GMAW Forces at Droplet

8/11/2019 GMAW Forces at Droplet

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Analyses of Electrode Heat Transfer in

Gas Metal Arc Welding

In-depth investigation offers insight into the practicality

of modeling the GM AW process

BY Y.-S. KIM, D. M. McELIGOT AND T.

W.

EAGAR

ABSTRACT. Heat and fluid flow in the

electrod e during gas metal arc welding are

considered approx imate ly , exper imen

tally, analytically and nume ricallyforranges

of electrodes and materials of practical

importance. Est imat ion of the governing

nondimensional parameters and pert inent

time scales provides insight into droplet

format ion and detachment whi le demon

strat ing that the behavior of the solid

electrode may be considered to be quasi-

steady. The time scale estimates sho w that

a steady-state, spherical f low calculation

for the droplet would be inappropr iate

and possibly misleading. Experimental ob

servat ions of the format ion of a tapering

t ip ,

forming as electrical current is in

creased in steel electrodes shielded by ar

gon gas, are found quant itat ively consis

tent with numerical simulat ions based on

the hypothesis that addit ional thermal en

ergy is evolved along the cylindrical side

surface of the electrode due to electron

condensat ion.

Introduction

Cas metal arc (CMA) welding is the

mos t common method fo r a rc we ld ing

steels and aluminum alloys. Ab ou t 40 % of

the product ion welding in this country is

accomp lished by this process in wh ich the

thermal phenomena and melt ing of the

solid electrode are coupled to the plasma

arc and theweld poo l .Thus, the the rmo-

fluid behavior of the e lect rode and de

taching drops can have significant effects

on the subsequent weld quality and pro

duct ion rate.

Whi le a number of qual i ta t ive hypoth

eses concern ing me tal transfer have been

suggested andinsome instances acce pted,

quantitative proof of their validity is still

K-S.KIM is

a.Research

Associate,Materials

Sci

ence and

Engineering,

University of Florida,

Gainesville,

Fla.

D. M.McELIGOT iswith West

inghouse NavalSystems Division, Cleveland,

Ohio. T. W.EAGAR is a

Professor,

Materials

Science

an d

Engineering, Massachusetts Insti

tute of

Technology,

Cambridge, Mass.

lacking (Ref. 1).The purpo se of the present

paper is to provide quantitative analyses,

concentrat ing on the thermal behavior of

the electrode, to aid in the fundamental

understanding of the process. Main em

phasis is on the commercially important

application of spray transfer (Refs. 2, 3)

from

steel electrodes w ith argon shielding.

In particular, it is sh ow n that simple e nerg y

balances are inadequate to explain the

observed melt ing phenomena. Instead,

heat t ransfer between the arc and the

elect rode involves a number of coupled

processes. This paper outlines which heat

transfer mechanisms predominate and in

which regimes each is important.

For a general review of recent work on

metal t ransfer, the reader is referred to

Lancaster's chapter in the text by Study

Cro up 212 of the Internat ional Inst itute of

We lding (Ref. 4). The pion eering study of

metal transfer by Lesnewich (Refs. 2, 3)

has been recent ly summ arized by h im in a

letter (Ref. 5) . Cooksey and Miller (Ref. 6)

descr ibed six modes, and Needham and

Carte r (Ref. 7) de fine d the ranges of m etal

transfer. The axial spray transfer mode is

often preferred to ensure maximum arc

stabil i ty and minimum spatter.

Analyses and experiments have been

conducted by Greene (Ref. 8), Halmoy

(Ref. 9), W oo d s (Ref. 1 0), Ue gur i, Hara and

Komura(Ref .

11),

Allum (Refs. 12,13)and

by Waszink and coworkers (Refs. 14-17).

These studies have predominant ly ad-

K E Y W O R D S

Gas Metal Arc Weld ing

Electrode Heat

Heat Transfer

Electron Condensat ion

Numerical Simulat ion

Time-Scale Estimates

Tapering Tip

Thermocapil lary Flow

Thermal Energy Flow

Nondimension Bond No.

dressed steady or static conditions, al

though Lancaster and Allum did consider

transient instabilit ies for possible explana

tions of the final stage of the droplet de

tachment process.

Possible thermal processes that may in

teract with the forces on the droplet to

cause detachment are descr ibed sche

matically in Fig. 1 for an idealized droplet.

The process is t ransient, proce edin g fro m

detachment of one droplet through melt

ing,

format ion and detachment of the

next, so there ischange in the thermal en

ergy s torage , S. Heating is caused by elec

trical a resistance heating G and by inter

act ion with the plasma q

p

.Heat losses oc

cur via conduct ion in the solid rod qi


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and the transient terms must be retained

(as they might be for the solid wire, since

the me lting interface also must be

affected

by the transient droplet) . Boundary con

di t ions for the momentum equat ions in

clude treatment of the surface tension

forces that can be dominant. Solut ion for

the droplet f ields is thus much more diff i

cult than analysis of the thermal behavior

of the solid wire and is be yo nd the scope

of the present work.

