*3.1. E*ff*ect of Arc and Droplet Transfer on Weld Pool*

During the welding process, the arc pressure and the impingement of droplet agitate weld pool intensify the convection in the weld pool. Hence, the study on heat and mass transfer process definitely is the premise of that on the dynamic behavior of pool in DP-GMAW. In P-GMAW, the current pulse frequency is constant. In DP-GMAW, the frequency of the current pulse changes periodically. Typical electrical signal waveforms of P-GMAW and DP-GMAW.

A thermal pulse cycle of DP-GMAW consists of peak period, base period and transition period of thermal pulse, as shown in Figure 6. The peak and base period of thermal pulse differ in the frequency and the peak of current pulse, leading to variational heat input, arc pressure and droplet impingement force. Therefore, it is necessary to analyze the heat input and force acting on the weld pool during a single current pulse period, then analyze the variational process of the heat input and the force acting on the pool during the whole thermal period of DP-GMAW. The thermal nature of the DP-GMAW weld pool is largely controlled by the heat content of the droplet and the arc heating. Assuming that the current distribution is homogeneous on the arc projection plane on the pool surface, the arc heat during one current pulse (*Earc*) is expressed as follows [16]:

$$E\_{\rm arc} = \int\_0^{1/f} I(V\_w - \varphi)dt\tag{9}$$

where *Vw* is the cathode voltage when the cathode material is stainless steel and ϕ is the electronic work function of stainless steel. Y Yokomizu [17] points out that for stainless steel, *Vw* is about 16.7 v, ϕ is 4.77 v. *Parc* is the instantaneous power of heat input of arc to weld pool. The heat content of the droplet (*Edroplet*) can be estimated by the following Equation [14]:

$$E\_{droplet} = \rho h \frac{4}{3} \pi \left(\frac{D\_d}{2}\right)^3 \tag{10}$$

where ρ is the density of the liquid stainless steel, *h* is the enthalpy of the droplet and *Dd* is the diameter of the droplet. Considering overheating of the droplets, the assumed temperature before the droplets enter the molten pool is 2900 K, and the enthalpy of the droplets *h* [16] is:

$$h = \int\_{300}^{2900} \mathbb{C}\_p dT \tag{11}$$

where *Cp* is the specific heat capacity of the droplet and T is the temperature. According to the research data of Davim [18], h = 1.578 × 106 J/kg. The total heat input (*Etotal*) and the power of heat input (*Ptotal*) acting on weld pool in a single current pulse period are:

$$E\_{\text{total}} = \rho h \frac{4}{3} \pi \left(\frac{D\_d}{2}\right)^3 + \int\_0^{1/f} I(V\_{\text{iv}} - q\rho) dt\tag{12}$$

$$P\_{\text{total}} = E\_{\text{total}} \times f \tag{13}$$

where *f* is the instantaneous frequency of the current pulse. The arc force (*Farc*) during welding process is as follows [18]:

$$F\_{\rm arc} = \frac{\mu}{4\pi} l^2 \log \frac{D\_d}{D\_R} \tag{14}$$

where <sup>μ</sup> is the space permeability of the arc area, <sup>μ</sup> = 4.073 <sup>×</sup> 10−<sup>4</sup> N/A2 [19]. The momentum of the droplet (*pdroplet*) and the droplet impingement pressure on weld pool (*Pd*) are shown as follows [16]:

$$p\_{droplet} = \frac{4}{3}\pi \left(\frac{D\_{droplet}}{2}\right)^3 \rho \text{ V}\_d \tag{15}$$

