*5.2. The E*ff*ects of Arc Length on the Droplet Impact Force*

The droplet impact force is the cumulative effect of droplets. If the types of droplet transfer were changed, the droplet impact force would be different as well [33]. According to Ref. [34], the droplet was considered approximately to be a sphere and the droplet impact force (*P*d) was regarded as a force per unit area or pressure, which was relative to the droplet mass (*m*d), velocity (*v*d), frequency (*f* d) and diameter (*d*d), as displayed in Equation (1).

$$P\_{\rm d} = \frac{4m\_{\rm d}v\_{\rm d}f\_{\rm d}}{\pi d\_{\rm d}^2}. \tag{1}$$

According to the mass formula of the sphere, the *m*<sup>d</sup> can be calculated by Equation (2).

$$m\_{\rm d} = \frac{\rho \pi d\_{\rm d}^3}{6}.\tag{2}$$

Therefore, Equation (1) can be further written as Equation (3) (density ρ = 7.8 g/cm3).

$$P\_{\rm d} = \frac{2\rho v\_{\rm d} f\_{\rm d} d\_{\rm d}}{3}.\tag{3}$$

However, Equation (3) is only applicable to the single-mode droplet transfer. For the mixture of different types of projected transfer, the droplet impact force should be the sum of each droplet impact force in MDPP, ODPP and ODMP (Equation (4)).

$$P\_{\rm d} = P\_{\rm d,MDPP} + P\_{\rm d,ODPP} + P\_{\rm d,ODMP}.\tag{4}$$

The droplet frequency of MDPP, ODPP and ODMP are noted as *f*MDPP, *f*ODPP and *f*ODMP, while the percentage of the pulses' number are noted as ϕMDPP, ϕODPP and ϕODMP respectively. Therefore, the droplet frequency of ODPP equals the percentage of the pulses' number (ϕ) times the frequency of pulse current wave (*f*) (Equation (5)).

$$f\_{\text{ODPP}} = \varphi\_{\text{ODPP}} f. \tag{5}$$

In addition, the frequency of the big droplet and the small droplet in MDPP (see Figure 11) are equal to the frequency of current pulses (Equation (6)). Multiple sized droplets can be found in

the MDPP process, but the biggest droplet was much larger than the others (see Figure 11). Thus, the droplet impact force was approximately regarded as that of the biggest droplets in MDPP process.

$$f\_{\rm MDPP} = \varphi\_{\rm MDPP} f. \tag{6}$$

In the ODMP process, a droplet may detach from the wire after severe pulses. After observation and calculation from the high-speed photographs, the average pulses for every MDPP are 2.2 and 2.3 in Test 5 and Test 6, respectively. Thus, the droplet frequency in Test 5 and Test 6 can be calculated by Equations (7) and (8).

$$f\_{\text{ODMP}} = \varphi\_{\text{ODMP}} f / 2.2. \tag{7}$$

$$f\_{\text{ODMP}} = \varphi\_{\text{ODMP}} f / 2.3. \tag{8}$$

Moreover, the percentage of the pulses' number (ϕ) and the frequency of pulse current wave (*f*) can be read from Figure 12 and Table 1, respectively. The image-processing method in Ref. [35] was used to estimate the droplet velocity (*v*d) and diameter (*d*d). By using Equations (1)–(8) simultaneously, the average droplet impact force of each test was obtained in Figure 13. It can be seen that the droplet impact force of Test 3 was the highest, while the droplet impact force of Test 6 is the lowest. The former was about 50% larger than the latter, indicating that the arc length has an important influence on the droplet impact force. The droplet impact force declined with the growth of the arc length. In addition, the main part of the droplet impact force was contributed from ODPP.

**Figure 13.** The average droplet impact force of projected transfer.

#### **6. Discussion**

The characteristics of weld bead formation and droplet transfer in pulsed GMAW with different arc lengths (about 1–11 mm) by changing the base current time were studied in this work. Because enough arc space was needed when a droplet detached from the wire and dropped into the molten pool, the mixture of projected transfer and short circuits would be obtained if the arc length were shorter than 3 mm. However, spatters would inevitably be produced from short circuits, especially instantaneous short circuits (Section 4.1). To reduce the spatters and improve the weld bead formation, the shortest arc is recommended to be limited to avoid the partial projected transfer zone.

Additionally, in the projected transfer zone, the quality of weld bead surface formation became worse gradually with the increase of the arc length. When the arc length was over 10 mm, dozens of droplets directly dropped outside the molten pool and became large spatters near the bead (Section 4.2). In addition, the penetration offset in pulsed GMAW will become more sensitive with the increase of

arc length. The penetration offset was less than 0.5 mm when the arc length was no more than 5 mm. However, when the arc length exceeded 10 mm, the penetration offset can reach 3 mm, which is not conducive to the positioning and alignment of the bead.

On one hand, Figure 10 in Section 4.2 indicates that the increase of arc length contributes to the fall of energy density and increase of heat dissipation of arc. On the other hand, Figure 13 in Section 5.2 implies that the droplet impact force declined with the growth of the arc length. According to Ref. [34], large droplet impact force can promote the increase of weld penetration. Therefore, because of the above three factors (the increase of arc heat dissipation, the fall of arc energy density and droplet impact force), the penetration tended to become shallower.

As a result, it is suggested that the arc length should be limited to a shorter range (less than 5 mm) in the projected transfer zone. So that the welding formation can be improved, the penetration offset can be reduced and the larger penetration can be obtained. Additionally, Table 1 shows that the average current of shorter arc was smaller, which can reduce heat input and save electric energy when compared with the longer arc.

In our preliminary experiment, the tensile properties of welded joints were also affected under difference arc lengths. According to AWS: B4 specifications [36], the tensile test specimens were prepared from the butt joints in the perpendicular direction to the welded seam. Figure 14 shows the average tensile strengths and elongations of the welded joints with different arc lengths in the projected transfer zone. It can be seen that the tensile strengths were approximately constant. However, with the growth of arc length, the elongations fell gradually. This implied that the short arc is also beneficial for obtaining weld joints with high elongations.

**Figure 14.** The tensile strengths and elongations of the welded joints with different arc lengths in the projected transfer zone.

In addition to the above discussion, the power law relationship (*I* n <sup>p</sup>*t*<sup>p</sup> = constant) has been used in many studies to determine the peak current and time of ODPP transfer mode [16–18], ignoring the influence of the base current time. However, in this work, it was found that the types of droplet transfer in pulsed GMAW changed a lot by only adjusting the base current time, even though the peak current and time were constant. More than 90% (but not 100%) ODPP transfer mode can be obtained when the pulse parameters were selected properly. The arc length can be adjusted by the base current time. The short arc trended to rise the proportion of MDPP, and the long arc trended to rise the proportion of ODMP.
