## 3 Results and Discussions
### SLM AlSi10 Mg  
Table 1 presents the scanning speed and laser power applied in SLM simulations. The other parameters, such as emissivity, coefficient exchange, initial conditions, and so on are the same as those used by [PERSON] et al. [33]. The experimental results of sample 1# are used to calibrate \(z_{0}\) (\(z_{0}=0.66*\eta_{t}\)). The simulation results of V200-P200 (scanning speed labeled V: 200 mm/s and laser power labeled P: 200 Watt) are used to illustrate certain characters of the proposed heat source. Figure 13 shows the melting pool shape at different moments during the simulation, and the contours are shown at the symmetrical plane. The melting pool depth increases progressively over time, since the heat source increases its penetration automatically. The final simulated melt pool shape is shown in Figure 14, and two stages can be clearly identified. The melt pool depth keeps increasing in the transient stage, while the melt pool depth is almost constant in the steady-state stage. A slight increase of the melt pool depth can be observed in the steady-state stage, which is perhaps due to the boundary effect as the model is short. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample No.** & **1 \#** & **2 \#** & **3 \#** & **4 \#** & **5 \#** & **6 \#** & **7 \#** \\ \hline Scanning speed (mm/s) & 200 & 400 & 600 & 800 & 1000 & 600 & 600 \\ \hline Laser power (W) & 200 & 200 & 200 & 200 & 200 & 180 & 160 \\ \hline Beam radius (\(\mu\)m) & \multicolumn{6}{c}{50} \\ \hline Layer thickness (\(\mu\)m) & \multicolumn{6}{c}{20} \\ \hline Absortivity & \multicolumn{6}{c}{0.6} \\ \hline Initial temperature (\({}^{\circ}\)C) & \multicolumn{6}{c}{25} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Process parameters used in SLM AlSi10 Mg [33]. Figure 12: Schematic diagram to illustrate the sizes of the molten pool. Another investigation concerns the sensibility of the time step, as it is known that \(\eta_{t}\) is calculated in an explicit way. Figure 15 shows the molten profiles simulated with different time steps, where the maximal recommended time step is \(dt=\dfrac{r_{0}}{3*V_{scanning}}=0.06\) ms. The comparison of the melt pool depths shows that a temperature-dependent heat source is stable and slightly sensitive to the time step. A maximum difference of 3.8% is observed, and the increase of melt pool depth in \(dt\) = 0.125 ms is perhaps due to the boundary effect. Even though the time step is different in this study, the number of time steps required to achieve the steady-state stage is almost the same (about 29 transient time steps). Figure 14: Final melt pool depth simulated in SLM AlSi10 Mg (V200-P200) (**a**) and the evolution of melt pool depth in scanning direction (**b**). Figure 13: Melting pool shape simulated in SLM AlSi10 Mg (V200-P200) at t = 0.1 ms (**a**); t = 0.5 ms (**b**); t = 1 ms (**c**); t = 1.5 ms (**d**). Figure 16 provides the comparison of the cross-section morphology of three melt pool shapes. The dimensions of the melt pool given by experiment and simulation are quite similar, and the relative error between the experimental and simulated data is 4.8% for width and 2% for depth. One should note that the heat source parameters are adjusted automatically without any manual intervention. The comparison of the molten pool dimensions of the experimental and numerical results is presented in Figure 17, and good correlations among experimental results (ExpWidth and Exp-Depth) [33], numerical results with the proposed heat source (Auto-Width and Auto-Depth), and with the anisotropic conductivity method (Anisotropic-Width and Anisotropic-Depth) [33] are found. The proposed heat source is capable of predicting the melting pool dimension with different process parameters correctly. Compared to the experimental results, the average relative errors given by the proposed model are generally less than 4.8% for depth and 5.2% for width. A better precision of prediction than the anisotropic conductivity method is thus observed.