*3.2. The VPPA Pressure and its Influence Mechanism on Keyhole and Weld Pool Evolution*

Figure 12 is the radial distribution of VPPA pressure as the function of elapsed time from the beginning of the EP phase. The currents in EP and EN phase both are 150 A. The pressure is the Gaussian distribution in the radial direction. The radial distribution width of arc pressure has little difference in the EP and EN phases. However, there is an obvious difference between two polarities in the plasma arc center. The pressure of the EP phase is clearly lower than that of the EN phase. Combining with pressure evolution in arc center region shown in Figure 13, we can understand the pressure difference between EN and EP more clearly. In the EN phase, the pressure can keep at a stable value about 3.3 kPa. After the polarity switches from EN to EP, the pressure firstly drops quickly, then gradually decreases. The minimum pressure appears at the moment of polarity switching from EP to EN. Then it increases to the stable value of EN phase, which takes about 6 ms. Therefore, we can

conclude that the difference between the two polarities is mainly due to the arc pressure decreasing process and the rising process in the start segment of each phase.

**Figure 12.** Radial distribution of plasma arc pressure as a function of elapsed time from the beginning of EP phase with the current of 150 A.

**Figure 13.** The evolution of plasma arc pressure and current in the center region of arc with 150 A in EN and EP phase.

In order to understand the evolution mechanism of the VPPA pressure and adjust the pressure output reasonably, the energy and momentum balance between electrodes and plasma arc in different polarities is analyzed in Figure 14. The balance items in the start moment of the EP phase are listed out in Figure 14a, based on which the variation tendencies of the tungsten electrode temperature field and the plasma arc shape are also described, marked by the pink solid line. In the start of the EP phase, the tungsten becomes positive polarity and begins to absorb electrons with the high temperature that comes from the arc column, leading to the temperature of tungsten gradually increasing. Therefore, the melting region becomes larger as shown in Figure 14b. Tanaka et al. [29] synchronously measured the electrode temperature and work function of the tungsten electrode. They found that the work function of the tungsten electrode with the temperature above melting point is obviously lower than that of a solid electrode. Therefore, due to the low work function, the region of current outflow increases. Current density decreases with the increase of the melting region. The plasma arc pressure gradually decreases because of the changing of the current density.

**Figure 14.** The energy and momentum balance of plasma arc in different polarities. (**a**) start of EP pahse; (**b**) end of EP phase; (**c**) start of EN phase; (**e**) end of EN phase.

Another reason for the pressure reduction in the EP phase is the different physical process on the interaction of the plasma arc and the base metal in EN and EP phases. Tashiro et al. [30] pointed out that the cathode spot tended to be produced on the oxide layer. The current flowing between the arc and base metal is conducted mainly through the cathode spots. The gradual cleaning of the oxide film from the center to the circumference of the arc also leads to the expansion of the arc shape, causing the current density to decrease further. As shown in Figure 14c,d, the opposite process occurs in the EN phase, which makes the pressure of the EN phase higher.

Moreover, Basins et al. [31] pointed out that the arc pressure can be calculated by the following equation.

$$P\_{\rm arc} = \frac{\mu\_0 I^2}{4\pi^2 r^2} \tag{1}$$

where *Parc* is arc pressure, *μ*<sup>0</sup> is the space permeability, *I* is the current, *r* is the radius of plasma arc. Therefore, the difference of pressure between EN phase and EP phase can be got.

$$P\_{\rm arc}^{EN} - P\_{\rm arc}^{EP} = \frac{\mu\_0}{4\pi^2 r\_{EN}^2} \left( I\_{EN}^2 - \frac{I\_{EP}^2}{q r^2} \right) \tag{2}$$

Expressed in terms of current density, Equation (2) gives

$$P\_{\rm arc}^{EN} - P\_{\rm arc}^{EP} = \frac{\mu\_0}{4} \left( j\_{\rm EN}^2 r\_{\rm EN}^2 - j\_{\rm EP}^2 r\_{\rm EP}^2 \right) \tag{3}$$

where *PEN arc* is the plasma arc pressure of the EN phase, *PEP arc* is the plasma arc pressure of the EP phase, *rEN* is the radius of the EN plasma arc, *rEP* is the radius of the EP plasma arc, *IEN* is the current of the

EN phase, *IEP* is the current of the EP phase, ϕ is the radius ratio of the EP arc to the EN arc, *jEN* is the current density of the EN phase, *jEP* is the current density of the EP phase.

