Theoetical model and expeimental investigation of cuent density bounday condition fo welding ac study A. Boutaghane, K. Bouhadef, F. Valensi, S. Pellein, Y. Benkedda To cite this vesion: A. Boutaghane, K. Bouhadef, F. Valensi, S. Pellein, Y. Benkedda. Theoetical model and expeimental investigation of cuent density bounday condition fo welding ac study. Euopean Physical Jounal: Applied Physics, EDP Sciences, 2011, 54 (1), <10.1051/epjap/2011100146>. <hal-00687330> HAL Id: hal-00687330 https://hal.achives-ouvetes.f/hal-00687330 Submitted on 13 Ap 2012 HAL is a multi-disciplinay open access achive fo the deposit and dissemination of scientific eseach documents, whethe they ae published o not. The documents may come fom teaching and eseach institutions in Fance o aboad, o fom public o pivate eseach centes. L achive ouvete pluidisciplinaie HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau echeche, publiés ou non, émanant des établissements d enseignement et de echeche fançais ou étanges, des laboatoies publics ou pivés.
Theoetical model and expeimental investigation of cuent density bounday condition fo welding ac study A Boutaghane 1,3, K Bouhadef 2, F Valensi 3,4, S Pellein 3 and Y Benkedda 1 1 Cente de echeche scientifique et technique en soudage et contôle, CSC, Alge, Algéie 2 Univesité des sciences et de la technologie, Houai Boumediene, USTHB, Alge, Algéie 3 GREMI-Site de Bouges, Univesité d Oléans/CNRS, BP 4043, 18028 Bouges cedex 2 - Fance 4 LAPLACE-AEPPT, Univesité Paul Sabatie/CNRS, 31062 Toulouse cedex 9 - Fance Coespondent's email addess: stephane.pellein@univ-oleans.f Coespondent's fax numbe: (33) [0]2 48 70 75 41 Abstact. This pape pesents esults of theoetical and expeimental investigation of the welding ac in Gas Tungsten Ac welding (GTAW) and Gas Metal Ac Welding (GMAW) pocesses. A theoetical model consisting in simultaneous esolution of the set of consevation equations fo mass, momentum, enegy and cuent, Ohm s law and Maxwell equation is used to pedict tempeatues and cuent density distibution in agon welding acs. A cuent density pofile had to be assumed ove the suface of the cathode as a bounday condition in ode to make the theoetical calculations possible. In stationay GTAW pocess, this assumption leads to fai ageement with expeimental esults epoted in liteatue with maximum ac tempeatues of ~ 21000 K. In contast to the GTAW pocess, in GMAW pocess, the electode is consumable and non-themionic, and a ealistic bounday condition of the cuent density is lacking. Fo establishing this cucial bounday condition which is the cuent density in the anode melting electode, an oiginal method is setup to enable the cuent density to be detemined expeimentally. High-speed camea (3000 images/sec) is used to get geometical dimensions of the welding wie used as anode. The total aea of the melting anode coveed by the ac plasma being detemined, the cuent density at the anode suface can be calculated. Fo a 330 A ac, the cuent density at the melting anode suface is found to be of 5 10 7 A.m -2 fo a 1.2 mm diamete welding electode. Keywods: themal plasma, magnetohydodynamic, agon ac, GTAW, GMAW pocess PAC s numbe: 52.50.-b, 52.65.Kj, 52.70.K, 52.75.Hn, 52.77.Fv Submitted to: Euopean Physical Jounal - Applied Physics
1. Intoduction In ac welding, an electic ac is buning between a wokpiece and an auxiliay electode: - Fo gas metal ac welding (GMAW) pocess the auxiliay electode is welding wie, which is usually the anode (evese polaity). Heat tansfe fom the ac and Ohm s heating in the wie melt its tip foming doplets, tansfeed though the ac to the wokpiece used as a cathode. - Fo gas tungsten ac welding (GTAW) pocess, the wokpiece, which is usually the anode (staight polaity), locally melts due to heat tansfe fom the ac, foming a weld pool. Themal behaviou of welding acs and thei electodes can have significant effects on the subsequent weld quality and poduction ate. Hence, it is desiable to have a theoetical method which can pedict the popeties of both electodes and ac plasma as functions of the ac opeating conditions. The behaviou of an ac is govened by a coupled set of physical laws, i.e., Ohm s Law, Maxwell s equations and consevation equations of mass, momentum, enegy and electical chage [1, 2]. The modelling of ac welding pocesses has been epoted by a numbe of eseaches [2-16]. Most ealy numeical models have teated eithe only the ac plasma [2-7] o only the weld pool [8-14]. Fo the ac plasma, a plane suface of the solid anode has been set to be a bottom bounday fo the electic potential and tempeatue which ae given as the bounday conditions. The tungsten cathode has been assumed to be at a unifom tempeatue as a bounday condition and the cuent density distibution on the cathode has been also given as anothe bounday condition to the calculations of the ac plasma. Fo calculations of the weld pool, the distibutions of heat flux and cuent density to be specified at the anode suface have been equied. Moe ecent models have combined the ac plasma and the weld pool fo stationay welding [15, 16], but the calculations of the ac plasma and the weld pool wee made sepaately, without inteaction between the plasma and the weld pool. The fist completely unified models of the gas tungsten ac wee fo acs with solid anodes made of coppe cooled by wate [17, 18]. The unified models give tempeatues and cuent densities in the whole egion of the ac, i.e. fo the tungsten cathode, the