# Research of a Multi-Frequency Waveform Control Method on Double-Wire MIG Arc Welding
## 5 Experimental Results and Analyses
### Process and Quality Analyses Using Probability Density Function  
Apart from the figure of transient voltage and current waveforms, the welding current probability density function (pdf) can be also employed to evaluate the welding stability [25; 26]. Figure 6 shows the pdf of experiment 1. It can be observed that the pdf of leading current was 1% around 20 A, which showed that the current sharply varied when arc interruption occurred at trailing current and the possibility of small current appearing increased. Two small convex peaks appeared at 75 A and 336 A in pdf curve of leading current, the corresponding setting value of the base of leading wire and peak of leading wire were, respectively, 78 A and 340 A, which showed the differences were very small. The two convex peaks were gentle, and the pdf of 75 A was 2.86%, while the pdf of 336 A was only 0.88%, and the pdf between peak and base was beyond 0.1%, which showed that the overall current distribution was dispersive. The pdf curve of trailing current also had two convex peaks at 62 A and 210 A. The first convex peak was broad and the maximum pdf value was 2.12%. However, the pdf was 1.5% between 55 A and 80 A of trailing current, which showed that the current in the base stage was unstable, and the current was very dispersive. The difference between actual value 62 A and setting value 78 A was large. It may because that the current was unstable when arc interruption occurred, which increased the possibility of small current appearing. The second convex peak was also gentle with low slope, which showed that current distribution was not concentrative and the switch between base stage and peak stage was not prompt. Hence, it can be shown that, in experiment 1, the welding current distribution was dispersive and the welding process was unstable. Figure 5: Current waveform of experiment 1. The corresponding welding seam in Figure 7 shows that quality of welding seam was not satisfactory, and the phenomena of arc interrupt and undercut frequently appeared. Because the heat for metal transfer was not enough, the welding seam was not sufficiently formed. The defects appeared at 6-7 cm and 11 cm. In addition, some splashes occurred during the process, and the surface of the seam was poorly smooth. The best welding quality was obtained from experiment 13 according to Table 2. Transient current waveforms in Figure 8 shows that the currents were much more regular than that of experiment 1, and no arc interruption and short circuit occurred during the process. Corresponding pdf of the currents is shown in Figure 9. It can be seen that leading current had two convex peaks at 77 A and 336 A, which corresponded, respectively, to the currents in base stage and peak stage. The pdf of 77 A in the curve was 8.79%, and the convex peak was steep and narrow,  
Figure 8: Current waveform of experiment 13. Figure 6: Probability density function (pdf) figure of experiment 1. Figure 7: Welding seam of experiment 1.  
which showed that leading current in base stage was concentrative with small variation, corresponding to a stable welding process. The pdf of 336 A in the curve was 0.88%, and slope was steeper than that in Figure 6. The corresponding pdf between two peaks was between 0.01% and 0.1%. The pdf of current in peak value was small, which was because the \(DC_{T}\) of experiment 1 was 36.6%, while the value in experiment 13 was only 19.8%. It is because its duty cycle was much smaller than that of experiment 1, and the corresponding pdf was also decreased. According to Figure 9, the maximum pdf of trailing current in base stage appeared when the current was 80 A, the convex peak was also steep, and the shape was uniform with that of trailing current in base stage. Moreover, the second convex peaks had a difference, which denoted that peak of the trailing current was smaller, whose value was 239 A. However, the shapes of two convex peaks were uniform and the slopes were steep, which showed that the switch between peak stage and base stage was prompt.