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CFD simulations of GMA welding of horizontal fillet joints based on coordinate rotation of arc models
Accepted Manuscript Title: CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models Author: Ligang Wu Jason Cheon Degala Venkata Kiran Suck-Joo Na PII: DOI: Reference:
S0924-0136(15)30243-0 http://dx.doi.org/doi:10.1016/j.jmatprotec.2015.12.027 PROTEC 14674
To appear in:
Journal of Materials Processing Technology
Received date: Revised date: Accepted date:
14-9-2015 20-12-2015 24-12-2015
Please cite this article as: Wu, Ligang, Cheon, Jason, Kiran, Degala Venkata, Na, Suck-Joo, CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models.Journal of Materials Processing Technology http://dx.doi.org/10.1016/j.jmatprotec.2015.12.027 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models
Ligang Wu, Jason Cheon, Degala Venkata Kiran, Suck-Joo Na*
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea
*Corresponding author. Tel.: +82 42 350 3216 Fax: +82 42 350 3210. E-mail address: [email protected] (Suck-Joo Na).
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Abstract This study conducted both experiments and simulations of gas metal arc welding of horizontal fillet joints with different welding speeds and wire feed rates. Front and side arc images were respectively captured by a CCD camera placed in front of the workpiece and beside it in each experiment. The arc models, including surface heat flux, electromagnetic force, arc pressure and drag force, were formulated in a rotated (x'-y'-z') coordinate system whose z'-axis was consistent with the arc axis. A higher welding speed made the arc behaviors less stable and may induce undercut on the vertical plate, whereas a higher wire feed rate enhanced the stability of arc behaviors. The arc images were analyzed to determine the effective arc radii of the arc models by applying both the Abel inversion technique and Fowler-Milne method. The radial distance, vertical distance and material thickness were calculated respectively to approximate the electromagnetic force distributions, and the resultant electromagnetic force distributions were analyzed in details. The resultant arc models were subsequently used to simulate each welding experiment. The molten pool behaviors by different welding speeds and wire feed rates were compared and analyzed, and the simulation models were verified by comparing the experimental and simulation results.
Keywords Gas metal arc welding; Horizontal fillet joint; Welding simulation; Coordinate rotation; Computational fluid dynamics; Volume of fluid.
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1.
Introduction Welding is one of the most widely used material processing technologies in modern manufacturing
industries, and is applied in various fields, such as shipbuilding, the construction of offshore structures, and the production of automobiles and pressure vessels. One of the major objectives of welding research is to optimize the welding parameters, such as welding speed, current, voltage and wire feed rate. For example, Karadeniz et al. (2007) investigated the influence of various welding parameters on penetration depth in robotic gas metal arc (GMA) welding through experiments. Optimal welding parameters can be determined by analyzing the resultant bead profiles. Even though this method can yield optimal welding parameters, it is impossible to experimentally analyze the molten pool behaviors that significantly affect the bead formation. Finite element method (FEM) and computational fluid dynamics (CFD) are the two methods used for welding simulations. However, FEM is limited to modeling conduction heat transfer, and is insufficient for explaining some phenomena such as humping, melt-through and finger penetration. In contrast, CFD considers both conduction and convection heat transfer, making it possible to study the molten pool behaviors and weld bead formation. The FLOW-3D software package equipped with the volume of fluid (VOF) technique is widely adopted to solve both heat flow and fluid flow for various welding processes. Cao et al. (2004) studied the bead formation of GMA welding considering the effects induced by molten droplets impinging on the molten pool surface. Cho et al. (2006) modeled the pulsed GMA welding process with parameters, such as droplet radius, droplet velocity and arc length, obtained from video images. Cho et al. (2010) combined the process models of laser and arc welding to simulate the distributions of alloying elements in CO2 laser-GMA hybrid welding, neglecting the laser-arc interactions. Cho et al. (2013a) studied the molten pool behaviors in vacuum gas hollow tungsten arc welding under various gas flow rates. Han et al. (2013) investigated the effects of various driving forces on molten pool behaviors in gas tungsten arc (GTA) welding, laser welding, and laser-GTA hybrid welding. All of the above reports were about bead on plate (BOP) welding, which is rarely used in real production. Recently, CFD models have been applied to more popular and advanced welding processes. Cho et al. (2013b) studied the molten pool behaviors in V-groove GMA welding with and without a root gap for various welding positions. Cho et al. (2013c) analyzed the influence of torch angle and polarity on molten pool behaviors in single-electrode submerged arc welding, considering the thermal energy transferred by molten slag as an additional heat input.
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Fillet welding refers to the process of joining two flat steel plates at a 90-degree angle, in which the weld metal fills the area where the two steel plates meet. It is a widely used welding process; for instance, Jeong and Cho (1997) indicated that in the shipbuilding industry more than 80% of the welded joints are fabricated as a fillet shape. Due to the complex V-shaped fillet geometry and arc characteristics, it is rather difficult to develop a CFD simulation model for fillet welding compared with that for BOP welding. Until now, only a very limited number of works on fillet welding simulation have been reported. Kim et al. (2003) modeled the temperature field and solidified surface profile in GMA fillet welding by solving the energy conservation equation in a boundary fitted coordinate system. Zhang et al. (2004) solved the governing equations in a boundary fitted curvilinear coordinate system and studied heat flow and fluid flow in GMA fillet welding. However, no detailed research on employing CFD simulation for horizontal fillet welding has ever been reported, and it is urgent to build such a simulation model. In this study, a CFD simulation model based on coordinate rotation was developed to study the molten pool behaviors in horizontal fillet welding. Two coordinate systems, namely the original (x-y-z) and the rotated (x’y’-z’) coordinate systems, were used. In this model the x-axis is the same as the x’-axis, and the y’-z’ plane results from the rotation of the y-z plane with respect to the x-axis. The FLOW-3D software package inputs and outputs all of the data in the original coordinate system, whereas the formulations of the arc models, including surface heat flux, arc pressure, EMF and drag force, are given in the rotated coordinate system where the z’-axis is consistent with the arc axis. In the case of BOP and V-groove welding, the arc axis is the same as the z-axis, so that coordinate rotation is not needed; all of the previous studies were done in the original coordinate system. However, the arc axis is different from the z-axis in horizontal fillet welding. To calculate the scalars and vectors this study formulated the arc models in the rotated coordinate system. The calculated scalars are directly input into the FLOW-3D software package, whereas the calculated vectors are converted to the original coordinate system. The previous model can also be adopted to perform fillet welding simulation by rotating the fillet joint instead of the arc models, but it is limited to single-sided fillet welding. Compared with the previous method, the one proposed in this study can be expanded for the simulation of double-sided fillet welding.
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2.
Experimental procedure Table 1 gives the welding parameters used to perform horizontal fillet welding with steel plates of 25.0 cm
10.0 cm × 0.6 cm, using the GMA welding process with direct current electrode positive polarity. It should be noted that the magnitudes of current and voltage in Table 1 are the average values of the transient signals measured from the experiments. Table 2 outlines the chemical composition of the workpiece and electrode used in this study. The diameter of the electrode was 0.12 cm and the distance between the contact tip and the workpiece was maintained at 1.95 cm. A mixture of 95% Ar-5% CO2 was used as the shielding gas at a flow rate of 20 L/min. The material properties used in this study are shown in Table 3. The vertical and the horizontal plates were firstly joined by two spots at the two ends of the fillet joint by manual metal arc welding, after which GMA welding was performed to lay the weld bead. Fig. 1 shows the details of the experimental setup. A CCD camera was placed in front of the workpiece and beside it to capture the front and side arc images respectively. Regarding the alignment of the fillet joint and welding wire, the electrode tip was intentionally shifted around 0.1 cm away from the location where the vertical and horizontal plates meet, to reduce undercut on the vertical plate. During experiments, the arc torch was kept stationary, and the platform carrying the workpiece moved at a constant speed. The welding process was initiated at a location about 2 cm away from one end of the fillet joint and stopped at a location about 2 cm away from the other end. The measured welding parameters are listed in Table 2.
3. Mathematical formulation 3.1 Mesh size and boundary type Cho et al. (2013b) indicated that the droplet volume could be lost if a mesh size larger than 0.025 cm/mesh was used, which would lead to inaccurate simulation results. For this reason, a uniform mesh density of 0.025 cm/mesh was assigned to the whole calculation domain. The mesh system comprises only one mesh block, which is 4.0 cm in length, 1.625 cm in width and 1.625 cm in depth. The continuative boundary type was selected for all mesh boundaries. A continuative boundary condition consists of zero normal derivatives at the boundary for all quantities. The zero-derivative condition is intended to represent a smooth continuation of the flow through the boundary.
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3.2 Governing equations In this study, the molten pool is assumed to be an incompressible Newtonian viscous laminar flow. The governing equations given as Eqs. (1)-(4) are solved by the FLOW-3D software package. -
Mass conservation equation:
m ·V s ρ
(1)
s is the mass source term by molten droplets. where V is the velocity vector and m
-
Momentum conservation equation:
m f V 1 V·V - P υ 2V s Vs V b t ρ ρ ρ
(2)
where ρ is the fluid density, p is the pressure, υ is the dynamic viscosity, Vs is the velocity vector for the mass source, and fb is the body force. -
Energy conservation equation:
h 1 V·h ·κT h s t ρ ρ s C sT T Ts h h(Ts ) hsl Tl Ts h(Tl ) ρl Cl (T-Tl )
(3)
T Ts Ts T Tl
(4)
Tl T
where h is the enthalpy, κ is the thermal conductivity, T is the local temperature, hs is the enthalpy source term due to the mass source term, ρs is the solid density, ρl is the liquid density, Cs is the specific heat of solid, Cl is the specific heat of liquid, Ts is the solidus temperature, Tl is the liquidus temperature, and hsl is the latent heat of fusion.
3.3 The volume of fluid method The FLOW-3D software package uses the VOF method to model the free surfaces. The VOF method was initially reported by Nichols and Hirt (1975), and more completely by Hirt and Nichols (1981). It consists of three ingredients: a scheme to locate the fluid surface, an algorithm to track the surface as a sharp interface moving through a computational grid, and a means of applying boundary conditions at the surface. The fluid
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surface configuration is defined by a fluid volume fraction function that states the VOF per unit volume and is governed by the following conservation equation:
F VF Fs t
(5)
where F is the volume of fluid and Fs is the change of the volume fraction of fluid associated with the mass
s in the continuity equation. source m The volume of fluid in a cell is normalized to the volume of the computing cell so that the value of F means the fraction of the cell occupied by the fluid. A unit value of F means that the cell is full of fluid and a zero value represents that the cell is empty. A cell with an F greater than zero and smaller than one indicates that it is partially filled with fluid, and is identified as a surface cell.
