A Study on the Modeling of Magnetic Arc Deflection and Dynamic Analysis of Arc Sensor

7/29/2019 A Study on the Modeling of Magnetic Arc Deflection and Dynamic Analysis of Arc Sensor

1/6

ABSTRACT. This investigation presentstheoretical predictions and experimentalresults of the effect of a magnetic field in-tensity, initial arc length, and arc currenton the deflection of a welding arc in amagnetic field. The sensitivity character-istics of an arc sensor using magnetic arc

oscillation were also analyzed for gastungsten arc welding. First, a mathemati-cal model of the magnetic arc deflectionfor theoretical prediction was introduced,then the model was confirmed by corre-sponding experiments. Finally, a modelof an arc sensor using magnetic arc oscil-lation was set up mathematically by con-sidering the model of magnetic arc de-flection and electromagnet, as well aswelding arc and welding power source.Experiments and simulations were car-ried out to investigate how welding con-ditions such as initial arc length and arccurrent affect the sensitivity of the arc

sensor. The simulated results based onthe model showed good agreement withexperimental ones.

Introduction

A magnetic field externally applied tothe welding arc deflects the arc by elec-tromagnetic force (Lorentz force) in theplane normal to the field lines. The mag-netic field exerts force on the electronsand ions within the arc, which causes thearc to be deflected away from the normalarc path. The welding arc can be de-flected forward, backward, or sideways

with respect to electrode and welding di-rection, depending upon the direction ofan external magnetic field. A transversemagnetic field deflects the arc in thewelding direction, whereas a longitudinalmagnetic field deflects the arc perpendic-ular to the bead. If unidirectional mag-netic field is applied to an AC arc, or an

alternating field is applied to a DC arc,then the arc can be oscillated in the posi-tion normal to the direction of welding.

This has been used to improve weldingwith both gas tungsten arc welding( GTAW) and gas metal arc welding(GMAW) processes (Ref. 1).

Deminskii, et al. (Ref. 2), conductedexperiments using a GMAW process onan aluminum-magnesium alloy while alongitudinal magnetic field was applied tothe welding arc. The magnetic fields ap-plied were alternating and of the order of40 gauss. They reported the arc oscillatedacross the weld axis. They also applied analternating, transverse magnetic field tothe welding arc. I t was reported this re-sulted in a change in the shape of the weldpool. Not only was the solidification af-fected but the mechanical properties wereimproved by the application of a magneticfield to the gas metal arc welding of alu-

minum and magnesium alloys.Serdyuk, et al. (Ref. 3), reported the

metal transfer when magnetic arc oscilla-tion was applied to gas metal arc welding.Images of the metal transfer indicated thedroplets were emitted from the electrodeat the moment of maximum arc deflec-tion and the path of the molten drop wasthe same as the direction of the arc de-flection just prior to the time the drop wasdetached from the electrode.

Oscillating the arc sideways with re-spect to welding direction could be usedfor strip cladding (Ref. 4) and welding ofa material that is sensitive to hot cracking(Ref. 5), because this gives a wide beadand uniform and shallow penetration.The results indicate encouraging trends

in increasing the melt-off rate/beadheight by 15% and decreasing joint pen-etration by 20%, and hence dilution by23%. No significant improvement in beadcharacteristics was observed by increas-ing peak magnetic flux density beyond 40gauss. Metallographic examination (Ref.5) of the solidification substructureshowed arc oscillation decreases the sizeof the solidification substructure and thusprovides a more desirable pattern of mi-crosegregation in the weld metal. In gen-eral, increasing either the frequency orthe amplitude of arc oscillation had anadvantageous influence on the weld

metal microstructure. This was found tobe true whether the oscillation was per-formed parallel or perpendicular to thewelding direction.

Subjecting the welding arc to trans-verse magnetic fields has beneficial ef-fects only when the arc is deflected for-ward with respect to the direction ofelectrode travel (Refs. 6, 7). Applying anoptimum magnetic field to a welding arcon both nonmagnetic and magnetic ma-terials increases welding speed severaltimes at which undercut-free and no-porosity welds can be made.

