2.2.3. EMF model

EMF can be induced from the two different arc plasmas; therefore EMF model used in the twowire SAW process can be followed [18]:

$$J\_{zL} = \frac{I}{2\pi} \int\_0^\pi \lambda I\_0(\lambda r\_a) \exp\left(-\lambda^2 \sigma\_{AL}^2 / 4d\_d\right) \frac{\sinh\left[\lambda(c-z)\right]}{\sinh\left(\lambda c\right)} d\lambda \tag{33}$$

$$J\_{rL} = \frac{I}{2\pi} \int\_0^\infty \lambda I\_1(\lambda r\_d) \exp\left(-\lambda^2 \sigma\_{AL}^2 / 4d\_d\right) \frac{\cosh\left[\lambda(c-z)\right]}{\sinh\left(\lambda c\right)} d\lambda \tag{34}$$

$$B\_{\theta L} = \frac{\mu\_m I\_L}{2\pi} \left[ f\_1(\lambda r\_d) \exp\left(-\lambda^2 \sigma\_{AL}^2 / 4d\_d\right) \frac{\sinh\left[\lambda(c-z)\right]}{\sinh\left(\lambda c\right)} d\lambda \right] \tag{35}$$

Figure 8. Arc interaction effect of the two wire tandem SAW [17, 28].

Figure 9. Droplet flights due to the arc interaction effect in two wire SAW process [18].

$$F\_{rL} = f\_{zL} B\_{\theta L} \tag{36}$$

JrT <sup>¼</sup> <sup>I</sup> 2π ð ∞

<sup>B</sup>θ<sup>T</sup> <sup>¼</sup> <sup>μ</sup>mIT 2π

3. Simulation results for SAW process

3.1. Single wire SAW process

3.1.1. Spray mode of metal transfer

Figure 10. Electrode angle used in the simulation [28].

2.2.4. Other models

• Single DC

and bead width.

0

ð ∞

0

<sup>λ</sup>J1ð Þ <sup>λ</sup>ra exp �λ<sup>2</sup>

<sup>J</sup>1ð Þ <sup>λ</sup>ra exp �λ<sup>2</sup>

σ2 AT=4da � � cosh ½ � λð Þ c � z

Modeling and Analysis of Molten Pool Behavior for Submerged Arc Welding Process with Single and Multi-Wire…

σ2 AT=4da � � sinh ½ � λð Þ c � z

The same surface tension and buoyance force models in equation (24) and (25) are applied.

Cho et al. [15] simulated the molten pool behaviors for single DC SAW process which compared the molten pool behaviors for different electrode angles as shown in Figure 10. They found that electrode angle plays on important role to form the bead shapes such as penetration

When the negative electrode angle is applied, the penetration of weld bead increases deeper because the droplet impingement direction is very similar to the molten poo circulation. Thus the momentum can be transferred sufficiently to the weld pool. Specifically, the molten pool flows downward and backward in the dotted box between droplet generations (Figure 11(a) and (b)) and then forms a sharp and deep penetration on a transverse cross-section by convection heat transfer as shown in Figure 12(a). However, the positive electrode angle induces

sinh ð Þ λc

sinh ð Þ λc

FrT ¼ JzTBθ<sup>T</sup> (41)

FzT ¼ JrTBθ<sup>T</sup> (42)

dλ (39)

17

http://dx.doi.org/10.5772/intechopen.76725

dλ (40)

$$F\_{zL} = f\_{rL} B\_{\theta L} \tag{37}$$

$$J\_{zT} = \frac{I}{2\pi} \left[ \lambda I\_0(\lambda r\_d) \exp\left(-\lambda^2 \sigma\_{AT}^2 / 4d\_d\right) \frac{\sinh\left[\lambda(c-z)\right]}{\sinh\left(\lambda c\right)} d\lambda \right] \tag{38}$$

Modeling and Analysis of Molten Pool Behavior for Submerged Arc Welding Process with Single and Multi-Wire… http://dx.doi.org/10.5772/intechopen.76725 17

$$J\_{rT} = \frac{I}{2\pi} \left[ \lambda I\_1(\lambda r\_a) \exp\left(-\lambda^2 \sigma\_{AT}^2 / 4d\_d\right) \frac{\cosh\left[\lambda(c-z)\right]}{\sinh\left(\lambda c\right)} d\lambda \right] \tag{39}$$

$$B\_{\theta T} = \frac{\mu\_m I\_T}{2\pi} \left[ \int\_1 (\lambda r\_a) \exp\left(-\lambda^2 \sigma\_{AT}^2 / 4d\_a\right) \frac{\sinh\left[\lambda(c-z)\right]}{\sinh\left(\lambda c\right)} d\lambda \right] \tag{40}$$

$$F\_{\rm rT} = f\_{\rm zT} B\_{\theta \rm T} \tag{41}$$

$$F\_{zT} = f\_{rT} B\_{\theta T} \tag{42}$$

#### 2.2.4. Other models

The same surface tension and buoyance force models in equation (24) and (25) are applied.