3.4 Coordinate rotation Fig. 2 shows the shape of the fillet joint together with the original and the rotated coordinate systems. The FLOW-3D software package adopted in this study inputs and outputs all of the data in the original coordinate system where the z-axis is parallel to the gravity direction, while the z'-axis is parallel to the arc axis in the rotated coordinate system. The modeling of fillet welding needs coordinate rotation, and the same was developed in this study. This scheme was executed in three steps. Firstly, the data output in the original coordinate system was adopted from the FLOW-3D software package; secondly, the data was converted into the rotated coordinate system and used to formulate the arc models to calculate the scalars and vectors; finally, the calculated scalars were directly input into the FLOW-3D software package, but the calculated vectors were converted into the original coordinate system before being input. For modeling the moving arc models, the local coordinate of the fluid cell is needed, and it can be derived using the following matrix equation:
0 0 x S x vt xlocal 1 y 0 cos α - sin α y S y local z local 0 sin α cos α z S z
(6)
where (xlocal, ylocal, zlocal) is the local coordinate of fluid cell given in the rotated coordinate system, α is the angle between the arc axis and the vertical plate, (x, y, z) is the coordinate of fluid cell given in the original coordinate
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system, (Sx, Sy, Sz) is the coordinate of the starting point of welding given in the original coordinate system, v is the welding speed, and t is the welding time. The calculated local coordinate of the fluid cell is subsequently used to formulate the arc models, including the surface heat flux, EMF, arc pressure and drag force. The detailed explanation of the coordinate rotation scheme for each arc model is given in the following sections.
3.5 Thermal boundary conditions The surface heat flux is applied on the top corner surface marked in Fig. 3 and modeled as an asymmetric Gaussian distribution expressed as Eq. (7).
If xlocal 0 and y local 0 , Qarc (xlocal , y local )
x2 η arcVI y2 exp local2 local 2σ 2πσ x σ y 2σ 2y1 x1
If xlocal 0 and y local 0 , Qarc (xlocal , y local )
x2 η arcVI y2 exp local2 local 2σ 2πσ x σ y 2σ y22 x1
If xlocal 0 and y local 0 , Qarc (xlocal , y local )
2 x2 η arcVI y local exp local 2σ 2 2πσ x σ y 2σ y21 x2
2 x2 η arcVI y local exp local 2σ 2 2πσ x σ y 2σ 2y 2 x2 σ y2 ) 2
If xlocal 0 and y local 0 , Qarc (xlocal , y local ) where σ x (σ x1 σ x 2 ) 2 , σ y (σ y1
(7)
where Qarc is the surface heat flux, ηarc is the arc efficiency, V is the arc voltage, I is the welding current, σx1 is the effective radius in x’-direction for xlocal greater than zero, σx2 is the effective radius in x’-direction for xlocal smaller than zero, σy1 is the effective radius in y’-direction for ylocal greater than zero, and σy2 is the effective radius in y’-direction for ylocal smaller than zero. By using the local coordinate, the moving surface heat flux is modeled in the rotated coordinate system. The thermal energy transfer rate from the electric arc to the fluid cell can be determined with Eqs. (8)-(9).
n 'x 1 0 0 n x ' n y 0 cos α sin α n y ' 0 sin α cos α n z n z
(8)
E arc Qarc xlocal , y local , z local Atotal n'z
(9)
where (nx, ny, nz) is the unit surface normal given in the original coordinate system, (n' , n'y , n' ) is the unit x z surface normal given in the rotated coordinate system, and Atotal is the total free surface area in cell.
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Additionally, the convection heat loss approximated by Newton’s law of cooling and the radiation heat loss estimated by the Stefan-Boltzmann law are considered for both the top and bottom corner surfaces as Eqs. (10)(11). Thus, the heat loss rate is expressed as Eq. (12).
Qconv hc T T0
Qrad σ T 4 T 04
(10)
(11)
Eloss Qconv Qrad Atotal
(12)
where Qconv is the convection heat loss, T0 is the ambient temperature, Qrad is the radiation heat loss, hc is the convection coefficient, σ is the Stefan-Boltzmann constant, and ε is the material emissivity. Therefore, the thermal energy absorption rate of the fluid cells on the top corner surface is expressed as Eq. (13).
Etop E arc -Eloss Qarc xlocal ,y local Atotal n'z -Qconv Qrad
(13)
The thermal energy loss rate of the fluid cells on the bottom corner surface is expressed as Eq. (14).
Ebot Eloss Qconv Qrad Atotal
(14)
Dhingra and Murphy (2005) stated that the total heat transfer efficiency in GMA welding ranges from 0.60 to 0.85 and this study assumes the total arc efficiency to be 0.7. The total heat transfer to the weld pool consists of the thermal energy transferred by the electric arc and that by molten droplets. The droplet efficiency and arc efficiency are determined by Eqs. (15)-(18).
f d 3rw2WFR 4rd3
qd
(15)
4 3 ππd ρC s Ts T0 Cl Td Tl f d 3
(16)
ηd qd VI
(17)
ηarc 0.7 ηd
(18)
where fd is the droplet frequency, rw is the wire radius, WFR is the wire feed rate, rd is the droplet radius, qd is the thermal energy transferred by the molten droplets, Td is the droplet temperature, and ηd is the droplet efficiency.
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3.6 Arc pressure model This study assumes that the effective radii of arc pressure are the same as those of the surface heat flux due to the physical relationship described by Cho et al. (2013a). The arc pressure model is expressed as Eq. (19). 2 2 xlocal μ0 I 2 ylocal exp 2σ 2 2σ 2 4π 2 σ x σ y x1 y1
2 2 xlocal μ0 I 2 ylocal exp 2σ 2 2σ 2 4π 2 σ x σ y x1 y2 x2 μ I2 y2 0 , Parc(xlocal , ylocal ) 20 local exp local 2 2σ 4π σ x σ y 2σ 2y1 x2
x2 μ0 I 2 y2 local exp local 2 2 2σ 4π σ x σ y 2σ 2y 2 x2
If xlocal 0 and ylocal 0 , Parc(xlocal , ylocal ) If xlocal 0 and ylocal 0 , Parc(xlocal , ylocal ) If xlocal 0 and ylocal
If xlocal 0 and ylocal 0 , Parc(xlocal , ylocal )
(19)
where Parc is the arc pressure and µo is the permeability of vacuum. The arc pressure in a single cell is assumed to be uniform, and the total arc pressure force equals the arc pressure multiplied by the total free surface area in the cell. Subsequently, the arc pressure force vector can be determined by the unit surface normal given in the original coordinate system as Eq. (20).
Fpx nx Fpy Parc xlocal , ylocal Atotal n y F n z pz
(20)
3.7 EMF model 3.7.1 Formulation of the EMF model This study adopts the EMF model proposed by Kou and Sun (1985), which is formulated based on the magnetic field and current flow inside the material substrate. Regarding the magnetic vector, only the angular component is non-zero. The current density and the magnetic field are expressed as Eqs. (21)-(23). The EMF vector can be derived as Eqs. (24)-(26). The radial distance of the fluid cell can be calculated by Eq. (27). It should be noted that the EMF model proposed by Kou and Sun (1985) follows an axisymmetric Gaussian distribution with only one effective radius, and it is taken as the average of the four effective arc radii in this study as Eq. (28).
Jz
I sinh λc zv λJ 0 λr' exp λ 2 σ r2 2 dλ 0 2π sinh λc
10
(21)
Jr
I cosh λc zv λJ1 λr' exp λ 2 σ r2 2 dλ 0 2π sinh λc
Bθ
μm I 2π
0
λJ1 λr' exp λ 2 σ r2 2
λc z dλ sinhsinh λc v
(22)
(23)
Fex' J z Bθ xlocal r'
(24)
Fey' J z Bθ ylocal r'
(25)
Fez' J r Bθ
(26)
2 2 r' xlocal ylocal
(27)
σ r σ x1 σ x 2 σ y1 σ y 2 4
(28)
where Jr is the radial current density, Jz is the vertical current density, J0 is the Bessel function of the first kind of zero order, J1 is Bessel function of the first kind of first order, c is the plate thickness, r’ is the radial distance, zv is the vertical distance, (Fex' , Fey' , Fez' ) is the EMF vector given in the rotated coordinated system, Bθ is the angular magnetic field, σr is the effective radius of EMF model, and µm is the material permeability.
3.7.2 Calculation of the vertical distance The vertical distance of a fluid cell is essential for determining its EMF value. The vertical distance in Sun and Kou’s EMF model equals the distance from the fluid cell to the plate surface, because the model was originally developed for BOP GTA welding, where the bead height is negligible. The calculation of vertical distance is different in BOP GMA welding due to the non-negligible bead height. In previous study (Cho et al., 2013b), the distance between the fluid cell and the surface cell right above it was regarded as its vertical distance. In the case of fillet welding, the logic used to determine the vertical distance should be similar to that in BOP GMA welding. This study considers four steps to calculate the vertical distance, as explained in Fig. 4. a)
Assume one line (Line 1) that goes through a random surface cell A, and is parallel to the z’-axis.
b) Assume another line (Line 2) that goes through the current cell, and is also parallel to the z’-axis. c)
The distance d between Line 1 and Line 2 can be calculated.
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d) Find the surface cell B that derives the smallest d. The distance between the current cell and surface cell B is approximated as the vertical distance. This study assumes that the current cell and surface cell B are in the same y’-z’ plane for the purpose of reducing calculation efforts.
3.7.3 Redefinition of material thickness In fillet welding, the current is initially released from the V-shaped joint surface, and then flows perpendicularly into the steel plates (Cho et al., 2013d). Because the material thickness is crucial to calculating the EMF, this study redefines the material thickness by following five steps, described as follows: a)
Output the data from the FLOW-3D software package and determine the leg lengths on both the vertical
and horizontal plates on any transverse cross sections so that Point C can be confirmed. b) As shown in Fig. 5(a), the vertical plate is divided into 21 segments with respect to Point C and Point B20. For the cells within Triangle CEiEi+1, the material thickness is approximated as the length of Line BiEi, where 0 ≤ i ≤ 19. c)
As shown in Fig. 5(b), the horizontal plate is divided into 21 segments with respect to Point C and Point A20.
For the cells within Triangle CDiDi+1, the material thickness is approximated as the length of Line AiDi, where 0 ≤ i ≤ 19. d) For the cells in the remaining part of the fillet joint, the material thickness is defined as the plate thickness.
3.7.4 Conversion of the calculated EMF vector By using the local coordinate, the resultant EMF vector is given in the rotated coordinate system. For this reason, the EMF vector should be converted into the original coordinate system before being input into the FLOW-3D software package as in Eq. (29). ' Fex 1 0 0 Fex ' Fey 0 cos α sin α Fey F 0 sin α cos α F ' ez ez
(29)
where (Fex, Fey, Fez) is the EMF vector given in the original coordinated system.
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3.8 Drag force model Drag force is a shear force induced by the plasma jet flow that impinges on the molten pool surface. It is independent of the effective arc radii and drives the fluid outward from the arc center in a radial direction. In this study, the analytical solutions of the wall shear stress for a circular jet impingement predicted by Phares et al. (2000) were adopted to estimate the drag force. Since only the universal functions for several integer H/D ratios are available in the reference paper, the ones needed for this study were fitted. The calculation of other terms in the drag force model, including the Reynolds number and the initial velocity of the arc plasma, are the same as in the previous study (Cho et al., 2006). The empirical equation is expressed as Eq. (30).
H r' τ ρ u g 2 Re10/ 2 D H
2
2 p 0
(30)
where τ is the shear stress, ρp is the density of arc plasma, µ0 is the initial velocity of arc plasma, Re0 is the Reynolds number, H is the nozzle height taken as the arc length, D is the nozzle diameter taken as the electrode diameter, and g2 is the universal function. With the radial distance calculated using the local coordinate, the resultant drag force vector is given in the rotated coordinate system as Eqs. (31)-(33), and Eq. (34) is employed to convert it into the original coordinate system.