ac plasma and the anode. These basic models and pocedues wee extended to include melting of the anode, with inclusion of convective effects in the molten anode, fo pedicting the GTAW popeties [18]. A unified electode-ac weld-pool teatment, including effects of depession of the weld-pool suface due to the ac pessue, has been pesented by Haida [19]. Geneally, it is assumed that the ac plasma at atmospheic pessue is a fluid [2-7, 15-17]. The magnetohydodynamic (MHD) appoximation, which includes foce tems due to the magnetic field in the momentum equations, solves fo pessue, tempeatue, velocity and electic potential though the fou consevation equations of mass, momentum, enegy and cuent. If we assume otational symmety aound the ac axis, the system can be epesented by cylindical coodinates. Compaed with the GTAW ac plasma, modelling of the GMAW has been fa less addessed. Relatively few eseaches have attempted to combine the vaious aspects of the physical modelling in ode to detemine the oveall behaviou of the GMAW pocess. In these pevious papes, the anode melting ate has not been consideed and doplets have been simply epesented eithe by tuncated ellipsoids o by tuncated sphees. This is only an indication of tends athe than the actual behaviou of doplets fomation, since a numbe of seve simplifications and assumptions have been intoduced [24, 31]. Hence it is desiable to develop a GMAW model that takes the popeties of the welding ac, the melting anode as well as the doplet fomation into consideation. In the fist pat of this pape, solutions of the consevation equations in the magnetohydodynamic (MHD) appoximation ae pesented in stationay state fo GTAW pocess with agon shielding gas at atmospheic pessue. Detailed calculations ae pesented fo 100 A, 200 A and 300 A acs in agon at atmospheic pessue. In the second pat of this pape, paticula attention to the molten welding wie of Gas Metal Ac Welding (GMAW) pocess is made fo futhe GMAW model. The GTAW ac model is adapted to epesent the GMAW ac, taking into account the change of polaity, to calculate the ac column tempeatues by assuming a ealistic cuent density distibution on the anode spot which is detemined expeimentally. An oiginal method is poposed in this second pat of this pape
to detemine the shape and the dimensions of the molten anode by using high-speed camea (3000 images/sec). Geometical dimensions of a 1.2 mm molten welding wie ae makedly pesented fo a 330 A ac. It is woth mentioning that cuent density in GMAW highe than 10 7 A.m -2 seems to be not justified fo welding cuent less than 330 A. To the best of ou knowledge, it is fo the fist time the molten electode dimensions ae thooughly pesented. The boundaies of the wie anode egion change with time, depending upon the shape of the doplet and the melting ate of the anode. Contou detection of ac images, obtained by high-speed video camea, is pefomed to epesent these geometical bounday conditions which ae of key impotance fo futhe semi-empiical GMAW model. 2. Theoy Figue 1 shows the computational domain used in the GTAW pocess. The pesence of an electic field between the cathode (a tungsten od) and the anode (metal wokpiece) causes the passage of an electic cuent though the ionied plasma egion. The inteaction of the ac cuent with its own magnetic field leads, in ac egimes of vaiable coss section, to the phenomena of induced plasma jets. The cathode egion of a fee-buning ac, fo example, acts as an electomagnetic pump dawing gas fom the suoundings and ejecting it towad the anode in the fom of a jet. Due to the electical esistance of the plasma, the enegy poduced by the cuent keeps the plasma in the ionied state and povides the heating mechanism fo the welding pocess. Fo modelling this complex welding ac, some assumptions must be made: 1. The ac is axially symmetic so that the equations can be witten in two-dimensional cylindical coodinates. 2. The plasma is in local themodynamic equilibium (LTE). 3. The ac is in the steady state and the flow is lamina. 4. The plasma is optically thin. 2.1. Govening equations Figue 1. Ac-electode domain. Based on these assumptions, the consevation equations govening the ac egion may be expessed in cylindical coodinates as follow [2, 24]: - Cuent continuity equation in tems of electic potential: V 1 V 2 V = σ σ = 0 (1) whee σ is the electical conductivity; and V the electical potential. - The cuent density is given by:
V σ J = and V σ J = (2) whee J and J ae the adial cuent density and the axial cuent density, espectively. - Since the cuent distibution is axisymmetic, the self-induced magnetic field is given by the following elation fom Ampee s law: = 0 0 θ ξdξ J µ B (3) whee µ 0 = 4 10-7 H.m -1 is the pemeability of fee space. - The Loen foce components ae given as: J B F θ = and J B F θ = (4) whee F is the adial component and F is the axial component - Mass consevation: 0 u) ( v) ( 1 = ρ ρ (5) whee ρ is the gas density; and u and v ae the axial and adial velocities, espectively. - Radial momentum equation: 2 θ 2 v 2µ ) u µ v (µ ) v (2µ 1 B j P uv) ( ) v ( 1 t (ρu) = ρ ρ (6) and axial momentum equation: ρg ) u µ v (µ 1 ) u (2µ B j P ) u ( vu) ( 1 t (ρv) θ 2 = ρ ρ (7) whee P is the pessue; µ is the dynamic viscosity; and g is the gavitational acceleation. - Enegy equation: R B 2 2 p S T J T J e k 2 5 σ J J T k 1 T k T v T u ρc = (8) whee T is the tempeatue; S R is the adiation heat loss; c p is the specific heat at constant pessue; k is the themal conductivity; k B is the Boltmann constant; and e is the electonic chage. The enegy equation contains, fom left to ight, two convection tems, two conduction tems, the joule-heating tem, an additional tem that epesents the tanspot of electon enthalpy
