*3.1. The Metal Transfer Process and Impact on the Weld Pool*

During the short circuit period, the heat source of weld pool is mainly the resistance heat of the filler material and the molten filler material. Arc heat is the main heat source during the arc period. In order to compare the heating power of different waveform control methods to the weld pool, Equation (1) was used to calculate the welding power for all waveform control methods, Equations (2) and (3) were used to calculate the welding line energy on the base metal [12,13].

$$P\_w = \frac{1}{t\_a + t\_s} \left[ \left( \int\_0^{t\_a} u(t)i(t)dt \right) + \left( \int\_0^{t\_s} u(t)i(t)dt \right) \right] \tag{1}$$

$$Q\_b = P\_w \ast \eta\_{\rm eff} \ast \left(t\_d + t\_s\right) = P\_w \ast \eta\_{\rm eff} \ast t\_w \tag{2}$$

$$Q\_{pl} = \frac{Q\_b}{v \ast t\_w} = \frac{P\_w \ast \eta\_{\rm eff}}{v} \tag{3}$$

where *u*(*t*) is the voltage curve during welding, *i*(*t*) is the current curve, *tw* is the welding time, *tarc* is the burning-arc time, *ts* is the arc-shorting time, *Pw* is the welding power during single a droplet transfer cycle, *Qb* is the heat in the base material, ηeff is the thermal efficiency of the welding process, *Qpl* is the heat power applied to the weld pool per unit length, and *v* is the welding speed.

The arc length of S-GMAW is short hence the heat losses to the surrounding atmosphere are low. The effective thermal efficiency is high and the ηeff of S-GMAW is 0.85 [14] which is higher than that of Pulsed GMAW and Spray GMAW.

Figure 5 shows the combination of voltage and current waveform and metal transfer process of different S-GMAW processes. In order to ensure the comparability of waveforms, the volume of the drops was similar at the time of waveforms acquisition. The arc current curve of traditional S-GMAW process is influenced by two factors: Inductance of the welding circuit and re-striking current. The re-striking current determines the peak current in the arc period. Then the current declined to the background current, this period was *tarc*<sup>1</sup> as shown in Figure 5a. Inductance of the welding circuit

determined the rate of current decline. The LSC process maintained the large current for a defined short period of time after the arc ignites to ensure that the arc had sufficient energy to heat the welding wire and the base material. Then the current decreased to the background current by the current control to regulate and initiate the next detachment, this period was *tarc*<sup>1</sup> as shown in Figure 5b. As for Cold Arc process, the current was decreased dramatically to permit a smooth break of the bridge of the molten metal at the end of short-circuit period. After the arc had been stabilized, the current was raised for a defined short period of time, known as melt pulse, to heat the welding wire and the base material. Then the current decreased to the background current, this period was *tarc*<sup>1</sup> as shown in Figure 5c. The average heating power to the base material and weld pool outlines of three waveforms is shown in Table 3.

**Figure 5.** The droplet transition process: (**a**) conventional process; (**b**) LSC; and (**c**) Cold Arc.


**Table 3.** The effective heating power to the base material and weld pool outlines.

Figure 6 shows the profile of the weld pool during the transition period of a single molten drop. The first column of Figure 6 is the surface profiles of the weld pools at the short circuit stage, the second at the time when the liquid bridge exploded, the third at the arc stage, and the fourth at the short circuit stage of next droplet transition stage. The weld pools size was shown in Table 2. The area of the weld pool was measured by the Photoshop software, the border between the liquid and the solid was outlined manually, which could not be found by the software for tiny gray scale differences. The pool size can be obtained imprecisely by measuring the image, but the influence trend of waveform control mode on the pool size can be obtained under the same shooting condition. The results show that there was no obvious difference in the width of the weld pool, but there was a great difference in the length of the weld pool. These differences were directly related to the impact of electrical explosion at the end of short circuit.

**Figure 6.** Variation of weld pool profile of short circuit gas metal arc welding (S-GMAW) under different waveforms (wire feed rate: 3 m/min, thickness of base plates: 4 mm): (**a**) conventional waveform, (**b**) LSC waveform, and (**c**) Cold Arc waveform.

As shown in Figure 6, strong arc light appeared at the moment of electric explosion. There was no obvious change in the size of the weld pool before and after the electric explosion, but there was obvious difference between the surface of different weld pools. The glitters in the blue circles of Figure 6 were due to backlight and weld pool surface, which was the mirror-like reflection. The weld pool fluctuation resulted in the change of surface curvature. The more violent the surface fluctuation of the weld pool, the greater the chance of mirror reflection and the more glitters there were. The surface of the weld pool with traditional waveform fluctuated the most, which was followed by LSC, and the weld pool of Cold Arc basically did not change. In the transition period of a single melt droplet, the energy carried by electric explosion was mainly propagated to the melt pool in the form of momentum, which changes the flow state of the metal inside the weld pool.