Fdx' τAtotal n'z xlocal r'
(31)
Fdy' τAtotal n'z ylocal r'
(32)
Fdz' 0
(33)
' Fdx 1 0 0 Fdx ' Fdy 0 cos α sin α Fdy F 0 sin α cos α F ' dz dz
(34)
where (Fdx' , Fdy' , Fdz' ) is the drag force vector given in the rotated coordinated system and (Fdx, Fdy, Fdz) is the drag force vector given in the original coordinated system.
3.9 Other models In this study, the other arc models, such as surface tension and buoyancy force, are the same as those used in the previous study (Han et al., 2013).
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4. Result and discussion 4.1 Arc behavior Fig. 6 presents the representative arc images captured in the experiments with different welding speeds. The molten droplets transfer into the molten pool in a stable spray transfer mode when the welding speed is as low as 0.4 cm/s. The droplet transfer mode switches to a transition mode between a spray transfer mode and a globular transfer mode as the welding speed increases with temporal fluctuation of current and voltage signals. It should be noted that the simulation model in this study is limited to spray transfer mode. For this reason, the arc behaviors during spray transfer mode are selected to simulate Case 2 and Case 3. The arc lengths in Cases 13 are similar to each other, and are measured to be 0.54 cm, 0.51 cm and 0.55 cm, respectively. On the other hand, angle α fluctuates slightly with the increase in welding speed, whereas angle β greatly increases. Fig. 7 presents arc images captured in the experiments with different wire feed rates. The molten droplets transfer onto the vertical plate in Case 2, the corner in Case 4 and the horizontal plate in Case 5, respectively. To simulate this phenomenon, the starting points of welding in Eq. (6) for Case 2, Case 4 and Case 5 were set to be (0, 0, 0.06), (0, 0, 0) and (0, 0.1, 0) respectively. The arc lengths in Case 2, 4 and 5 decrease with the increase in wire feed rate, and are measured to be 0.51 cm, 0.43 cm and 0.35 cm, respectively. Angle α fluctuates slightly with the increase in wire feed rate, whereas angle β greatly decreases. This is probably because the arc length becomes shorter when the wire feed rate is higher, and it makes the arc stiffness greater. As mentioned in the previous paragraph, the molten droplets transfer into the molten pool in a transition mode in Case 2. The stability of droplet transfer is greatly improved as the wire feed rate increases, and the droplets transfer into the molten pool in a stable spray transfer mode in Case 4 and Case 5. In a nutshell, it is easier to produce a stable spray transfer mode with low welding speed and high wire feed rate in horizontal fillet welding.
4.2 Droplet generation Droplet temperature, radius, frequency, initial position and velocity are needed for droplet generation in the simulation. The droplet temperature was set to be 2400 K (Cho et al., 2013b), the droplet radius was measured from the front arc images, and the calculation of droplet frequency has been discussed in Section 3.5. In the simulation, molten droplets are generated at the arc center above the molten pool surface. For this reason, they should be assigned the velocity just before impingement. This study measures the 2D impingement velocity Vyz from the front arc images to approximate the 3D impingement velocity. The arc image where the droplet is
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about to impinge the molten pool surface and the one before it are selected. The 2D impingement velocity Vyz can be found by dividing the traveling distance measured from these two arc images over their time difference. Subsequently, the 3D droplet impingement velocity can be approximated by Eqs. (35)-(38).
Vdz V yz2 1 tan α
(35)
Vdx Vz tan β
(36)
Vdy Vz tan α
(37)
Vd Vdx2 Vdy2 Vdz2
(38)
2
where (Vdx, Vdy, Vdz) is the droplet impingement velocity vector and Vd is the magnitude of the droplet impingement velocity. The approximated impingement velocities for Cases 1-5 are listed in Table 4. As can be seen from Fig. 6, the distance from the position where the droplets are created to the molten pool surface is too short to be measured in Case 4 and Case 5 so that it becomes impossible to estimate the droplet impingement velocity with the method described above. Lin et al. (2001) found a positive correlation between the droplet velocity and the welding current. Based on this information, the impingement velocity magnitudes of Case 4 and Case 5 were calculated to be 111.8 cm/s and 166.4 cm/s respectively.
4.3 Modeling the surface heat flux and arc pressure Fig. 8 shows the modeling procedure for the surface heat flux and arc pressure. The Abel inversion technique and Fowler-Milne method were combined to calculate the effective arc radii. Due to the complex Vshape of fillet joint and the inclination of the torch, four effective arc radii are measured from the front and side arc images. It should be noted that the dotted lines in Fig. 8 used to extract the light intensity distribution are not straight lines because of the presence of pre-flow. Five steps were taken, explained as follows. a)
The light intensity distribution was obtained along the dotted line, which was 0.1 mm above the plate
surface or fluid surface in the arc images. b) The emissivity distribution was calculated with the Abel inversion technique. c)
The calculated emissivity distribution was processed with the Fowler-Milne method to calculate the arc
temperature distribution.
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d) Gaussian fitting was performed for the arc temperature distribution data, to derive the effective arc radii; the resultant values are listed in Table 5. e)
The asymmetric surface heat flux and arc pressure were modeled with the four effective arc radii.
4.4 EMF results 4.4.1 Calculated radial distance, vertical distance, material thickness distributions As explained in Section 3.7, the radial distance, vertical distance and material thickness are essential to determining the EMF of a fluid cell. The calculation of radial distance can be simply done using Eq. (27). Fig. 9(a) presents the calculated radial distance distribution on the transverse cross section at the arc axis. The radial distance equals zero at the arc axis and reaches its maximum at the locations farthest away from arc axis. Fig. 9(b) displays the calculated vertical distance distribution on an arbitrary transverse cross section. The vertical distance equals zero at the molten pool surface and reaches its maximum at the bottom. Fig. 9(c) shows the calculated material thickness distribution on an arbitrary transverse cross section. The material thickness becomes larger as the cell gets closer to the arc axis. The calculated radial distance and vertical distance distributions are consistent with their respective physical meanings, and the calculated material thickness distribution also follows its definition, as introduced in Section 3.7.3.
4.4.2 Analysis of EMF EMF is caused by the current flow and magnetic field inside the material substrate. The direction of the magnetic vector can be confirmed by Ampere's right-hand screw rule, and that of EMF can be determined by the left-hand rule. As a result, the direction of radial EMF is toward the arc center in the radial direction and that of vertical EMF is downward along the direction parallel to the arc axis. Fig. 10 shows the 3D and 2D radial EMF distributions in the weld pool. The radial EMF mainly concentrates on the molten pool surface. The radial EMF is decomposed into two components, namely the x'EMF and y'-EMF, to input into the software. Fig. 11 shows the 3D and 2D x'-EMF distributions. The x'- EMF is positive behind the arc center and negative ahead of the arc center so that it drives the fluid behind the arc center forward in the welding direction, and the fluid ahead of the arc center is driven backward against the welding direction.
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Fig. 12 presents the 3D and 2D y'-EMF distributions. The y'-EMF is positive on the left side and negative on the right side so that it drives the fluid on the left side to the right and that on the right side to the left. Therefore, the fluid is driven towards the arc center in the radial direction by the x'-EMF and y'-EMF, which is the same direction as the radial EMF mentioned in the previous paragraph. Fig. 13 displays the 3D and 2D vertical EMF distributions. The vertical EMF also concentrates on the molten pool surface, and its negative value indicates that it drives the fluid downward along the direction parallel to the arc axis. The direction is also the same as that of the vertical EMF mentioned in the previous paragraph. Therefore, it can be concluded with confidence that the calculated EMF vector follows its physical meaning.
4. 5 Fluid flow analysis Cases 1-3 were performed to investigate the influence of welding speed on molten pool behaviors. Fig. 14 shows the temperature profile and streamlines on the transverse cross section at x=1.013 cm in Case 1. Before droplet impingement as in Fig. 14(a), the arc is away from this location, and the fluid is mainly driven by the surface tension gradient force. The fluid flows outward from the arc center, and this kind of flow pattern makes the molten pool wide and shallow. When the arc arrives, as in Fig. 14(b)-(c), the influence of droplet impingement, EMF and arc pressure becomes dominant. The molten droplets, carrying a large amount of thermal energy and momentum, continually impinge on the molten pool surface. That fluid, which has already absorbed a great quantity of thermal energy from the arc on the free surface, and the fluid inside the molten pool flows downward along the direction parallel to the arc axis, striking the bottom of the molten pool and making the penetration deeper. Subsequently, the fluid travels away from the center of the bottom, which then meets and totally reduces that driven by surface tension gradient force. After the arc leaves, as in Fig. 14(d), the fluid in the molten pool flows upward. Fig. 15 presents the temperature profile and streamlines on the transverse cross section at x=1.013 cm in Case 2, and they are quite similar to those in Case 1. The only difference occurs during the droplet impingement period. The outward flow by surface tension gradient force is not totally reduced because of the reduced influence of droplet impingement, EMF and arc pressure due to the increase in welding speed. On the other hand, the molten pool behaviors on the transverse cross section in Case 3 are almost the same as those in Case 2. Fig.16 shows the temperature profile and streamlines on the longitudinal cross sections at y=0.06 cm in Cases 1-3. The length of the molten pool decreases with the increase in welding speed because less thermal
17
energy accumulates in the molten pool as the welding speed increases. In Case 1, the fluid in the rear part of the molten pool is driven to the right side while that in the top part flows in a counterclockwise direction because of the surface tension gradient force. At the same time, the fluid in the front part flows backward due to droplet impingement, EMF and arc pressure. In Case 2, the backward fluid flows in a clockwise direction due to the dominance of droplet impingement, EMF and arc pressure. The different fluid flow patterns in Cases 1 and 2 result from the fact that the thermal energy accumulated in the molten pool is reduced due to the increase in welding speed, and the temperature gradient becomes smaller, so that the influence of surface tension gradient force becomes weaker. The longitudinal molten pool behaviors in Case 3 show similar characteristics as those in Case 2. Cases 2, 4 and 5 were performed to study the influence of wire feed rate on molten pool behaviors. Regarding the molten pool behaviors on the transverse cross sections in Cases 4 and 5, they are almost same as those in Case 2. Fig.17 shows the temperature profile and streamlines on the longitudinal cross sections at y=0.06 cm in Cases 2, 4 and 5. The length of the molten pool increases with the increase in wire feed rate because more momentum and molten metal are transferred into the molten pool. In the longitudinal cross section view of Case 2, a large portion of the molten pool is affected by droplet impingement, EMF and arc pressure because the molten pool is short in size. However, a relatively smaller portion of the molten pool is observed to be affected probably due to the longer length of the molten pool and the different droplet impingement positions as displayed in the front views in Fig. 7. In Case 5, only the forefront part of the molten pool is affected by droplet impingement, EMF and arc pressure, whereas the rear part is dominated by surface tension gradient force.
