## 3 Results and Discussion
### The Welding Pool Oscillation Process
[12] derived the relationship between the energy attenuation factor \(\alpha\) and the viscosity \(\eta\) of the weld pool fluid, based on the principle of energy conservation in fluid mechanics, as shown in Equation (2):  
\[\alpha=\frac{8\eta\pi^{2}}{\rho\lambda^{2}}\times\frac{\sqrt[2]{\frac{2\pi g}{ \lambda}+\frac{8\sigma\pi^{3}}{\rho\lambda^{2}}}}{g+\frac{12\sigma\pi^{2}}{ \rho\lambda^{2}}} \tag{2}\]  
where, \(\rho\) is the density of the liquid metal in the weld pool, \(\sigma\) is the surface tension of the liquid metal, \(g\) is the acceleration of gravity, \(\lambda\) is the wavelength, \(\eta\) is the viscosity, and \(\eta=4.3\) mPa\(\cdot\)s.  
The study of [PERSON] et al. showed that the wavelength \(\lambda\) of the oscillating wave generated by the impact of a droplet is equal to the diameter of the droplet [13]. The transmission speed of surface traveling waves \(v\) mainly depends on the surface tension and density of the weld pool [13], as shown in Equation (3):  
\[v=\sqrt{2\pi\sigma/\lambda\rho} \tag{3}\]  
where, the surface tension (\(\sigma\)) of the fluid of Q235 steel is 1.0 N\(\cdot\)m\({}^{-1}\), the energy attenuation factor (\(\alpha\)) obtained by Equation (2) is 0.05, and the surface wave velocity obtained by Equation (3) is 0.77 m/s. Then, the relationship among the weld pool oscillation amplitude (\(A\)), the initial oscillation amplitude (\(A_{0}\)), and time is shown in Equation (4):  
\[A=A_{0}\times\mathrm{e}^{-\alpha\eta t}=A_{0}\times e^{-0.39t} \tag{4}\]  
It should be noted that the residual oscillation phenomenon in the weld pool can also affect the decay process of the oscillation amplitude, but this effect is difficult to measure and analyze based on existing methods. It can be seen from Equations (2)-(4) that the attenuation process of the main wave of the weld pool mainly depended on the density and surface tension of the weld pool metal, but the initial oscillation amplitude (\(A_{0}\)) of the main wave is related to the size of the weld pool and the magnitude of the impact from the electric explosion. Although reference [6] have shown that the weld pool has different oscillation modes with different penetration states in GTAW, few studies have analyzed the differences in the oscillation phenomenon of the S-GMAW weld pool in different penetration states. Figure 5 shows the oscillation process and oscillation signal of the full penetration weld pool in the S-GMAW process, the wire feeding speed and the plate thickness of which is 3 m/min and 2 mm, respectively. It can be found from Figure 5a that the weld pool in the fully penetrated state also forms oscillating waves under the impact of the electric explosion, similar to the partially penetrated state. Figure 5: (**a**) The oscillation process of fully penetrated S-GMAW weld pool (wire feeding speed is 3 m/min, plate thickness is 2 mm); (**b**) The oscillation signal at reference point of fully penetrated S-GMAW weld pool. It can be found that the weld pool of the short-circuit transition process in the full penetration and non-penetration states forms the main wave under the impact of the electric explosion, and moves to the tail of the molten pool, due to the damping caused by the viscosity of the molten pool metal. As shown in Figure 5b, the oscillation amplitude of the fully penetrated molten pool is higher than that of the non-penetrated molten pool. At the same time, the oscillation signal shows a large amplitude. The low-frequency oscillatory waves carry multiple high-frequency oscillatory waves with small amplitudes.