due to the dift of the electons and the adiation tem S R. 2.2. Bounday conditions The calculation domains and the bounday conditions used in this analysis ae specified with efeence to Figue 1 in Table 1. The calculation domain fo u, v and T is chosen as the aea ABCD. Theefoe, the domain fo V is chosen as the smalle aea ABCD, since the exact bounday condition fo V along the line FA is unknown. V V = 0 Table 1. Bounday Conditions AB BC CE EF FA DA V = V = C te 0 u u ρu u = 0 u = 0 = 0 = 0 u = 0 v v v = 0 v = 0 = 0 v = 0 v = 0 T T = T 0 exp =2200 K [20, 21, 26] 1000 K[22] 1000 K [2, 6, 17] 3000 K [2, 6, 17] Equation (9) Due to symmety, only a half of the flow domain was consideed fo the calculation. Along the centeline AB, symmety conditions ae used, eo velocities ae specified along the solid boundaies BC and FA. Along the fa field bounday CE, eo adial gadients fo all vaiables ae specified unless fo the tempeatue, which is set to 1000 K [22]. A constant electical potential is specified along the anode suface BC because the anode is assumed to be a pefect conducto elative to the plasma. Expeimental data of Bloch-Bolten and Eaga [20] and Cieslak et al. [21] showed that the maximum suface tempeatue fo steel weld pool is appoximately 500 K below the boiling tempeatue. In this study, theefoe, we set a constant tempeatue of 2200 K at the cathode suface as suggested by Tanaka and Lowke [26]. Along the bounday EF, the tempeatue is taken as 1000 K [2, 6, 17] and the adial velocity component is neglected. At the cathode suface FA, the tempeatue is assumed to be 3000 K [2, 6, 5, 17] except at the point whee the cuent emeges fom the cathode. The cathode spot itself cannot be easily modelled because of non-lte effects. The cathode sheath is typically 0.1 mm wide, and in this egion, electons ae heated fom 3000 K to 21000 K [5, 22, 30]. Since ou model descibes only the positive column, we do not take into account cathode sheath effects, and thus we assume that the tempeatue of the cathode spot is 21000 K [2, 5] fo all cuents. As the cathode spot adius depends on the cuent, its values ae taken fom expeimental measuements: we set to h = 0.6 mm, h = 0.51 mm, h = 0.45 mm fo ac cuents of 300 A, 200 A and 100 A espectively [2, 5, 30]. The most citical bounday condition in this modelling is the cuent density distibution along the line DA. Fo this egion, the cuent density defines a bounday condition fo V. The pofile of the cuent density is fomulated following the epesentation of Hsu et al [2] and Kovitya et al [5]. It is assumed to be of the fom: = J exp( b) (9a) Jc 0 whee b is a constant and the maximum cuent density is I J0 = (9b) 2 2π h The constant b is detemined fom:
R c I = 2π J0exp( b)d (10) 0 whee R c is the cut-off adius of the ac along DA. R c is taken as 3 mm [2] fo the evaluation of b. This choice, howeve, is not citical because of the assumed exponential decay of the cuent density in the adial diection. The mateial popeties of the plasma (density, constant pessue specific heat, viscosity, electical and themal conductivities) have been taken fom liteatue [31]. 3. Numeical method The method of epesenting the consevation equations is the finite contol volume method fomulated fo ectangula gid system. The patial diffeential equations (1) to (8) ae solved iteatively by the SIMPLEC numeical pocedue as oiginated by Patanka [1] and used theeafte in seveal wok [2, 27, 31, 35]. To pevent instabilities, we have used upwind method of evaluating the convective tems on the left-hand sides of equations (6)-(8). It is necessay to use elaxation paamete to avoid numeical instabilities. With a elaxation paamete of ~ 0.8, convegence is geneally achieved in ~ 300 iteations. Actually the electical potential and the cuent density calculated by this method, equations (1, 2), have to be adjusted so that the calculated intensity I *, equation (12), can be matched with the imposed intensity of the cuent I. The intensity of the cuent I *, on one o moe sections of the ac, can be calculated by: I * = 1 n n p p i= 1 Σ i * J.dS whee n P is the numbe of plan and Σ i is the sectional suface of the plan i. We define a constant C V which epesents the atio of the imposed cuent intensity ove the calculated cuent: I C V = (13) * I Then the electical potential and the cuent density can be adjusted by: * V = C V V and (12) = * (14) 4. Results Results ae pesented fo 100 A, 200 A and 300 A acs in agon with a tungsten cathode of 3.2 mm diamete and electode spacing of L = 10 mm at atmospheic pessue. In the ac egion, the plasma was assumed to be in local themodynamic equilibium (LTE), even if depatue fom LTE can occu in the egion immediately suounding the cathode. Depatue fom LTE esults fom a combination of the lage tempeatue gadients and the magnetohydodynamic popeties occuing in the egion close to the ac-cathode attachment egion. If the electodes ae at tempeatues below thei melting point, the tempeatues of egions adjacent to the electodes ae less than 4000 K and the equilibium electon density and electical conductivity ae nea eo. Howeve, it is believed by many investigatos that in pactice, non-equilibium effects such as themionic emission and ambipola diffusion can make these egions highly conducting [29, 19, 24]. This egion is divided into two subones [29, 37]: the ioniation one and the space chage one. The fome is used to account fo the geneation of ions and electons and extends ove a distance of aound 0.0075 cm. The latte extents ove a distance equivalent to a Debye length, λ D = 10-6 cm, and is used fo explaining the sheath fomation. Thus, vey close to the cathode, the usual continuum appoach is no longe valid. In ou calculation both the cathode and the anode one ae neglected, this is J C V J