4.6 Comparisons of experimental and simulation results Fig. 18(a)-(c) shows the comparisons of the experimental and simulation results for different welding speeds. The leg length, penetration and actual throat decrease with the increase in welding speed. Moreover, undercut occurs on the vertical plate when the welding speed is as high as 1.0 cm/s. Fig. 18(b), (d) and (e) shows comparisons of the experimental and simulation results for different wire feed rates. A higher wire feed rate results in a deeper penetration because of the greater droplet impingement velocity, arc pressure and EMF due to the higher welding current. The simulated fusion zone geometries for Cases 1, 4 and 5 are in fair agreement with the experimental results, whereas those for Cases 2 and 3 are inconsistent with the experimental ones. This is
18
probably because the arc behaviors in Case 2 and 3 are unstable, and this study only selects the arc behaviors during the spray transfer mode for simulation. For the quantitative analysis of the simulation model, the leg length and actual throat of the experimental and simulation results are compared, as shown in Fig. 19. It should be noted that the experimental data in Fig. 19(a) are average values. As shown in Fig. 19(b), the cross section views of Case 1 at different longitudinal locations in a single experiment are almost same with each other, whereas those of Case 2 and Case 3 are observed to be different. Regarding Case 2 and Case 3, different cross section views are also observed when the experiments are repeated, as can been seen by comparing the cross section views in Fig. 18 and Fig. 19(b). This may have been induced by the unstable arc behaviors observed in Case 2 and Case 3, and it is difficult to repeat the experiments when the arc behaviors are unstable. In addition, the difference between the experimental and simulation results may also have been induced by the following aspects: a)
The difficulty in measuring the effective arc radii. Theoretically, the light intensity distribution 0.1 mm
above the plate surface or fluid surface in the arc images should be extracted for Abel inversion. However, it is impossible to take a line that exactly follows this criterion in real practice because of the extremely irregular shape of the molten pool. b) The arc models are assumed to be different shapes. The surface heat flux and arc pressure are modeled as asymmetric Gaussian distributions because of the four mutually different effective arc radii measured from the arc images. However, the EMF follows an axisymmetric Gaussian distribution, and this study takes the average of the four radii as its effective radius. c)
A constant total arc efficiency of 0.7 is assumed for all cases. Stenbacka (2013) reported that the total arc
efficiency was reduced with an increase in arc length. The arc lengths in the five cases are mutually different so that fixing the total arc efficiency as 0.7 may not be appropriate.
19
5. Conclusions This study systematically presented a method to formulate arc models, based on coordinate rotation, for CFD simulations of GMA welding of horizontal fillet joints. Welding experiments with different welding speeds and wire feed rates were performed to validate the simulation models. This work can be summarized as follows: a)
Surface heat flux and arc pressure were modeled as asymmetric Gaussian distributions. The four effective
arc radii were determined from arc images captured by a CCD camera by applying both the Abel inversion technique and Fowler-Milne method, whereas the EMF was modeled as an axisymmetric Gaussian distribution with its effective radius being the mean of the four effective arc radii. b) The arc models, including the surface heat flux, EMF, arc pressure and drag force, were formulated in the rotated coordinate system. The calculated scalars were directly input into the FLOW-3D software package, whereas the calculated vectors were converted into the original coordinate system. This calculation method was verified by comparing the experimental and simulation results. c)
The leg length, penetration and actual throat decreased with an increase in the welding speed. A higher
welding speed made the arc behaviors less stable and may induce undercut on the vertical plate, whereas a higher wire feed rate enhanced the stability of arc behaviors and produced a deeper penetration. d) The weld pool was widened by the outward flow resulting from the surface tension gradient force, and was deepened by the downward flow along the direction parallel to the arc axis by droplet impingement, EMF and arc pressure. The outward flow due to surface tension force was totally reduced when the welding speed was as low as 0.4 cm/s, but partially reduced when the welding speed was increased. On the other hand, the length of the molten pool decreased with the increase in welding speed but increased with the increase in wire feed rate.
Acknowledgements The authors gratefully acknowledge the support of the Brain Korea 21 and Mid-career Researcher Program through NRF of Korea (Grant No. 2013R1A2A1A01015605).
20
References Cao, Z., Yang, Z., Chen, X. L., 2004. Three-dimensional simulation of transient GMA weld pool with free surface. Welding Journal (Miami, Fla) 83(6): 169s-176s. Cho, D.W., Lee, S.H., Na. S.J., 2013a. Characterization of welding arc and weld pool formation in vacuum gas hollow tungsten arc welding. Journal of Materials Processing Technology 213(2): 143-152. Cho, D. W., Na, S.J., Cho, M.H., Lee, J.S., 2013b. A study on V-groove GMAW for various welding positions. Journal of Materials Processing Technology 213(9): 1640-1652. Cho, D.W., Na, S.J, Cho, M.H, Lee, J.S., 2013d. Simulations of weld pool dynamics in V-groove GTA and GMA welding. Welding in the World 57(2): 223-233. Cho, D.W., Song, W.H., Cho, M.H, Na, S.J., 2013c. Analysis of submerged arc welding process by threedimensional computational fluid dynamics simulations. Journal of Materials Processing Technology 213(12): 2278-2291. Cho, M. H., Lim, Y.C., Farson, D.F., 2006. Simulation of weld pool dynamics in the stationary pulsed gas metal arc welding process and final weld shape. Welding Journal (Miami, Fla) 85(12): 271s-283s. Cho, W.I., Na, S.J., Cho, M.H., Lee, J.S., 2010. Numerical study of alloying element distribution in CO2 laser– GMA hybrid welding. Computational Materials Science 49(4): 792-800. Dhingra, A., Murphy, C., 2005. Numerical simulation of welding-induced distortion in thin-walled structures. Science and Technology of Welding & Joining 10(5): 528-536. Han, S.W., Cho, W.H., Na, S.J., Kim, C.H., 2013. Influence of driving forces on weld pool dynamics in GTA and laser welding. Welding in the World 57(2): 257-264. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of computational physics 39(1): 201-225. Jeong, S.K., Cho, H.S., 1997. An analytical solution to predict the transient temperature distribution in fillet arc welds. Welding Journal (Miami, Fla) 76(12): 223s. Karadeniz, E., Ozsarac, U., Yildiz, C., 2007. The effect of process parameters on penetration in gas metal arc welding processes. Materials & Design 28(2): 649-656. Kim, C.H., Zhang, W., Debroy, T., 2003. Modeling of temperature field and solidified surface profile during gas–metal arc fillet welding. Journal of Applied Physics 94(4): 2667.
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Kou, S., Sun, D., 1985. Fluid flow and weld penetration in stationary arc welds. Metallurgical Transactions A 16(2): 203-213. Lin, Q., Li, X., Simpson, S.W., 2001. Metal transfer measurements in gas metal arc welding. Journal of Physics D: Applied Physics 34(3): 347. Nichols, B., Hirt, C., 1975. Methods for calculating multi-dimensional, transient, free surface flows past bodies. Proc., 1st Int. Conf. Ship Hydrodynamics, DTIC Document. Phares, D. J., Smedley, G.T., Flagan, R.C., 2000. The wall shear stress produced by the normal impingement of a jet on a flat surface. Journal of Fluid Mechanics 418: 351-375. Stenbacka, N., 2013. On arc efficiency in gas tungsten arc welding. Soldagem & Inspeção 18(4): 380-390. Zhang, W., Kim, C.H., Debroy, T., 2004. Heat and fluid flow in complex joints during gas metal arc welding— Part I: Numerical model of fillet welding. Journal of Applied Physics 95(9): 5210.
22
List of Figures
Fig. 1. Experimental setup of GMA welding for horizontal fillet welding.
Fig. 2. Schematic sketch of horizontal fillet joint.
23
Fig. 3. Schematic sketch of the top and bottom corner surfaces of the fillet joint.
Fig. 4. Determination of the vertical distance in fillet welding.
Fig. 5. Redefinition of the material thickness.
24
Fig. 6. Arc images captured in the experiments with different welding speeds.
Fig. 7. Arc images captured in the experiments with different wire feed rates.
25
Fig. 8. Modeling procedure of the surface heat flux and arc pressure.
26
Fig. 9. Calculated radial distance, vertical distance and material thickness distributions.
Fig. 10. 3D and 2D radial EMF distributions.
27
Fig. 11. 3D and 2D x'- EMF distributions.
Fig. 12. 3D and 2D y'-EMF distributions.
28
Fig. 13. 3D and 2D vertical EMF distributions.
29
Fig. 14. Temperature profile and streamlines on the transverse cross section at x=1.013 cm in Case 1.
30
Fig. 15. Temperature profile and streamlines on the transverse cross section at x=1.013 cm in Case 2.
31
Fig. 16. Temperature profile and streamlines on the longitudinal cross sections at y=0.06 cm in Cases 1-3.
32
Fig. 17. Temperature profile and streamlines on the longitudinal cross sections at y=0.06 cm in Cases 2, 4 and 5.
33
Fig. 18. Comparisons of the experimental and simulation results for Cases 1-5.
34
Fig. 19. a) Quantitative comparisons of the experimental (averaged value) and simulation results for Cases 1-5, (b) experimental cross section views of repeated experiments for Cases 1-3.
35
Table 1 Welding parameters used in the experiments. Voltage Current Welding speed [V] [A] [cm/s]
WFR [m/min]
Case 1
25.8
255.4
0.4
7.5
Case 2
25.4
249.0
0.7
7.5
Case 3
25.6
258.5
1.0
7.5
Case 4
25.8
266.3
0.7
8.5
Case 5
26.2
298.8
0.7
9.5
Table 2 Chemical composition of ASTM AH36 steel and SM70 solid wire. Chemical composition C Si Mn P S Cr Ni wt. %
Cu
Nb
Ti
V
Al
AH36
0.157
0.392
1.501
0.014
0.003
0.03
0.01
0.015
0
0.003
0.003
0.042
SM70
0.07
0.83
1.48
0.017
0.02
-
-
-
-
-
-
-
Table 3 Material properties of ASTM AH36 steel. Properties
Value
Density of solid
7.86 g/cm3
Density of liquid
6.90 g/cm3
Latent heat of fusion
2.47×109 erg/g s
Thermal conductivity of solid
2.60×106 erg/cm s K
Thermal conductivity of liquid
3.30×106 erg/cm s K
Specific heat of solid
4.70×106 erg/g s K
Specific heat of liquid
6.97×106 erg/g s K
Viscosity
0.06 g/cm s
Heat transfer coefficient
105 erg/cm2 s K
Surface tension coefficient
1870 dyne/ cm
Surface tension gradient
-0.35 dyne/cm K
Liquidus temperature
1791 K
Solidus temperature
1688 K
Emissivity
0.2
Coefficient of thermal expansion
1.20×10-5 cm/cm K
Permeability of vacuum
1.20×106 H/m
Material permeability
1.20×106 H/m
36
Table 4 Droplet velocities measured in Cases 1-5. Vd [cm/s]
Vdx [cm/s]
Vdy [cm/s]
Vdz [cm/s]
Case 1
98.7
-20.2
-79.1
-55.4
Case 2
96.3
-34.3
-75.5
-49.0
Case 3
89.0
-33.2
-67.7
-47.4
Case 4
111.8
-27.5
-90.9
-59.0
Case 5
166.4
-32.4
-136.9
-88.9
Table 5 Effective arc radii measured in Cases 1-5. σx1 [cm] σx2 [cm] σy1 [cm] σy2 [cm] Case 1
0.176
0.168
0.091
0.123
Case 2
0.160
0.146
0.104
0.107
Case 3
0.153
0.142
0.130
0.148
Case 4
0.162
0.148
0.096
0.160
Case 5
0.153
0.137
0.092
0.143
37
S0924-0136(15)30243-0 http://dx.doi.org/doi:10.1016/j.jmatprotec.2015.12.027 PROTEC 14674
To appear in:
Journal of Materials Processing Technology
Received date: Revised date: Accepted date:
14-9-2015 20-12-2015 24-12-2015
Please cite this article as: Wu, Ligang, Cheon, Jason, Kiran, Degala Venkata, Na, Suck-Joo, CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models.Journal of Materials Processing Technology http://dx.doi.org/10.1016/j.jmatprotec.2015.12.027 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
CFD Simulations of GMA Welding of Horizontal Fillet Joints based on Coordinate Rotation of Arc Models
Ligang Wu, Jason Cheon, Degala Venkata Kiran, Suck-Joo Na*
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea
*Corresponding author. Tel.: +82 42 350 3216 Fax: +82 42 350 3210. E-mail address: [email protected] (Suck-Joo Na).
