**4. Results and discussion**

In this chapter, the comprehensive model [44, 45] is used to simulate a spot GMAW welding of a mild steel workpiece with a mild steel electrode under a constant current of 220 A shielded by argon. The electrode has a diameter of 0.16 cm and the workpiece is a mild steel disk with a 3-cm diameter and a 0.5-cm thickness. The contact tube is set flush with the bottom of the gas nozzle and has a contact tube to workpiece distance of 2.54 cm. The wire feed rate is 4.5 cm/s and the initial arc length is 0.8 cm. The shielding gas flow rate is 24 l/min and the inner diameter of the nozzle is 1.91 cm.

The temperature-dependent material properties of argon and the radiation loss term (SR) in Eq. (4) are taken from [58] and are plotted in **Figure 2**. **Table 2** lists the properties of

the solid and liquid mild steel taken from [7] and other parameters used in the computa‐ tion.

22 2 2

*r R Rr RR <sup>Q</sup> RR Rr v r <sup>V</sup>*

<sup>=</sup> - + - - +

*n nw*


4 4

p

FG, uniform current density along AB specified as *J <sup>z</sup>* = −*σ<sup>e</sup>*

calculate the velocity and temperature fields.

**4. Results and discussion**

diameter of the nozzle is 1.91 cm.

the other surfaces.

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solution.

**3. Numerical methods**

*n w*

electrode and the internal radius of the shielding gas nozzle, respectively.

the new free surface using the VOF method, Eq. (12), in the metal region.

2 22

*n w*

where *Q* is the shielding gas flow rate, *Vw* is the wire feed rate, *Rw* and *Rn* are the radius of the

The temperature boundaries along AD, DE, and EG are set as the room temperature. The boundary conditions for current flow include a zero voltage at the bottom of the workpiece

At each time step, the calculation involves separate calculations in the arc region and the metal region, the coupling of the two regions through the interface boundary conditions described in Sections 2.4 and 2.5, and updating the arc and metal regions after obtaining

The arc plasma region uses a fully implicit formulation and an upwind scheme for the combined convection/diffusion coefficients, and the SIMPLE algorithm [65] for the velocity and temperature fields. The metal region uses the method developed by Torrey et al. [59] to

The computational domain is 5 cm in radius and 3.04 cm in length. A nonuniform grid sys‐ tem is used with finer meshes near the electrode tip, in the arc column and the weld pool, where a fine mesh of 0.01 cm is used. Time step size is set as 5 × 10−6 s for a stable numerical

In this chapter, the comprehensive model [44, 45] is used to simulate a spot GMAW welding of a mild steel workpiece with a mild steel electrode under a constant current of 220 A shielded by argon. The electrode has a diameter of 0.16 cm and the workpiece is a mild steel disk with a 3-cm diameter and a 0.5-cm thickness. The contact tube is set flush with the bottom of the gas nozzle and has a contact tube to workpiece distance of 2.54 cm. The wire feed rate is 4.5 cm/s and the initial arc length is 0.8 cm. The shielding gas flow rate is 24 l/min and the inner

The temperature-dependent material properties of argon and the radiation loss term (SR) in Eq. (4) are taken from [58] and are plotted in **Figure 2**. **Table 2** lists the properties of

*R R R R R R R R*

*n*

*n w n w n w n w*

> ∂*ϕ* <sup>∂</sup> *<sup>z</sup>* <sup>=</sup> *<sup>I</sup> πRw*

(24)

<sup>2</sup> , and zero current flow along

ln( / )

ln( / ) ( ) <sup>2</sup> ln( / ) ln( / ) ( ) ( ) ln( / )

**Figure 2.** Temperature-dependent material properties of argon and the volume radiation heat loss taken from [58].



inward and axially downward electromagnetic force toward the workpiece. The maximum axial velocity in the arc column is found to be 230 m/s on the axis. The corresponding current density distribution in **Figure 5** clearly shows that current diverges from the electrode tip and converges at the cathode in the workpiece, which results in inward and downward electro‐ magnetic forces around the droplet and the inward and upward electromagnetic forces near

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**Figure 4.** The corresponding velocity distributions in the arc plasma for the cases shown in **Figure 3**.

**Figure 5.** The corresponding current distributions in the arc plasma for the cases shown in **Figure 3**.

After the droplet is detached from the electrode at *t* = 118 ms, a new arc plasma is struck between the electrode tip and the top surface of the detached droplet. During the transfer of the detached droplet to the workpiece, the existence of the moving droplet greatly distorts the arc shape and flow pattern. Between *t* = 118 and 133 ms, current flow through the moving

the workpiece.