suppoted by the fact that the influence of diffusion pocesses in the main plasma is small. Besides, a compaison with the expeimental esults indicates that an optimum mesh sie could be used so that, fo appoximate calculations, non-equilibium sheaths nea the electodes can be neglected. Lowke et al. [27, 29] epoted in thei modeling of a single tempeatue agon plasma that neglecting sheath egion has little effect on the validity of the esults if the mesh sie is small enough, and that smalle mesh sies cause an incease in the eo because of significant diffusion effects. In the pesent calculation, a unifom mesh was used in the whole domain of calculation, this mesh sie being 0.05 mm in both the axial and the adial diections. In ou case, this value epesents the lowe cell sie to pevent instabilities. Howeve, this mesh sie was caefully chosen to epesent physical pocess. Hee, we ae limited to cases in which convection dominates ove diffusion pocesses, which is usually valid fo most pats of the ac. Figue 2. Electical potential and axial cuent density along the ac axis in a GTAW pocess. Figue 2 shows the centeline distibution of the electical potential and the cuent density. The calculated total ac voltage is 12.5 V fo an ac of 200 A. The coesponding measued value is aound 13.1 V [23, 25]. The value calculated by Lowke et al [27] is 12.7 V. The compaison indicates that effects in the cathode sheath of ohmic heating and ioniation due to the electic field, which wee omitted fo the pesent investigation, wee small. The cuent density is vey high nea the cathode tip, but deceases apidly with inceasing distance fom the cathode. A steep gadient of electical potential nea the cathode tip esults in the high cuent density, which geneates a stong magnetic foce, and thus, esulting in high ac constuction leading to a stong plasma flow. Thus, the cold neutal atoms injected into the ac due to this effect, caused the cathode one to be in no LTE state. It has been found that in this cold one n e /n e LTE is less than 0.5 [19], whee n e is the electon numbe density in the cathode egion and n e LTE is the equilibium electon numbe density. Actually, it is well known that the sheath-voltage dop is lowe fo lowe electon numbe densities in the plasma. In contast, the high electon numbe densities at the sheath edge would esult in a highe sheath voltage dop [19, 24, 37]. As a esult, magnetohydodynamic models based on LTE assumption may lead to an oveestimation of both the tempeatue and the total voltage dop. In ou teatment LTE is assumed thoughout the ac plasma, esulting in high electon numbe densities (n e =n e LTE ) which may lead to oveestimation of a sheath voltage. Fo 200 A ac, the total voltage deived fom calculation diffes by about 4.5 V, which is almost the sum of the cathode and the anode dop voltage. Hsu et al. [37] found the voltage dop in ioniation one of aound 4.5 V. Hsu et al. [22] found the sum of the cathode and anode fall voltage dop of about 8.7 V. Lowke et al. [29] calculated the effect of back diffusion of electons to the cathode and found that the sheath voltage is inceased fom 1.5 to 3 V and the total ac voltage is coespondingly inceased by 1.5 V. Sansonnens et al. [28] estimated that the sum of the cathode and anode voltage is aound 2.6 V. Thus, the diffeence between calculated and measued ac
voltage can be explained by the fact that ou calculations do not account fo both the cathode and the anode egions. The calculated isothems ae shown in Figues 3 to 5. The tempeatue shows a apid incease in font of the cathode due to ohmic heating, and as the ac speads (decease of the cuent density) the tempeatue dops to values bellow 11000 K close to the anode. As expected, the highest tempeatues, fom 21000 K down to 19000 K, occued close to the cathode tip fo all consideed cuents as we can see in Figues 3(a) to 5(a). Results ae to some extent dependent on the cathode tempeatue as showed in figues 3(b) to 5(b). Highe cathode tempeatues influence the calculations, because the hot cathode tends to boaden the whole ac column and educes cuent densities within the ac. At the cente line of the ac and close to the anode and the cathode the ac pesents almost the same tempeatues fo all cuents as it can be seen in Figue 6. Howeve, in the column ac the tempeatues diffe by ~ 1000 K when cuent changes by 100 A. The ac behaviou is mainly contolled by the welding cuent: all calculated data, tempeatues, voltage dop and axial cuent density incease when inceasing cuent. The pedicted isothems ae in ageement with pevious calculations [2, 5, 25]. The discepancy value at the cathode egion is tentatively ascibed to depatues fom LTE and sheath effects in this one. Figue 3. Pedicted isothems of a 100 A ac, 10 mm long in agon (GTAW pocess - P = 1 atm). Figue 4. Pedicted isothems of a 200 A ac, 10 mm long in agon (GTAW pocess - P = 1 atm).