1
Abstract This study conducted both experiments and simulations of gas metal arc welding of horizontal fillet joints with different welding speeds and wire feed rates. Front and side arc images were respectively captured by a CCD camera placed in front of the workpiece and beside it in each experiment. The arc models, including surface heat flux, electromagnetic force, arc pressure and drag force, were formulated in a rotated (x'-y'-z') coordinate system whose z'-axis was consistent with the arc axis. A higher welding speed made the arc behaviors less stable and may induce undercut on the vertical plate, whereas a higher wire feed rate enhanced the stability of arc behaviors. The arc images were analyzed to determine the effective arc radii of the arc models by applying both the Abel inversion technique and Fowler-Milne method. The radial distance, vertical distance and material thickness were calculated respectively to approximate the electromagnetic force distributions, and the resultant electromagnetic force distributions were analyzed in details. The resultant arc models were subsequently used to simulate each welding experiment. The molten pool behaviors by different welding speeds and wire feed rates were compared and analyzed, and the simulation models were verified by comparing the experimental and simulation results.
Keywords Gas metal arc welding; Horizontal fillet joint; Welding simulation; Coordinate rotation; Computational fluid dynamics; Volume of fluid.
2
1.
Introduction Welding is one of the most widely used material processing technologies in modern manufacturing
industries, and is applied in various fields, such as shipbuilding, the construction of offshore structures, and the production of automobiles and pressure vessels. One of the major objectives of welding research is to optimize the welding parameters, such as welding speed, current, voltage and wire feed rate. For example, Karadeniz et al. (2007) investigated the influence of various welding parameters on penetration depth in robotic gas metal arc (GMA) welding through experiments. Optimal welding parameters can be determined by analyzing the resultant bead profiles. Even though this method can yield optimal welding parameters, it is impossible to experimentally analyze the molten pool behaviors that significantly affect the bead formation. Finite element method (FEM) and computational fluid dynamics (CFD) are the two methods used for welding simulations. However, FEM is limited to modeling conduction heat transfer, and is insufficient for explaining some phenomena such as humping, melt-through and finger penetration. In contrast, CFD considers both conduction and convection heat transfer, making it possible to study the molten pool behaviors and weld bead formation. The FLOW-3D software package equipped with the volume of fluid (VOF) technique is widely adopted to solve both heat flow and fluid flow for various welding processes. Cao et al. (2004) studied the bead formation of GMA welding considering the effects induced by molten droplets impinging on the molten pool surface. Cho et al. (2006) modeled the pulsed GMA welding process with parameters, such as droplet radius, droplet velocity and arc length, obtained from video images. Cho et al. (2010) combined the process models of laser and arc welding to simulate the distributions of alloying elements in CO2 laser-GMA hybrid welding, neglecting the laser-arc interactions. Cho et al. (2013a) studied the molten pool behaviors in vacuum gas hollow tungsten arc welding under various gas flow rates. Han et al. (2013) investigated the effects of various driving forces on molten pool behaviors in gas tungsten arc (GTA) welding, laser welding, and laser-GTA hybrid welding. All of the above reports were about bead on plate (BOP) welding, which is rarely used in real production. Recently, CFD models have been applied to more popular and advanced welding processes. Cho et al. (2013b) studied the molten pool behaviors in V-groove GMA welding with and without a root gap for various welding positions. Cho et al. (2013c) analyzed the influence of torch angle and polarity on molten pool behaviors in single-electrode submerged arc welding, considering the thermal energy transferred by molten slag as an additional heat input.
3
Fillet welding refers to the process of joining two flat steel plates at a 90-degree angle, in which the weld metal fills the area where the two steel plates meet. It is a widely used welding process; for instance, Jeong and Cho (1997) indicated that in the shipbuilding industry more than 80% of the welded joints are fabricated as a fillet shape. Due to the complex V-shaped fillet geometry and arc characteristics, it is rather difficult to develop a CFD simulation model for fillet welding compared with that for BOP welding. Until now, only a very limited number of works on fillet welding simulation have been reported. Kim et al. (2003) modeled the temperature field and solidified surface profile in GMA fillet welding by solving the energy conservation equation in a boundary fitted coordinate system. Zhang et al. (2004) solved the governing equations in a boundary fitted curvilinear coordinate system and studied heat flow and fluid flow in GMA fillet welding. However, no detailed research on employing CFD simulation for horizontal fillet welding has ever been reported, and it is urgent to build such a simulation model. In this study, a CFD simulation model based on coordinate rotation was developed to study the molten pool behaviors in horizontal fillet welding. Two coordinate systems, namely the original (x-y-z) and the rotated (x’y’-z’) coordinate systems, were used. In this model the x-axis is the same as the x’-axis, and the y’-z’ plane results from the rotation of the y-z plane with respect to the x-axis. The FLOW-3D software package inputs and outputs all of the data in the original coordinate system, whereas the formulations of the arc models, including surface heat flux, arc pressure, EMF and drag force, are given in the rotated coordinate system where the z’-axis is consistent with the arc axis. In the case of BOP and V-groove welding, the arc axis is the same as the z-axis, so that coordinate rotation is not needed; all of the previous studies were done in the original coordinate system. However, the arc axis is different from the z-axis in horizontal fillet welding. To calculate the scalars and vectors this study formulated the arc models in the rotated coordinate system. The calculated scalars are directly input into the FLOW-3D software package, whereas the calculated vectors are converted to the original coordinate system. The previous model can also be adopted to perform fillet welding simulation by rotating the fillet joint instead of the arc models, but it is limited to single-sided fillet welding. Compared with the previous method, the one proposed in this study can be expanded for the simulation of double-sided fillet welding.
4
2.
Experimental procedure Table 1 gives the welding parameters used to perform horizontal fillet welding with steel plates of 25.0 cm
10.0 cm × 0.6 cm, using the GMA welding process with direct current electrode positive polarity. It should be noted that the magnitudes of current and voltage in Table 1 are the average values of the transient signals measured from the experiments. Table 2 outlines the chemical composition of the workpiece and electrode used in this study. The diameter of the electrode was 0.12 cm and the distance between the contact tip and the workpiece was maintained at 1.95 cm. A mixture of 95% Ar-5% CO2 was used as the shielding gas at a flow rate of 20 L/min. The material properties used in this study are shown in Table 3. The vertical and the horizontal plates were firstly joined by two spots at the two ends of the fillet joint by manual metal arc welding, after which GMA welding was performed to lay the weld bead. Fig. 1 shows the details of the experimental setup. A CCD camera was placed in front of the workpiece and beside it to capture the front and side arc images respectively. Regarding the alignment of the fillet joint and welding wire, the electrode tip was intentionally shifted around 0.1 cm away from the location where the vertical and horizontal plates meet, to reduce undercut on the vertical plate. During experiments, the arc torch was kept stationary, and the platform carrying the workpiece moved at a constant speed. The welding process was initiated at a location about 2 cm away from one end of the fillet joint and stopped at a location about 2 cm away from the other end. The measured welding parameters are listed in Table 2.
3. Mathematical formulation 3.1 Mesh size and boundary type Cho et al. (2013b) indicated that the droplet volume could be lost if a mesh size larger than 0.025 cm/mesh was used, which would lead to inaccurate simulation results. For this reason, a uniform mesh density of 0.025 cm/mesh was assigned to the whole calculation domain. The mesh system comprises only one mesh block, which is 4.0 cm in length, 1.625 cm in width and 1.625 cm in depth. The continuative boundary type was selected for all mesh boundaries. A continuative boundary condition consists of zero normal derivatives at the boundary for all quantities. The zero-derivative condition is intended to represent a smooth continuation of the flow through the boundary.
5
3.2 Governing equations In this study, the molten pool is assumed to be an incompressible Newtonian viscous laminar flow. The governing equations given as Eqs. (1)-(4) are solved by the FLOW-3D software package. -
Mass conservation equation:
m ·V s ρ
(1)
s is the mass source term by molten droplets. where V is the velocity vector and m
-
Momentum conservation equation:
m f V 1 V·V - P υ 2V s Vs V b t ρ ρ ρ
(2)
where ρ is the fluid density, p is the pressure, υ is the dynamic viscosity, Vs is the velocity vector for the mass source, and fb is the body force. -
Energy conservation equation:
h 1 V·h ·κT h s t ρ ρ s C sT T Ts h h(Ts ) hsl Tl Ts h(Tl ) ρl Cl (T-Tl )
(3)
T Ts Ts T Tl
(4)
Tl T
where h is the enthalpy, κ is the thermal conductivity, T is the local temperature, hs is the enthalpy source term due to the mass source term, ρs is the solid density, ρl is the liquid density, Cs is the specific heat of solid, Cl is the specific heat of liquid, Ts is the solidus temperature, Tl is the liquidus temperature, and hsl is the latent heat of fusion.
3.3 The volume of fluid method The FLOW-3D software package uses the VOF method to model the free surfaces. The VOF method was initially reported by Nichols and Hirt (1975), and more completely by Hirt and Nichols (1981). It consists of three ingredients: a scheme to locate the fluid surface, an algorithm to track the surface as a sharp interface moving through a computational grid, and a means of applying boundary conditions at the surface. The fluid
6
surface configuration is defined by a fluid volume fraction function that states the VOF per unit volume and is governed by the following conservation equation:
F VF Fs t
(5)
where F is the volume of fluid and Fs is the change of the volume fraction of fluid associated with the mass
s in the continuity equation. source m The volume of fluid in a cell is normalized to the volume of the computing cell so that the value of F means the fraction of the cell occupied by the fluid. A unit value of F means that the cell is full of fluid and a zero value represents that the cell is empty. A cell with an F greater than zero and smaller than one indicates that it is partially filled with fluid, and is identified as a surface cell.
