fig. 1ymzhang/papers/2005 england.pdfusing the model, the whole gas tungsten arc welding (gtaw)...

Modelling the transient behaviours ofa fully penetrated gas–tungsten arcweld pool with surface deformationP C Zhao1, C S Wu1*, and Y M Zhang2

1Institute of Materials Joining, MOE Key Laboratory for Liquid Structure and Heredity of Materials, Shandong

University, Jinan, People’s Republic of China2Centre for Manufacturing and Department of Electrical and Computer Engineering, University of Kentucky,

Lexington, Kentucky, USA

The MS was received on 30 December 2003 and was accepted after revision for publication on 2 September 2004.

DOI: 10.1243/095440505X8073

Abstract: Numerical analysis of the dynamic behaviours of a gas–tungsten arc (GTA) weld poolwith full penetration is of great significance to designing the process control algorithm. In thispaper, a three-dimensional transient numerical model is developed to investigate the dynamicbehaviours of a fully penetrated GTA weld pool with surface deformation. A body-fittedcoordinate system is used to transform the complex physical boundaries resulted from thesurface deformation into regular boundaries. A separated algorithm is employed to solve thestrongly coupling problems between the surface deformation, fluid flow, and heat transfer. Byusing the model, the whole gas–tungsten arc welding (GTAW) process (including arc ignition,weld pool formation and growth, penetration, quasi-steady state, and arc extinguishments) aresimulated, and the transient development of a three-dimensional weld pool shape and fluidflow inside the pool are obtained. The predicted weld geometry matches the experimentalresults. It provides useful basic data for the development of sensing and control systems of GTAW.

Keywords: transient behaviours, weld pool, full penetration, surface deformation, numericalsimulation

1 INTRODUCTION

Gas–tungsten arc welding (GTAW) has become indis-pensable as a tool for many industries because of thehigh-quality welds produced and the basic role ofmaterials joining in manufacturing industry. Thisprocess is typically used for critical and accurate join-ing where the weld quality must be ensured, such asfor the root pass and for the welding of advancedmaterials, thin and ultra-thin section materials, andpressure vessels, because of its capability in precisioncontrol of the welding fusion process [1]. Accuratewelding and production of quality welds will involvea complex operation. Typical practice is first toselect and design the welding process, welding

parameters, fixture, joint geometry, etc., based onmaterials used and the specified requirements.However, for GTAW, simply following the establishedprocedure is not adequate because normally 100 percent of full penetration must be ensured withoutburn-through or over-penetration which damagesmaterials properties. To this end, automated sensingand control of GTAW process must be realized [2].The design of the control algorithm requires thatthe underlying process be described using a dynamicmodel such as a transfer function. However, thewelding process is an extremely complex process inwhich different types of phenomenon occur in acoupled way. Thus, numerical analysis for modellingthe dynamic behaviour of the GTAW process is ofgreat significance to designing the process controlalgorithm.

Although there have been significant advancesin the numerical simulation of the GTAW process[3–5], most studies have entailed general simulation

99

B24203 # IMechE 2005 Proc. IMechE Vol. 219 Part B: J. Engineering Manufacture

*Corresponding author: Institute of Materials Joining, MOE Key

Laboratory for Liquid Structure and Heredity of Materials,

Shandong University, 73 Jingshi Road, Jinan 250061, People’s

Republic of China; email: [email protected]

of the process under constant welding parametersand a quasi-steady state, and little attention hasbeen paid to the transient dynamics of the weldpool. Zacharia et al. developed a three-dimensionaltransient model for the arc welding process [6], butit either was only concerned with partial penetrationor did not consider the weld pool surface deformationin the full penetration. Wu and Yan conductednumerical simulation of transient development anddecrease in the gas–tungsten arc (GTA) weld pool,but they assumed flat surfaces at both the front andthe back sides of the weld pool [7]. In fact, the weldpool surfaces at both the front and the back sidesare depressed under the condition of full penetration,and the amplitude of this depression could beconsidered to reflect the penetration extent. Fordynamic control, models are required to reveal howthe process variables (weld pool geometry and sur-face depression) change with the welding parameters(welding current and velocity). In this paper, anumerical model is developed to describe the transi-ent behaviour of a three-dimensional GTA weld poolwith full penetration and surface deformation.

