so clear. Therefore, in Figure 9, a percentage variation respect the reference value (level 3) of the extrusion force is shown.