学术论文-脉冲式点焊钨极气体保护焊过程中电弧 - 熔池耦合的瞬态统一模型
A Transient Unified Model of Arc-Weld Pool Couplings during Pulsed Spot Gas Tungsten Arc Welding
A. Traidia1, 2, F. Roger*, 1
1ENSTA Paristech, Department of Mechanics UME
2AREVA NP, Technical Center
*Corresponding author: ENSTA Paristech, Department of Mechanics UME, Chemin de la hunière, 91761 Palaiseau ,
FRANCE, frederic.roger@ensta-paristech.fr
Abstract:
A transient finite element model has been developed to study the heat transfer and fluid flow during pulsed spot GTA welding on stainless steel. Temperature field, fluid velocity and electromagnetic fields are computed inside the cathode, arc-plas ma and anode using a unified MHD formulation. The evolution of the heat flux and current density at the top surface of the anode are studied during the welding process. The electric heating flux at the anode which represents the energy absorbed by the workpiece from the electrons coming from the cathode is found to be the major mechanis m of heating. The proposed numerical model also permits to study the time evolution of the weld pool dimensions for both constant and pulsed current. A comparison shows that the use of a pulsed current welding gives a wider and deeper weld shape than the mean constant current welding. The present work lays a foundation for the future development of a three-dimensional model for moving torch arc welding.
Keywords:
Heat transfer, Fluid flow, Arc plas ma, Unified model, Marangoni effect.
1、Introduction
Due to the widespread use of GTA welding in the manufacturing industry, the numerical simulation of such a process is currently in great progress. The main goal is to study the impact of the welding parameters (welding current, arc length, pulse frequency, welding speed …) on the final weld shape in order to improve the welding quality and increase productivity. The complexity of the numerical modeling is due the strong couplings between many physics involved in this process. The ionization of the shielding gas ensures the current flow between the two electrodes, then the heating Joule effect creates a thermal plas ma composed of electrons, ions and neutral species at a large temperature range; from 300 K to more than 20 000 K. The workpiece is then heated from both the arc-plas ma conduction, and the electrons flow at the top surface. Depending on the melting temperature of the workpiece, a weld pool is formed in which the fluid flow is governed by the Marangoni effect at the top surface, the buoyancy forces and the electromagnetic forces created by the current flow. The fluid flow inside the weld pool is also strongly coupled to the temperature field and the deformation of the top free surface.
Many numerical models of spot GTAW are available in the literature [1-5]. Most of them consider only one part of the welding process [1 4] (either the cathode, or the arc plas ma, or the anode) which leads to fix some boundary conditions that do not represent the real situations. The best way to deal with the problem is to take into account the three parts (anode, cathode and arc-plas ma) in a unified formalis m. The interfaces between the plas ma and the electrodes are then considered as internal boundaries. This approach was proposed by Lowke and Tanaka et al [5] and gives satisfying results for constant current welding.
In the present work, a unified finite element model is introduced taking into account the three parts of the welding process. The time-dependent model can simulate pulsed current welding in which the welding current varies with time at a given frequency between two constant values; the peak current and the background current. This permits to study the transient evolution of some physical quantities at the transition between the peak and background times but also to compare welding under pulsed current with welding under the mean corresponding constant current.
2. Mathematical formulation
1.1 Governing equations
The mathematical formulation is based on the following assumptions:
The study is restricted to spot GTAW; an axisymmetric coordinate system is used.
The arc column is assumed to be pure argon at Local Thermodynamic Equilibrium.
The gas plas ma and molten metal are incompressible.
A weak coupling is considered between the free surface deformation and the Magneto Hydrodynamic (MHD) calculations.
The temperature, velocity and pressure fields are calculated in the three domains using the classical conservation equations written in a unified transient formalis m as follows:
Where 
is velocity, T is temperature, ρ is
pressure, ρ is density,
is an
equivalent specific heat that takes into account
the latent heat of fusion 
is the liquid
fraction assumed to vary linearly with
temperature in the mushy zone and 
equals 1
in the weld pool and 0 elsewhere. k is thermal
conductivity and μ is the viscosity. The
Boussinesq approximation is used to compute
the convection forces inside the weld pool. β is
the metal thermal expansion and
is taken as
the solidus temperature.
In the weld pool the volumetric heat source is the
Joule effect and the enthalpic flux, and in the arc
plas ma we take in addition the radiation losses,
usually approximated by
, where 
is the net emission coefficient of argon that varies with
temperature.
The determination of the electromagnetic forces
and the joule effect in both arc plas ma and work
piece requires the computation of the current
density j and the magnetic fluxB. To achieve
this, the coupled current continuity and the
magnetic potential equations are computed as
function of the electric potential V and the
magnetic potential vector A as follows:
The current density, electric field and magnetic flux are then computed from V and A as follows:
It is important to notice that the eddy current
created by the time variation of the
welding current is taken into account in the
above expressions.
The free surface deformation φ(r) is described by
the following PDE obtained from [2]:
Where φ is the free surface depression, Pa is the
arc pressure, γ is the molten metal surface
tension and λ is a Lagrangian multiplier used to
take into account the mass conservation
constraint:
1.2 Boundary conditions
The computational domain is shown in Figure 1. As seen the worpiece is made of two subdomains in order to use a finer mesh size for the weld pool formation. All the boundary conditions are listed in Table 1; the most important points are discussed below;
At the interface between arc plas ma and the anode (GD) the following conditions must be satisfied [5]:
Figure 1. Computational domain (dimensions in mm)
The first condition shows that the normal heat
flux at the anode is composed by the heating
conduction flux from the plas ma, the heating
electric flux (which represents the energy
transferred from the electrons to the anode) and
the cooling radiation losses. 
is the anode
work function and 
is the Stefan-Boltzmann
constant.