**Table 2.** Thermophysical properties of mild steel and other parameters.

#### **4.1. Arc plasma evolution**

**Figure 3** shows the distributions of arc plasma temperature and pressure before and after the first droplet is detached and transferred to the workpiece. The shape of the electrode and workpiece are marked with thick lines. At *t* = 100 ms, the first droplet is formed at the electrode tip and the workpiece is still flat before a weld pool is formed. The arc shown in **Figure 3(a)** has a bell-shaped envelope with a maximum temperature of 19,300 K underneath the droplet. The high-temperature arc covers the droplet and expands as it moves toward the workpiece. The arc pressure contours at *t* = 100 ms in **Figure 3(b)** has two high-pressure regions. One is underneath the droplet caused by the pinch effect of the electromagnetic force, and the other is near the workpiece due to the stagnation of the plasma flow impinging onto the workpiece. The velocity field and streamlines in **Figure 4** show that shielding gas flows downward from the gas nozzle along the electrode surface and then is drawn to the electrode around the electrode tip. The ionized shielding gas around the electrode tip is pinched by the radially

**Figure 3.** Arc plasma evolution during the first droplet formation, detachment, transfer, and impingement onto the workpiece: (a) temperature distributions in the arc plasma and (b) pressure distributions in the arc plasma.

inward and axially downward electromagnetic force toward the workpiece. The maximum axial velocity in the arc column is found to be 230 m/s on the axis. The corresponding current density distribution in **Figure 5** clearly shows that current diverges from the electrode tip and converges at the cathode in the workpiece, which results in inward and downward electro‐ magnetic forces around the droplet and the inward and upward electromagnetic forces near the workpiece.

**Nomenclature Symbol Value (unit)** Latent heat of vaporization *Hev* 7.34×106

Solidus temperature *Ts* 1750 (K) Liquidus temperature *Tl* 1800 (K) Ambient temperature *T<sup>∞</sup>* 300 (K) Vaporization temperature *Tev* 3080 (K) Surface tension coefficient *γ* 1.2 (N m−1) Surface tension temperature gradient *∂γ*/*∂T* 10−4 (N m−1 K−1)

Work function *ϕ<sup>w</sup>* 4.3 V Electrical conductivity *σ<sup>e</sup>* 7.7 × 105

**Figure 3** shows the distributions of arc plasma temperature and pressure before and after the first droplet is detached and transferred to the workpiece. The shape of the electrode and workpiece are marked with thick lines. At *t* = 100 ms, the first droplet is formed at the electrode tip and the workpiece is still flat before a weld pool is formed. The arc shown in **Figure 3(a)** has a bell-shaped envelope with a maximum temperature of 19,300 K underneath the droplet. The high-temperature arc covers the droplet and expands as it moves toward the workpiece. The arc pressure contours at *t* = 100 ms in **Figure 3(b)** has two high-pressure regions. One is underneath the droplet caused by the pinch effect of the electromagnetic force, and the other is near the workpiece due to the stagnation of the plasma flow impinging onto the workpiece. The velocity field and streamlines in **Figure 4** show that shielding gas flows downward from the gas nozzle along the electrode surface and then is drawn to the electrode around the electrode tip. The ionized shielding gas around the electrode tip is pinched by the radially

**Figure 3.** Arc plasma evolution during the first droplet formation, detachment, transfer, and impingement onto the

workpiece: (a) temperature distributions in the arc plasma and (b) pressure distributions in the arc plasma.

**Table 2.** Thermophysical properties of mild steel and other parameters.

**4.1. Arc plasma evolution**

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(J kg‒1)

(Ω–1m–1)

