numerical analysis of metal transfer in gas metal arc welding

Numerical Analysis of Metal Transfer in Gas Metal Arc Welding under Modified Pulsed Current Conditions

G. WANG, P.G. HUANG, and Y.M. ZHANG

A method has been proposed to pulsate current in gas metal arc welding (GMAW) to achieve a specifictype of desirable and repeatable metal transfer mode, i.e., one drop per pulse (ODPP) mode. This methoduses a peak current lower than the transition current to prevent accidental detachment and takes advantageof the downward momentum of the droplet oscillation to enhance the detachment. A numerical model withadvanced computational fluid dynamics (CFD) techniques, such as a two-step projection method, volumeof fluid (VOF) method, and continuum surface force (CSF) model, was used to carry out the simulationfor the metal transfer process. The Gauss-type current density distribution was assumed as the boundarycondition for the calculation of the electromagnetic force. The calculations were conducted to demonstratethe effectiveness of the proposed method in achieving the desired metal transfer process in comparisonwith conventional pulsed current GMAW. Also, the critical conditions for effective use of this proposed methodwere identified by the numerical simulation. Comparison showed good agreement between calculationand experimental results.

I. INTRODUCTION

IN gas metal arc welding (GMAW), several different modesof the metal transfer have been classified.[1] At low current,the globular transfer occurs if the arc length is sufficient. Thedrops grow at the tip of the electrode with a classic pendantdrop shape, due to the competition between gravity and surfacetension in the presence of relatively small electromagneticforces. The large drops with diameter much greater than thediameter of the electrode are detached primarily by the gravity.When the welding current increases, the electromagnetic forcebecomes the dominant droplet force so that small drops withdiameter equal or less than the diameter of the electrode canbe detached. This is referred to as the spray transfer mode. Itis found that there is an abrupt transition in the current, whichdivides the globular and spray transfer modes. This currentor current range is referred to as the transition current. Highirregularity in the drop detachment frequency and the dropsize occurs in the middle of the transition current range.[2,3,4]

The globular transfer mode typically causes significantspatters and poor welding quality.[5] Its application in pro-duction is rare. The spray transfer mode takes advantage overthe globular mode by its regular detachment, directionaldroplet transfer, and low spatters.[3] However, spray transferis only achieved at high current, which causes a thermal loadtoo high to apply to thin sectioned or heat-sensitive materials.In an effort to overcome this difficulty, pulsed current GMAWwas introduced in 1962.[6] By using a pulsed current, a con-trolled spray transfer mode can be achieved at low averagecurrent, which typically results in globular transfer. To fur-ther achieve the desirable one drop per pulse (ODPP) mode,which characterizes a stable, periodical, and controllable metaltransfer process, the necessary conditions were investigatedin a number of works.[7–18] To this end, Ueguri et al.[9] sug-

gested the peak current should be set above a critical current,while Amin[10] identified this critical current as the transitioncurrent between the globular and spray transfer mode. Quintinoand Allum[11,12] and Smati[13] showed that the peak durationshould be increased to get the ODPP when the peak currentdecreases. The work of Kim[15,16,17] and his associates pointedout that there was a range of operational parameters withinwhich one droplet was transferred per current pulse. This wasfurther proved by the work conducted by Nemchinsky.[18]

A novel active control technology was recently proposedby Zhang et al.[7,8] in order to achieve a modified ODPP metaltransfer process. The drop is detached by the combination ofthe downward momentum of the drop oscillation and theincreased electromagnetic force, which is induced by an excit-ing pulse and a detaching pulse, respectively. The synchroni-zation between the downward momentum and the increase ofthe detaching electromagnetic force is referred to as phasematch. The phase match must be satisfied to ensure dropdetachment and to realize one drop detached by every detach-ing pulse. This method introduces a number of additionalwelding parameters, which make it difficult to select optimumcombinations of parameters for a wide range of welding con-ditions. A trial-and-error method was used to determine theseparameters experimentally. However, this empirical approachis very time-consuming.