2 FORMULATION

2.1 Surface deformation

The weld pool surface is deformed under the action ofthe arc pressure, surface tension, gravity, and so on.When full penetration is established, pool surfacesat both the top and the bottom are deformed. Asshown in Fig. 1, the functions Ztop ¼ ’ðx‚ yÞ andZbottom ¼ ðx‚ yÞ are used to describe the configura-tion of the top and bottom surfaces respectively ofthe weld pool.In the case of partial penetration [Fig. 1(a)], the

surface deformation occurs only at the top surfaceof the workpiece. The top surface of the weld pool isgoverned by the equation [8]

Parc � �g’þ C1

¼ ��ð1þ ’2yÞ’xx � 2’x’y’xy þ ð1þ ’2xÞ’yy

ð1þ ’2x þ ’2yÞ3=2ð1Þ

where Parc is the arc pressure, � is the density, g isthe gravitational acceleration, � is the surface tension,C1 is a constant, ’x ¼ q’=qx, ’xx ¼ q2’=qx2, ’xy ¼q2’=ðqx qyÞ, and so on. At the other area of the topsurface, ’ðx‚ yÞ ¼ 0. Because the total volume of theweld pool is not changed before or after the surfacedeformation, there is the constraintðð

�1

’ðx‚ yÞdx dy ¼ 0 ð2Þ

where �1 is the surface area of weld pool at the topsurface. The arc pressure can be expressed as [9, 10]

Parc ¼�0I

2

8p2�2jexp

�� r2

2�2j

�ð3Þ

where �0 is permeability in free space, I is the welding

current, �j is the current distribution parameter, and

r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx� u0tÞ2 þ y2

p, where u0 is the welding speed

and t is the time.For a fully penetrated weld pool [Fig. 1(b)], two

equations are required to describe the configurationof the top and bottom surfaces respectively, namely

Parc � �g’þ C2

¼ ��ð1þ ’2yÞ’xx � 2’x’y’xy þ ð1þ ’2xÞ’yy

ð1þ ’2x þ ’2yÞ3=2ð4aÞ

�gð þ L� ’Þ þ C2

¼ ��ð1þ 2yÞ xx � 2 x y xy þ ð1þ 2xÞ yy

ð1þ 2x þ 2yÞ3=2ð4bÞ

where L is the thickness of the workpiece,C2 is a con-stant, x ¼ q =qx, xx ¼ q2 =qx2, xy ¼ q2 =ðqx qyÞ,and so on. At the other area out of the weld pool,’ðx‚ yÞ ¼ 0 and ðx‚ yÞ ¼ 0. The total volume of theweld pool does not vary in full penetration. Thereforeðð

�1

’ðx‚ yÞdx dy ¼ðð�2

ðx‚ yÞdxdy ð5Þ

where �1 is the surface area of the weld pool at thetop surface, while �2 is the surface area of the weldpool at the bottom surface.

Fig. 1 Schematic diagram of the weld pool surface deformation

100 P C Zhao, C S Wu, and Y M Zhang

Proc. IMechE Vol. 219 Part B: J. Engineering Manufacture B24203 # IMechE 2005

C1 and C2 are the total sum of other forces that acton the weld pool surface except for arc pressure,gravity, and surface tension. In the calculation, C1 isderived from equations (1) and (2) while C2 is derivedfrom equations (4) and (5) according to

C1

ðð�1

dx dy

¼ðð�1

ð�ParcÞ dxdy

�ðð�1

�ð1þ ’2yÞ’xx � 2’x’y’xy þ ð1þ ’2xÞ’yy

ð1þ ’2x þ ’2yÞ3=2dxdy

ð6Þ

C2

�ðð�1

dx dyþðð�2

dx dy

�

¼ðð�1

ð�ParcÞ dxdy

�ðð�1

�ð1þ ’2yÞ’xx � 2’x’y’xy þ ð1þ ’2xÞ’yy

ð1þ ’2x þ ’2yÞ3=2dxdy

� �g

ðð�2

ðL� ’Þ dx dy

�ðð�2

�ð1þ 2yÞ xx � 2 x y xy þ ð1þ 2xÞ yy

ð1þ 2x þ 2yÞ3=2dx dy

ð7Þ

The iterative method is used to calculate the surfacedeformation of the weld pool. Firstly, the guessedvalues of C1 and C2 are employed. Then ’ðx‚ yÞ and ðx‚ yÞ are obtained through solving equations (1)and (4) and the improved values of C1 and C2 are

found by solving equations (6) and (7). Based on thenew values of C1 and C2, equations (1) and (4) aresolved again to obtain the improved functions’ðx‚ yÞ and ðx‚ yÞ. The above procedure is repeateduntil it meets the criterion of convergence and theconstraint conditions are satisfied. In addition, thefunctions ’ðx‚ yÞ and ðx‚ yÞ are calculated in Carte-sian coordinates.