The resistance heat is the main factor that causes the liquid bridge explosion during short circuit period. Due to the highest resistance at the neck of the liquid bridge, it was the location where the electric explosion occurred. The instantaneous heat generation power per unit volume of the metal at the neck of the liquid bridge is calculated, the process is shown as follows:

$$R = \frac{\rho \ast dl}{\pi r^2} \tag{4}$$

$$P\_h = I^2 \ast R = I^2 \ast (\rho \ast dl) / \left(\pi r^2\right) \tag{5}$$

$$P\_{\upsilon} = \frac{P\_h}{V} = \frac{I^2 \ast \frac{\rho \circ dl}{\pi r^2}}{\pi r^2 \ast dl} = \frac{I^2 \ast \rho}{\pi^2 \ast r^4} \tag{6}$$

where *R* is the resistance at liquid bridge neck, ρ is the resistivity of metal at liquid bridge, *r* is the radius of liquid bridge neck which was extracted by image processing system which was mentioned above, *dl* is the fluid bridge neck differential length, *Ph* is the thermal power of resistance at neck of liquid bridge, and *Pv* is the instantaneous power density of the liquid bridge. The electrical explosion is caused by overheating of the metal at the neck of the bridge. The diameter of the liquid bridge changes gently in a small area near the neck constriction whose volume can be replaced by a cylinder whose diameter is equal with the diameter of the neck of the liquid bridge. *V* is the differential volume of the fluid bridge neck length.

The image processing system was used to extract the diameter of the shrinking neck of the liquid bridge in the short circuit period. Figure 7 are the relationship curves that show the diameter of the neck of the liquid bridge along with time.

**Figure 7.** The diameter of the neck of the liquid bridge as a function of time.

It has been pointed out that the surface tension and electromagnetic pinch force are the main forces to make droplet transfer which have close relation with formation, destabilization, and break-up of short circuit liquid bridge. The curves in Figure 7 all showed a process of rapid rise, then stability, and finally rapid decline. The rapid decline stage of diameter was the process of destabilization and break-up of liquid bridge. The sharp slumping stage of three curves lasted nearly the same time as shown in Figure 7. At that time, the current in the welding loop were 280 A, 210 A, and 50 A in conventional, LSC, and Cold Arc, respectively, as shown in Figure 5. The results showed that electromagnetic shrinkage force had little effect on the duration of destabilization and break-up of short circuit liquid bridge. The difference of stability times of liquid bridges was obvious, which indicated that the rising rate of loop current in the short circuit stage can effectively promote the formation of neck of liquid bridge and greatly reduce the short circuit stage time.

Figure 8 shows the relationship curves of the instantaneous power density of liquid bridge neck with time under three waveform conditions. As shown in Figure 8, The curve of the instantaneous power density of the liquid bridge along with time was acquired by substituting the diameter of the shrinking neck of the liquid bridge and the current corresponding to it into Equation (6).

**Figure 8.** The instantaneous power density of the liquid bridge as a function of time.

It can be seen from Figure 8 that the instantaneous power density of the liquid bridge was extremely low during short circuit period for most of the time. The energy accumulated in a very short time before the liquid bridge explosion is the main factor influencing the impact of electric explosion. Therefore, the instantaneous power density of the liquid bridge during the burst can effectively measure the magnitude of the electric explosive impact force. The instantaneous power density of liquid bridge metal in cold arc power supply was relatively small. The instantaneous power density of liquid bridge metal at the end of short circuit in LSC process was about half of that of traditional process, and the electric explosion impact force was less than that of traditional process. The impact force of electric

explosion determines the dynamic characteristics of weld pool. Figure 9 shows the probability density distribution of oscillation amplitude of weld pool:

The amplitude of weld pool is proportional to the impact of electric explosion. The probability of large amplitude of weld pool in traditional process was greater than that of LSC and Cold Arc. The impact of electric explosion on the weld pool in Cold Arc process was very small, and the liquid level of the weld pool had no obvious fluctuation.

The results of the statistics of oscillation amplitude are in good agreement with Figure 6. The amplitude was proportional to the impact of surface traveling wave on the boundary of weld pool. This can explain the obvious difference in the length of weld pool with little difference in the width of weld pool. The oscillation amplitude of weld pool was affected by the state of weld pool. The full penetration pool had larger amplitude of the weld pool was affected by the state of the weld pool; compared with the partial penetration. When the weld pool was impacted, the bottom of the full weld pool was liquid metal level, which had little effect on the downward movement of metal flow. As a result, the amplitude of full penetration pool was larger than that of partial penetration pool under the same welding parameters.