3.4 Coordinate rotation Fig. 2 shows the shape of the fillet joint together with the original and the rotated coordinate systems. The FLOW-3D software package adopted in this study inputs and outputs all of the data in the original coordinate system where the z-axis is parallel to the gravity direction, while the z'-axis is parallel to the arc axis in the rotated coordinate system. The modeling of fillet welding needs coordinate rotation, and the same was developed in this study. This scheme was executed in three steps. Firstly, the data output in the original coordinate system was adopted from the FLOW-3D software package; secondly, the data was converted into the rotated coordinate system and used to formulate the arc models to calculate the scalars and vectors; finally, the calculated scalars were directly input into the FLOW-3D software package, but the calculated vectors were converted into the original coordinate system before being input. For modeling the moving arc models, the local coordinate of the fluid cell is needed, and it can be derived using the following matrix equation:
0 0 x S x vt xlocal 1 y 0 cos α - sin α y S y local z local 0 sin α cos α z S z
(6)
where (xlocal, ylocal, zlocal) is the local coordinate of fluid cell given in the rotated coordinate system, α is the angle between the arc axis and the vertical plate, (x, y, z) is the coordinate of fluid cell given in the original coordinate
7
system, (Sx, Sy, Sz) is the coordinate of the starting point of welding given in the original coordinate system, v is the welding speed, and t is the welding time. The calculated local coordinate of the fluid cell is subsequently used to formulate the arc models, including the surface heat flux, EMF, arc pressure and drag force. The detailed explanation of the coordinate rotation scheme for each arc model is given in the following sections.
3.5 Thermal boundary conditions The surface heat flux is applied on the top corner surface marked in Fig. 3 and modeled as an asymmetric Gaussian distribution expressed as Eq. (7).
If xlocal 0 and y local 0 , Qarc (xlocal , y local )
x2 η arcVI y2 exp local2 local 2σ 2πσ x σ y 2σ 2y1 x1
If xlocal 0 and y local 0 , Qarc (xlocal , y local )
x2 η arcVI y2 exp local2 local 2σ 2πσ x σ y 2σ y22 x1
If xlocal 0 and y local 0 , Qarc (xlocal , y local )
2 x2 η arcVI y local exp local 2σ 2 2πσ x σ y 2σ y21 x2
2 x2 η arcVI y local exp local 2σ 2 2πσ x σ y 2σ 2y 2 x2 σ y2 ) 2
If xlocal 0 and y local 0 , Qarc (xlocal , y local ) where σ x (σ x1 σ x 2 ) 2 , σ y (σ y1
(7)
where Qarc is the surface heat flux, ηarc is the arc efficiency, V is the arc voltage, I is the welding current, σx1 is the effective radius in x’-direction for xlocal greater than zero, σx2 is the effective radius in x’-direction for xlocal smaller than zero, σy1 is the effective radius in y’-direction for ylocal greater than zero, and σy2 is the effective radius in y’-direction for ylocal smaller than zero. By using the local coordinate, the moving surface heat flux is modeled in the rotated coordinate system. The thermal energy transfer rate from the electric arc to the fluid cell can be determined with Eqs. (8)-(9).
n 'x 1 0 0 n x ' n y 0 cos α sin α n y ' 0 sin α cos α n z n z
(8)
E arc Qarc xlocal , y local , z local Atotal n'z
(9)
where (nx, ny, nz) is the unit surface normal given in the original coordinate system, (n' , n'y , n' ) is the unit x z surface normal given in the rotated coordinate system, and Atotal is the total free surface area in cell.
8
Additionally, the convection heat loss approximated by Newton’s law of cooling and the radiation heat loss estimated by the Stefan-Boltzmann law are considered for both the top and bottom corner surfaces as Eqs. (10)(11). Thus, the heat loss rate is expressed as Eq. (12).
Qconv hc T T0
Qrad σ T 4 T 04
(10)
(11)
Eloss Qconv Qrad Atotal
(12)
where Qconv is the convection heat loss, T0 is the ambient temperature, Qrad is the radiation heat loss, hc is the convection coefficient, σ is the Stefan-Boltzmann constant, and ε is the material emissivity. Therefore, the thermal energy absorption rate of the fluid cells on the top corner surface is expressed as Eq. (13).
Etop E arc -Eloss Qarc xlocal ,y local Atotal n'z -Qconv Qrad
(13)
The thermal energy loss rate of the fluid cells on the bottom corner surface is expressed as Eq. (14).
Ebot Eloss Qconv Qrad Atotal
(14)
Dhingra and Murphy (2005) stated that the total heat transfer efficiency in GMA welding ranges from 0.60 to 0.85 and this study assumes the total arc efficiency to be 0.7. The total heat transfer to the weld pool consists of the thermal energy transferred by the electric arc and that by molten droplets. The droplet efficiency and arc efficiency are determined by Eqs. (15)-(18).
f d 3rw2WFR 4rd3
qd
(15)
4 3 ππd ρC s Ts T0 Cl Td Tl f d 3
(16)
ηd qd VI
(17)
ηarc 0.7 ηd
(18)
where fd is the droplet frequency, rw is the wire radius, WFR is the wire feed rate, rd is the droplet radius, qd is the thermal energy transferred by the molten droplets, Td is the droplet temperature, and ηd is the droplet efficiency.
9
3.6 Arc pressure model This study assumes that the effective radii of arc pressure are the same as those of the surface heat flux due to the physical relationship described by Cho et al. (2013a). The arc pressure model is expressed as Eq. (19). 2 2 xlocal μ0 I 2 ylocal exp 2σ 2 2σ 2 4π 2 σ x σ y x1 y1
2 2 xlocal μ0 I 2 ylocal exp 2σ 2 2σ 2 4π 2 σ x σ y x1 y2 x2 μ I2 y2 0 , Parc(xlocal , ylocal ) 20 local exp local 2 2σ 4π σ x σ y 2σ 2y1 x2
x2 μ0 I 2 y2 local exp local 2 2 2σ 4π σ x σ y 2σ 2y 2 x2
If xlocal 0 and ylocal 0 , Parc(xlocal , ylocal ) If xlocal 0 and ylocal 0 , Parc(xlocal , ylocal ) If xlocal 0 and ylocal
If xlocal 0 and ylocal 0 , Parc(xlocal , ylocal )
(19)
where Parc is the arc pressure and µo is the permeability of vacuum. The arc pressure in a single cell is assumed to be uniform, and the total arc pressure force equals the arc pressure multiplied by the total free surface area in the cell. Subsequently, the arc pressure force vector can be determined by the unit surface normal given in the original coordinate system as Eq. (20).
Fpx nx Fpy Parc xlocal , ylocal Atotal n y F n z pz
(20)
3.7 EMF model 3.7.1 Formulation of the EMF model This study adopts the EMF model proposed by Kou and Sun (1985), which is formulated based on the magnetic field and current flow inside the material substrate. Regarding the magnetic vector, only the angular component is non-zero. The current density and the magnetic field are expressed as Eqs. (21)-(23). The EMF vector can be derived as Eqs. (24)-(26). The radial distance of the fluid cell can be calculated by Eq. (27). It should be noted that the EMF model proposed by Kou and Sun (1985) follows an axisymmetric Gaussian distribution with only one effective radius, and it is taken as the average of the four effective arc radii in this study as Eq. (28).
Jz
I sinh λc zv λJ 0 λr' exp λ 2 σ r2 2 dλ 0 2π sinh λc
10
(21)
Jr
I cosh λc zv λJ1 λr' exp λ 2 σ r2 2 dλ 0 2π sinh λc
Bθ
μm I 2π
0
λJ1 λr' exp λ 2 σ r2 2
λc z dλ sinhsinh λc v
(22)
(23)
Fex' J z Bθ xlocal r'
(24)
Fey' J z Bθ ylocal r'
(25)
Fez' J r Bθ
(26)
2 2 r' xlocal ylocal
(27)
σ r σ x1 σ x 2 σ y1 σ y 2 4
(28)
where Jr is the radial current density, Jz is the vertical current density, J0 is the Bessel function of the first kind of zero order, J1 is Bessel function of the first kind of first order, c is the plate thickness, r’ is the radial distance, zv is the vertical distance, (Fex' , Fey' , Fez' ) is the EMF vector given in the rotated coordinated system, Bθ is the angular magnetic field, σr is the effective radius of EMF model, and µm is the material permeability.
3.7.2 Calculation of the vertical distance The vertical distance of a fluid cell is essential for determining its EMF value. The vertical distance in Sun and Kou’s EMF model equals the distance from the fluid cell to the plate surface, because the model was originally developed for BOP GTA welding, where the bead height is negligible. The calculation of vertical distance is different in BOP GMA welding due to the non-negligible bead height. In previous study (Cho et al., 2013b), the distance between the fluid cell and the surface cell right above it was regarded as its vertical distance. In the case of fillet welding, the logic used to determine the vertical distance should be similar to that in BOP GMA welding. This study considers four steps to calculate the vertical distance, as explained in Fig. 4. a)
Assume one line (Line 1) that goes through a random surface cell A, and is parallel to the z’-axis.
b) Assume another line (Line 2) that goes through the current cell, and is also parallel to the z’-axis. c)
The distance d between Line 1 and Line 2 can be calculated.
11
d) Find the surface cell B that derives the smallest d. The distance between the current cell and surface cell B is approximated as the vertical distance. This study assumes that the current cell and surface cell B are in the same y’-z’ plane for the purpose of reducing calculation efforts.
3.7.3 Redefinition of material thickness In fillet welding, the current is initially released from the V-shaped joint surface, and then flows perpendicularly into the steel plates (Cho et al., 2013d). Because the material thickness is crucial to calculating the EMF, this study redefines the material thickness by following five steps, described as follows: a)
Output the data from the FLOW-3D software package and determine the leg lengths on both the vertical
and horizontal plates on any transverse cross sections so that Point C can be confirmed. b) As shown in Fig. 5(a), the vertical plate is divided into 21 segments with respect to Point C and Point B20. For the cells within Triangle CEiEi+1, the material thickness is approximated as the length of Line BiEi, where 0 ≤ i ≤ 19. c)
As shown in Fig. 5(b), the horizontal plate is divided into 21 segments with respect to Point C and Point A20.
For the cells within Triangle CDiDi+1, the material thickness is approximated as the length of Line AiDi, where 0 ≤ i ≤ 19. d) For the cells in the remaining part of the fillet joint, the material thickness is defined as the plate thickness.
3.7.4 Conversion of the calculated EMF vector By using the local coordinate, the resultant EMF vector is given in the rotated coordinate system. For this reason, the EMF vector should be converted into the original coordinate system before being input into the FLOW-3D software package as in Eq. (29). ' Fex 1 0 0 Fex ' Fey 0 cos α sin α Fey F 0 sin α cos α F ' ez ez
(29)
where (Fex, Fey, Fez) is the EMF vector given in the original coordinated system.
12
3.8 Drag force model Drag force is a shear force induced by the plasma jet flow that impinges on the molten pool surface. It is independent of the effective arc radii and drives the fluid outward from the arc center in a radial direction. In this study, the analytical solutions of the wall shear stress for a circular jet impingement predicted by Phares et al. (2000) were adopted to estimate the drag force. Since only the universal functions for several integer H/D ratios are available in the reference paper, the ones needed for this study were fitted. The calculation of other terms in the drag force model, including the Reynolds number and the initial velocity of the arc plasma, are the same as in the previous study (Cho et al., 2006). The empirical equation is expressed as Eq. (30).
H r' τ ρ u g 2 Re10/ 2 D H
2
2 p 0
(30)
where τ is the shear stress, ρp is the density of arc plasma, µ0 is the initial velocity of arc plasma, Re0 is the Reynolds number, H is the nozzle height taken as the arc length, D is the nozzle diameter taken as the electrode diameter, and g2 is the universal function. With the radial distance calculated using the local coordinate, the resultant drag force vector is given in the rotated coordinate system as Eqs. (31)-(33), and Eq. (34) is employed to convert it into the original coordinate system.