Figue 5. Pedicted isothems of a 300 A ac, 10 mm long in agon (GTAW pocess - P = 1 atm). Figue 6. Pedicted tempeatues in ac axis fo a 10 mm long ac in agon (GTAW pocess - P = 1 atm). It was mentioned above that the themal behaviou of the GTAW ac is dominated by the cuent ac, and thus by the cuent density. Spot adius and hence ac attachment aea is of key impotance to detemine the cuent density. As showed in section 2, it was necessay to specify the cuent density pofile on the cathode as a bounday condition in ode to make the theoetical calculations possible. We showed that the Gaussian distibution of the cuent density fo themionically emitting cathodes leads to a good pediction of ac popeties. In contast of the GTAW pocess, the cathode is nonthemionic in GMAW pocess. The physics of the cathode fall egion and the themal balance at a non-themionic cathode ae not vey well undestood and thus the cuent density cannot be easily modeled. In the following sections, expeimental model of the anode electode in GMAW pocess, electode positive, is detemined fo high ac cuents, and expeimental method of detemining cuent density fo a melting electode is thooughly pesented. 5. Expeimental electode model in Gas Metal Ac Welding (GMAW) pocess In GMAW pocess, low-voltage electic ac plasma is maintained between a wokpiece and a wie electode, both of which ae melted by the ac. Dops of molten metal detach fom the wie electode in vaious modes such as globula, epelled globula, pojected spay, steaming and otating tansfe.
In contast with the GTAW pocess, GMAW pocess is usually used in evese polaity i.e. the welding wie electode is connected to the positive pole (anode). Actually, the ac configuation is moe stable in the evese polaity (positive wie) than in the diect polaity (negative wie) as showed in figue 7. (a) GMAW in evese polaity (b) GMAW in diect polaity Figue 7. Ac attachment to the melting welding electode, I = 330 A, in Agon In Zielinska et al. [32] wok, a high-speed camea (157 images/sec) has been used to investigate the metal tansfe and the ac plasma shape in GMAW pocess. It has been found that the ac plasma in GMAW pocess is composed of two ones. A bight one in the cente has fom of a cone which is suounded by a peipheal one of much smalle bightness. Photogaphy of the gas metal ac welding pocess [32] shows that the anode spot vaies makedly with diffeent welding cuents. At low welding cuents, the anode spot is attached to the bottom of the pendant dop on the end of the electode. At high welding cuents, the anode spot is moe diffuse and gows noticeably in sie. At sufficiently high cuents (fo example, above 280 A with 1.2 mm diamete steel electode) the anode spot fills the dop and begins to climb the cylindical side walls of the electodes. Since most of the heat caied to the anode is caied by the welding cuent, the cuent in the anode spot causes the cylindical side walls of the electode to melt. The end of the electode foms a tapeed geomety. But detailed about the tapeed electode ae not clealy distinct. In this second pat, we extend the ealie teatment of Zielinska et al. [32] by impoving the optical layout and by using a faste camea (3000 images/sec). Geometic popeties of the melting welding electode fo GMAW pocess, electode positive opeating in spay mode, ae thooughly detemined so that the cuent density in the anode is expeimentally quantified. Theeafte, this expeimental cuent density is used as a bounday condition at the anode suface in conjunction with the theoetical ac model descibed in the fist pat of this pape. 5. 1 Expeiment pocedue The most impotant welding paamete in GMAW pocess influencing the doplet fomation and the molten electode is cuent intensity at its suface. The cuent density dives the dynamic evolution of the dop and also depends on the instantaneous shape of the dop. The shape pofiles of dops detaching fom a GMAW electode can be measued fom images of the electode. Howeve measuing the suface-cuent emission density along these pofiles equies special teatment since a moe pecise desciption of whee the cuent emeges fom the electode and how the cuent density is distibuted ove the dop is lacking. Even though significant bightness about the dop is obseved unde cetain conditions, this bightness is moe an indicato of the ac tempeatue and composition