During the transient development of the weld pool,�1 and�2, i.e. the action areas of the arc pressure andsurface tension, change with time. The volume of theweld pool varies with time, and so does the gravity.Thus, the configurations of the weld pool surfaces’ðx‚ yÞ and ðx‚ yÞ change with time until the quasi-steady state of the weld pool is achieved.

2.2 Governing equations

A schematic sketch of a typical GTAW process systemis shown in Fig. 2. In order to describe the develop-ment of the weld pool shape, surface deformation,thermal field, and fluid flow field, a time-dependentmodel is required. Therefore, it is a transient problem.

For a three-dimensional transient problem, thegoverning equations include the energy, momentum,and continuity equations. Because of the surfacedeformation, some newly added boundaries appearat both the top and the bottom surfaces, and theirpositions change with time. Therefore, the calculateddomain is no longer a perfect cube for bead-on-platewelding, which causes some boundary conditionsthat are difficult to deal with. In this study, based onthe Cartesian coordinate, the body-fitted coordinatesystem (x�‚ y�‚ z�) is introduced [Fig. 1(b)] to trans-form the deformed domain to a regular domainaccording to

x� ¼ x‚ y� ¼ y‚ z� ¼ z� ’ðx‚ yÞLþ ðx‚ yÞ � ’ðx‚ yÞ

ð8Þ

Fig. 2 Schematic diagram of the GTA process system

Modelling the transient behaviours of a fully penetrated GTA weld pool 101


Thus, the governing equations in body-fitted coor-dinate are expressed as

�Cp

�qTqt

þUqTqx

þ VqTqy

þWt

qTqz�

�

¼ qqx

�kqTqx

�þ qqy

�kqTqy

�þ S

qqz�

�kqTqz�

�

þ kCT ð9Þ

�

�qUqt

þUqUqx

þ VqUqy

þW1

qUqz�

�

¼ ��qPqx

þ qPqz�

qz�

qx

�þ �

�q2Uqx2

þ q2Uqy2

þ Sq2Uqz�2

�

þ CU þ Fx ð10aÞ

�

�qVqt

þUqVqx

þ VqVqy

þW1

qVqz�

�

¼ ��qPqy

þ qPqz�

qz�

qy

�þ �

�q2Vqx2

þ q2Vqy2

þ Sq2Vqz�2

�

þ CV þ Fy ð10bÞ

�

�qWqt

þUqWqx

þ VqWqy

þW1

qWqz�

�

¼ � qPqz�

qz�

qxþ �

�q2Wqx2

þ q2Wqy2

þ Sq2Wqz�2

�

þ CW þ Fz ð10cÞ

qUqx

þ qVqy

þ qWqz�

qz�

qzþ Cm ¼ 0 ð11Þ

where T is the temperature, U, V , and W are thethree components of velocity in the x, y, and z direc-tions respectively, t is the time, � is the density, Cp isthe specific heat, k is the thermal conductivity, P isthe pressure in the liquid, L is the thickness of theworkpiece, Fx, Fy, and Fz are the components ofbody forces in the x, y, and z directions respectively,and � is the dynamic viscosity of liquid metal. Someterms in governing equations are defined as