A theoretical description of the metal transfer in GMAW canprovide a better understanding of the technology’s mechanismand a better means to determine the optimum operation param-eters. Some numerical studies have been performed forconstant-current and traditional pulsed-current GMAW.[15–24]

Such studies evolve from the earliest static models to themost recent dynamic models. In this work, a transient two-dimensional model developed based on RIPPLE[25] was usedto simulate the droplet formation, detachment, and transportin GMAW. The transient shape of the droplet was calculatedusing the fractional volume of fluid (VOF) method.[26] Thecontinuum surface force (CSF) model[27] used here simplifiedthe calculation of surface tension and enabled accurate mod-eling of fluid flows driven by surface forces. The electro-magnetic force, which was generated by the welding current,

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 35B, OCTOBER 2004—857

G. WANG, Graduate Student, and P.G. HUANG, Professor, Departmentof Mechanical Engineering, and Y.M. ZHANG, Associate Professor,Department of Electrical and Computer Engineering, are with the Universityof Kentucky, Lexington, KY 40506. Contact e-mail: [email protected]

Manuscript submitted July 29, 2003.

858—VOLUME 35B, OCTOBER 2004 METALLURGICAL AND MATERIALS TRANSACTIONS B

was calculated by assuming Gauss-type current density distri-bution over the free surface of the droplet.

II. PROPOSED APPROACH IN MODIFIEDPULSED CURRENT GMAW

In conventional pulsed GMAW using pulse waveform, asshown in Figure 1(a), the drop is detached by the combina-tion of the gravitational force and electromagnetic force. Thedetachment of a drop is still a natural detachment process.Under the current lower than the transition current, a naturaldetachment can occur only when the droplet is significantlylarger than the diameter of the electrode. Hence, the peakcurrent Ip must be higher than the transition current in orderto guarantee that the droplet naturally detaches with a sizesimilar to the diameter of the electrode.[9,10] On the other hand,the use of a peak current higher than the transition current fre-quently brings accidental detachment, which causes multipledroplets per pulse (MDPP).

To guarantee ODPP with the droplet size similar to thediameter of electrode, while the peak current is lower thanthe transition current to prevent the accidental detachment,a novel active control technology was recently proposed.[8]

In this modified pulsed current GMAW, a pulse repetitioncycle is composed of two periods: the growth period andthe detachment period, as shown in Figure 1(b). An excitingpulse edge is applied at the end of the growth period when thecurrent is switched to the base level so that a sudden changein electromagnetic force is imposed to the droplet. As a result,an oscillation of the droplet is introduced. After a periodTb2, as shown in Figure 1(b), a detaching pulse is applied.

The downward momentum of the oscillating droplet enhancesdetachment and eliminates the need for a higher current todetach the droplet. (The detachment of the droplet is nolonger a natural transition in this proposed approach but aresult of current control.) Hence, the peak current can be lowerthan the transition current to detach the droplet, while at thesame time, accidental detachment is prevented. The achieved“one drop in per pulse cycle” metal transfer, which has simi-lar periodical and controllable characteristics as ODPP, isreferred to as the modified ODPP mode or simply ODPPfor convenience of discussion.

From the parameters of the modified pulsed current GMAWshown in Figure 1(b),

[1]

[2]

[3]

[4]

where f is the pulse frequency, Iavg is the average current, Ip

is the peak current, Ib is the background current, and Tp andTb represent the peak and base duration, respectively. Anyfour of them are given as preset parameters. The other twoparameters can be determined accordingly. The waveform ofthe welding current can be changed by adjusting Tp1, Tp2, Tb1,and Tb2 without changing the preset parameters. By properlychoosing the waveform of the welding current, the proposedmethod takes advantage of synchronization between the down-ward momentum of the droplet oscillation and the detachingpulse to realize ODPP.

Experiments have demonstrated the effectiveness of the pro-posed approach. But a significant limitation of the developedcontrol system found by experiment is the use of a high-costimaging system, which monitors the oscillating droplet to guar-antee the phase match. Numerical simulations can provide abetter understanding of the mechanism of this process and hencelead to a better choice of optimum operation parameters.

III. NUMERICAL SCHEMES

The numerical schemes used are based on a finite-differencesolution of a coupled set of partial differential equationsgoverning unsteady incompressible fluid flow:

[5]

[6]

where v is the velocity, � is the fluid density, p is the scalarpressure, � is the viscous stress tensor, and Fb is body force,which includes the gravitational force and the electromagneticforce. The two-step projection method[25] was used as the basicalgorithm for solving this set of partial differential equations.The transient shape of the droplet was calculated using thefractional VOF[26] method. The free surface profile is recon-structed by employing the function F(x,t), which representsthe fluid volume ratio of each cell. The function F takes thevalue of unity for the cell filled with the fluid and zero forthe empty cell. For incompressible flow, the VOF function

rDvDt

� �§p � § # t � Fb

§ # v � 0

� (Ip * Tp � Ib * Tb) * f

Iavg � (Ip * Tp1 � Ip * Tp2 � Ib * Tb1 � Ib * Tb2)/T

T � Tb1 � Tb2 � Tp1 � Tp2 � Tb � Tp � 1/f

Tp � Tp1 � Tp2

Tb � Tb1 � Tb2

(a)