It is known the extent of arc deflection

is dependent upon the flux density of theapplied magnetic field, the arc current,arc length, and so on (Refs. 6, 8, 9). Toapply magnetic arc oscillation to weldingautomation such as weld quality controland joint tracking, therefore, quantita-tive information has to be obtained aboutthe effect of welding conditions on arcde fle ctio n .

Mathematically and empirically de-veloped expressions of arc deflection, byBachelis and Kovalev, respectively, incor-

A Study on the Modeling of Magnetic ArcDeflection and Dynamic Analysis

of Arc Sensor

BY Y. H. KANG AND S. J. NA

A magnetic field applied to a welding arc produced an output signalbeneficial for an arc sensor

KEY WORDS

Magnetic ArcDeflection/OscillationArc PhysicsWeld Process SimulationArc SensorGTAW

Y. H. KANG and S. J. NA are with the Dept. of

Mechanical Engineering, KAIST, Taejon, Korea.

J ANUARY 20028-S


2/6

porate similar dependencies, i.e., on ini-tial arc length (lo), magnetic field inten-sity (H) and arc current (i) (Refs. 8, 9).

These relationships are as follows:

(1)where c and k are dimensionless con-stants representing arc rigidity and isthe arc deflection measured by the move-ment of the center of the anode spot with

the application of a magnetic field. Be-cause the rigidity constants are usuallyunknown, these equations have found lit-tle practical use.

The arc sensor is based on a sensingtechnique developed by using a funda-mental arc property, which is that arc cur-rent and voltage characteristics vary withvariations in torch height (electrode ex-tension length + arc length). The practi-cal advantages, such as the absence of anywelding torch and robot arm additions, its

status as a cheap and simple technique,good real-time operability, and little sus-ceptibility to the effect of electrode wirebending, have made this approach emi-nently applicable to automatic jointtracking (Refs. 1012).

Weaving frequency of mechanicalunits such as a robot arm is limited toabout 10 Hz because the inertia of thearm and welding torch causes overshootand dynamic instability of the system.

Therefore, real-time joint tracking usinga mechanically induced weaving methodlimits the attainable welding speed. Butmagnetic arc oscillation could be appliedto high-speed joint tracking because the

magnetically oscillating arc possesses vir-tually no inertia and a weaving frequencyof up to 200 Hz is permitted (Ref. 1). Themagnetic arc oscillation method easilycontrols weaving width and frequency bythe control of magnitude and frequencyof applied current to the electromagnet.

The frequency of oscillation of the arc isthe same as that of the controlling mag-netic field.

In this study, a mathematical model ofmagnetic arc deflection was introduced

for theoretical prediction; the model wasconfirmed by corresponding experi-ments. Also, the effects of magnetic fieldintensity, initial arc length, and arc cur-rent on the deflection of the gas tungstenwelding arc in a magnetic field were in-vestigated. The arc sensor using magneticarc oscillation was also modeled mathe-matically by considering the model ofmagnetic arc deflection and electromag-net as well as the welding arc and weldingpower source. Experiments and simula-tions were carried out in order to clarifyhow welding conditions affect the sensi-tivity characteristics of the arc sensor.

Model of Magnetic Arc Deflection

Since electron density ne is approxi-mately equal to that of ionsni in the col-umn of an arc plasma except where veryclose to the electrodes, the welding arccan be assumed to be electrically neutral,or ne ni (= n). Mass density , chargedensity s, mass velocity u , and currentdensity j in an arc plasma satisfying aelectrically neutral condition are there-fore expressed as follows:

=ci

4H1 1

16H2lo

2

c 2i2

1 / 2

and

=kHlo

2

i2 k2H2lo

2( )1 / 2

Fig. 1 Magnetic field externally applied on the welding arc. Fig. 2 Distributions of temperature, electrical potential, and arcpressure along the arc axis.

Fig. 3 Arc deflection calculated for various external magneticflux densities.

Fig. 4 Experimental setup for measurement of magnetic arc de-flection.

9-SWELDING J OURNAL


3/6

= niM + nem n(M+ m) nM (2)

= (ni ne)q (3)

(4)

(5)wherem, Mare the electron and ion massrespectively, ui the ion velocity, the ueelectron velocity, and q the electroniccharge.