Wt ¼ Uqz�

qxþ V

qz�

qyþW

qz�qz

� k

�Cp

�q2z�

qx2þ q2z�

qy2þ q2z�

qz2

�ð12aÞ

W1 ¼ Uqz�

qxþ V

qz�

qyþW

qz�

qz

� �

�

�q2z�

qx2þ q2z�

qy2þ q2z�

qz2

�ð12bÞ

S ¼�qz�

qx

�2þ�qz�

qy

�2þ�qz�

qz

�2ð12cÞ

CT ¼ 2�

q2Tqz� qx

qz�

qxþ q2Tqz� qy

qz�

qy

�ð12dÞ

CU ¼ 2��

q2Uqz� qx

qz�

qxþ q2Uqz� qy

qz�

qy

�ð12eÞ

CV ¼ 2��

q2Vqz� qx

qz�

qxþ q2Vqz� qy

qz�

qy

�ð12fÞ

CW ¼ 2��

q2Wqz� qx

qz�

qxþ q2Wqz� qy

qz�

qy

�ð12gÞ

Cm ¼ qUqz�

qz�

qxþ qVqz�

qz�

qyð12hÞ

where qz�=qx, qz�=qy, and qz�=qz can be obtainedfrom equation (8).

Although using the body-fitted coordinates cancompletely avoid the newly added boundaries result-ing from the surface deformation, the governingequations in the body-fitted coordinate system arequite complex, which causes many difficulties in thediscretization of governing equations. Some specialtechniques are employed to overcome these difficul-ties.

2.3 Boundary conditions

Owing to the energy transferred from the arc (qarc) tothe workpiece, the weld pool forms and grows subse-quently. At the same time, some energy is transferredinto the solid metal out of the weld pool, and some islost into the ambient medium by radiation (qrad) andconvection (qconv). Also evaporation (qevap) occurs atthe surface of the weld pool.

The net heat transfer input at the top surface is

q ¼ qarc � qconv � qrad � qevap ð13ÞAt the symmetric surface, both sides have no net heatsurplus. Therefore

qTqy

¼ 0 ð14Þ

At all other surfaces, there are only convection, radia-tion, and evaporation losses. Thus,

q ¼ �qconv � qrad � qevap ð15Þ

For the heat source, an elliptical thermal flux distri-bution was used in this study, which can be written asfollows [11]: when x � u0t 5 0

qarcðx‚ yÞ ¼6EI

paðb1 þ b2Þexp

�� 3ðx� u0tÞ2

b21

�

� exp�� 3y

2

a2

�ð16aÞ



and, when x� u0t < 0

qarcðx‚ yÞ ¼6EI

paðb1 þ b2Þexp

�� 3ðx� u0tÞ2

b22

�

� exp�� 3y

2

a2

�ð16bÞ

where is the efficiency of the arc power, E is the arcvoltage, I is the welding arc current, and b1, b2, and aare the parameters related to the welding process.The constraint

aðb1 þ b2Þ ¼ 12�2q ð17Þ

exists where �q is the characteristic radius of the archeat flux. In this research, a ¼ 1:87�q, b1 ¼ 2:51�q,and b2 ¼ 3:91�q.The heat loss includes convection, radiation, and

evaporation losses. They are in the forms [12]

qconv ¼ hcðT � T0Þ ð18aÞ

qrad ¼ �"ðT4 � T40 Þ ð18bÞ

qevap ¼ WvHv ð18cÞ

where hc is the convective heat-transfer coefficient,T is the temperature of the workpiece, T0 is theambient temperature, � is the Stefan–Boltzmannconstant, " is the radiation emissivity, Wv is theliquid-metal evaporation rate, and Hv is the latentheat of evaporation. For the materials SS304, anapproximate equation for Wv in equation (18c) [13,14] is given by

logWv ¼ 2:52þ�6:121� 18 836

T

�� 0:5 logT

ð19Þ

The required boundary conditions for the solutionof equation (10) are

�qUqz�

qz�

qz¼ � q�

qTqTqx

�qVqz�

qz�

qz¼ � q�

qTqTqy

‚ at z� ¼ 0‚ z� ¼ 1 ð20Þ

where � is the surface tension of liquid metal, and

V ¼ 0‚ qUqy

¼ 0‚ qVqy

¼ 0‚ at y ¼ 0 ð21Þ

U ¼ 0‚ V ¼ 0‚ W ¼ 0‚ at other boundaries

ð22Þ

The components of the body forces, Fx, Fy, and Fz,may be obtained from reference [15].