**Figure 4.** The corresponding velocity distributions in the arc plasma for the cases shown in **Figure 3**.

**Figure 5.** The corresponding current distributions in the arc plasma for the cases shown in **Figure 3**.

After the droplet is detached from the electrode at *t* = 118 ms, a new arc plasma is struck between the electrode tip and the top surface of the detached droplet. During the transfer of the detached droplet to the workpiece, the existence of the moving droplet greatly distorts the arc shape and flow pattern. Between *t* = 118 and 133 ms, current flow through the moving droplet decreases and the temperature of the arc plasma underneath the droplet also decreases. The arc plasma above the droplet is driven by the electromagnetic force and accelerates above the electrode. The high-velocity arc plasma flow impinges onto the top surface of the relatively slow-moving droplet and then flows around it. The flow pattern of the arc plasma around the droplet is similar to a flow around a sphere, including a high-pressure region formed at the droplet top surface due to the impingement and a low-pressure wake region below the droplet. The pressure drag is the main driving force for the droplet acceleration in the arc plasma. These arc plasma transport phenomena are confirmed by the experimental results of [30–32], but are significantly different from the numerical results in [43]. The unified GMAW model in [43] predicted current tended to flow through the detached droplet and a strong arc plasma flow formed beneath the droplet. However, the flow pattern in [43] failed to push the detached droplet downward in the arc plasma and thus an empirical equation was used to calculate the arc plasma drag force.

weld-pool surface at *t* = 133 ms when there is a detached droplet in the arc column, whereas high and concentrated arc pressure distribution is observed at *t* = 400 s when the weld-pool surface is projected and the arc column has no detached droplet. These distributions signifi‐ cantly deviate from the assumed Gaussian distribution in many weld-pool models [7–29]. Similarly, their assumed Gaussian distributions of current and heat flux cannot represent the

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Droplet formation is determined by the concentrated heating due to the recombining electrons at the electrode surface and the flow pattern within the droplet caused by a balance of forces acting on the droplet, which includes electromagnetic force, surface tension force, gravity, arc pressure, and plasma shear stress. To clearly illustrate the heat transfer and fluid flow within the droplet at the electrode tip, the distributions of temperature, velocity, electrical potential, current, and electromagnetic force within the droplet at *t* = 100 ms are drawn in **Figure 7**. A vortex flow forms in the droplet with a downward flow along the centerline and an upward flow at the surface. The fluid circulation enhances the mixing of cold fluid at the center with the hot surface fluid. The downward flow is caused by the inward and downward electro‐ magnetic force at the upper part of the droplet near the melt line marked as a dashed line. The electromagnetic force and current density are determined by the electrical potential distribu‐ tion. Current slightly diverges in the upper part of the droplet and converges in the lower part and then flows out of the droplet surface from the lower part of the droplet. The current flow pattern results in an electromagnetic force that is radially inward and axially downward at the upper part and upward at the bottom part. The upward electromagnetic force, surface tension, and arc pressure at the droplet bottom change the fluid to flow upward along the surface. At the balance of electrons heating, arc plasma heating, evaporation and radiation cooling, and convection cooling, the maximum temperature at the droplet surface is found to be 2936 K,

**Figure 7.** Distribution of physical variables within the droplet at *t* = 100 ms. (a) Temperature, (b) velocity, (c) electrical

dynamic boundary conditions at the weld-pool surface.

which is close to the experimental result of [58].

potential, (d) current density, and (e) electromagnetic force.

**4.2. Droplet formation and transfer**

The first droplet reaches the workpiece around *t* = 136 ms, and a weld pool with an oscillating surface forms at the workpiece. The current distribution at the workpiece is greatly influenced by the weld-pool surface shape. The current tends to converge on the projected area at the workpiece, which may be at the workpiece center as in the cases of both *t* = 136 and 400 ms or not at the center as that of *t* = 150 ms.

**Figure 6.** Arc pressure distributions along the radial direction at the workpiece surface.

In many of the weld-pool models [7–29], the arc pressure distribution at the center of the workpiece surface was assumed to be a Gaussian distribution with a fixed amplitude and distribution radius. However, the arc pressure distribution at the workpiece surface changes dramatically during the welding process as shown in **Figure 6**. Both the magnitude and distribution region varies with the evolution of the electrode and weld-pool surfaces and the presence of the detached droplet. Low arc pressure with a flat-top distribution is found at the weld-pool surface at *t* = 133 ms when there is a detached droplet in the arc column, whereas high and concentrated arc pressure distribution is observed at *t* = 400 s when the weld-pool surface is projected and the arc column has no detached droplet. These distributions signifi‐ cantly deviate from the assumed Gaussian distribution in many weld-pool models [7–29]. Similarly, their assumed Gaussian distributions of current and heat flux cannot represent the dynamic boundary conditions at the weld-pool surface.