Fdx' τAtotal n'z xlocal r'
(31)
Fdy' τAtotal n'z ylocal r'
(32)
Fdz' 0
(33)
' Fdx 1 0 0 Fdx ' Fdy 0 cos α sin α Fdy F 0 sin α cos α F ' dz dz
(34)
where (Fdx' , Fdy' , Fdz' ) is the drag force vector given in the rotated coordinated system and (Fdx, Fdy, Fdz) is the drag force vector given in the original coordinated system.
3.9 Other models In this study, the other arc models, such as surface tension and buoyancy force, are the same as those used in the previous study (Han et al., 2013).
13
4. Result and discussion 4.1 Arc behavior Fig. 6 presents the representative arc images captured in the experiments with different welding speeds. The molten droplets transfer into the molten pool in a stable spray transfer mode when the welding speed is as low as 0.4 cm/s. The droplet transfer mode switches to a transition mode between a spray transfer mode and a globular transfer mode as the welding speed increases with temporal fluctuation of current and voltage signals. It should be noted that the simulation model in this study is limited to spray transfer mode. For this reason, the arc behaviors during spray transfer mode are selected to simulate Case 2 and Case 3. The arc lengths in Cases 13 are similar to each other, and are measured to be 0.54 cm, 0.51 cm and 0.55 cm, respectively. On the other hand, angle α fluctuates slightly with the increase in welding speed, whereas angle β greatly increases. Fig. 7 presents arc images captured in the experiments with different wire feed rates. The molten droplets transfer onto the vertical plate in Case 2, the corner in Case 4 and the horizontal plate in Case 5, respectively. To simulate this phenomenon, the starting points of welding in Eq. (6) for Case 2, Case 4 and Case 5 were set to be (0, 0, 0.06), (0, 0, 0) and (0, 0.1, 0) respectively. The arc lengths in Case 2, 4 and 5 decrease with the increase in wire feed rate, and are measured to be 0.51 cm, 0.43 cm and 0.35 cm, respectively. Angle α fluctuates slightly with the increase in wire feed rate, whereas angle β greatly decreases. This is probably because the arc length becomes shorter when the wire feed rate is higher, and it makes the arc stiffness greater. As mentioned in the previous paragraph, the molten droplets transfer into the molten pool in a transition mode in Case 2. The stability of droplet transfer is greatly improved as the wire feed rate increases, and the droplets transfer into the molten pool in a stable spray transfer mode in Case 4 and Case 5. In a nutshell, it is easier to produce a stable spray transfer mode with low welding speed and high wire feed rate in horizontal fillet welding.
4.2 Droplet generation Droplet temperature, radius, frequency, initial position and velocity are needed for droplet generation in the simulation. The droplet temperature was set to be 2400 K (Cho et al., 2013b), the droplet radius was measured from the front arc images, and the calculation of droplet frequency has been discussed in Section 3.5. In the simulation, molten droplets are generated at the arc center above the molten pool surface. For this reason, they should be assigned the velocity just before impingement. This study measures the 2D impingement velocity Vyz from the front arc images to approximate the 3D impingement velocity. The arc image where the droplet is
14
about to impinge the molten pool surface and the one before it are selected. The 2D impingement velocity Vyz can be found by dividing the traveling distance measured from these two arc images over their time difference. Subsequently, the 3D droplet impingement velocity can be approximated by Eqs. (35)-(38).
Vdz V yz2 1 tan α
(35)
Vdx Vz tan β
(36)
Vdy Vz tan α
(37)
Vd Vdx2 Vdy2 Vdz2
(38)
2
where (Vdx, Vdy, Vdz) is the droplet impingement velocity vector and Vd is the magnitude of the droplet impingement velocity. The approximated impingement velocities for Cases 1-5 are listed in Table 4. As can be seen from Fig. 6, the distance from the position where the droplets are created to the molten pool surface is too short to be measured in Case 4 and Case 5 so that it becomes impossible to estimate the droplet impingement velocity with the method described above. Lin et al. (2001) found a positive correlation between the droplet velocity and the welding current. Based on this information, the impingement velocity magnitudes of Case 4 and Case 5 were calculated to be 111.8 cm/s and 166.4 cm/s respectively.
4.3 Modeling the surface heat flux and arc pressure Fig. 8 shows the modeling procedure for the surface heat flux and arc pressure. The Abel inversion technique and Fowler-Milne method were combined to calculate the effective arc radii. Due to the complex Vshape of fillet joint and the inclination of the torch, four effective arc radii are measured from the front and side arc images. It should be noted that the dotted lines in Fig. 8 used to extract the light intensity distribution are not straight lines because of the presence of pre-flow. Five steps were taken, explained as follows. a)
The light intensity distribution was obtained along the dotted line, which was 0.1 mm above the plate
surface or fluid surface in the arc images. b) The emissivity distribution was calculated with the Abel inversion technique. c)
The calculated emissivity distribution was processed with the Fowler-Milne method to calculate the arc
temperature distribution.
15
d) Gaussian fitting was performed for the arc temperature distribution data, to derive the effective arc radii; the resultant values are listed in Table 5. e)
The asymmetric surface heat flux and arc pressure were modeled with the four effective arc radii.
4.4 EMF results 4.4.1 Calculated radial distance, vertical distance, material thickness distributions As explained in Section 3.7, the radial distance, vertical distance and material thickness are essential to determining the EMF of a fluid cell. The calculation of radial distance can be simply done using Eq. (27). Fig. 9(a) presents the calculated radial distance distribution on the transverse cross section at the arc axis. The radial distance equals zero at the arc axis and reaches its maximum at the locations farthest away from arc axis. Fig. 9(b) displays the calculated vertical distance distribution on an arbitrary transverse cross section. The vertical distance equals zero at the molten pool surface and reaches its maximum at the bottom. Fig. 9(c) shows the calculated material thickness distribution on an arbitrary transverse cross section. The material thickness becomes larger as the cell gets closer to the arc axis. The calculated radial distance and vertical distance distributions are consistent with their respective physical meanings, and the calculated material thickness distribution also follows its definition, as introduced in Section 3.7.3.
4.4.2 Analysis of EMF EMF is caused by the current flow and magnetic field inside the material substrate. The direction of the magnetic vector can be confirmed by Ampere's right-hand screw rule, and that of EMF can be determined by the left-hand rule. As a result, the direction of radial EMF is toward the arc center in the radial direction and that of vertical EMF is downward along the direction parallel to the arc axis. Fig. 10 shows the 3D and 2D radial EMF distributions in the weld pool. The radial EMF mainly concentrates on the molten pool surface. The radial EMF is decomposed into two components, namely the x'EMF and y'-EMF, to input into the software. Fig. 11 shows the 3D and 2D x'-EMF distributions. The x'- EMF is positive behind the arc center and negative ahead of the arc center so that it drives the fluid behind the arc center forward in the welding direction, and the fluid ahead of the arc center is driven backward against the welding direction.
16
Fig. 12 presents the 3D and 2D y'-EMF distributions. The y'-EMF is positive on the left side and negative on the right side so that it drives the fluid on the left side to the right and that on the right side to the left. Therefore, the fluid is driven towards the arc center in the radial direction by the x'-EMF and y'-EMF, which is the same direction as the radial EMF mentioned in the previous paragraph. Fig. 13 displays the 3D and 2D vertical EMF distributions. The vertical EMF also concentrates on the molten pool surface, and its negative value indicates that it drives the fluid downward along the direction parallel to the arc axis. The direction is also the same as that of the vertical EMF mentioned in the previous paragraph. Therefore, it can be concluded with confidence that the calculated EMF vector follows its physical meaning.
4. 5 Fluid flow analysis Cases 1-3 were performed to investigate the influence of welding speed on molten pool behaviors. Fig. 14 shows the temperature profile and streamlines on the transverse cross section at x=1.013 cm in Case 1. Before droplet impingement as in Fig. 14(a), the arc is away from this location, and the fluid is mainly driven by the surface tension gradient force. The fluid flows outward from the arc center, and this kind of flow pattern makes the molten pool wide and shallow. When the arc arrives, as in Fig. 14(b)-(c), the influence of droplet impingement, EMF and arc pressure becomes dominant. The molten droplets, carrying a large amount of thermal energy and momentum, continually impinge on the molten pool surface. That fluid, which has already absorbed a great quantity of thermal energy from the arc on the free surface, and the fluid inside the molten pool flows downward along the direction parallel to the arc axis, striking the bottom of the molten pool and making the penetration deeper. Subsequently, the fluid travels away from the center of the bottom, which then meets and totally reduces that driven by surface tension gradient force. After the arc leaves, as in Fig. 14(d), the fluid in the molten pool flows upward. Fig. 15 presents the temperature profile and streamlines on the transverse cross section at x=1.013 cm in Case 2, and they are quite similar to those in Case 1. The only difference occurs during the droplet impingement period. The outward flow by surface tension gradient force is not totally reduced because of the reduced influence of droplet impingement, EMF and arc pressure due to the increase in welding speed. On the other hand, the molten pool behaviors on the transverse cross section in Case 3 are almost the same as those in Case 2. Fig.16 shows the temperature profile and streamlines on the longitudinal cross sections at y=0.06 cm in Cases 1-3. The length of the molten pool decreases with the increase in welding speed because less thermal
17
energy accumulates in the molten pool as the welding speed increases. In Case 1, the fluid in the rear part of the molten pool is driven to the right side while that in the top part flows in a counterclockwise direction because of the surface tension gradient force. At the same time, the fluid in the front part flows backward due to droplet impingement, EMF and arc pressure. In Case 2, the backward fluid flows in a clockwise direction due to the dominance of droplet impingement, EMF and arc pressure. The different fluid flow patterns in Cases 1 and 2 result from the fact that the thermal energy accumulated in the molten pool is reduced due to the increase in welding speed, and the temperature gradient becomes smaller, so that the influence of surface tension gradient force becomes weaker. The longitudinal molten pool behaviors in Case 3 show similar characteristics as those in Case 2. Cases 2, 4 and 5 were performed to study the influence of wire feed rate on molten pool behaviors. Regarding the molten pool behaviors on the transverse cross sections in Cases 4 and 5, they are almost same as those in Case 2. Fig.17 shows the temperature profile and streamlines on the longitudinal cross sections at y=0.06 cm in Cases 2, 4 and 5. The length of the molten pool increases with the increase in wire feed rate because more momentum and molten metal are transferred into the molten pool. In the longitudinal cross section view of Case 2, a large portion of the molten pool is affected by droplet impingement, EMF and arc pressure because the molten pool is short in size. However, a relatively smaller portion of the molten pool is observed to be affected probably due to the longer length of the molten pool and the different droplet impingement positions as displayed in the front views in Fig. 7. In Case 5, only the forefront part of the molten pool is affected by droplet impingement, EMF and arc pressure, whereas the rear part is dominated by surface tension gradient force.