2.4 Numerical method

An implicit control volume-based finite differencemethod combined with the SIMPLEC algorithm [16,17] is used for the solution of equations (9) to (11).A special grid system is utilized for discretization ofthe welding domain. A uniform grid is used in the zdirection because of the thin plate, while grids ofvariable spacing are used in the x direction and ydirection, i.e. finer spacing near the heat sourcebecause of the higher temperature and velocitygradients, and coarser away from it. The governingequations with the boundary conditions are trans-formed into finite difference equations. To deal withthe boundary conditions conveniently, the so-called‘inner grid node’ method is employed to discretizethe welding domain; i.e. the nodes are located atthe centre of the control volumes, and grid linesconstitute the faces of the control volumes. The‘staggered grid’ where the velocity components U,V , and W are calculated for the points that lie onthe faces of the control volumes for temperature Tand pressure P is required for numerical stability influid flow calculations. The additional source termmethod [18] is applied to process the boundaryconditions.

The calculation of the fluid flow field has to bemade first in order to solve the thermal energyequation. The velocity components are governed bythe momentum equations. Since the pressuregradient forms a term for a momentum equation,and there is no obvious equation for obtainingpressure, the difficulty in the calculation of thevelocity field lies in the unknown pressure field. Thepressure field is indirectly specified via the continuityequation. When the correct pressure field is substi-tuted into the momentum equation, the resultingfield satisfies the continuity equation. The SIMPLECalgorithm converts the indirect information in thecontinuity equation into direct information for thecalculation of pressure [16, 17]. The alternative direc-tion iteration method [19] is used in the solutions ofdiscretized equations, and so the time step mustsatisfy the criterion

k

�Cp

dt�1

dx2þ 1

dy2þ 1

dy2

�4 1:5 ð23Þ

where dt is the time step, and dx, dy, and dz are thespacing of grid along the x, y, and z directions respec-tively. In this study, the time step is 0.001 s.

In order to implement the calculations men-tioned above, the computer program is designedand debugged. As mentioned above, since thesurface deformation of the weld pool and theintroduction of the body-fitted coordinate system,the calculation of heat and fluid flow fields intransient state are much more complex than in



steady and quasi-steady conditions. A separatedalgorithm is employed to solve the surface defor-mation, fluid flow, and heat transfer in transientconditions; i.e. these three problems are calculatedseparately and improved in turn. In this way thestrongly coupling problems between the surfacedeformation, fluid flow, and heat transfer aresolved successfully. The code is written as a modu-lar structure. The whole calculation procedure con-sists of the following main steps:

(a) performing domain discretization and gridsystem formation;

(b) calculating the temperature distribution based onthe initial conditions;

(c) determining the three-dimensional weld poolgeometry based on the temperature profiles;

(d) calculating the surface deformation of the weldpool;

(e) conducting the coordinate system transforma-tion;

(f) calculating the fluid velocity field inside the weldpool under the body-fitted coordinate system andobtaining convergent results;

(g) calculating the temperature field over thewhole domain and obtaining the convergentresults;

(h) repeating steps (c) to (g) and improving thecalculation accuracy until the convergentcriterion for the weld pool surface deformation,fluid flow field, and temperature distribution areall met;

(i) going to the next time step, and repeating steps(c) to (h).

3 RESULTS AND DISCUSSION

Numerical simulations are performed for GTAWon type 304 stainless steel and low-carbon steelQ235. A half-workpiece with a welding domain of200mm� 50mm� 3 or 2mm is divided into a meshof 352� 60� 10 grid points. A finer grid spacing isutilized in the molten region. The specific heat Cp,dynamic viscidity �, and thermal conductivity k aretemperature dependent, and can be expressed asfollows [15, 20]. For type 304 stainless steel

k ðW=mKÞ

¼

10:717þ 0:014 955T ‚

12:076þ 0:013 213T ‚

217:12� 0:1094T ‚

8:278þ 0:0115T ‚

8>>>>><>>>>>:

T 4 780K

780K4T 4 1672K

1672K4T 4 1727K

1727K4T

ð24Þ

� ð�10�3 kg=msÞ

¼

37:203� 0:0176T ‚

20:354� 0:008T ‚

34:849� 0:0162T ‚

13:129� 0:0045T ‚

8>>>>><>>>>>:

1713K4T 4 1743K

1743K4T 4 1763K

1763K4T 4 1853K

1853K4T 4 1873K

ð25Þ

Cp ðJ=kgÞ

¼

438:95þ 0:198T ‚

137:93þ 0:59T ‚

871:25� 0:25T ‚

555:2þ 0:0775T ‚

8>>>>><>>>>>:

T 4 773K

773K4T 4 873K

873K4T 4 973K

973K4T

ð26Þ

For Q235 steel

k ðW=mKÞ

¼

60:719� 0:027 857T ‚

78:542� 0:0488T ‚

15:192þ 0:0097T ‚

349:99� 0:1797T ‚

8>>>>><>>>>>:

T 4 851K

851K4T 4 1082K

1082K4T 4 1768K

1768K4T 4 1798K

ð27Þ

� ð�10�3 kg=msÞ

¼

119:00� 0:061T ‚

10:603� 0:025T ‚

36:263� 0:0162T ‚

8>><>>:

1823K4T 4 1853K

1853K4T 4 1873K

1873K4T 4 1973K

ð28Þ

Cp ðJ=kgÞ

¼

513:76� 0:335Tþ6:89� 10�4T2‚

�10 539þ 11:7T ‚

11 873� 10:2T ‚

644‚

354:34þ 0:21T ‚

8>>>>>>>>><>>>>>>>>>:

T 4 973K

973K4T 4 1023K

1023K4T 4 1100K

1100K4T 4 1379K

1379K4T

ð29Þ

Other thermophysical properties and parametersused in the calculation are summarized in Table 1.

The development of the weld pool includes thefollowing stages: the weld pool forming after the arcignition, the pool expanding, and the pool reachingthe quasi-steady state. Figure 3 shows the transientdevelopment of the weld pool geometry and fluid



flow field inside the pool. Figures 3(a), (b), and (c) arethe top surface, longitudinal section, and transversecross-section respectively of the weld pool. Thewidth and length of the weld pool at the top surfaceincrease quickly after the arc ignition [Fig. 3(a)].When the weld pool reaches the quasi-steady state,the pool geometry is kept nearly constant. When theworkpiece is partially penetrated, the penetrationdepth increases with time. After the workpiece isfully penetrated, the lower part of the weld poolexpands quickly, and the expanding rate of bothpool width and pool length at the top surface slowsdown [Fig. 3(b)]. Figure 3(c) is the cross-section ofthe weld pool 1.2mm behind the arc centre-line.The maximum fluid velocity is at the region nearthe electrode centre-line (x¼ 0), and the value is0.007m/s at t¼ 2:0 s and 0.040m/s at t¼ 4:12 s.Figure 4 demonstrates the variations in the poollength, width, and depth with time. For the usedwelding conditions (workpiece, Q235; thickness,2mm; arc voltage, 16 V; welding current, 110 A; weld-ing speed, 160mm/min), the weld pool emerges att¼ 1:62 s, the workpiece is penetrated at t¼ 2:88 s,and the quasi-steady state is reached at t¼ 4:20 s.The transient behaviours of the weld pool when the

arc is extinguished is also calculated. This process isactually the cooling and solidifying of the weld pool.For the used welding conditions (workpiece, type304 stainless steel; thickness, 3mm; arc voltage,14 V; welding current, 100 A; welding speed,120mm/s), the quasi-steady state is achieved att¼ 4:0 s; then the arc is intentionally extinguishedand both the welding current and the speedbecome zero. Because there is no heat input, theweld pool decreases very quickly. The calculationresult shows that the weld pool disappears totally att¼ 4:6 s. Figure 5 illustrates the transient contractionbehaviour of the weld pool geometry at the topsurface, bottom surface, longitudinal section, andtransverse cross-section. During the cooling process,the weld pool moves backwards relative to the

electrode centre-line (x¼ 0). The penetration depthchanges slowly at first and then more rapidly thanthe pool width and length. Figure 6 shows the transi-ent variation in the fluid flow field after the arc hasbeen extinguished. Because of the disappearance ofthe arc pressure and electromagnetic forces, thefluid flow is driven only by the surface tension gradi-ent and buoyancy; therefore it lasts a very short time,and the amplitude of flow velocity is much lower thanin the quasi-steady state.