Generally, arc plasma consists of un-countable electrons and ions, so theequations of motion about electron andion have to be solved separately to calcu-late the motion of plasma. In highly ion-ized plasma, coulomb collisions domi-nate over collisions with neutral atoms.

Thus, the two momentum balance equa-tions only considering the coulomb colli -sions are referred to as the individualfluid equations of motion.

(6)

where E, B are the electric and magnetic

field, pi, pe the ion and electron pressure

and Rie and Rei describe the collisional

transfer of momentum between two

species (Ref. 13). These two equations

are added together, to produce the com-

bined equation of motion.

(7)where p = pe+ pi is the total pressure. Inadding the two individual fluid equationsof motion, the collision terms cancel eachother since R ie= Rei.

In practice, however, mass velocity ofa plasma is generally dominated by theions, being much heavier than the elec-trons, so there is no distinction between uand the ion mean velocity ui. Momentumtransfer from ions to electrons is ex-pressed in terms of velocity differenceand average collision frequency (or, theplasma resistivity).

(8)Welding arc plasma can be assumed to beelectrically neutral. So, Equation 7 maybe rewritten

(9)Also, the diffusion by external mag-

netic field can be assumed to be a suffi-ciently static process that the plasma is al-ways in a state of equilibrium. These

assumptions allow us to neglect the iner-tia of the ions as well as that of electrons,and to replace Equation 7 as follows:

(10)Assuming the external magnetic field

Bx is only in the x-direction and the pres-sure gradient dp/dz and the electric fieldEz are only in the z-direction, then theequations of perpendicular componentsof the plasma velocity are obtained fromEquations 9 and 10 as follows:

(11)Equation 11 can be used only in cal-

culating the diffusion perpendicular to amagnetic field in highly ionized plasma.Arc deflection is, therefore, as follows:

(12)where z is the axial distance. Equation 12shows the magnitude of magnetic arc de-flection is linearly proportional to the ex-ternal magnetic flux density.

The external magnetic field appliedon arc plasma was assumed to be uniformand only in x-direction perpendicular tothe electrode axis as shown in Fig. 1. Thecoordinate system shown in F ig. 1 indi-cates x is the direction of welding, y istransverse to welding direction in theplane of the workpiece, and z coincideswith the axis of the electrode. Distribu-tions of pressure gradient, temperature,and electric field in the arc plasma wereobtained by numerical analysis of the gastungsten welding arc under argon shield-ing gas by using a code based on a finitedifference method developed in an ear-

lier study (Ref. 14). In the study, a two-di-mensional, steady-state mathematicalmodel of the arc assuming the currentdensity distribution along the cathodesurface was applied to GTAW in an argonatmosphere for investigating the influ-ences of parameters such as electrodeangle, welding current, and arc length onthe welding arc. The current density dis-tribution was assumed to have a Gaussianform characterized by the maximum cur-rent density at the electrode tip or the dis-

=uy

uzz =

Ez 1

2nq

dp

dz

dpdz

Bx z

uy =Ez

Bx

1

2nqBx

dp

dz

uz =

Bx2

dpdz

j B

= p

E+ u B

= j

+

j B

pe

nq

Rei

= mn ei ui

ue

=

n2

q2

u

i ue

= nq j

d u

dt=

u

t+ u u

=

E

+ j

B

p

Mni

d ui

dt= qni E

+ u

i B

pi + Rie

mnedu e

dt= qne E+ ue B

pe + R ei

j

= q ni u

i ne u

e

nq u

i u

e

u

= ni M u

i + ne

mue

M u

i+ mue

M + m u

i+m

Mu

e

Table 1 Physical Constants Used inCalculating Arc Deflection

Electronic charge q = 1.602 x 1019coulombBoltzmann k = 1.38 x 1023J /K

constantElectronic mass m = 9.108 x 1031 kgPermittivity of o = 8.854 x 1012 farad/m

free space

Table 2 Experimental Conditions

Welding current 100300 AArc length 510 mmMagnetic flux density 07 gaussShielding gas Pure ArElectrode 2.4- mm-diameter,

60-deg thoriatedtungsten

Fig. 5 Arc column images captured by high-speed camera. A Undeflected arc col-umn; B arc column deflected by constant magnetic field.

