All these models describe convection in tungsten-inert gas (TIG) weld pools where no wire is consumed. The metal-inert gas (MIG) welding process is rapidly ...
ENGINEERING COMPUTATIONS, VOL. 9, 5 2 9 - 5 3 7 (1992)
COMPUTER SIMULATION OF THREE-DIMENSIONAL CONVECTION IN TRAVELLING MIG WELD POOLS CHUAN SONG WU Department of Welding Engineering, Harbin Institute of Technology, Harbin, People's Republic of China
ABSTRACT Mathematical models of the metal-inert gas (MIG) welding process may be used to study the influence of various welding parameters on weld dimensions, to assist in the development of welding procedures, and to aid in the generation of process control algorithms for automated applications. A three-dimensional model for convection and heat transfer in MIG weld pools has been formulated and solved using the finite difference technique. The energy exchange between the pool and the molten filler metal droplets via spray transfer, and the interaction of electromagnetic, buoyant, surface tension, droplet impact and plasma jet forces were considered. MIG welding was carried out using mild steel plate with heat input from 7 to 17.5 KJ/cm. The calculated and experimentally observed weld bead dimensions were compared. Occurrence of finger penetration phenomena only in MIG welds are adequately explained through the application of the proposed model. Good agreement is demonstrated between predicted weld dimensions and experimentally measured ones. KEY WORDS MIG welding 3-D convection
INTRODUCTION Weld pool convection can strongly affect the structure and properties of the resultant welds. Variations in weld characteristics which are likely to occur from changes in weld pool convection are weld penetration, macro-segregation, gas porosity, solidification structure, undercutting, and surface smoothness. Apparently, the quantitative understanding of convection and heat flow in weld pools is of considerable practical interest. Mathematical models describing convection and heat flow in weld pools are essential, not only because of the quantitative understanding they provide, but also because of the difficulties associated with the experimental measurements of weld pool convection. These difficulties are mainly due to the fact that only surface flow, rather than the overall convection pattern in the weld pool, can be observed. In fact, due to arc glow even the observation of surface flow can be rather inconvenient1. Several weld pool convection models have been developed by investigators in USA 1-7 . All these models describe convection in tungsten-inert gas (TIG) weld pools where no wire is consumed. The metal-inert gas (MIG) welding process is rapidly becoming popular for semi-automatic and automatic welding applications where commercially important metals, such as carbon steels, stainless steels, aluminium and copper alloys must be joined 8 . However, there are fewer precedents of numerical modelling of MIG welding because of the additional difficulty posed by the deposition of filler metal. Tsao and Wu 9 have analysed the idealized case of stationary MIG welding with coupled fluid flow and thermal effects. In this paper, the computer simulation of three-dimensional convection in travelling MIG weld pools is addressed. 0264-4401 /92/050529-09$2.00 © 1992 Pineridge Press Ltd
Received November 1990 Revised June 1991
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MATHEMATICAL MODEL A schematic diagram of the MIG welding process is shown in Figure 1. The plasma arc at the tip of the consumable electrode wire was assumed to move in the x direction along the top surface of the plate at a constant welding velocity, Μ0. At the same time, the electrode was fed into the weld at a constant wire feed rate, melted, and reformed as the MIG weld reinforcement. The coordinate system (x, y, z) moves with the heat source at the same speed as welding velocity u0, and its origin coincides with the centre of the electrode. Molten filler metal migrates across the arc into the weld pool as fine droplets. When arc current is beyond a certain critical value, metal transfer is in the way of spray transfer. An amount of heat ∆H is transferred into the weld pool by this spray transfer of the molten filler metal droplets. Since a droplet has a higher heat content in comparison with the weld pool liquid, the excess heat AH of a droplet will diffuse in the weld pool as soon as the droplet is in contact with the weld pool. In MIG welding, besides the three distinct driving forces for weld pool convection, i.e. the electromagnetic force, the buoyancy force, and the surface tension gradient at the weld pool surface, there are several driving forces which may affect fluid flow in pools, such as arc pressure, droplet impact and plasma jet force. The convective heat and fluid flow, driven by all these forces, occurs in the MIG weld pool. The definitions of all the symbols are presented in the Appendix. The flow field in the MIG weld pool should satisfy the mass continuity equation:
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The x-, y- and z-direction momentum equations are in the following forms:
The temperature distribution (in and out of MIG weld pools) around the MIG are is defined by energy equation:
For MIG welding, the body force can be expressed as: The electromagnetic field in the specimen is obtained from the solution of Maxwell's equations10 give by:
In the solution of the electromagnetic force, the current distribution j(x, y) at the weld pool surface is in the following form4:
The solution of Maxwell's equations is described in Reference 11 and will not be described here. Equation (5) shows that in MIG welding process, the overheated filler metal droplets deliver their excess heat (AH) to the weld pool, besides the same spatial distribution of heat flux on the top surface as in TIG welding process. The diffusion of AH is not homogeneous throughout the molten pool. On the other hand, in addition to electromagnetic force, the bouyancy force and the surface tension gradient at the weld pool surface, there are no ways and means at present to measure and analyse other forces exerted on the weld pool, such as arc pressure, droplet impact, plasma jet force and so on. In order to consider the influence of these forces on fluid flow and heat transfer in MIG weld pools, it is considered that AH is non-uniformly distributed in x, y and z directions. The non-uniform distribution of ∆H in z direction shows the effect of forces exerted by the arc and droplets, while the non-uniform distribution of ∆H in x, y directions represents the diffusion of ∆H. Hd and Hv are used to represent the average values of heat content of a droplet and a weld pool, respectively. Thus, filler metal droplets transfer the following amount of heat into a weld pool per second:
where f is the spray transfer frequency in units of droplets per second. ∆S can theoretically be calculated. However, in order for the computed results to be of practical relevance, the value of
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AS is based on experimental results. According to Reference 16, ∆S = 2.286f (W/mm3). The heat transfer rate into the weld pool by spray transfer of molten filler droplets are assumed to follow the distribution function:
where the definition of xb and Dz is shown in Figure 2. It considers the heat flux from the arc to the anode (metal) surface as a specified radially symmetric Gaussian distribution given by:
The Gaussian distribution for the heat flux from the arc with the arc spot radius ra, defined as the distance at which the heat flux decays to 0.05 of the maximum value, was suggested by Rykalin12. In addition, the experimental work by Smart et al.13 also found the heat flux from the arc to fit the Gaussian distribution. The boundary conditions take the following form:
Equation (11b) expresses the physical fact of symmetry about the x-axis. u = v = w = 0, at the melt-solid interface and in the solid The surface shear stress components are formulated as 14 :
(12)
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METHODS OF SOLUTION The governing equations and the boundary conditions are transformed into finite difference equations which are solved by using a calculation domain that includes both the fluid and solid regions. The problem is solved as a convection-conduction problem throughout the entire calculation domain; but, since the velocities in the solid are zero, in effect, a pure-conduction calculation would be performed in the solid region. The resulting solution would thus give temperature distributions in the solid and in the fluid, and they would have been automatically matched at the solid-fluid interface. Due to symmetry with respect to the centre plane, the velocity and temperature fields were calculated on only one side of the centre plane. In order to enhance the accuracy of calculation grids of variable spacing are used, i.e. finer spacing near the heat source and coarser away from it. For calculations where steep velocity gradient ∂u/∂z and ∂v/∂z are induced by the surface tension gradient at the pool surface, the use of fine grid spacing near the surface is essential. Equations (l)-(5) were solved using the SIMPLER algorithm15. The application of the SIMPLER algorithm to weld pool convection has been described elsewhere14 and hence will not be repeated here. The physical properties of lCr/18Ni/9Ti stainless steel (i.e., the workpiece material) and other parameters used in the calculation are shown in Table 1. The computational procedure is similar to that described in Reference 14. The heat flow and convection were calculated by solving (l)-(5) with their proper boundary conditions until the
Table 1 Parameters used in calculation
Physical property parameters in this Table are for stainless steel lCr/18Ni/9Ti. Those for mild steel used in calculation are referred to in Reference 14.
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following convergence criteria were met: for velocities and pressure and |T(new)- T(old)|max ≤0.5 °C for temperature where Σ denotes summation over all grid points and max denotes the maximum value of all grid points. RESULTS AND DISCUSSION Experiments were carried out for measuring weld dimensions so that the validity of the model is verified. MIG welding was done using DC electrode positive with Ar shielding gas. Wire of 1.2 mm in diameter was employed. The study was limited to spray transfer, because of the wide usefulness of spray transfer for good penetration. Bead-on-plate welds were deposited on steel plate 6 mm thick. Weld bead dimensions were measured from polished cross-sections of the welds (Figure 3). Figure 4 shows the theoretical and experimental weld width, penetration and cross-sectional area versus welding current. When other parameters are kept constant, weld width, penetration and cross-sectional area increases with rising welding current. Indicated in Figure 5 is the relationship between weld dimensions and welding speed. If other conditions are identical, the increment of welding speed makes the energy input (often expressed as the ratio of arc power to welding speed, with units J/mm) decrease. Thus, the weld dimensions also come down. It can be seen that the weld bead dimensions calculated by the model matches well with the experimental measurements over a wide range of welding energy input values. Figure 6 shows that the MIG weld pool configuration is different from that of TIG welding even if they are under identical operating conditions. In Table 2, it makes a comparison between the maximum and average fluid velocities in MIG and TIG weld pools with the same welding energy input. It indicates that with the same conditions, the fluid velocity in MIG weld pool is higher than that in TIG weld pool, and MIG welding process results in distinctfingerpenetration. The reason is that in MIG welding there are several other driving forces, such as droplet impact