than it is of the envelope of cuent flow. The ac plasma was obseved though a naow band intefeence filte which tansmits at 469.2 nm wavelength (3 nm spectal bandwidth). The system setup and the equipment specifications ae detailed by Zielinska et al. [32]. The filte cited above is of key impotance since it eliminates spectal lines which depend on both the tempeatue and the electonic density theeby only the continuum of the plasma ac can be seen though. Since the continuum depends mainly on the squae of the electonic density and hence on cuent density, the cuent-caying egion nea the anode cannot be extended substantially beyond the ac bounday suggested by the envelope of bightness. In addition, a diode lase is used to obseve the metal-tansfe pocess. The melting wie is illuminated with a H-C3830/40-F4 diode lase and the camea is fitted with an intefeential filte cented on the lase wavelength. Then most of the light emitted by the plasma is cut and only the lase light eflected by the melting wie is ecoded. The lase souce, which is not focused, has a powe of 30 W and a wavelength of 838 nm. Successive images wee assembled in figue 8 to illustate the detachment of dops fom the electode. The electode geometic paametes wee measued fom the images analysis and aveaged. The images ecoded in this expeiment ae of bead-on-plate gas metal ac welding opeated in constant cuent mode (330 A), that is, the welding cuent was contolled independently and the welding voltage was egulated about a set point by vaying the wie feed speed. In all of the expeiments, the electode was 1.2 mm diamete solid wie (AWS A5.17) shielded with agon, fed at 9 m.mn -1 though a 21.8 mm diamete gas nole. A coppe contact tube was mounted flush with the bottom of the gas nole and the gas nole was always 20 mm above the base plate. The base plate is not visible in all of the images and, using the electode diamete as a efeence, the geometic chaacteistics of both the ac and the melting electode can be measued diectly fom the images. The images wee ecoded with a high-speed video system at 3000 images pe second using the optical technique descibed in [32], thus the time between images was 333 µs. 5.2 Results and discussion The collection of well-specified, clea images pesented hee illustates the condition of a steel GMAW electode shielded with agon gas opeating at constant cuent of 330 A. The images obtained when the ac plasma is illuminated by the lase light ae pesented in Figue 8. In the othe hand, the aea of whee the cuent emeges is clealy obseved in figue 9. Figue 8. The tapeing of the welding wie electode at high welding cuent, in GMAW pocess. (Constant cuent I = 330 A and V = 32 V, evese polaity; Electode diamete: 1.2 mm; shielded gas: Agon. Image inteval = 333 µs. Filte: 838.0 nm). Fom the successive pictues shown in figues 8 and 9, we can see that in GMAW shielded with agon gas, and at high cuent, the ac is stable, the ac length can be consideed invaiable, and futhemoe, small doplets fomed fom a tapeed electode. Such a tapeed electode tip geomety, which is shown schematically on Figue 10, does not develop at low welding cuents. The tapeed tip ceates a smalle diamete fo attachment of the doplet to the electode by suface tension foces. This would poduces smalle doplets than would be pesent in the absence of tape fomation. Thee ae a
numbe of consequences of this tape fomation. Kim [34] has shown that the melting ate of the electode is contolled by heat tansfe acoss the liquid-solid bounday between the dop and the solid electode. Since the tape educes the aea of this bounday, tape fomation educes the ate of melting of the electode. Figue 9. Successive pictues of plasma ac in GMAW pocess. (Constant cuent I = 330 A and V = 32 V, evese polaity; Electode diamete: 1.2 mm; shielded gas: Agon. Image inteval = 333 µs. Filte: 469.2 nm). Thus the discepancy of the calculated tempeatues fom the MHD model in GMAW pocess as compaed with the expeimental data [33] may be explained by examining the validity of the assumptions made in the calculation of the calculated tempeatues fom the MHD model. One of the most impotant assumptions is that the electode should emain cylindical and maintain its full diamete at the point whee the dop is fomed. If the geometical dimensions of the electode ae changed eithe by suface melting o by defomation, the calculated tempeatues will be affected [33]. In figues 8, 9 and 10, we can see that the geomety of the dop holding neck is significantly changed due to fomation of a tape at the electode tip. The tapeing of the electode occus because the anode spot eaches this suface of the electode and geneates condensation heating on the cylindical suface of the electode. Figue 10. Doplet fomation at the tapeed electode and ac-anode attachment. (Constant cuent I = 330 A and V = 32 V, evese polaity; Electode diamete: 1.2 mm; shielded gas: Agon. a/ Filte: 838.0 nm, b/ Filte: 469.2 nm).