#### **4.2. Droplet formation and transfer**

droplet decreases and the temperature of the arc plasma underneath the droplet also decreases. The arc plasma above the droplet is driven by the electromagnetic force and accelerates above the electrode. The high-velocity arc plasma flow impinges onto the top surface of the relatively slow-moving droplet and then flows around it. The flow pattern of the arc plasma around the droplet is similar to a flow around a sphere, including a high-pressure region formed at the droplet top surface due to the impingement and a low-pressure wake region below the droplet. The pressure drag is the main driving force for the droplet acceleration in the arc plasma. These arc plasma transport phenomena are confirmed by the experimental results of [30–32], but are significantly different from the numerical results in [43]. The unified GMAW model in [43] predicted current tended to flow through the detached droplet and a strong arc plasma flow formed beneath the droplet. However, the flow pattern in [43] failed to push the detached droplet downward in the arc plasma and thus an empirical equation was used to calculate the

The first droplet reaches the workpiece around *t* = 136 ms, and a weld pool with an oscillating surface forms at the workpiece. The current distribution at the workpiece is greatly influenced by the weld-pool surface shape. The current tends to converge on the projected area at the workpiece, which may be at the workpiece center as in the cases of both *t* = 136 and 400 ms or

**Figure 6.** Arc pressure distributions along the radial direction at the workpiece surface.

In many of the weld-pool models [7–29], the arc pressure distribution at the center of the workpiece surface was assumed to be a Gaussian distribution with a fixed amplitude and distribution radius. However, the arc pressure distribution at the workpiece surface changes dramatically during the welding process as shown in **Figure 6**. Both the magnitude and distribution region varies with the evolution of the electrode and weld-pool surfaces and the presence of the detached droplet. Low arc pressure with a flat-top distribution is found at the

arc plasma drag force.

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not at the center as that of *t* = 150 ms.

Droplet formation is determined by the concentrated heating due to the recombining electrons at the electrode surface and the flow pattern within the droplet caused by a balance of forces acting on the droplet, which includes electromagnetic force, surface tension force, gravity, arc pressure, and plasma shear stress. To clearly illustrate the heat transfer and fluid flow within the droplet at the electrode tip, the distributions of temperature, velocity, electrical potential, current, and electromagnetic force within the droplet at *t* = 100 ms are drawn in **Figure 7**. A vortex flow forms in the droplet with a downward flow along the centerline and an upward flow at the surface. The fluid circulation enhances the mixing of cold fluid at the center with the hot surface fluid. The downward flow is caused by the inward and downward electro‐ magnetic force at the upper part of the droplet near the melt line marked as a dashed line. The electromagnetic force and current density are determined by the electrical potential distribu‐ tion. Current slightly diverges in the upper part of the droplet and converges in the lower part and then flows out of the droplet surface from the lower part of the droplet. The current flow pattern results in an electromagnetic force that is radially inward and axially downward at the upper part and upward at the bottom part. The upward electromagnetic force, surface tension, and arc pressure at the droplet bottom change the fluid to flow upward along the surface. At the balance of electrons heating, arc plasma heating, evaporation and radiation cooling, and convection cooling, the maximum temperature at the droplet surface is found to be 2936 K, which is close to the experimental result of [58].

**Figure 7.** Distribution of physical variables within the droplet at *t* = 100 ms. (a) Temperature, (b) velocity, (c) electrical potential, (d) current density, and (e) electromagnetic force.

The first droplet formation is shown in **Figures 3**–**5** and **8** from *t* = 20 to 116 ms. A round droplet forms at the electrode tip and grows larger. After a neck is formed at *t* = 116 ms, the velocity within the droplet increases due to the increased electromagnetic pinch force at the neck. After the first droplet is detached at *t* = 118 ms, the second droplet begins to form at the electrode tip. The droplet is detached and transferred to the workpiece from *t* = 118 to 133 ms. The detached droplet is accelerated by the plasma arc and gravity and reaches the workpiece with an axial velocity of about 60 cm/s. The center positions of the first detached droplet shown in **Figure 8** are plotted as a function of time and compared with the flight trajectory taken by Jones et al. [32] in **Figure 9**. The droplet trajectory from the computation matches the experi‐ mental results. The droplet acceleration obtained by taking the second derivative of the curve

**Figures 3** and **8** show the first droplet impingement onto the workpiece and form a weld pool. The weld pool grows wider and deeper with more droplets deposited into it. The final weld-

**Figure 10.** A sequence of temperature distributions in the metal showing droplet generation, detachment, transfer in

the arc, impingement onto the weld pool, and weld-pool dynamics.

in [32].

