## 3 Results and Discussion
### Analysis of Frequency Characteristics of Welding Pool Oscillation
The above research results show that the oscillation mode of the GMAW short-circuit transition weld pool can be analogous to the oscillation mode of the GTAW weld pool. [PERSON] analyzed the relationship between the oscillation frequency and the size of the GTAW weld pool [14], as shown in Equation (6):  
\[f=\left(\frac{2\pi\sigma}{\rho\lambda^{3}}+\frac{g}{2\pi\lambda}\right)^{0.5} \tan\left(h\left(\frac{2\pi h}{\lambda}\right)\right) \tag{6}\]  
where, \(h\) is the depth of the weld pool, and the relationship between wavelength (\(\lambda\)) and wavenumber (\(K\)) is \(K=2\pi/\lambda\). The wavenumber (\(K\)) of the partially penetrated weld pool can be solved by the First Kind Bessel function equation (\(J_{m}\)) [14], as shown in Equation (7):  
\[J_{m}\left(KR_{pool}\right)=0 \tag{7}\]  
In Equation (6), \(R_{pool}\) is the equivalent radius of weld pool. The solution of \(J_{m}\) under different oscillation modes of the weld pool is shown in Figure 9 [15]. According to Figures 2 and 5, the oscillation mode corresponding to the partially penetrated weld pool in S-GMAW is shown on the right side of Figure 8, \(KR_{pool}=14.03\), and Equation (6) can be evolved into Equation (8):  
\[f=\left(\frac{1}{4\pi^{2}}\left(\frac{14.03}{B}g+\frac{2761.7}{B^{3}}\frac{ \sigma}{\rho}\right)\tan\left(28.06\frac{h}{B}\right)\right)^{0.5} \tag{8}\]  
where, \(B\) is the equivalent diameter of weld pool, \(B=(W\times L)^{0.5}\), \(W\) is the pool width, and \(L\) is the pool length. It can be found from Figures 2 and 5 that there is no significant difference between the oscillation modes of the weld pool with different penetration states. [PERSON] [6] proved that the weld pools oscillation phenomenon with different penetration state were similar when the ratio of the equivalent diameter of the bottom to the top is less than 0.5 in a fully penetrated weld pool. In S-GMAW, the ratio between the bottom diameter and the top surface of the full penetration part is less than 0.5, so, Equation (7) can be used to describe the frequency characteristics of both the fully and partially penetrated weld pool oscillation phenomenons. In order to verify the accuracy of Equation (7), the base plates with 2 mm and 4 mm are used to prepare the welds with fully and partially penetrated states. The calculated oscillation frequency is compared with the actual measured oscillation frequency of the weld pool, as shown in Figure 10.  
Figure 6:0 Solutions of Bessel Functions with different oscillation modes [15]. It can be found from Figure 10 that the actual oscillation frequency of the weld pool with different penetration states under different wire feeding speeds is close to the calculated result of Equation (7). However, the deviation between the measured value and the calculated value of the full penetration weld pool is significantly higher than that of the partial penetration weld pool. When the wire feeding speed is 3.3 m/min, the deviation is significant. The increase in wire feeding speed caused the width of the full penetration part at the bottom of the weld pool to increase, and the free oscillation area expanded, which, in turn, affected the oscillation process of the weld pool, resulting in deviations.