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The numerical model was developed using a SPH (Smoothed Particle Hydrodynamics) method and the projected transfer phenomena during a GMA (Gas Metal Arc) welding were simulated by the model to clarify mechanisms of the phenomena. As a result, the droplet transfer mode obtained from this calculation was regarded as a projected transfer mode in which the liquid column grew about 1 mm and a droplet grew up until its diameter became large the same as a wire diameter , after that it was detached from the tip of the column. In addition, 10 droplets were formed for 0.1 s through these growth and detachment processes at the tip of a wire. To compare with the numerical results, actual GMA welding was carried out and molten metal droplet transfers were taken by high speed camera. The diameter of a wire, the length of a liquid column, the velocity of a droplet right before it reached a weld pool obtained by simulation showed good agreement with experiment.

GMA (Gas Metal Arc) welding is one of the joining processes in which the welding is conducted with heating and melting of a wire electrode. This process is widely used in the industry because it is easy to automatize and apply to various materials. In GMA welding process, a wire is heated and melted by mainly the Joule heating and the electron inflow. Then, a molten metal droplet is formed at the tip of a wire. The droplet grows with time evaluation and it is detached by influences of the gravity and the electromagnetic force. Then, it is transported to a weld pool by the shielding gas and the gravity. These behaviors are called molten metal droplet transfer phenomena and it is one of the important factors to determine the amount of spatters during a welding. These phenomena are changed from the globular transfer mode to the spray transfer mode with increase in a welding current [

However to track the free surface of a molten metal smoothly, some high level techniques such as a VOF method [

In this study, the density homogenizing algorithm is used in order to apply a SPH method [

In the SPH method, physical quantities such as mass, energy, and so on are transported by fluid particles. A physical quantity A at a certain position a is written as

A a = ∑ b m b A b ρ b W a b , (1)

as the interactions with the adjacent particles b. Here, a and b are the indices of particles, m is the mass, ρ is the density, W is the kernel function. In this study, M4-spline function is used as the kernel function, which is described as

W a b = 1 π h 3 { 1.0 − 1.5 ( | l a b | h ) 2 + 0.75 ( | l a b | h ) 3 ( 0 ≤ | l a b | < h ) 2.0 − 3.0 | l a b | h + 1.5 ( | l a b | h ) 2 − 0.25 ( | l a b | h ) 3 ( h ≤ | l a b | < 2 h ) 0 ( 2 h ≤ | l a b | ) , (2)

where h is the kernel radius which is the same as the particle diameter and l is the relative distance between particle a and b. Using Equation (1), Equation (2) and the Navier-Stokes equation which expresses the motion of fluid, the acceleration of a particle is written as

D u a D t = − ∑ b m b ( p a ρ a 2 + p b ρ b 2 ) ∇ a W a b + 2 δ λ a n a ρ a ∑ b ≠ a μ a + μ b 2 ( u b − u a ) W a b + F a ρ a , (3)

where u is the velocity, t is the time, p is the pressure, dim is the dimension number, λ is the parameter of moving particle semi-implicit method [

∇ a W a b = 10 7 π h 4 { − 3.0 | l a b | h + 2.25 ( | l a b | h ) 2 ( 0 ≤ | l a b | < h ) − 3.0 + 3.0 | l a b | h − 0.725 ( | l a b | h ) 2 ( h ≤ | l a b | < 2 h ) 0 ( 2 h ≤ | l a b | ) . (4)

When a droplet is regarded as a perfect hard sphere, the drag force F D acting on the sphere is expressed as,

F D = 1 2 V ρ ¯ u ¯ 2 C D π 4 d 2 . (5)

Here, V is the volume of a particle, ρ ¯ and u ¯ are averaged density and averaged relative velocity of the shielding gas around a droplet. d is the diameter of a droplet, which is set to be 1.5 mm as an imaginary droplet diameter. C_{D} is the coefficient of the drag force [

C D = { 24 R e D ( R e D < 0.1 ) 24 R e D ( 1 + 3 16 R e D − 19 1280 R e D 2 ) ( 0.1 ≤ R e D < 1 ) 20.4 R e D ( 1 + 0.136 R e D 0.803 ) ( 1 ≤ R e D < 20 ) R e D 20.4 ( 1 + 0.138 R e D 0.793 ) ( 20 ≤ R e D < 100 ) 24 R e D ( 1 + 0.125 R e D 0.72 ) ( 100 ≤ R e D < 1000 ) 0.44 ( 1000 ≤ R e D ) , (6)

R e D is the Reynolds number and it can be described as,

R e D = ρ ¯ u ¯ d μ ¯ . (7)

Where μ ¯ is the averaged viscosity coefficient of a shielding gas around a molten metal droplet. The drag force in this model is calculated considering the effects of the shielding gas not only near the droplet but also around it. Therefore, the velocity, the temperature, the iron vapor concentration, the viscosity coefficient and the density of the shielding gas which are used to calculate Equation (5), Equation (6) and Reynolds number respectively should be obtained from not much on the grid point, but averaged value within some area. In this study, averaged velocity, averaged density and averaged viscosity coefficient at each z coordinate on r = 0 m are obtained using grid points within an area (from r = 0 m to 2.25 ´ 10^{−}^{3} m in radial direction, z = z ± 2.25 ´ 10^{−}^{3} m in axial direction) in the result of previous study [

^{−}^{3} m means the base metal surface.