(b)

Fig. 1—Current waveforms for pulsed GMAW: (a) current waveform forconventional pulsed GMAW and (b) current waveform for modified pulsedGMAW.


might be regarded as the normalization F(x,t) � �(x,t)/�f,where �f is the constant fluid density. The discontinuity in Fis a Lagrangian invariant, propagating according to

[7]

Therefore, Eq. [7] implies that the function F should be solvedsimultaneously with Eqs. [5] and [6]. The surface tension offree surfaces was modeled as a localized volume force derivedfrom the CSF model.[27] The surface tension with volume formFsv(x) � ��(x)�F(x)g(x) can be easily counted by applyingan extra body force term in the momentum Eq. [6], where �,�,and g are surface tension coefficient, local free surface cur-vature, and optional function, respectively. The electromag-netic force, Fm � J � B, generated by the welding currentshould also be included in the body force in the momentumEq. [6]. The terms J and B represent the current density andmagnetic flux density, respectively. The current density is cal-culated from the electric potential, which satisfies the Laplaceequation by assuming the electric field is quasi-steady-stateand the electrical conductivity is constant. The boundary con-ditions for the Laplace equation are important to the determi-nation of the distributions of the potential and current densitywithin the drop and hence to the profile and magnitude of theresultant electromagnetic force. Since experimental data con-cerning the current distribution on the drop’s surface are notavailable in the literature due to the difficulty in performingmeasurements in the arc next to the free surface, an assumptionof a Gaussian distribution was made based on our pervioustheoretical study.[24] The current density on the drop surfacecell (i, j) was assumed following a Gaussian distribution:

[8]

where Jsij represents the current density on the surface cell(i, j), I the welding current, Sij the area of the free surface cell(i, j), X the arc (curve) length on the drop surface betweenthe lowest point on the drop and the free surface cell (i, j),and D the diameter of the electrode when the welding cur-rent is constant. It has been shown in our previous study[24]

that the results calculated by using a Gaussian current den-sity distribution yield a better agreement with the experimentaldata than the results based on other distributions such as aconstant or linear assumption.

When the initial and boundary conditions are given, the flowvelocity, pressure, and potential distributions and free surfaceprofile can be calculated. The metal transfer process in GMAWwith initial and boundary conditions is illustrated in Figure 2.Assumptions made here include the following: (1) the problemis axisymmetric, (2) the input velocity of molten metal is thesame as the wire feed rate no matter the current in peak orbase duration, (3) there is free slip at the solid boundaries,(4) the velocities of the surrounding gas are set to zero with pres-sure of atmospheric condition, (5) an isopotential line ( � 0)is set at the inlet section, and (6) there is a Gaussian currentdensity distribution on the droplet surface.

j �X

D

f (i, j) �112p

exp (�j2/2)

Jsij � I # f (i, j)/an

1Si,j# f (i, j)2

dF

dt�

F

t� (v # §)F � 0

As mentioned earlier, the proposed approach takes advan-tage of the downward momentum of the excited oscillationto reduce the current level for the droplet detachment and

(a)

(b)

Fig. 2—Schematic sketch of the metal transfer process in GMAW with initialand boundary conditions: (a) a schematic of metal transfer process and(b) initial and external boundary conditions.


Table I. Material Properties of the Electrode

Mass density, � 7860 kg/m3

Kinematic viscosity, v 2.8 � 10�7 m2/sSurface tension coefficient, � 1.2 N/mElectrical conductivity, � 8.54 � 105 mho/mPermeability, � 4 � 10�7 H/m

prevent accidental detachment. In order to guarantee thedetachment and realize ODPP, the phase match between thedownward momentum and the detaching action is crucial.The proper selection of Tb2, time interval between the excitingpulse and detaching pulse, determines whether the phasematch condition between the downward momentum and thedetaching action can be met. Because of the importance ofthe time interval Tb2, a numerical solution is introduced hereto determine it and guarantee phase match. Since the oscil-lation of the droplet is induced by the exciting pulse, theexcited oscillation of the droplet is numerically simulatedfirst. Based on analysis of the calculated results, the propertime interval is then determined to assure ODPP.