A B

J ANUARY 200210-S


4/6

tribution parameter. Because the elec-trode shape is curved and the size small

compared to the arc region, it is difficultto represent electrode configuration bythe rectangular grid. Thus, a boundary-fitted coordinate system was adopted toprecisely describe the electrode surface.A more detailed description of the math-ematical model can be found in the ear-lier publication (Ref. 14). For this inves-tigation, the numerical analysis of a gastungsten welding arc under argon shield-ing gas was carried out for a welding cur-rent of 100 ~ 300 A, arc length of 5 ~10

mm and electrode angle of 60 deg. Figure2 shows distributions of pressure gradi-

ent, temperature, and electric field alongthe arc center axis with a welding currentof 200 A and an arc length of 10 mm. Arcpressure and temperature near the cath-ode are higher than near the anode (Refs.14, 15). A steep gradient of electrical po-tential near the cathode tip results in highcurrent density, which generates a strongmagnetic force. This strong magneticforce acting upon the welding arc gener-ates a steep pressure gradient near thecathode tip, which in turn accelerates the

argon plasma toward the anode plate.Physical constants used in calculating

arc deflection are shown in Table 1. Fig-ure 3 shows the calculated results of arccenterline deflection for various mag-netic flux densities with a 100-A weldingcurrent and 10-mm arc length. Althoughthe deflection of arc centerline increasednonlinearly with axial location from cath-ode tip to anode plate, total deflection in-creased almost linearly with magneticflux density. As shown in the figure, themagnitude of deflection at an axial dis-tance halfway between the electrode and

A B

Fig. 6 Calculated and experimental results of arc deflection. A Effects of externally applied magnetic flux density on arc deflectionfor various welding currents; B effects of externally applied magnetic flux density on arc deflection for various arc lengths.

Fig. 7 Welding voltage waveforms with magnetic arc oscillation for various oscillation frequencies.

11-SWELDING J OURNAL


5/6

workpiece was much more than at thevicinity of the cathode and anode.

Experiment of MagneticArc Deflection

To verify the model of magnetic arcdeflection, corresponding experimentswere carried out under various weldingconditions as listed in Table 2. Figure 4shows the experimental apparatus ofGTA welding for investigating the extentof arc deflection. The water-cooled cop-per anode, which would not melt duringwelding, was used in the experiments forgenerating a constant and stable arc. Thecopper-anode was cooled down by aforced water flow to prevent it from rising

above its melting temperature. The mag-nitude of magnetic arc deflection wasmeasured with a high-speed video cam-era. Figure 5 shows the characteristic im-ages of undeflected arc column and de-flected arc column by a constantmagnetic field as captured by the high-speed camera. The magnitude of the de-flection is defined as the offset of arccenterline at the anode plate, as shown inFig. 5B.

Figure 6 shows the effects of exter-

nally applied mag-netic flux density on

arc deflection forvarious welding cur-rents and arclengths. As the mag-netic flux density andarc length increase,the magnitude of arcdeflection also in-creases, while it de-creases with increas-ing welding current.This is probably due

to the fact an increase in current and a de-crease in arc length makes arc stiffness in-crease. In Fig. 6, calculated arc deflec-

tions based on the model were comparedwith experimental ones. A lthough mag-netic flux density and arc deflection wererelated linearly in the calculated results,they showed a nonlinear relation in theexperimental ones. The linear relation-ship between magnetic flux density andarc deflection is probably attributable tothe calculation that considered only thecenterline deflection. Consequently, theproposed model cant represent the non-linearity of experiments with sufficientexactness.

Variation of WeldingVoltage with

Magnetic Arc Oscillation

Magnetic arc oscillation changes arclength, which periodically changes thewelding voltage and current. An alternat-ing parallel magnetic field causes the arcto oscillate in position normal to the di-rection of welding, which takes effect likea mechanical weaving. There is, however,a difference between magnetic arc oscil-lation and mechanical weaving on the flatplate. In mechanical weaving, the welding

voltage and current are constant duringbead-on-plate welding, while in magnetic

arc oscillation they change periodically.The welding voltage variation was inves-tigated during bead-on-plate GTA weld-ing using magnetic arc oscillation.