$$P\_d = \frac{2f\rho D\_d V\_d}{3} \tag{16}$$

where *Vd* is the velocity of the droplet. Combined with the above formula, the arc behavior, droplet transition behavior, heat input and force acting on the weld pool during a current pulse period were analyzed, as shown in Figures 7 and 8. The arc size increases first and then decrease with the change of current during a current pulse, as shown in Figure 8a. At the beginning of the current pulse, the current and voltage rise rapidly to the peak, the size of the arc, the pressure and the heat power of the arc acting on weld pool rises synchronously. During peak time, current, arc size, arc pressure rise to the maximum in the pulse period. The arc transmits most of the heat to the weld pool during peak time, as shown in Figure 8b. With the decrease of current, the size of arc decreases gradually. The arc pressure and the heating power also decreases synchronously with current. While the size of the arc increased after the time of the droplet detached from the wire. It was caused by metal vapor concentration increasing in arc space when the droplets detach from the wire, and the phenomenon of arc jumping is also one of the factors, as shown in Figure 7(5,6). While this increase of arc size has no obvious effect on arc force and heating process at low current. The heat contained by the droplet and its impact force acting on weld pool can be calculated by Equations (5) and (11). Based on the above data, the total heat input, the arc pressure and the droplet impingement force acting on the weld pool in a single pulse period can be calculated, as shown in Figure 8b.

**Figure 6.** Welding electrical signal waveform of (**a**) P-GMAW(No.12); (**b**) DP-GMAW(No.3).

**Figure 7.** Combination of arc behavior, droplet transition behavior and electrical signals: 1–9 are the arc profile, 10–18 are images of the droplet transfer process (No.3).

**Figure 8.** (**a**) Arc size and droplet diameter; (**b**) heat input and pressure acting on weld pool.

DP-GMAW process periodically adjusts the output welding current, pulse waveform and pulse frequency vary with the current on the basis of "one droplet one pulse". Figure 9 shows the peak pulse current and pulse frequency with different output welding current. With the increase of the output current, the pulse frequency increases significantly, while the peak current of the pulse increases slightly. The main way to control output current for DP-GMAW process is to adjust the current pulse frequency. The purpose of adjusting the peak of the current pulse is to maintain the stability of the transition under different welding currents.

**Figure 9.** Peak current and frequency of pulses with different welding currents.

Figure 10 shows the heat content, the power of heat input, the pressure of arc, the droplet impingement force and momentum per unit current pulse with different output welding current. As shown in Figure 10a, the heat content of droplet was similar under different output welding current the arc heat had the same trend. Due to the uneven composition of the welding wire and the unstable wire feed speed during welding process, the size of the droplets cannot be consistent. However, the difference in droplet size with different average currents were small due to the consistency of the current pulse waveform. However, the heating power acting on weld pool increased obviously due to a clear growth of current pulse frequency. The momentum carried by the droplets were similar under different output welding currents, as shown in Figure 10b. Many studies can contribute to explaining it. The research of Emanuel [1]. Found that the droplet speed depends on the ratio between base to peak current of P-GMAW, which is different from the traditional GMAW. A slight change in the peak current could not significantly affect the droplet velocity. P.K. Ghosh's study [18] came to a similar conclusion that the diameter and speed of droplet in P-GMAW process predominantly depends upon Ip irrespective of mean current and arc voltage. The increase of droplet transition frequency leads to an obvious increase of equivalent droplet impact force, as shown in Figure 10b. It is worth noticing that the arc pressure acting on the weld pool was much less than the droplet impingement force. Other researchers have described similar phenomena that liquid waves in P-GMA welding are triggered primarily by the impact of droplet, not by arc pressure [20]. Therefore, this paper only considers the droplet impingement force on weld pool.

**Figure 10.** Heat input (**a**), pressure and momentum (**b**) of arc and droplet during single current-pulse with different welding currents.

Figure 11 shows the heat input and the droplet impingement force acting on the weld pool during the thermal pulse period with different ΔI. As shown in Figure 11, the process of thermal and pressure acting on the weld pool demonstrated the characteristic periodically fluctuation same with the thermal frequency. The heat input rate of the different stage of the thermal pulse were the average heat input rate during Tp or Tb. This paper compares the heat input rate and the thermal gradient of weld pool (G) at different period under all parameters, as shown in Table 3. It should be noted that the thermal gradient of weld pool (G) along the welding direction calculated by Equation (7) is without considering the pool convection.

**Figure 11.** Changes of heat input (**a**) and droplet impingement force (**b**) in thermal pulse of DP-GMAW.


**Table 3.** Heat input rate (KJ/m) and the thermal gradient of weld pool (K <sup>×</sup> mm<sup>−</sup>1) with different parameters.
