## 3 Results and Discussion
### Analysis of Frequency Characteristics of Welding Pool Oscillation  
The free oscillation process of the weld pool could be interrupted by the droplet transition process, which will greatly disturb the continuity of the oscillation signal. In order to analyze the frequency characteristics of the weld pool oscillation signal of S-GMAW, continuous wavelet transform is used to extract discontinuous frequency features of the oscillation process. Figure 6 is the wavelet quantity diagram of the weld pool oscillation signal under different penetration states, and the corresponding oscillation signal component at the scale vector with stable frequency characteristics. Equation (5) is the conversion relationship between scale vector (\(\alpha\)) and the corresponding stable frequency characteristics (\(f\)):  
\[f=\frac{f_{a}f_{s}}{\alpha} \tag{5}\]  
where, the sampling frequency of high-speed photography (\(f_{s}\)) is 10 kHz, (\(\alpha\)) is the scale vector, and \(f_{a}\) is the frequency of the wavelet basis function selected. The frequency of the wavelet basis function used in this paper is 0.796. Figure 6: Wavelet Quantity Diagrams and Corresponding Oscillating Signal Components of Melt\(-\) Pool Oscillations: (**a**) The wavelet quantity diagram of Figure 2b; (**b**) The wavelet quantity diagram of Figure 5b; (**c**) The corresponding oscillating signal components at the wavelet ridges of (**a**); (**d**) The corresponding oscillating signal components at wavelet ridges 1 of (**b**); (**e**) The corresponding oscillating signal components at wavelet ridges 2 of (**b**). It can be found from Figure 6a that a stable continuous wavelet ridge line appears in the wavelet quantity diagram of the oscillation signal of the partially penetrated weld pool, which indicates that the oscillation process has only one frequency characteristic. The corresponding oscillating signal components at the wavelet ridges are shown in Figure 6c, and the oscillation frequency is 26.5 Hz. As for the fully penetrated weld pool, the wavelet quantity diagram has two stable continuous wavelet ridges, indicating that the oscillation signal has two frequency characteristics, 20 Hz and 53 Hz, respectively. The component diagrams of the oscillating signal corresponding to the two frequencies are shown in Figures 6d,e, respectively. Under mobile welding conditions, the GTAW weld pool is prolonged in the length direction, causing asymmetrical back and forth \"sloshing\" on the free surface of the weld pool [14], as shown in Figure 7. The oscillation phenomenon in the GMAW welding process was similar to that of the GTAW. The front part of the weld pool in the S-GMAW welding process was subjected to the \"surface impact\" from the electric explosion, and the whole weld pool oscillated in a swaying mode. The difference in weld pool oscillation modes and boundary conditions between the partially penetrated and fully penetrated weld pool is shown in Figure 8. Figure 8a,c are the cross-sections of the incomplete penetration weld and the full penetration weld, respectively, Figure 8b,d are the corresponding oscillation mode, respectively. In a fully penetrated weld pool, where the front of the weld pool bottom is fully penetrated, the oscillation phenomenon is similar to that of a partially penetrated weld pool. However, the freedom of oscillation in a fully penetrated weld pool increases, and the liquid above the penetration point can move vertically. This results in a greater amplitude for the oscillations, making the fully penetrated weld pool more susceptible to high-amplitude oscillations. This phenomenon also appears in the oscillation phenomenon of the GTAW weld pool [6; 14]. Figure 8: (**a**) Partial penetration weld cross section; (**b**) Partial penetration weld pool oscillation mode; (**c**) Full penetration weld cross section; (**d**) Full penetration weld pool oscillation mode. Figure 7: The weld pool oscillation mode [11].