Using the drag force obtained by

F a = j × B + F a L + F a L S + F a D + ρ a g . (8)

j , B show the current density vector and the magnetic flux vector at each particle

position and this term expresses the electromagnetic force acting on particles. In this calculation, the electromagnetic force distribution shown in

F a L = 1.2 ( 1 − ψ ) γ h V ∑ b f a b attract | a , b ∈ Liquid , (9)

F a L S = 1.2 ψ γ h V ∑ b f a b attract | a , b ∈ ( Liquid ∪ Solid ) . (10)

ψ is the constant to decide a contact angle. In this study, it is used as the parameter to express the relationship between solid and liquid, which is set to be 0.8. γ is the surface tension coefficient that is 1.0 N/m. f a b attract is the weighted function which is determined by the distance between particle a and b [

In this study, the temperature change is not considered for simplification based on the assumption in which height of the solid-liquid interface is kept constant. This assumption means that the wire feed rate balances with the wire melting speed [

Diameter of particle | f 0.1 mm |
---|---|

Density of particle | 7850 kg/m^{3} |

Time step | 1.0 × 10^{−2} ms |

Acceleration of gravity | −9.8 m/s^{2} |

Surface tension coefficient | 1.0 N/m |

Viscosity coefficient | 4.0 × 10^{−3} Pa・s |

Wire feed rate | 7.9 m/min |

On the other hand, height of the solid-liquid interface becomes lower by increase wire feed rate which is the velocity to feed the wire. To express this wire melting phenomena in this simulation, solid particles which make the wire become liquid state instantaneously when they move to the position that is lower than the solid-liquid interface.

To compare with actual projected transfer mode, the GMA welding process with typical conditions (welding current was 313 A, arc voltage was 36.8 V) was carried out and molten metal droplet transfers were taken by high speed camera

(MIROeX). Frame rate and exposure time of the camera were 2000 fps and 2 μs, respectively. In this experiment, the mixture gas was used because the transfer mode in pure Ar atmosphere became from the streaming transfer to the globular transfer by reducing a welding current and the projected transfer mode was not obtained.

Simulation | Experiment | |
---|---|---|

Diameter of droplet [mm] | 1.26 | 1.14 |

Velocity of droplet [m/s] | 1.56 | 1.40 |

Length of fluid column [mm] | 1.13 | 1.15 |

As stated above, the diameter of a wire, the length of a liquid column, the velocity of a droplet right before it reached a weld pool obtained by simulation showed good agreement with experiment.

In this study, three-dimensional computational model was developed by an incompressible SPH method in which it was easy to track the free surface and calculated motion of the fluid with large deformation stably. Then, the numerical simulation of the molten metal droplet transfer during a GMA welding was carried out. The conclusions of this study can be summarized as follows:

1) An incompressible SPH method simulated that 10 droplets were formed for 0.1 s through growth and detachment processes at the tip of a wire.

2) The droplet transfer mode obtained from this calculation was regarded as a projected transfer mode, in which the liquid column grew about 1 mm and a droplet grew up until its diameter became large the same as a wire diameter, after that it was detached from the tip of the column.

3) The diameter of a wire, the length of a liquid column, the velocity of a droplet right before it reached a weld pool obtained by simulation showed good agreement with experiment.

Komen, H., Shigeta, M. and Tanaka, M. (2018) Numerical Simulation of Molten Metal Droplet Behavior in Gas Metal Arc Welding by Three-Dimensional Incompressible Smoothed Particle Hydrodynamics Method. Journal of Flow Control, Measurement & Visualization, 6, 66-81. https://doi.org/10.4236/jfcmv.2018.62007

a : index

b : index

A : physical quantity

m : mass [kg]

ρ : density [kg・m^{−3}]

W : kernel function [m^{−3}]

l : relative distance [m]

h : kernel radius [m]

u : velocity [m・s^{−1}]

t : time [s]

p : pressure [N・m^{−2}]

δ : dimension number

λ : parameter [m^{2}]

n : number density [m^{−3}]

μ : viscosity coefficient [Pa・s]

F : body force [N・m^{−3}]

V : volume [m^{3}]

C D : drag coefficient

d : diameter [m]

R e D : Reynolds number

j : current density [A・m^{−2}]

B : magnetic flux density [N・A^{−1}・m^{−1}]

g : acceleration of gravity [m・s^{−2}]

ψ : constant

γ : surface tension coefficient [N・m^{−1}]

f : weighted function