Experimental measurements are made to validatethe model. The common commercial charge-coupleddevice camera combined with a special narrow-bandfilter is used to capture the images of the weld poolduring the GTAW process. Once the image of theweld pool captured by the camera is digitized througha frame grabber, it is stored in a computer as a matrixin which one element represents a dot of image. Aspecial image-processing algorithm has been devel-oped to extract the weld pool edges so that the weldpool geometry of the top side is determined [21].Figure 7 shows the comparison of the experimentaland predicted results. It can be seen that the pre-dicted weld pool surface geometry generally agreeswith the measured geometry except for the trailingpart. Because the latent heat is not considered inthe model, the calculated weld pool trail is not elon-gated. Figure 8 shows a comparison of the calculatedand experimentally observed geometries of the weldpool in cross-section. The experimental and the pre-dicted cross-section configurations of the weld areconsistent with each other although the weld widthhas a slight difference. Further studies are continuingto improve the accuracy of simulation.

4 CONCLUSIONS

1. A three-dimensional transient numerical model isdeveloped to investigate the dynamic behavioursof the weld pool geometry, surface deformation,

Table 1 Other thermophysical properties and parameters used in the calculation

Value

Property or parameter (units) Symbol 304 stainless steel Q235 steel

Melting point (K) Tm 1763 1789Density (kg/m3) � 7200 6900Ambient temperature (K) T1 293 293Convective heat-transfer coefficient (W/m2 K) Hc 80 80Latent heat of vaporization (J/kg) Hv 73:43� 105 73:43� 105

Stefan–Boltzmann constant (W/m2 K4) � 5:67� 10�8 5:67� 10�8

Current flux radius parameter (mm) �j 1.5 1.5Heat flux radius parameter (mm) �q 2.25 2.25Surface radiation emissivity " 0.4 0.4Magnetic permeability (H/m) �0 1:66� 10�6 1:66� 10�6

Surface tension (N/m) � 1.0 1.0Arc power efficiency 0.65 0.65Gravitational acceleration (m/s2) g 9.8 9.8



Fig.3

Transientvariationin

thethree-dim

ensionalweld

poolsh

apeandfluid

flow

field

(workpiece,

Q235;thickness,2mm;arc

voltage,16V;weldingcu

rrent,110A;weldingsp

eed,160mm/m

in)



heat transfer, and fluid flow in a fully penetratedGTA weld pool. The simulation results lay thefoundation for process control of the GTAWprocess.

2. For GTAW on a low-carbon steel Q235 plate of2mm thickness with an arc voltage of 16 V, awelding current of 110 A, and a welding speedof 160mm/min, the weld pool emerges at

t ¼ 1.62 s, the workpiece is penetrated att¼ 2:88 s, and the quasi-steady state is reachedat t¼ 4:20 s. The maximum fluid velocity is inthe region near the electrode centre-line (x¼ 0),and the value is 0.007m/s at t¼ 2:0 s and0.040m/s at t¼ 4:12 s.

3. For the welding conditions used (type 304 stainlesssteel plate with a thickness of 3mm, a welding

Fig. 4 The weld pool dimensions versus time (workpiece, Q235; thickness, 2mm; arc voltage, 16 V;welding current, 110A; welding speed, 160mm/min)

Fig. 5 Transient variation in the three-dimensional shape of a weld pool after the arc has been extin-guished (workpiece, type 304 stainless steel; thickness, 3mm; arc voltage, 14 V; welding current,100A; welding speed, 120mm/s)



current of 100A, an arc voltage of 14V, and awelding speed of 120mm/s), the quasi-steadystate is achieved at t¼ 4:0 s; then the arc is inten-tionally extinguished and both the welding current

and the welding speed become zero. The transientbehaviours of the weld pool when the arc isextinguished are also calculated. It is found thatthe weld pool disappears totally at t¼ 4:6 s.

Fig. 6 (continued over)



4. GTAW experiments are carried out to obtain thecross-section of weld. The predicted andmeasured data are in agreement.

ACKNOWLEDGEMENTS

The authors are grateful for financial support for thisproject from the US National Science Foundationunder Grant DMI-0114982, and the National NaturalScience Foundation of China under Grant 57405131.

REFERENCES

1 Swaim, W.Gas tungsten arc welding made easy.Weld. J.,1998, 77(9), 51–52.

2 Zhang, Y. M., Kovacevic, R., and Lin, L. Adaptive controlof full penetration GTA welding. IEEE Trans. ControlSystems Technol., 1996, 4(4), 394–403.