Through the analysis of momentum and energy balance in the interface between electrodes and plasma arc, we can know that the tungsten temperature increase and cleaning of oxide layer on the surface of base metal during EP phase both result in the decrease of current density. Thus, the arc pressure depends not only on the square of the current but also on the square of arc radius based on the Equations (2) and (3). However, Lin et al. [32] pointed out that welding parameters have little effect on the arc pressure distribution radius. Therefore, the best method to balance the pressure of the EP and EN phases is to adjust the current of different phases to change the arc current density separately.

### *3.3. The Optimization of Plasma Arc Pressure and the Molten POOL Stability*

In this section, the current of the EP phase is adjusted to balance the pressure output. Figure 15 is the evolution of plasma arc pressure in the arc center with a different EP current. The current in the EN phase is fixed to 150 A. The EP current changes from 160 A to 200 A at intervals of 20 A. When the EP current is 160 A as shown in Figure 15a, the pressure of the EP phase is lower than that of the EN phase. The average pressure difference between two phases is around 0.25 kPa. When the EP current increases to 180 A as shown in Figure 16b, the pressure of the EP phase is still lower than that of the EN phase. The pressure between two phases gets closer and the average difference is 0.15 kPa. When the EP current is 200 A, the pressure of the EP phase already becomes a little bigger than that of the EN phase.

**Figure 15.** The plasma arc pressure and current waveform with different current of EP phase. (**a**) 150 A in EN phase and 160 A in EP phase; (**b**) 150 A in EN phase and 180 A in EP phase; (**c**) 150 A in EN phase and 200 A in EP phase.

The variation of plasma arc pressure with the change in current can be clearly presented by the distribution contour shown in Figure 16. By comparison, it is found that there is no obvious expansion of the arc pressure distribution radius with the changing current. The difference of arc pressure between two polarities is obvious when the EP current is 160 A as shown in Figure 16a. When

continuously increasing the current of the EP phase to 180 A and 200 A, the arc pressure of the EP and EN phases tend to be consistent, as shown in Figure 16b,c. Therefore, it can be inferred that the balance of pressure output between the EP and EN phases is achievable by separately adjusting the current in two polarities. Thus, the keyhole weld pool instability during the digging process of VPPA welding can be weakened.

**Figure 16.** Radial distribution of plasma arc pressure as a function of elapsed time from the beginning of the EP phase with different EP currents. (**a**) 150 A in EN phase and 160 A in EP phase; (**b**) 150 A in EN phase and 180 A in EP phase; (**c**) 150 A in EN phase and 200 A in EP phase.

Figure 17 shows the distribution point and fitting line of the average pressure in EP and EN phases with the change of the EP current. The pressure of the EP phase gradually increases and there's a small fluctuation in the EN pressure. According to the fitting equation, the current of EP phase is 196 A if the pressure of two polarities is equal to each other, when the current of EN phase is 150 A.

The weld pool free surface with different EP currents is shown in Figure 18. The influence of balanced pressure output on the weld pool fluctuation is analyzed by comparing the different case. The time 0 in the figures with EN results in around 5 s from arc ignition. Four weld pool statuses in one current cycle are presented: EN, EN to EP, EP, EP to EN, respectively. When the current of EN phase is 150 A and EP current is 160 A as shown from Figure 18a to Figure 18d, the difference of the weld pool free surface between two polarities is obvious. Due to the decrease of plasma arc pressure in the EP phase, the weld pool free surface moves up and close to the upper surface of the base metal. When the current of EP phase is 180 A which is 30 A bigger than that of the EN phase, the difference of

free surface deformation in different polarities becomes very small, as shown in Figure 18e–h. When the EP current increases to 200 A, there is also a small weld pool fluctuation between two polarities, which is shown in Figure 17i–l. Therefore, the keyhole and weld pool of the digging process can be stabilized by separately adjusting the current to balance the pressure output.

**Figure 17.** Average plasma arc pressure at different EP currents.

**Figure 18.** The evolution of weld pool upside surface in one cycle with different EP current: (**a**–**d**) EP = 160 A; (**e**–**h**) EP = 180 A; (**i**–**l**) EP = 200 A.

Through a large amount of welding experiments, it is found that the success rate of forming weld bead is low if the keyhole weld pool fluctuates. It is easy to form cutting. As Figure 19 shows, when the current of EN and EP phase is 150 A, all the liquid metal falls to the workpiece bottom in the keyhole generation segment, which makes it difficult to close the keyhole, resulting in cutting. After balancing the pressure output (EN: 150 A, EP: 180 A), the keyhole is more easily closed by avoiding a liquid metal overall drop due to the weak fluctuation. Thus, the weld bead is easier to form.

**Figure 19.** The weld formation with different EP current.