IV. RESULTS AND DISCUSSION

Calculations were performed based on the experimentalwork of Zhang et al.[8] Simulations were carried out for astainless steel electrode with a diameter of 1.2 mm. Thephysical properties of the stainless steel electrode are listedin Table I. A uniform computational mesh with a spacingof 0.1 mm in each coordinate direction was used. Whilethe mesh spacing was varied between 0.08 and 0.16 mm, itwas found that the calculated results remained unchanged.

A. Problems in Traditional Single Pulsed GMAW

The calculations were performed for the metal transferprocess under constant current to estimate the transition cur-rent first. The wire feed rate was selected to be 70 mm/s. Fig-ure 3 shows the predicted average drop sizes detached at

different welding currents. As the welding current increases,the metal transfer mode changes from the globular modewith a large drop detached to the spray mode with a smalldrop detached. There exists a narrow current range overwhich the transition from the globular transfer mode to thespray transfer mode occurs. The transition current rangefor the stainless steel electrode with diameter of 1.2 mm ispredicted from 220 to 230 A. It agrees well with the experi-mental results.

Figure 4 shows the dynamic drop development and detach-ment processes under traditional single pulsed currentGMAW. There are two cases presented here. In these twocases, the average current Iavg is set to 100 A, where thepulse frequency f is 30 Hz, and the base current Ib is set to40 A. According to the experimental data taken from thework of Zhang et al.,[7] the wire feed rate was selected as110 in./min (46.5 mm/s) for an average current of 100 A.In the first case, one drop multiple pulses occur when thepeak current Ip is 220 A, as shown in Figure 4(a). This resultsupports the general consensus that the peak current mustbe larger than the transition current in order to guaranteethat the droplet detaches with a size similar to the diameterof the electrode in conventional single pulsed GMAW. Also,the droplet oscillation introduced by the current pulse canbe easily visualized from Figure 4(a), which shows that everytime after the current pulse drags the droplet downward, thedroplet rebounds to a new high position and this reboundbecomes stronger as the mass of the droplet increases. Inaddition, the frequency of droplet oscillation after the currentpulse is decreased with the increase of the mass of thedroplet. In the second case, the use of a 250 A pulsatingcurrent has led to an undesirable MDPP detachment, asshown in Figure 4(b).

B. Modified Pulsed Current GMAW

1. Advantages for modified pulsed current GMAWBy simply splitting the pulse used in the first case in Sec-

tion A into two parts, one exciting pulse and the other detach-ing pulse, and keeping all other parameters unchanged(Figure 5a), the modified pulsed current GMAW takes advan-tage of the phase match between the downward momentumof the oscillating droplet introduced by the exciting pulseand the increased electromagnetic force brought by thedetaching pulse. The current level, which is required to detacha drop with a size similar to the diameter of the electrode,is reduced by introducing the downward momentum of theoscillating droplet. Figure 5(b) shows the ODPP achievedwith a droplet size similar to the diameter of the electrodeunder the peak current, which is lower than the transitioncurrent, by using the modified pulsed current GMAW.

2. Parameter Diagnoses for Phase MatchAs can be observed in Figure 5, when the time interval

between two pulses Tb2 is 4 ms, the ODPP is realized. How-ever, if a shorter duration Tb2 � 3 ms or a longer durationTb2 � 5.5 ms is used, the ODPP cannot be realized, as shownin Figure 6. In these two cases, the failure of ODPP is causedby the unsatisfied phase match condition. In the first case, asshown in Figure 6(a), the time interval between the excitingpulse and detaching pulse is too short to let the drop bounceto its highest position before the detaching pulse is added.Fig. 3—The relationship between the detached drop sizes and welding currents.


(a)

(b)

Fig. 4—Metal transfer processes under conventional pulsed current GMAW: (a) drop profiles at peak current of 220 A and (b) drop profiles at peak currentof 250 A.

Hence, the drop continues, moving to the higher positionduring part of the period of detaching pulse application. Theupward momentum of drop offsets the electromagnetic forceand makes the drop detachment process more difficult. Inthe second case, the longer time interval between the excit-ing pulse and detaching pulse allows the drop to reach itshighest position and move a long way down before thedetaching pulse presence. The downward momentum of

the droplet decreases when the drop moves down from itshighest position. Due to the ill matching of the pulse, thecombined effect of the decreasing downward momentumand the increasing electromagnetic force is not large enoughto detach the droplet. Phase match is a necessary conditionfor the proposed approach to be effective. Phase match can beachieved by the proper selection of Tb2. It is expensive todetermine Tb2 experimentally due to the use of the high-cost


(a)

(b)

Fig. 5—Metal transfer process in modified pulsed current GMAW: (a) current waveform and (b) droplet profiles.