The present study examines the thermal

processes occurr ing in moving electrodes

for GM AW with the object ives of 1) de

termin ing which phenomena are impor

tant in controlling the melting rate and 2)

explaining the format ion of a tapering t ip

observed for some combinat ions of elec

trode materials and shielding gases.

Nondimensional Parameters and

Time Scales

Determinat ion of the nondimensional

parameters and relative time scales helps

to quant i fy w hich therm of lu id ef fects are

important for which transfer mode. I t fur

ther provides part of the nondimensional

descr ipt ion , wh ich w il l help generalize the

ult imate solut ion and, thereb y, reduce the

total number of calculat ions that wil l be

necessary to descr ibe the overall behav

ior.

To quant ify the typical orders of mag

ni tude inc luded, the approx imate proper

t ies and welding parameters for steel are

emp loyed .

Inapplications for steel, typical

wire diameters are in the range 0.8 to 2

mm (0.03 to 0.09 in.) and wire speeds are

of the order 0.04 to 0.2 m/s (100 to 400

in. /min) . The wire extens ion beyond the

electrical contact t ip is about 10 to 30 mm

(V2t o1in.). Typical thermo f luid propert ies

of steel (or iron) in solid and liquid phases

have been given by Greene (Ref. 8) and

Waszink and Piena (Ref. 16) and others.

The Prandt l num ber o f the l iquid metal,

Pr = Cp^/k , is a measure of the rate at

which viscous ef fects propagate across

the f luid relat ive to thermal conduct ion

(Ref. 18), or the rate at whic h the flo w field

approaches steady state compared to the

temperature

fiejd.

For steel and most

liq

uid metals Pr > 1 . An d fo r spray-sized drop le ts,

Marangon i convect ion wou ld be s ign i f i

cantly greater than natural convection

(B o

d

< < 1). The value o f Bd~ 0.2 for

spray transfer would be an indication that

a force(s) other than gravity (such as elec

t romagnet ic fo rces and/or so-ca l led

plasma jet drag) is involved in droplet de

tachment in that mode, since surface cur

vature would cause greater pressure (and

restoring force) than the weight of the

d r o p .

Greene (Ref. 8) and Waszink and

Piena (Ref. 16) have concluded from dif

ferent argume nts that the addit ional forces

are e lectromagnet ic and, there fore , M ax

well 's equations should be included in the

com plete solutio n. W hile plasma jet drag

can be expected to be signif icant as the

free droplet passes through the arc re

g ion ,

i t is not clear that i t would have an

impo rtant e ffect while the dro plet is st il l

attached. It is anticipated that i t wou ld pr i

marily act indirectly through its upstream

influence on the shielding gas around the

drop, part ia l ly countering the deceleration

of the gas at the bottom of the drop I.e.,

pressure recovery and negative drag).

Treatment of th is aspect would require a

more complete analysis, including the

plasma arc, that is beyond the scope of

this paper.

The discussion of the nondimensional

governing parameters above applies

pr i

marily to steady processes. However,

drop le t fo rmat ion and detachment is a

nonsteady event, so t ime scales or re

sponse times of the phenom ena must also

be considered to estimate whether steady

or quasi-steady condit ions may be ap

proached during the process (Ref. 24).

For1.6-mm

(Vi6-in.)

diameter mild steel,

Lesnewich (Ref. 3) shows droplet detach

ment frequencies to be of the order of

15/s

fo r curren ts be low 240 A and 250-

300/s above 280 A. These values repre

sent globular and spray metal transfer and

corresp ond to per iods o f about 70 ms and

3 ms, respectively. Kim (Ref. 19) obs erve d

frequencies rang ing f rom about 3 to 4 50 /

22-s |

JA N U A R Y 1 9 9 1


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Tab le

1Estimated

O r d e r s of M a g n i t u d e

Tab le 2Orders of M a g n i t u d e of Elect rode Time Scales'* '

Pe

Globular 4

Spray 40

Bd Bo

0.001

0.001

2

0.2

10

1

Bo

d

0.8

0.08

s.For hise x p e r i m e n t s w i t h 1.1-mm ( 0 . 0 4 5 -

i n .) d i a m e t e r s t e e l , M o r r i s ( R e f . 25)r e p o r t s

t yp i ca l va l u e sof 50 ms for g l o b u l a r and 4

m s for sp r a y t r a n s f e r but hass e e n up to

2 0 0 0 d r o p s / s or d r o p l e t p e r i o d s as shor t

as Vi ms.