Figure 7 shows the raw and filteredwelding voltage signals for various oscil-lation frequencies during bead-on-platewelding. As shown in the figure, the sig-nals consist of two frequency compo-nents: a high-frequency noise componentvarying faster than the arc oscillation anda basic signal component varying at thesame frequency as the arc oscillation. A l-though the ripple voltage of a weldingpower source is about 23 V, the welding

voltage fluctuation still shows the mag-netic arc oscillation clearly. The arc sen-sor makes use of the basic signal compo-nents in these waveform signals. Thebasic signal components were thereforeextracted by a digital low-pass filter. InFig. 7, the solid line marks the waveformafter low-pass filtering. This welding volt-age variation can be used for the outputsignal of the arc sensor.

The arc sensor using magnetic arc os-cillation was mathematically modeled fortheoretical prediction. F igure 8 shows theequivalent electrical circuit of a conven-tional GTA welding system composed of

a welding power source, welding arc, andcables. A conventional welding powersource can be considered as generallyequivalent to a constant Ussource with anoutput resistance Ks and inductance L s.

The welding cable is also characterized byits resistance Rc and inductance L c. Thearc voltage Uaconsists of voltage drops inthe anodic zone, cathodic zone, and arccolumn. Based on the experimental re-sults, it is characterized by a constantcomponent uao, resistance Ra, and elec-

Fig. 8 Equivalent circuit of GTAW system with constant cur-rent power source.

Fig. 9 Comparison of welding voltage waveform obtained bysimulation and experiment during magnetic arc oscillation

Fig. 10 Experimental and theoretical frequency characteristicsof arc sensor during bead-on-plate welding with magnetic arc os-cillation.

J ANUARY 200212-S


6/6

tric field intensity Ea(= Eal + EaiI) of arccolumn. Thus, the voltage equations forthe whole loop of welding circuit can bewritten as follows:

(13)where I is the welding current and La thearc length (Ref. 12). As shown in F ig. 8,the arc length La is expressed as a func-tion of deflection angle and can be writ-ten as follows:

(14)where Lao is the initial arc length.

With increasing the alternating fre-quency of voltage applied to the electro-magnet coil, the current through the coildecreases gradually due to the coil induc-tance, which means the magnetic flux den-

sity generated from the electromagnetalso decreases. Finally, the arc deflectionand the welding voltage variation are low-ered. This phenomenon was taken intoaccount for simulation of the arc sensor.

Figure 9 shows the experimental andcalculated results of welding voltage vari-ation when magnetic arc oscillation isused. L and R represent the left and theright end position of the arc, while Crefers to the central position in the arc os-cillation. The voltages were maximizedboth at L and R and minimized at C dueto the variation of arc length. The differ-ence between maximum and minimum

voltage, or the variation amplitude ofwelding voltage, was about 2 V. The sim-ulation result was in a fairly good agree-ment with the experimental one.

Figure 10 shows the variations ofwelding voltage sensitivity for various os-cillation frequencies and welding cur-rents. The low-pass filtering techniquewas used in experimental results to en-sure a correct determination of the weld-ing voltage variation amplitude. The vari-ation increased with the decrease ofwelding current at the same magnetic fluxdensity because of the increase in arc de-flection. As the oscillation frequency in-

creased, the magnetic flux density gener-ated from the electromagnet was reduceddue to the electromagnet inductance, asdiscussed above. In the case of the elec-tromagnet used in the present work, themagnetic flux density decreased remark-ably at an oscillation frequency of morethan 15 Hz. Consequently, welding volt-age variations were reduced considerablyover 15 Hz, as shown in Fig. 10. If the re-duction of magnetic flux density can becompensated, the variation, or sensitivity,

of the arc sensor will likely remain almostconstant even over a 15-Hz oscillationfrequency.

Conclusions

Through the simulation and experi-ment of magnetic arc deflection and arcsensor using magnetic arc oscillation, thefollowing conclusions were obtained:

1) A magnetic arc deflection modelconsidering only arc centerline deflectionwas obtained. From the experimental andsimulation results, it was found magneticflux density and arc deflection are relatedlinearly in lower magnetic flux density forboth results.