When enough heat is geneated on the suface, the suface will melt and the liquid metal will be swept downwad by eithe the gavitational foce and/o the plasma dag foce. When this melting and sweeping action occus ove a significant length of cylinde, a tape will develop at the end of the electode, as it is shown in figue 10. Thus, the assumption of cylindical electode which maintains its full diamete at the point whee the dop is fomed is not justified. The expeimental electode welding model that we popose in GMAW pocess consists of two pats: solid and liquid, as shown in figue 11. The solid pat is the welding wie of 1.2 mm diamete. The liquid pat, which is the tapeed electode, consists of thee ones as it is shown in figues 10 and 11. The neck of the tape, which has conical fom, is of 1.41 mm length, and the small diamete of the cone is about 0.36 mm. The liquid column has cylindical fom of 0.36 mm diamete and 2.54 mm length. At the end of this liquid column, the doplet with a spheical shape of 0.56 mm diamete is fomed. Details of aea calculation of these thee ones ae pesented in table 2. As it can be seen in figues 8, 9 and 10, the ac doesn t attach totally the neck of the tapeed electode. Only one sixth of the suface of the tapeed neck one S 1 is consideed to be attached by the ac, let this suface be Σ 1, Σ 1 = 1/6 S 1 as shown in table 2. In addition, the doplet has athe a tuncated spheical suface Σ 3 than a spheical suface S 3. Thus, the total aea fom which the welding cuent emeges is: S Tot = Σ 1 S 2 Σ 3. Figue 11. A schematic desciption of the poposed melting welding electode model used as an anode (evese polaity) in GMAW pocess. (Constant cuent I = 330 A and V = 32 V, evese polaity; Electode diamete: 1.2 mm; shielded gas: Agon). Table 2. Aea of the thee ones of the melting electode Σ Aea 1 : the tape neck S 2 : the liquid column (Cone) (Cylinde) Aea of the melting anode one coveed by the ac plasma (mm 2 ) Total aea (mm 2 ) 6.18 ± 0.01 Σ 3 : doplet (Tuncated sphee) 2.38 ± 0.01 2.87 ± 0.01 0.93 ± 0.01 Finally, the welding electode steel of 1.2 mm diamete, in GMAW pocess shielded with agon gas,
flowed by a 330 A welding cuent, has an ac-anode attachment aea of 6.18 mm 2 and hence the cuent density is of 5 10 7 A.m -2. Following the expeimental model of the melting-anode pesented above, the cuent density is detemined athe than be specified as an abitay condition as commonly assumed in liteatue. In the following section, the MHD model in conjunction with the expeimental cuent density is used to pedict tempeatue distibution in GMAW ac. 5. 3 Ac column calculations In GMAW, both the cathode and the anode ae melted by the ac. Hence, the cathode is nonthemionic and the cathode egion is unde high pessue due to the impinging plasma jet. The physics of the cathode-fall egion and the themal balance at a non-themionic cathode ae not well undestood. Theefoe, we have chosen to use a simila teatment of the enegy souce tem at the cathode bounday as used in GTAW [38]. Fo GMAW, emission of electons fom the cathode might be due to themo-field emission and thee may be impotant space chage effects in font of the cathode suface [19, 24]. Theeby, except fo the cuent density that flows though the anode suface, the cathode potential and the anode tempeatue, all the othe bounday conditions ae the same one that those descibed in section 2.2. Thus, we set a unifom cuent density J 0 of 5 10 7 A.m -2 on the anode suface, defined by the input cuent divided by the aea of coss section of the anode, as mentioned above, wheeas the potential is set to eo at the wokpiece used as the cathode. The value of the anode tempeatue detemined expeimentally in GMAW is lacking, while the calculated values show a high dispaity (see fo example [24], [36] and [43]); but anyway it is not eally necessay fo the calculation. Nevetheless it is equied to have an estimation of the plasma tempeatue just unde the wie: in a fist time, we have taken the value of about 21000 K obtained by Haida in simila conditions [24], which may seem high consideing the elatively low cuent densities. Figue 12a shows a lage ac column, which is due to the diffuse attachment mode. It is seen that the tends of the isothems ae in fai ageement with spectoscopic measuement [33], but the maximum tempeatue diffes noticeably. This is due to the fact that the metal vapos ae omitted in this study. Gleies et al. [39] showed that metal-vapo contamination to the ac leads to an incease in the enegy loss by the adiation, especially at lowe tempeatues. Zielinska et al. [33] and Valensi et al. [42] have shown that not only the maximum tempeatue is less than 15000 K but this maximum tempeatue is located away fom the ac axe as well, which suggest the pesence of metal vapos in the plasma paticulaly nea the cathode and the anode egions. a- T = 21000 K unde the wie, taken fom the liteatue [24]
b- T = 15000 K unde the wie, taken fom expeimental measuements [33, 42] Figue 12. Pedicted isothems of a 330 A ac, 10 mm long in agon (GMAW pocess in evese polaity - P = 1 atm - J 0 = 5 10 7 A.m -2 on the anode suface). Pedicted isothems of a 330 A ac, 10 mm long in agon fo this value ae shown in Figue 12b. It can be seen that fo lowe tempeatues the ac speads out less than fo highe tempeatues like in figue 12a which is in ageement with acs obtained by elatively low cuent densities. It should be noted that changing the cuent density esults in a low tempeatue on the axis of the ac column, which seems to have been obseved in the some expeimental woks that exist in the liteatue [32, 42]. Nevetheless, it is difficult to exactly compae with these expeimental data, because they ae difficult to pefom on the axis due to the passage of liquid metal doplets, and the authos geneally dismiss the cental one of the plasma. Figue 13. GMAW ac. Ac-attachment (Constant cuent I = 330 A and V = 32 V, evese polaity; Electode diamete: 1.2 mm; shielded gas: Agon. Filte: 469.2 nm).
