# Research of a Multi-Frequency Waveform Control Method on Double-Wire MIG Arc Welding
## 3 Proposed Multi-Frequency Double-Wire Impulse Welding Method  
During the double-wire MIG arc welding process, the distance between two wires is very small, generally 8-12 mm. The mutual electromagnetic force between the two electrical arcs can induce some unsteady phenomena and may change the electrical arc. If the change is very large, arc interruption, irregular metal transfer or considerable expulsion may occur during the process [15]. To reduce the mutual interference between two welding wires, the effect of the electromagnetic force on the process should be seriously considered. [PERSON] et al. [18] established an equation to calculate the electromagnetic force between two wires as follows:  
\[F=(\frac{I_{T}}{\pi\sigma_{T}^{2}})\times(\frac{\mu_{0}I_{L}}{2\pi D_{E}}), \tag{1}\]  
where \(F\) is the electromagnetic force, which is Lorentz force; \(I_{L}\) is the leading current; \(I_{T}\) is the trailing current  
employed in reality. The phase of the current waveforms have difference of 180\({}^{\circ}\), and under this circumstance, the mutual electromagnetic force may be one fourth of that in Figure 3a. In addition, the influence on metal transferring process in this case is much less. In addition, the duration of the currents holding the peak values should not be too long, otherwise, irregularity of metal transferring process and unsteady welding process may occur. Hence, the currents should be in base values for a certain time. However, when the two currents were in the base values at the same time, such as in Stage A and Stage B in Figure 3c, arc interruption may occur because the heat delivery was less, at the same time the welding process is unstable. Considering the different situations above and combining electromagnetic theories, relative experiments and corresponding analyses [19; 20; 21], a new multi-frequency double-wire waveform control method (Figure 3d) was proposed in this work. It can be seen from the figure that when the leading wire current switched from peak stage to base stage after one cycle, the central control system gave out a signal which made the trailing wire current turning from base stage to peak stage. In addition, the pulse of trailing wire current can be modulated to be a high-frequency pulse set which is composed of some high-frequency pulses. After one cycle, when the trailing wire current turned from peak stage to the base stage, the central control system made the leading wire current turning from base stage to peak stage. This process was a circling process and guaranteed the electrical arcs from the two wires are steadily stricken, and avoiding appearance of mutual interference. This new current waveform control method required two new variables, trailing wire high-frequency peak time \(T_{HTp}\) and trailing wire high-frequency base time \(T_{HTb}\). Moreover, the trailing wire current peak modulation frequency \(f_{TH}\) can be deducted from the above two times. The mutual relations between those variables can be shown as follows:  
\[f_{L}=f_{T}\leq f_{TH} \tag{4}\]  
Figure 3: (**a**) Current waveforms (same frequency and inverse phase pulse); (**b**) current waveforms (same frequency and same phase pulse); (**c**) current waveforms (different frequency and different phase pulse); and (**d**) multi-frequency double-wire waveforms. \[T_{pL} =T_{bT} \tag{5}\] \[T_{pT} =T_{bL} \tag{6}\]  
In addition, a duty cycle (\(DC\)), which denoted the ratio between the time of high current and the whole time, was also commonly used to describe the current waveform in double-wire MIG arc welding. We employed \(DC_{L}\) and \(DC_{T}\) to describe the duty cycles of leading wire and trailing wire currents, respectively; the mathematical descriptions are as follows:  
\[DC_{L}=\frac{T_{pL}}{T_{pL}+T_{bL}} \tag{7}\]  
\[DC_{T}=\frac{T_{pT}}{T_{pT}+T_{bT}} \tag{8}\]  
It can be obviously observed that:  
\[DC_{L}+DC_{L}=1 \tag{9}\]  
According to above analyses, this new current waveform control method may have the following advantages:  
1.