4.6 Comparisons of experimental and simulation results Fig. 18(a)-(c) shows the comparisons of the experimental and simulation results for different welding speeds. The leg length, penetration and actual throat decrease with the increase in welding speed. Moreover, undercut occurs on the vertical plate when the welding speed is as high as 1.0 cm/s. Fig. 18(b), (d) and (e) shows comparisons of the experimental and simulation results for different wire feed rates. A higher wire feed rate results in a deeper penetration because of the greater droplet impingement velocity, arc pressure and EMF due to the higher welding current. The simulated fusion zone geometries for Cases 1, 4 and 5 are in fair agreement with the experimental results, whereas those for Cases 2 and 3 are inconsistent with the experimental ones. This is
18
probably because the arc behaviors in Case 2 and 3 are unstable, and this study only selects the arc behaviors during the spray transfer mode for simulation. For the quantitative analysis of the simulation model, the leg length and actual throat of the experimental and simulation results are compared, as shown in Fig. 19. It should be noted that the experimental data in Fig. 19(a) are average values. As shown in Fig. 19(b), the cross section views of Case 1 at different longitudinal locations in a single experiment are almost same with each other, whereas those of Case 2 and Case 3 are observed to be different. Regarding Case 2 and Case 3, different cross section views are also observed when the experiments are repeated, as can been seen by comparing the cross section views in Fig. 18 and Fig. 19(b). This may have been induced by the unstable arc behaviors observed in Case 2 and Case 3, and it is difficult to repeat the experiments when the arc behaviors are unstable. In addition, the difference between the experimental and simulation results may also have been induced by the following aspects: a)
The difficulty in measuring the effective arc radii. Theoretically, the light intensity distribution 0.1 mm
above the plate surface or fluid surface in the arc images should be extracted for Abel inversion. However, it is impossible to take a line that exactly follows this criterion in real practice because of the extremely irregular shape of the molten pool. b) The arc models are assumed to be different shapes. The surface heat flux and arc pressure are modeled as asymmetric Gaussian distributions because of the four mutually different effective arc radii measured from the arc images. However, the EMF follows an axisymmetric Gaussian distribution, and this study takes the average of the four radii as its effective radius. c)
A constant total arc efficiency of 0.7 is assumed for all cases. Stenbacka (2013) reported that the total arc
efficiency was reduced with an increase in arc length. The arc lengths in the five cases are mutually different so that fixing the total arc efficiency as 0.7 may not be appropriate.
19
5. Conclusions This study systematically presented a method to formulate arc models, based on coordinate rotation, for CFD simulations of GMA welding of horizontal fillet joints. Welding experiments with different welding speeds and wire feed rates were performed to validate the simulation models. This work can be summarized as follows: a)
Surface heat flux and arc pressure were modeled as asymmetric Gaussian distributions. The four effective
arc radii were determined from arc images captured by a CCD camera by applying both the Abel inversion technique and Fowler-Milne method, whereas the EMF was modeled as an axisymmetric Gaussian distribution with its effective radius being the mean of the four effective arc radii. b) The arc models, including the surface heat flux, EMF, arc pressure and drag force, were formulated in the rotated coordinate system. The calculated scalars were directly input into the FLOW-3D software package, whereas the calculated vectors were converted into the original coordinate system. This calculation method was verified by comparing the experimental and simulation results. c)
The leg length, penetration and actual throat decreased with an increase in the welding speed. A higher
welding speed made the arc behaviors less stable and may induce undercut on the vertical plate, whereas a higher wire feed rate enhanced the stability of arc behaviors and produced a deeper penetration. d) The weld pool was widened by the outward flow resulting from the surface tension gradient force, and was deepened by the downward flow along the direction parallel to the arc axis by droplet impingement, EMF and arc pressure. The outward flow due to surface tension force was totally reduced when the welding speed was as low as 0.4 cm/s, but partially reduced when the welding speed was increased. On the other hand, the length of the molten pool decreased with the increase in welding speed but increased with the increase in wire feed rate.
Acknowledgements The authors gratefully acknowledge the support of the Brain Korea 21 and Mid-career Researcher Program through NRF of Korea (Grant No. 2013R1A2A1A01015605).
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References Cao, Z., Yang, Z., Chen, X. L., 2004. Three-dimensional simulation of transient GMA weld pool with free surface. Welding Journal (Miami, Fla) 83(6): 169s-176s. Cho, D.W., Lee, S.H., Na. S.J., 2013a. Characterization of welding arc and weld pool formation in vacuum gas hollow tungsten arc welding. Journal of Materials Processing Technology 213(2): 143-152. Cho, D. W., Na, S.J., Cho, M.H., Lee, J.S., 2013b. A study on V-groove GMAW for various welding positions. Journal of Materials Processing Technology 213(9): 1640-1652. Cho, D.W., Na, S.J, Cho, M.H, Lee, J.S., 2013d. Simulations of weld pool dynamics in V-groove GTA and GMA welding. Welding in the World 57(2): 223-233. Cho, D.W., Song, W.H., Cho, M.H, Na, S.J., 2013c. Analysis of submerged arc welding process by threedimensional computational fluid dynamics simulations. Journal of Materials Processing Technology 213(12): 2278-2291. Cho, M. H., Lim, Y.C., Farson, D.F., 2006. Simulation of weld pool dynamics in the stationary pulsed gas metal arc welding process and final weld shape. Welding Journal (Miami, Fla) 85(12): 271s-283s. Cho, W.I., Na, S.J., Cho, M.H., Lee, J.S., 2010. Numerical study of alloying element distribution in CO2 laser– GMA hybrid welding. Computational Materials Science 49(4): 792-800. Dhingra, A., Murphy, C., 2005. Numerical simulation of welding-induced distortion in thin-walled structures. Science and Technology of Welding & Joining 10(5): 528-536. Han, S.W., Cho, W.H., Na, S.J., Kim, C.H., 2013. Influence of driving forces on weld pool dynamics in GTA and laser welding. Welding in the World 57(2): 257-264. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of computational physics 39(1): 201-225. Jeong, S.K., Cho, H.S., 1997. An analytical solution to predict the transient temperature distribution in fillet arc welds. Welding Journal (Miami, Fla) 76(12): 223s. Karadeniz, E., Ozsarac, U., Yildiz, C., 2007. The effect of process parameters on penetration in gas metal arc welding processes. Materials & Design 28(2): 649-656. Kim, C.H., Zhang, W., Debroy, T., 2003. Modeling of temperature field and solidified surface profile during gas–metal arc fillet welding. Journal of Applied Physics 94(4): 2667.
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Kou, S., Sun, D., 1985. Fluid flow and weld penetration in stationary arc welds. Metallurgical Transactions A 16(2): 203-213. Lin, Q., Li, X., Simpson, S.W., 2001. Metal transfer measurements in gas metal arc welding. Journal of Physics D: Applied Physics 34(3): 347. Nichols, B., Hirt, C., 1975. Methods for calculating multi-dimensional, transient, free surface flows past bodies. Proc., 1st Int. Conf. Ship Hydrodynamics, DTIC Document. Phares, D. J., Smedley, G.T., Flagan, R.C., 2000. The wall shear stress produced by the normal impingement of a jet on a flat surface. Journal of Fluid Mechanics 418: 351-375. Stenbacka, N., 2013. On arc efficiency in gas tungsten arc welding. Soldagem & Inspeção 18(4): 380-390. Zhang, W., Kim, C.H., Debroy, T., 2004. Heat and fluid flow in complex joints during gas metal arc welding— Part I: Numerical model of fillet welding. Journal of Applied Physics 95(9): 5210.
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List of Figures
Fig. 1. Experimental setup of GMA welding for horizontal fillet welding.
Fig. 2. Schematic sketch of horizontal fillet joint.
23
Fig. 3. Schematic sketch of the top and bottom corner surfaces of the fillet joint.
Fig. 4. Determination of the vertical distance in fillet welding.
Fig. 5. Redefinition of the material thickness.
24
Fig. 6. Arc images captured in the experiments with different welding speeds.
Fig. 7. Arc images captured in the experiments with different wire feed rates.
25
Fig. 8. Modeling procedure of the surface heat flux and arc pressure.
26
Fig. 9. Calculated radial distance, vertical distance and material thickness distributions.
Fig. 10. 3D and 2D radial EMF distributions.
27
Fig. 11. 3D and 2D x'- EMF distributions.
Fig. 12. 3D and 2D y'-EMF distributions.
28
Fig. 13. 3D and 2D vertical EMF distributions.
29
Fig. 14. Temperature profile and streamlines on the transverse cross section at x=1.013 cm in Case 1.
30
Fig. 15. Temperature profile and streamlines on the transverse cross section at x=1.013 cm in Case 2.
31
Fig. 16. Temperature profile and streamlines on the longitudinal cross sections at y=0.06 cm in Cases 1-3.
32
Fig. 17. Temperature profile and streamlines on the longitudinal cross sections at y=0.06 cm in Cases 2, 4 and 5.
33
Fig. 18. Comparisons of the experimental and simulation results for Cases 1-5.
34
Fig. 19. a) Quantitative comparisons of the experimental (averaged value) and simulation results for Cases 1-5, (b) experimental cross section views of repeated experiments for Cases 1-3.
35
Table 1 Welding parameters used in the experiments. Voltage Current Welding speed [V] [A] [cm/s]
WFR [m/min]
Case 1
25.8
255.4
0.4
7.5
Case 2
25.4
249.0
0.7
7.5
Case 3
25.6
258.5
1.0
7.5
Case 4
25.8
266.3
0.7
8.5
Case 5
26.2
298.8
0.7
9.5
Table 2 Chemical composition of ASTM AH36 steel and SM70 solid wire. Chemical composition C Si Mn P S Cr Ni wt. %
Cu
Nb
Ti
V
Al
AH36
0.157
0.392
1.501
0.014
0.003
0.03
0.01
0.015
0
0.003
0.003
0.042
SM70
0.07
0.83
1.48
0.017
0.02
-
-
-
-
-
-
-
Table 3 Material properties of ASTM AH36 steel. Properties
Value
Density of solid
7.86 g/cm3
Density of liquid
6.90 g/cm3
Latent heat of fusion
2.47×109 erg/g s
Thermal conductivity of solid
2.60×106 erg/cm s K
Thermal conductivity of liquid
3.30×106 erg/cm s K
Specific heat of solid
4.70×106 erg/g s K
Specific heat of liquid
6.97×106 erg/g s K
Viscosity
0.06 g/cm s
Heat transfer coefficient
105 erg/cm2 s K
Surface tension coefficient
1870 dyne/ cm
Surface tension gradient
-0.35 dyne/cm K
Liquidus temperature
1791 K
Solidus temperature
1688 K
Emissivity
0.2
Coefficient of thermal expansion
1.20×10-5 cm/cm K
Permeability of vacuum
1.20×106 H/m
Material permeability
1.20×106 H/m
36
Table 4 Droplet velocities measured in Cases 1-5. Vd [cm/s]
Vdx [cm/s]
Vdy [cm/s]
Vdz [cm/s]
Case 1
98.7
-20.2
-79.1
-55.4
Case 2
96.3
-34.3
-75.5
-49.0
Case 3
89.0
-33.2
-67.7
-47.4
Case 4
111.8
-27.5
-90.9
-59.0
Case 5
166.4
-32.4
-136.9
-88.9
Table 5 Effective arc radii measured in Cases 1-5. σx1 [cm] σx2 [cm] σy1 [cm] σy2 [cm] Case 1
0.176
0.168
0.091
0.123
Case 2
0.160
0.146
0.104
0.107
Case 3
0.153
0.142
0.130
0.148
Case 4
0.162
0.148
0.096
0.160
Case 5
0.153
0.137
0.092
0.143
37