In the othe hand, Dunn et al. [40] showed that even small amounts of ion vapos incease the electical conductivity at low tempeatues of both helium and agon gases, which can significantly affect the ac configuation and cuent density distibution and, consequently, the enegy input to the wokpiece. Raafinimanana et al. [41] epoted that an incease in electical conductivity, esulting fom the pesence of metal vapos, leads to an expansion of the conduction channel of an electic cuent. Figue 13 shows ac configuation fo GMAW pocess, electode positive, opeating in spay mode. It can be seen that even if the cathode is a non-themionic electode, the ac speads ove a lage suface of the cathode, which could be explained by the pesence of metal vapos as intoduced above. Howeve, hee, ou pupose is to detemine the tends of the isothems vesus the cuent density assumed at the anode. The ac-anode attachment egion speads ove a lage aea of the melting anode, esulting in a cuent density of 5 10 7 A.m -2, which is ten times smalle than those poposed by Haida et al [24] and Hu et al [35-36]. In thei wok, they consideed that the totality of the cuent flows though the naow neck of the doplet, consequently, a high welding cuent that flows though a small suface, esults in an oveestimated cuent density and hence a naow ac column. Figue 14. Pedicted isothems of a 330 A ac, 10 mm long in agon (GMAW pocess in evese polaity - P = 1 atm T = 15000 K unde the wie [33, 42]). In figue14, we show esults fo calculations pefomed using smalle ac-anode attachment fo a tempeatue fixed to 15000 K unde the wie [33, 42]. Fo the ac attachment to the anode limited to an aea of S 2 Σ 3 = 2.870.93 = 3.8 mm 2, which epesents 61% of the total aea of the effective suface attachment (6.18 mm 2 ), the coesponding cuent density would be about 8.7 10 7 A.m -2, which epesents an incease in cuent density of 74% compaed with the case of full attachment. If the ac attach only on the doplet (Σ 3 = 0.93 mm 2 ), which epesents 15% of the total aea of the effective suface attachment, the cuent density would be about 3.55 10 8 A.m -2, which is ten times highe than ou new cuent density. Figue 14, shows isothems coesponding to these suface attachments. It can be seen clealy that little suface attachment esults in a naow ac. We showed in the section above that the cuent emeges fom a lage aea of the melting anode, thus, it is woth mentioning that cuent density in GMAW highe than 10 7 A.m -2 seems to be not justified fo welding cuent less than 330 A. Fo futhe impovement of quality contol in GMAW pocess, plasma tempeatue has to be estimated athe in situ. This could be done by using the poposed welding electode model in conjunction with the automatic detemination of the geometical electode paametes. The counte
detection, shown in the ight hand side of figue 15, seems to be a poweful method fo the instantaneous detemination of such geometical shapes. Figue 15. Automatic detemination of the geometic electode popeties in GMAW pocess (evese polaity), by using contou detection technique. 6. Conclusion A numeical model of a fee-buning ac in atmospheic-pessue agon plasma has been developed to analye a stationay Gas Tungsten Ac welding (GTAW) pocess. Solutions of the consevation equations with appopiate bounday conditions have been obtained fo atmospheic pessue agon acs in a cuent ange fom 100 A to 300 A and electode gap of 10 mm. Both the tempeatues and the cuent density ae extemely sensitive to the cuent density bounday condition close to the cathode. The pedicted ac tempeatue and cuent density distibutions ae in good ageement with the measuements in the liteatue. The discepancies, nea the cathode and anode egions may be due to ac-electode inteactions. The model developed has been extended to Gas Metal Ac Welding (GMAW) pocess. In GMAW pocess, the electodes have to be included as dynamic entities, so it will be inteesting to intoduce ealistic bounday conditions fo the cuent density in the anode. We showed in the second section of this wok that the cuent density bounday can easily be obtained if the shape of the welding electode used as an anode is known. High-speed camea (3000 images/sec) was used to get geometical dimensions of this melting anode, and by using specific naow intefeence filtes (469.2 nm, 838.0 nm) we managed to obseve the metal-tansfe pocess and how the cuent density is distibuted ove the dop. Thus, the total aea of whee the cuent emeges was thooughly detemined in the case of mild steel consumable electode (AWS A5.17) of 1.2 mm diamete shielded by agon gas, and flowed by a 330 A cuent. It is woth mentioning that cuent density in GMAW highe than 10 7 A.m -2 seems to be not justified fo welding cuent less than 330 A. It s hoped that melting electode model pesented hee will povide guidance of authos attempting to develop moe complete models of the GMAW melting pocess. 7. Refeences [1] Patanka S V, Numeical Heat Tansfe and Fluid Flow (McGaw-Hill, New yok,1980). [2] Hsu K C, Etemadi K and Pfende E 1983 J.Appl.Phys: Appl.Phys. 54 1293 301. [3] Kovitya P and Lowke J J 1985 J.Phys.D: Appl.Phys. 18 53 70. [4] Ushio M, Sekely J and Chang C W 1981 Ionmaking Steelmaking 6 279 86. [5] Kovitya P and Cam L E 1986 Welding Jounal 65 34-38.
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