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, which is comparable to 21 m/s2

is found to be 24 m/s2

**4.3. Weld-pool dynamics and solidification**

**Figure 8.** Velocity distributions in the metal showing droplet generation, detachment, transfer in the arc, and impinge‐ ment onto the weld pool.

**Figure 9.** Comparison of droplet flight trajectory with experiment results [32].

The first droplet formation is shown in **Figures 3**–**5** and **8** from *t* = 20 to 116 ms. A round droplet forms at the electrode tip and grows larger. After a neck is formed at *t* = 116 ms, the velocity within the droplet increases due to the increased electromagnetic pinch force at the neck. After the first droplet is detached at *t* = 118 ms, the second droplet begins to form at the electrode tip. The droplet is detached and transferred to the workpiece from *t* = 118 to 133 ms. The detached droplet is accelerated by the plasma arc and gravity and reaches the workpiece with an axial velocity of about 60 cm/s. The center positions of the first detached droplet shown in **Figure 8** are plotted as a function of time and compared with the flight trajectory taken by Jones et al. [32] in **Figure 9**. The droplet trajectory from the computation matches the experi‐ mental results. The droplet acceleration obtained by taking the second derivative of the curve is found to be 24 m/s2 , which is comparable to 21 m/s2 in [32].

### **4.3. Weld-pool dynamics and solidification**

**Figure 8.** Velocity distributions in the metal showing droplet generation, detachment, transfer in the arc, and impinge‐

**Figure 9.** Comparison of droplet flight trajectory with experiment results [32].

ment onto the weld pool.

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**Figures 3** and **8** show the first droplet impingement onto the workpiece and form a weld pool. The weld pool grows wider and deeper with more droplets deposited into it. The final weld-

**Figure 10.** A sequence of temperature distributions in the metal showing droplet generation, detachment, transfer in the arc, impingement onto the weld pool, and weld-pool dynamics.

pool shape and the resulting final weld shape are determined by weld-pool dynamics subject to periodic droplet impingement and several important forces, including electromagnetic force, arc pressure, plasma shear stress, surface tension, and gravity force. As shown in **Figures 10** and **11**, a droplet is ready to be detached from the electrode tip at *t* = 956 ms. Two vortices formed in the weld pool with an inward flow at the weld-pool surface and a downward flow at the center. The inward flow at the weld-pool surface is driven by the surface tension and the downward flow is mainly by the arc pressure force. When the arc pressure at the weldpool surface decreases due to a droplet stuck in the arc column, as shown in **Figures 12** and **13**, the fluid at the weld-pool center rises up at *t* = 960 ms. A crater is formed after a droplet impinges onto the weld pool at *t* = 982 ms. The high-temperature filler metal carried by the droplet reaches the bottom of the weld pool. The crater is then filled up by the surrounding fluid, and the weld pool first oscillates at high amplitude, then the oscillation gradually subsides. A sequence of experimental images is given in Ref. [43] showing the weld-pool oscillation after a droplet impinges onto the weld pool, which can be seen by the up-and-down movement of the weld-pool surface.

**Figure 12.** Temperature distributions in the arc plasma during the last droplet impingement and weld-pool dynamics.

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**Figure 13.** Pressure distributions in the arc plasma during the last droplet impingement and weld-pool dynamics.

At *t* = 1000 ms, the current is turned off and the temperature in the arc plasma decreases rapidly due to the high radiation loss and low heat capacity of the arc plasma. At *t* = 1004 ms, the hightemperature arc plasma is replaced by the nonionized shielding gas, which is continued to protect the solidifying weld pool. After a sudden removal of arc pressure and plasma shear stress at the electrode and weld-pool surfaces, the remnant droplet at the electrode and the weld pool oscillates and the oscillation is balanced by the surface tension. The sizes of the molten droplet and the weld pool become smaller with the heat loss to the solid metal by