The second condition means that the total shear
stress is the sum of the arc drag force and the
Marangoni force. 
and 
are respectively a
local tangent vector and the normal vector to the
top free surface (n is directed toward the plas ma
domain). 
is the surface tension
coefficient, which has been reported to have a
big impact on the flow directions inside the weld
pool [1-4]. Its dependence on temperature T and
sulfur activity 
is considered using the
expression developed by Sahoo and DebRoy et
al [6] as follows:
Along the interface between the arc plas ma and the cathode (HIJB), the normal discontinuity of the heat flux is expressed as follows:
Where i V and c are respectively the argon ionization potential and the cathode work function. i j and e j are respectively the ion current and electron current calculated from:
are respectively the Richardson’s
constant, the effective work function for
thermionic emission and the elementary charge.
Table 1: Boundary conditions
3. Numerical simulation results
The numerical model is applied to an AISI 304 stainless steel disk containing 290 ppm sulfur with 8 mm thickness. The thermophysical properties of AISI 304 ss are listed in the appendix. The properties of pure argon are taken from [7]. The gas inflow rate is fixed to 30 L/min. Table 2 lists the other welding parameters.
Table 2: Welding parameters
Figure 2 presents the time evolution of the computed solution at the end of the background time (left) and the peak time (right) every five periods. It is represented the temperature field and temperature contours inside the arc plas ma and the electrode, the normalized velocity field and streamlines inside the molten weld pool.
During the peak time the arc is bell-shaped and the maximum of temperature and velocity fields are higher than during the background time. The obtained values for the maximum of plas ma-jet velocity and plas ma temperature are in good agreement with the literature, in fact for a 150 A continuous current welding 17000 K for the maximum temperature and 150 m/s for the maximum velocity are reviewed [5]. We can also notice that the variations of temperature and velocity fields inside the plas ma column between the peak times are negligible; this is also the case for the background times.
The dynamic of the weld pool flow is studied by considering the streamlines of the velocity field. We can clearly identify in each figure two vortices named A and B. They results from the Marangoni effect at the top surface of the weld pool, the size of each vortex is related to both temperature distribution at the surface and sulfur content of the workpiece. Details about the dynamic variation of these vortices and their influence on the weld pool evolution are available in our previous works [4].
Figure 3 shows the anodic heat flux distribution
during the transition from the last peak time
(t=14.5 s) to the last peak time (15 s). During the
background time the maximum of anodic flux is
around 43 W/mm². The transition is then very
fast; in approximately 15 μs the heat flux seems
to stabilize especially at the center of the disk
and reaches a maximum of 56.6 W/mm².
The numerical model permits to study the energy
transfer between the arc plas ma and the
workpiece. Figure 4 shows the radial evolution
of the heat flux at the anode at the last peak and
background times (t=14.5 s and t=15 s). In each
figure it is represented the total heat flux and its
elementary contributions, namely; the electric
flux 
, the conduction from the arc plas ma
and the radiation losses
.
Figure 2. MHD solutions at background times (left) and peak times (right) for different periods
Figure 3. Evolution of the anodic heat flux at the transition between the background to the peak time
Figure 4. Anodic heat flux and its elementary contributions at the last period of heating
The electric flux is found to be the most significant factor in both peak and background times. It represents around 80 % of the total energy transferred to the workpiece. The contribution of the conductive heat flux from the plas ma represent around 30 % and the cooling radiation losses are under 10 % of the total heat flux.
Figure 5 shows the time evolution of the weld pool half-width and depth for the pulsed current 80/160 A and the continuous mean current 120 A Even though the two cases are energetically equivalent, the pulsed case produces a deeper and wider weld pool than the continuous case, especially for the weld pool depth. This conclusion goes with what is commonly observed by welders.
Figure 5. Evolution of the weld pool size for the pulsed current 80/160 A and the mean current 120 A
4. Conclusions
A transient unified model of pulsed spot GTAW has developed using COMSOL Multiphysics. The numerical simulation allowed a better understanding of the heat transfer between the arc plas ma and the electrodes. The heating thermionic emission at the anode was found to be the most important heating effect. The results showed that for a given level of energy, it is more interesting to use a pulsed current welding than the mean constant current to get a better weld size.
5. References
W.H. Kim and S.J. Na. Int. J. Heat Mass Tran. , 41, 3213-3227 (1998)
H.G. Fan, H.L. Tsai and S.J. Na. Int. J. Heat Mass Tran. , 44, 417-428 (2001)
F. Lu, S. Yao, S. Lou and Y. Li. Comput. Mater. Sci., 29, 371-378 (2004)
A. Traidia, F. Roger and E. Guyot. Int. J. Therm. Sci., 49, 1197-1208 (2010)
M. Tanaka and J.J. Lowke. J. Phys. D: Appl. Phys., 40, R1-R23 (2007)
P. Sahoo, T. DebRoy, M.T. McNallan. Metall. Trans. B., 19B, 483-491 (1988)
P. Fauchais, M. Boulos and E. Pfender, Thermal plas ma, fundamentals and applications, (1994)
6. Acknowledgements
This research was supported by the Technical Center of welding at AREVA NP, FRANCE. The authors are grateful to Lahcene Cherfa, Alexander Chidley and Catherine Holm for their help on the results processing.
Appendix
Table 3: Material properties of the used materials.
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