3 Kou, S., and Wang, Y. H. Weld pool convection and itseffect. Weld. J., 1986, 65(3), 63s–70s.

4 Choo, R. T. C., Szekely, J., and Westhoff, R. C. Modelingof high-current arcs with emphasis on free surfacephenomena in the weld pool. Weld. J., 1990, 69(9),346s–361s.

5 David, S. A., Vitek, J. M., Zacharia, T., and DebRoy, T.Weld pool phenomena. Document 212-829-93, Inter-national Institute of Welding, 1993, pp. 2–4.

Fig. 6 Transient variation in the fluid flow field after the archas been extinguished (workpiece, type 304 stainlesssteel; thickness, 3mm; arc voltage, 14V; weldingcurrent, 100A; welding speed, 120mm/s)

Fig. 7 Comparison between the predicted and experi-mental surface geometry of the weld pool (work-piece, type 304 stainless steel; thickness, 3mm; arcvoltage, 16 V; welding current, 100A; weldingspeed, 125mm/s)

Fig. 8 Comparison between the calculated and experi-mental cross-sections of the weld (workpiece, type304 stainless steel; thickness, 3mm; arc voltage,12 V; welding current, 110 A; welding speed,125mm/min)



6 Zacharia, T., Eraslan, A. H., Aidun, D. K., and David,S. A. Three-dimensional transient model for arc weldingprocess. Metall. Trans. B, 1989, 20(10), 645–659.

7 Wu, C. S., and Yan, F. Numerical simulation of transientdevelopment and diminution of weld pool in gastungsten arc welding. Modelling Simulation Mater. Sci.Engng, 2004, 12(1), 13–20.

8 Wu, C. S., and Dorn, L. Prediction of surface depressionof a tungsten inert gas weld pool in the full-penetrationcondition. Proc. Instn Mech. Engrs, Part B: J. EngineeringManufacture, 1995, 209(B3), 221–226.

9 Lancaster, J. F. The Physics of Welding, 2nd edition, 1986(International Institute of Welding, Pergamon, Oxford).

10 Tsai, N. S., and Eagar, T. W. Distribution of the heat andcurrent fluxes in gas tungsten arcs. Metall. Trans. B,1985, 16, 841–846.

11 Goldak, J. A new finite element model for welding heatsources. Metall. Trans. B, 1984, 15(6), 299–305.

12 Wang, Y., Shi, Q., and Tsai, H. L.Modeling of the effectsof surface-active elements on flow patterns and weldpenetration. Metall. Mater. Trans. B, 2001, 32, 145–161.

13 Zacharia, T., David, S. A., and Vitek, J. M. Effect ofevaporation and temperature dependent materialproperties on weld pool development. Metall. Trans. B,1991, 22, 233–241.

14 Choi, M., Greif, R., and Salcudean, M. A study of heattransfer during arc welding with applications to puremetals or alloys and low or high boiling temperaturematerials. Numerical Heat Transfer, 1987, 11(4), 477–489.

15 Wu, C. S., and Tsao, K. C. Modeling the three-dimensional fluid flow and heat transfer in a movingweld pool. Engng Computations, 1990, 7(3), 241–248.

16 Patankar, S. V. Numerical Heat Transfer and Fluid Flow,1980 (McGraw-Hill, New York).

17 Van Doormaal, J. P., and Raithby, G. D. Enhancement ofthe SIMPLE method for predicting incompressible fluidflows. Numer. Heat Transfer, 1984, 7, 147–163.

18 Jakobson, H. Th., and Chajar, A. J. Numerical solutionsof heat conduction and simple fluid flow problems. Int.Commun. Heat Mass Transfer, 1987, 14, 67–69.

19 Tao, W. Q. Numerical Heat Transfer, 1987 (Xi’an JiaotongUniversity, Xi’an, People’s Republic of China).

20 Wu, C. S. Computer simulation of three-dimensionalconvection in traveling MIG weld pools. Engng Compu-tations, 1992, 9(5), 529–537.

21 Wu, C. S., Gao, J. Q., Liu, X. F., and Zhao, Y. H. Vision-based measurement of weld pool geometry in con-stant-current gas tungsten arc welding. Proc. InstnMech. Engrs, Part B: J. Engineering Manufacture, 2003,217(B6), 879–882.



fig. 1ymzhang/papers/2005 england.pdfusing the model, the whole gas tungsten arc welding (gtaw)...

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