## 4 Results and Discussion
reduces along the rear, it reaches to 1.2 mm at \(x=-13\) mm. The above analysis indicates that there is a long weld pool at the rear but a narrow pool in the front. Figure 9 displays weld pool and temperature field on the longitudinal section (_xoy_ plane) at 3.2 s. It shows temperature field gradually shrink from the top surface to the bottom surface. The weld pool length is 16.2 mm at \(z=6\) mm, 5.6 mm at \(z=4\) mm, 3.8 mm at \(z=2\) mm, and 1.8 mm at \(z=0\) mm. The length drop rate (length reduction per unit height) reaches to 5.3 mm/mm, 0.9 mm/mm and 1.0 mm/mm in the three height ranges, respectively. The data indicates that the pool can maintain a long length at the top surface, but it shrinks fast at the upper part and smoothly at the lower part. Above research may benefit to the deep knowledge of the internal weld pool geometry. Figure 8: Weld pool and temperature field on the transverse cross-sections (\(t=3.2\) s). (**a**) \(x=1\) mm; (**b**) \(x=-2\) mm; (**c**) \(x=-3\) mm; (**d**) \(x=-4\) mm; (**e**) \(x=-6\) mm; (**f**) \(x=-13\) mm. In order to verify the model, a Fronius welding machine TranSynergic 5000 was used to conduct the experiment, as displayed in Figure 10. Experimental conditions are as follows: Welding current 150 A, Welding voltage 21.5 V, Welding speed 120 mm/min, Thickness of workpiece 6 mm, Orifice diameter 2.8 mm, Plasma gas flow rate 3 L-min\({}^{-1}\), Shielding gas flow rate 15 L-min\({}^{-1}\), Tungsten electrode shrinkage 2 mm, Distance from torch to workpiece 5 mm. Figure 11 displays comparison of captured image and calculated result of weld pool at the transverse cross-section. In the model, the solidus line (T = 1665 K) for the stainless-steel 304 is taken as the melting line. It can be found that the two agree well with each other. Figure 12 displays the calculated electric potential on the symmetry, and the maximum potential drop is 20.5 V. Meanwhile, the experimental welding voltage is 21.5 V, which is close to the calculated result. Previous PAW models never show the comparison of the welding voltage. Figure 10: Plasma arc welding system. Figure 9: Weld pool and temperature field on the longitudinal sections (\(t\) = 3.2 s). (**a**) \(z\) = 6 mm; (**b**) \(z\) = 4 mm; (**c**) \(z\) = 2 mm; (**d**) \(z\) = 0 mm. Arc pressure was also measured, and Figure 13 displays a comparison of the calculated arc pressure and measured pressure on the workpiece surface. It shows that the calculated pressure and measured pressure are in good agreement with each other at 110 A. The calculated arc pressure at 150 A shows similar distribution with that at 110 A. However, the pressure at 150 A was not measured since the detection probe will be fused at such a high current. In the unified model, the calculated arc pressure distribution at 150 A was used, where the maximum arc pressure is 6500 Pa at the center, but it reduces fast along the radial direction. The arc pressure is nearly zero beyond \(r=3\) mm. As shown in Figure 11, the \(P_{\text{max}}\) is 6500 Pa, and \(r_{0}\) is 3 mm in Equation (16). All above comparisons indicate the model is reliable in PAW engineering. Figure 11: Comparison of captured image and calculated result of weld pool at the transverse cross-section. Figure 5:0 Calculated electric potential on the symmetry. Figure 5:1 Comparison of calculated arc pressure and measured pressure on workpiece surface.