2) The magnetic arc oscillation re-sulted in a change of arc length, which inturn made the welding voltage signals pe-riodically change in GTAW. Although thesignals included ripple voltage of thewelding power source (high-frequencynoise component) of about 23 V, thewelding voltage fluctuation (the basic sig-

nal component) produced by the mag-netic arc oscillation was clearly shown.The basic signal components were, there-fore, extracted by a digital low-pass filter,which can be used for the output signal ofthe arc sensor.

3) Due to inductance, the magneticflux density generated from the electro-magnet was gradually reduced with an in-crease of oscillation frequency. It is nec-essary to compensate for the reducedmagnetic flux density to maintain a con-stant sensitivity of the arc sensor in thewhole frequency range.

Acknowledgments

This work was supported in part by theBrain Korea 21 Project. The authorswould like to thank the POSCO ResearchInstitute for providing matching funds forthis project.

References

1. Hughes, R. V., and Walduck, R. P. 1987.Electromagnetic arc path control in robotplasma welding. Robotic Welding. IFS Publica-tion and Springer-Verlag, pp. 243263.

2. Deminskii, Y . A., and Dyatlov, V. I . 1963.Magnetic control during gas shielded arc weld-

ing with a consumable electrode. Aut omat i cWelding(4): 6768.

3. Serdyuk, D. B., and Kornienko, A. N.1963. The welding arc in an alternating trans-verse magnetic field. Automatic Welding(10):713.

4. Mallya, U. D., and Srinivas, H. S. 1993.Magnetic steering of arc and bead characteris-tics in submerged arc strip cladding. WeldingJournal 72(11): 517-s to 522-s.

5. Tseng, C. F., and Savage, W. F. 1971. Theeffect of arc oscillation. Welding Journal 5 0(11): 777-s to 786-s.

6. Hicken, G. K ., and Jackson, C. E. 1966.The effect of applied magnetic fields on weld-ing arcs.Welding Journal 45(11): 515-s to 524-s.

7. Jayarajan, T. N., and J ackson, C. E. 1972.Magnetic control of gas tungsten arc weldingprocess. Welding Journal 51(8): 377-s to 385-s.

8. Ecer, G. M. 1980. Magnetic deflection ofthe pulsed current welding arc.Welding Journal59(6): 183-s to 191-s.

9. Lancaster, J . F. 1986.The Physics of Weld-ing.Oxford, Pergamon.

10. Sugitiani, Y ., Kobayashi, Y ., and Mu-rayama, M. 1991. Development and applica-tion of automatic high speed rotation arc weld-ing. Welding International 7(5): 577583.

11. Cook, G. E., Barnett, R. J ., Andersen,K., and Strauss, A. M. 1995. Weld modelingand control using artificial neural networks.IEEE Trans. Ind. Applicat.31(6): 14841491.

12. Ushio, M., and Mao, W. 1996. Model-ing of an arc sensor for DC MIG/MAG weld-ing in open arc mode: study of improvement ofsensitivity and reliability of arc sensors inGM A welding (1st Report).Q. J . Jpn. Weld Soc.14(1): 99107.

13. Goldston, R. J ., and Rutherford, P. H.1995. Introduction to Plasma Physics. Br i stol

and Philadelphia, Institute of Physics Publish-ing.14. Lee, S. Y ., and Na, S. J. 1996. A nu-

merical analysis of a stationary gas tungstenwelding arc considering various electrode an-gles. Welding Journal 75(9): 269-s to 279-s.

15. Hsu, K. C., Etemadi, K., and Pfender,E. 1983. Study of the free-burning high-inten-sity argon arc.J. Appl. Phys. 54(3): 12931301.

La =Laocos

dI

dt=U

s u

ao

Ls+ L

c

K

s+R

c+ R

a

Ls+ L

c

I

E

al+ E

aiI

Ls + L cL

a

13-SWELDING J OURNAL

Documents

A Study on the Modeling of Magnetic Arc Deflection and Dynamic Analysis of Arc Sensor