(a)

(b)

Fig. 6—Metal transfer processes with unsatisfied phase match condition: (a) drop profiles under a shorter duration Tb2 of 3 ms and (b) drop profiles undera longer duration Tb2 of 5.5 ms.


(a)

(b)

Fig. 7—The droplet response to the exciting pulse: (a) current waveformand (b) vertical coordinate of droplet tip.

(a)

(b)

Fig. 8—Development for vertical coordinate of droplet tip in modifiedpulsed current GMAW: (a) ODPP at Tb2 of 3.5 ms and (b) ODPP at Tb2

of 4.7 ms.

imaging system. But the diagnoses for phase match can beachieved efficiently through mathematic modeling. To ensurethe phase match, the calculation was carried out first to sim-ulate the response of the droplet under the stimulus of theexciting pulse.

Figure 7 shows the calculated vertical coordinate develop-ment of the droplet tip under the application of an excitingpulse Ip1. The oscillation of the droplet is introduced by theexciting pulse. In order to realize the phase match and takeadvantage of the downward momentum of the oscillatingdroplet, it has been determined that the proper time toadd the detaching pulse is when the vertical coordinate ofthe droplet tip reaches the highest point and begins to movedownward. Figure 7 shows that in this case the dropletrecoils back to its highest point 4 ms after the pulse. Asmentioned previously, ODPP is realized when Tb2 is setat 4 ms. Also, Figure 8 shows that ODPP is achieved whena shorter Tb2 of 3.5 ms or a longer Tb2 of 4.7 ms is adopted(instants for droplet detachment are marked with dots inthe figure). Hence, the value of Tb2 is determined accordingto analysis of the simulation results. There is a time rangeover which the ODPP can be achieved when the detach-ing pulse is added. Also, the optimum value of Tb2 usedto arrive at a proper phase match can be understood by the equation governing the frequency of droplet oscillation

. The proper value of Tb2 is increased

with increasing mass of droplet, as observed in Figure 4(a).

fdrop � 1/T � B km

3. Comparison with experimentFigure 9 shows the comparison between the calculated result

and experimental[12] data provided by Zhang et al. when theproposed active metal transfer control is employed. The averagecurrents were set at 100 and 165 A, respectively. The pulsefrequency was 30 Hz for 100A and 65 Hz for 165A. Accord-ing to experimental data from the work of Zhang et al.,[7] thewire feed speeds were set at 110 in./min (46.5 mm/s) for 100 Aand 180 in./min (76.2 mm/s) for 165 A. The waveform of thewelding current is shown in Figure 9(a). It was modeled as apulse cycle, which was composed of an exciting pulse withpeak current of 210 A and a detaching pulse with peak currentof 230 A. The peak duration for the detaching pulse was setto 6 ms, while the time interval Tb2 was set to 3 ms. The basecurrent was 40 A. The other parameters can be determinedaccordingly for both cases. The calculated and measured verticalcoordinates of the droplet tip increase with time, as shown inFigures 9(b) and (c), respectively. The predicted results agreewell with the experimental data. A ODPP cycle was realizedunder these two sets of conditions.


V. CONCLUSIONS

A novel pulsed current GMAW that has been proposedby experiment is simulated and analyzed by using advancedCFD techniques. The proposed method takes advantage ofsynchronization between the downward momentum of theoscillating drop and the increased electromagnetic force torealize a modified ODPP in GMAW. The robustness of themetal transfer process in GMAW provided by this technologyis significantly improved in comparison with the conventionalpulsed GMAW process. The calculation not only shows the

effectiveness of the proposed approach to achieve a ODPPcycle, but also provides an effective means to diagnose theoptimum operation parameters and paves the way for thisnew technique to become feasible in industry.

REFERENCES1. J.F. Lancaster: The Physics of Welding, 2nd ed., 1986, Pergamon Press,

Oxford, United Kingdom.2. L.A. Jones, T.W. Eagar, and J.H. Lang: Welding J., 1998, vol. 77,

pp. 135s-141s.

(a)

(b)

(c)

Fig. 9—Comparison between the calculated results and experimental data: (a) current waveforms, (b) vertical coordinate of droplet tip from experiment,and (c) vertical coordinate of droplet tip from calculation.


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numerical analysis of metal transfer in gas metal arc welding

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