**Figure 11.** The corresponding velocity distributions of the cases shown in **Figures 10**.

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pool shape and the resulting final weld shape are determined by weld-pool dynamics subject to periodic droplet impingement and several important forces, including electromagnetic force, arc pressure, plasma shear stress, surface tension, and gravity force. As shown in **Figures 10** and **11**, a droplet is ready to be detached from the electrode tip at *t* = 956 ms. Two vortices formed in the weld pool with an inward flow at the weld-pool surface and a downward flow at the center. The inward flow at the weld-pool surface is driven by the surface tension and the downward flow is mainly by the arc pressure force. When the arc pressure at the weldpool surface decreases due to a droplet stuck in the arc column, as shown in **Figures 12** and **13**, the fluid at the weld-pool center rises up at *t* = 960 ms. A crater is formed after a droplet impinges onto the weld pool at *t* = 982 ms. The high-temperature filler metal carried by the droplet reaches the bottom of the weld pool. The crater is then filled up by the surrounding fluid, and the weld pool first oscillates at high amplitude, then the oscillation gradually subsides. A sequence of experimental images is given in Ref. [43] showing the weld-pool oscillation after a droplet impinges onto the weld pool, which can be seen by the up-and-down

movement of the weld-pool surface.

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**Figure 11.** The corresponding velocity distributions of the cases shown in **Figures 10**.

**Figure 12.** Temperature distributions in the arc plasma during the last droplet impingement and weld-pool dynamics.

**Figure 13.** Pressure distributions in the arc plasma during the last droplet impingement and weld-pool dynamics.

At *t* = 1000 ms, the current is turned off and the temperature in the arc plasma decreases rapidly due to the high radiation loss and low heat capacity of the arc plasma. At *t* = 1004 ms, the hightemperature arc plasma is replaced by the nonionized shielding gas, which is continued to protect the solidifying weld pool. After a sudden removal of arc pressure and plasma shear stress at the electrode and weld-pool surfaces, the remnant droplet at the electrode and the weld pool oscillates and the oscillation is balanced by the surface tension. The sizes of the molten droplet and the weld pool become smaller with the heat loss to the solid metal by conduction and to the surroundings by radiation and convection. As steel is a good thermal conductor, the heat loss occurs mainly through conduction to the solid metal. Therefore, the liquid metal adjacent to the solid and liquid interface solidifies first and the solidus line moves outward toward the electrode and weld-pool surfaces. The solidification completes at *t* = 2600 ms in the electrode and at *t* = 2440 ms in the weld pool. **Figure 14** shows the final shape of the weld bead including the weld penetration, which is similar to the reported experimental results [7, 8, 43].

and the droplet generation, detachment, transfer, and impingement onto the workpiece, and the weld-pool dynamics and solidification. This model included all the three regions—the electrode, the arc plasma, and the weld pool—in the computational domain and modeled the interactive coupling between these three regions. The distributions of arc pressure, current density, and heat flux at the weld-pool surface are found to vary in a wide range, and thus cannot be represented by a fixed distribution in many published GMAW models. The simulation results have revealed physical insights which cannot be found with those isolated single-region models in the literature. The transient evolution of the arc plasma was found to influence and also to be influenced by the droplet formation, detachment, transfer in the arc, and weld-pool dynamics. Therefore, a comprehensive model is required to accurately take into account the coupling events in both the arc domain and metal domain. The comprehensive model can be used to study the effects of process parameters on the welding process and the final weld formation, such as droplet generation with pulse currents to achieve one droplet per pulse (ODPP) and the effects of shielding gas and wire feed rate on the welding process.

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and Hai-Lung Tsai3

1 Department of Mechanical Engineering, University of Bridgeport, Bridgeport, CT, USA

2 School of Energy Science and Engineering, Central South University, Changsha, China

3 Department of Mechanical and Aerospace Engineering, Missouri University of Science

[1] Choi S.K., Yoo C.D., Kim Y.-S. The dynamic analysis of metal transfer in pulsed current

[2] Choi S.K., Yoo C.D., Kim Y.-S. Dynamic simulation of metal transfer in GMAW, Part

[3] Choi S.K., Yoo C.D., Kim Y.-S. Dynamic simulation of metal transfer in GMAW, Part

[4] Wang G., Huang P.G., Zhang Y.M. Numerical analysis of metal transfer in gas metal

gas metal arc welding. J. Phys. D: Appl. Phys. 1998; 31: 207–215.

1: globular and spray transfer mode. Weld. J. 1998: 38–44s.

2: short-circuit transfer mode. Weld. J. 1998: 45–51s.

arc welding. Metall. Trans. 2003; 34B: 345–353.

**Author details**

**References**

Junling Hu1\*, Zhenghua Rao2

and Technology, Rolla, MO, USA

\*Address all correspondence to: jjhu@bridgeport.edu

**Figure 14.** The solidified weld-bead shape.
