## 5 Numerical Results and Discussion
### Simulation and Experimental Verification
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \(T\) (\({}^{\circ}\)C) & **20** & **100** & **200** & **300** & **400** & **500** & **600** & **700** & **800** \\ \hline \(\lambda\) (W/m\(\cdot\)\({}^{\circ}\)C) & 233 & 232 & 230 & 228 & 224 & 221 & 217 & 213 & 209 \\ \(\rho\) (Kg/m\({}^{3}\)) & 2780 & 2762 & 2746 & 2720 & 2698 & 2676 & 2536 & 2484 & 2310 \\ \(c\) (J/Kg\(\cdot\)\({}^{\circ}\)C) & 875 & 921 & 1047 & 1130 & 1180 & 1238 & 1292 & 1436 & 1476 \\ \(\alpha\) (\({}^{\circ}\)C\({}^{-1}\)) & 21.4 & 22.7 & 23.8 & 24.9 & 25.7 & 26.6 & 27.4 & 28.4 & 29.3 \\ \(E\) (GPa) & 70 & 65 & 49.4 & 38.9 & 28.5 & 18.2 & 7.8 & - & - \\ \hline \end{tabular}
\end{table} 
Table 1: Material properties. Figure 7: Temperature contour of the plane without cracks in the heating process (0 \(<\) \(t\)\(<\) 40 s). (**a**) \(t=5\) s; (**b**) \(t=10\) s; (**c**) \(t=18\) s.  
Figures 7 and 8 represent the temperature distribution of aluminum alloy plate in the welding heating and cooling processes. It can be seen that the high temperature area mainly concentrates on the welding center area; the highest temperature zone moves as the heat source. The heating quantity diffuses to the heating affected zone, of which the temperature of the workpiece tends to be balanced. The calculated results are in good agreement with the existing ones. In addition, it can be seen that the heat conduction on the workpiece is continuous, and the temperature gradient is distributed in the welding heating and cooling processes. In order to validate the effectiveness of the proposed method, the real-time temperature curve of the weldment surface is measured by the infrared thermal imager in the welding experiment [9; 19], which is shown in Figure 9.  
The plate surfacing MIG welding experiment of 2024 aluminum alloy sheet is done. The testing is carried out by the infrared thermal imaging instrument. The size of the base material is 80 mm \(\times\) 60 mm \(\times\) 2 mm. The three measuring points of the welding plate surface are measured by the infrared thermal imaging instrument, the layout of which is shown in Figure 10.  
The thermal cycle curve of the three measuring points is obtained, which is shown in Figure 11. It can be seen that the temperatures of the three measuring points rise rapidly as the welding heating source moves along the center zone of the workpiece. It reaches the maximum value in a very short time. Then, the temperature of each point descends slowly to be a value. The temperature rising rate of each point is higher than the falling one in the cooling process. In the welding heating process, the temperature of the welding seam zone is much greater than that of the heat affected zone. The maximum temperature value of point one is higher than that of the other points. The temperature of each point tends to be uniform as time goes on in the cooling process, which is consistent with the welding temperature field characteristics. Figure 8: Temperature contour of the plane without cracks in the cooling process (40 \(<t<\) 180 s). (**a**) \(t=50\) s; (**b**) \(t=80\) s; (**c**) \(t=100\) s.  
Figure 9: The temperature measured by the experiment. The effective heating radius of the Gauss heat source is adjusted to meet the agreement between the simulation and experiments [9]. The effective heating radius of the Gauss heat source is determined by an infrared thermal imaging temperature measurement experiment [9,19]. The appropriate radius is 4.0 mm corresponding to the welding parameters of \(I\) = 160 A, voltage \(U\) = 20 V and speed \(v\) = 2 mm/s. Figure 12 is the comparison of thermal cycle curves of the calculation and experiment at point one. The results show that the simulation results are close to the experimental results. Figure 11: Thermal cycle curves of the experiment. Figure 10: Temperature measuring point distribution.