## 3 Experimental Validation and Discussion
To demonstrate the presented method, these predicted results were compared with the experimental data, as shown in Figure 2. It can be observed that the predictions of molten pool width are very close to experimental data, and the predictions for depth have an acceptable agreement with the experimental results, which show the good prediction accuracy of the proposed analytical strategy. The normalized enthalpy \(\beta=\frac{AP}{\pi\rho cT_{m}\sqrt{Dua^{3}}}\) under various process conditions were calculated and shown in Table 1. The sensitivity of the molten pool width and depth to the normalized enthalpy is shown in Figure 3. It can be observed that both the experimental [22] and analytical results have a nearly linear relationship with the normalized enthalpy. An empirical formula obtained from the linear relationships may be an acceptable alternative to predict the molten pool dimensions [46]. A criterion derived by [PERSON] et al. in [12] was employed to calculate the threshold for the occurrence of the keyhole melting mode, which can be expressed as \(\beta>\frac{nT_{h}}{T_{m}}\), where \(\beta\) is the normalized enthalpy, \(T_{b}\) and \(T_{m}\) are the boiling point and the melting point of the material, respectively. When the normalized enthalpy is over 5.4, the melting mode of Ti6 Al4V will become keyhole mode, which is also shown in Figure 3. It can be observed that the predictions for molten pool depth are closer to the experimental results when the normalized enthalpy is lower than the threshold. When the process conditions enter the keyhole-mode melting regime, the predictions of molten pool depth cannot capture the variation of experimental results very well. This is mainly because the point moving heat source model only considers the thermal conduction [41], however, in the keyhole melting regime, the thermal convection plays an important role [11]. In addition, the predicted results with uniform absorptivity of 0.45 are shown in Figure 3 for comparison, which indicates that considering the variation of laser absorptivity can enhance the prediction accuracy. The computational time for the presented method is less than 200 s, which can save plenty of computational resources than finite element-based numerical methods. By virtue of the acceptable prediction accuracy and high computational efficiency, the presented analytical method can work as an efficient tool to predict the molten pool shapes and study the related defects in the powder bed fusion processes. In the future, the effects of temperature-dependent material properties and the thermal convection in keyhole regime can be considered to make the predictions more accurate. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Symbol** & **Value** & **Unit** \\ \hline Density & \(\rho\) & 4198 & kg/m\({}^{3}\) \\ Thermal conductivity & \(k\) & 27 & W/(m-\({}^{\circ}\)C) \\ Specific heat & \(c\) & 750 & J/(kg-\({}^{\circ}\)C) \\ Room temperature & \(T_{0}\) & 20 & \({}^{\circ}\)C \\ Boiling temperature & \(T_{b}\) & 3042 & \({}^{\circ}\)C \\ Melting temperature & \(T_{m}\) & 1655 & \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of Ti6 Al4V [34; 44; 45]. Figure 1: Calculated temperature profiles and molten pool shapes. Color bars show the temperature values. The green shapes are molten pool geometries. (**a**) Temperature distribution (**top**) and molten pool (**bottom**) of Case 1 (Power = 100 W, Speed = 500 mm/s). (**b**) Temperature distribution (**top**) and molten pool (**bottom**) of Case 7 (Power = 195 W, Speed = 500 mm/s). Figure 2: _Cont._  
Figure 3: Sensitivity of molten pool size to normalized enthalpy. (**a**): Molten pool width. (**b**): Molten pool depth. Figure 2: Comparison of predicted molten pool size with experimental data. (**a**): Molten pool width. (**b**): Molten pool depth.