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CHUAN SONG WU Table 2 Fluid velocity in weld pools
u0(mm/min)
Maximum velocity (mm/sec)
Average velocity (mm/sec)
600 600
101.02 140.72
26.51 45.88
Welding parameters Welding process
I(A)
Uw(V)
TIG MIG
180 180
20 20
Table 3 Relationship between fluid velocity and welding parameters
I(A)
Uw(V)
u0(mm/min)
Average fluid velocity (mm/sec)
200 200 210 220
20 20 20 20
420 600 600 600
30.05 22.48 29.80 30.05
MIG welding parameters
Maximum fluid velocity (mm/sec) 164.54 155.88 173.21 181.86
and plasma jet force, besides the same driving forces as in TIG welding, and the molten filler metal droplets transfer an excess amount of heat into the MIG weld pool. Previous models were unable to explain the phenomena of finger penetration in the MIG weld because they just employ a higher heat input efficiency η for MIG welding processes. If the momentum and energy of molten filler metal droplets via high frequency spray transfer are not considered, occurrences of finger penetration phenomena only in MIG welds are not numerically simulated. Table 3 shows that in MIG welding processes increasing the welding speed while keeping other welding parameters constant, the fluid velocity in the weld pool will decrease. With the increment of the welding current and the constant of other parameters, thefluidvelocity will rise. CONCLUSIONS (1) Three-dimensional convection in moving MIG arc weld pools can be simulated with the computer model developed. The model considers not only the same three distinct driving forces for weld pool convection as in TIG welding, but also the influence of droplet impact and plasma jet forces, and the energy exchange between the weld pool and molten filler metal droplets. (2) It is found that MIG weld pool configuration is different from that of TIG even if they are under identical welding conditions (i.e., welding parameters and efficiency η are same). MIG welding has a higher fluid velocity. The fluid velocity in MIG weld pools is directly proportional to welding current and inversely proportional to welding speed. (3) The calculated weld pool geometry parameters are in agreement with experimentally observed ones. REFERENCES 1 Kou, S. and Wang, Y. H. Computer simulation of convection in moving arc weld pools, Metall. Trans. (A), 17, 2271-2277(1986) 2 Kou, S. and Wang, Y. H. Weld pool convection and its effect, Weld. J., 65(3), 63s-68s (1986)
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3 Zacharia, T., David, S. A., Vitek, J. M. and Debroy, T. Weld pool development during GTA and laser beam welding of type 304 stainless steel, Part 1—Theoretical analysis, Weld J., 68(12), 499s-509s (1989) 4 Zacharia, T., Eraslan, A. H., Aidun, D. K. and David, S. A. Three-dimensional transient model for arc welding process, Metall. Trans. (B), 20, 645-659 (1989) 5 Thompson, M. E. and Szekeley, J. The transient behavior of weldpools with a deformed free surface, Int. J. Heat Mass Transfer, 32(6), 1007-1019 (1989) 6 Tsai, M. C. and Kou, S. Electromagnetic-force-induced convection in weld pools with a free surface, Weld. J., 69(6), 241s-246s(1990) 7 Choo, R. T. C, Szekeley, J. and Westhoff, R. C. Modeling of high-current arcs with emphasis on free surface phenomena in the weld pool, Weld. J., 69(9), 346s-360s (1990) 8 Pardo, E. and Weckman, D. C. Prediction of weld pool and reinforcement dimensions of GMA welds using a finite-element model, Metall. Trans. (B), 20, 937-947 (1989) 9 Tsao, K. C. and Wu, C. S. Fluid flow and heat transfer in GMAW weld pools, Weld. J., 67(3), 70s-75s (1988) 10 Jackson, J. D. Classical Electrodynamics, Wiley, New York (1962) 11 Szekely, J. Fluid Flow Phenomena in Metal Processing, Academic Press, New York (1979) 12 Rykalin, N. N. Weld. World, 9, 112-115 (1969) 13 Smart, H. B., Stewart, J. A. and Einerson, C. J. Am. Weld. Soc. 66th A. Conv. Las Vegas (1985) 14 Wu, C. S. and Tsao, K. C. Modelling the three-dimensional fluid flow and heat transfer in a moving weld pool, Eng. Comput., 7, 241-248 (1990) 15 Patankar, S. V. Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York (1980) 16 Nishiguchi, K. The Fundamentals and Recent Development in the Field of Arc and Plasma Welding Processes, Osaka University, Japan (1982)
APPENDIX B
cP
C1
D Dz F Fx Fy
Fz f
9 h Hd Hv I J
j
k P q
magnetic flux vector specific heat distribution parameter of excess heat content of a droplet weld penetration distribution parameter body force body force in x-direction body force in y-direction body force in z-direction frequency of spray transfer acceleration of gravity convection heat transfer coefficient heat content of molten filler droplet heat content of weld pool welding current welding current density vector current density at weld pool surface thermal conductivity pressure heat flux
r rb ra T To uo Uw u v
w x,y,z xb
β
σ δ
η
μ
μm
P
θ
radial distance current flux radius heat flux radius temperature initial temperature welding speed welding arc voltage x-component of velocity vector y-component of velocity vector z-component of velocity vector coordinates distribution parameter thermal expansion coefficient surface tension thickness of workpiece arc efficiency viscosity magnetic permeability density parameter
