## 3 Results and Discussion
### Correlation of Surface Profile Parameters and Dross Formation
#### 3.3.1 Obtained Roughness Model and Resulting Geometry Predictions  
The surface topography characterization, performed using 12 different surface profile parameters (see Section 3.3), showed that \(Pa\) can be considered as an appropriate parameter for describing the cross formation and magnitude of the associated roughness. The simple roughness prediction models obtained and the corresponding results, from following the approach described in Section 2.3.2, can be viewed in Figure 15.  
Figure 15a shows the roughness prediction model. The predicted roughness and geometry of a perfect CAD channel geometry with \(D_{nom}=6\) mm, together with the surface deviation map of the 6 mm A channel, can be seen in Figure 15b,c. Figure 15b shows that the roughness and shape are well predicted. The contour of the white area within the modeled channel (Figure 15b) is closely representing the contour of the white area within the X-ray CT characterized channel (Figure 15c), indicating a good geometric reproduction by the prediction methodology. The overall width of the dress formation area is slightly overestimated just as the local heights of the peaks are underestimated. This is likely due to the model being based on average \(Pa\)-values, which will smoothen out the predictions. The shown comparisons confirm the applicability of the parameter \(Pa\) for providing an appropriate description of the roughness and dress formation trends observed in the investigated aluminum LPBF channels.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Channel** & \begin{tabular}{c} \(Pa\) \\ [\(\mu\)m] \\ \end{tabular} & \begin{tabular}{c} \(P2\) \\ [\(\mu\)m] \\ \end{tabular} & \begin{tabular}{c} \(Pq\) \\ [\(\mu\)m] \\ \end{tabular} & \begin{tabular}{c} \(Pp\) \\ [\(\mu\)m] \\ \end{tabular} & \begin{tabular}{c} \(Ppk\) \\ [\(\mu\)m] \\ \end{tabular} & \begin{tabular}{c} \(Pku\) \\ [\(\mu\)m] \\ \end{tabular} & \begin{tabular}{c} \(Pku\) \\ [\(\mu\)m] \\ \end{tabular} & \begin{tabular}{c} \(Pmc\) \\ [\(\mu\)m] \\ \end{tabular} & \
\begin{tabular}{c} \(Pup\) \\ [\(\mu\)m] \\ \end{tabular} &
\begin{tabular}{c} \(Pup\) \\ [\(\mu\)m] \\ \end{tabular} \\ \hline mm & 44.17 & 239.8 & 260.2 & 55.63 & 149.0 & 0.610 & 3.52 & 1.642 & \(24.4\times 10^{3}\) & \(37.1\times 10^{3}\) & \(1.58\times 10^{3}\) & \(2.20\times 10^{3}\) \\ \hline
2 mm & 46.06 & 246.8 & 272.6 & 57.22 & 153.9 & 0.570 & 3.56 & 1.668 & \(26.3\times 10^{3}\) & \(37.8\times 10^{3}\) & \(1.41\times 10^{3}\) & \(2.10\times 10^{3}\) \\ \hline
3 mm & 45.05 & 217.5 & 248.9 & 55.67 & 127.4 & 0.240 & 2.92 & 1.550 & \(13.1\times 10^{3}\) & \(17.6\times 10^{3}\) & \(0.61\times 10^{3}\) & \(1.24\times 10^{3}\) \\ \hline
6 mm A & 40.85 & 171.2 & 219.8 & 49.96 & 98.54 & \(-0.040\) & 3.20 & 1.485 & \(5.92\times 10^{3}\) & \(7.51\times 10^{3}\) & \(0.20\times 10^{3}\) & \(0.60\times 10^{3}\) \\ \hline
6 mm B & 41.26 & 174.8 & 223.6 & 50.62 & 103.2 & \(-0.007\) & 3.12 & 1.452 & \(5.99\times 10^{3}\) & \(7.76\times 10^{3}\) & \(0.22\times 10^{3}\) & \(0.60\times 10^{3}\) \\ \hline
6 mm C & 40.75 & 170.8 & 215.8 & 49.95 & 96.63 & \(-0.039\) & 3.17 & 1.435 & \(6.00\times 10^{3}\) & \(7.54\times 10^{3}\) & \(0.19\times 10^{3}\) & \(0.61\times 10^{3}\) \\ \hline
6 mm D & 40.15 & 171.8 & 221.8 & 49.47 & 100.1 & \(-0.019\) & 3.30 & 1.423 & \(5.79\times 10^{3}\) & \(7.65\times 10^{3}\) & \(0.21\times 10^{3}\) & \(0.59\times 10^{3}\) \\ \hline
6 mm E & 39.85 & 169.1 & 220.5 & 48.99 & 100.7 & 0.025 & 3.21 & 1.470 & \(5.79\times 10^{3}\) & \(7.47\times 10^{3}\) & \(0.22\times 10^{3}\) & \(0.56\times 10^{3}\) \\ \hline
9 mm & 40.44 & 168.0 & 212.4 & 49.31 & 94.60 & 0.093 & 3.05 & 1.390 & \(5.83\times 10^{3}\) & \(7.79\times 10^{3}\) & \(0.18\times 10^{3}\) & \(0.57\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Calculated average profile parameters for all nine investigated channels.