T h e t i m e for a t h e r m a l c h a n g e to ap

p r o a c h s t e a d y s t a t e ( w i t h i n a b o u t 5%) by

c o n d u c t i o n in ther a d ia l d i r e c t i o n ( R e f .26),

t h e t h e r m a l c o n d u c t i v e t i m e s c a l e ,can be

e s t i m a t e d as0

T

~ 0.6

r / a .

T h e v i sco u s t i m e sca l e to a p p r o a c h

s t e a d y s t a t ecan be e x p e c t e d to be

ana l

o g o u s to the t h e r m a l c o n d u c t i v e t i m e

sca le , or 0

V

as 0.6rg/u = 0.6

0

T

/P r .

(Al

l u m

(Ref.

12) q u o t e s S o z o u

and

P i cke r i n g

(Ref .27) as sa y i n g t h a t for ) X Bf l o w s t o

a p p r o a c h s t e a d y s t a t e r e q u i r e s 0 ~ L

2

/u,

i.e., a n o t h e r v i s co u s t i m e sca l e . ) T e m p e r

a t u r e va r i a t i o n n e a r thesu r f a ce a f f e c t sthe

s u r f a c e t e n s i o n and,t h e r e f o r e , the

d r o p

l e t sh a p e p a r t i cu l a r l y n e a r then e c k at de

t a c h m e n t . C o n s e q u e n t l y , one m u s t

c o n

s ider the t i m e n e ce ssa r y to m o d i f y the

su r f a ce l a ye r s r a t h e r t h a n o n l y the ap

p r o a c h to s t e a d y s t a t e .Forr a d ia l c o n d u c

t i o n in a c y l i n d e r , a 90%c h a n g e in

t e m

p e r a t u r e isp r e d i c t e d at r / r

0

= 0.9 w i t h i n

n o n d i m e n s i o n a l t i m e (aO/r

2

,) = 0 . 1 ,ap

p r o x i m a t e l y . T h i s t i m e sca l e isa b o u t

Vb

of

t h a t

for

fu l l t h e r m a l p e n e t r a t i o n i.e.,

re

s p o n s e p e n e t r a t e s f r o m s u r fa c e t o c e n

t e r l i n e ) and we r e f e r t o it asr e s p o n s e of

t h e su r f a ce l a ye r .

F o r t h e i r w e l d p o o l s i m u l a t i o n Kou and

W a n g (Ref. 28) c l a i m the ch a r a c t e r i s t i c

t i m e a s s o c i a te d w i t h e l e c t r ic a l c o n d u c t i o n

a r e of the o r d e r of 10~

1 2

s. S ince these

t i m e s ca le s p r o b a b l y h a v e an r

2

d e p e n

d e n c e and the w e l d p o o l c o v e r s a l a rger

r e g i o n t h a n the d r o p l e t , the c o r r e s p o n d

i n g t i m e sc an bee x p e c t e d to ben e g l i g i b l e

in thep r e s e n t p r o b l e m . T y p i c a l l y , p o w e r

s u p p l i e s s h o w a r i p p l e of a b o u t 5% or

m o r e

in the

e l e c t r i c cu r r e n t ( u n l e ss t h e y

are s tab i l i zed)at 60, 120 or 360 Hz. This

s i t u a t i o n i m p l i e s a b o u t a 10%v a r i a t i o n in

i

2

w i t h ap e r i o d of 16 , 8 or 3 ms, r e s p e c

t i ve l y . T h u s , t h i s p r o ce ss is u su a l l y s l o w

r e l a t i ve

t o

s p ra y d e t a c h m e n t

but is

fast

r e l a t i vet og l o b u la r d e t a c h m e n t . N o n e t h e

less,i n e i t h e r ca se it c o u l d bee x p e c t e d to

i n f l u e n c e the d e t a c h m e n t p r o c e s s u p o n

w h i c h it is s u p e r p o s e d .

A t ime sca le for the p r o p a g a t i o n of

c a p i l l a r y w a v e s can be f o r m e d f r o m the

f l u i d p r o p e r t i e s as0

C

= [ 8 o 7 ( p g

3

) ]

1 / 4

.For

s tee lit is of t heo r d e r 30m s , w h i c h iss l o w

c o m p a r e d

to the

p e r i o d

for

sp r a y t r a n s f e r

a n d thes a m e o r d e r or f a s t e r t h a n the pe

r i o d for g l o b u l a r tr a n s f e r . T h e se r e l a t i ve

Globular

Spray

(Values inm il liseconds)

Droplet per iod

Electrical conduction

Current osci l lat ions (60, 120, 360 Hz)

Shieldinggasresidence t ime

Viscous dif fusion to center

Therma l conduct ion to center

Thermal surface layer (r >0 . 9 r d )

Capil lary waves

Surface osci l lat ion

Thermocapi l lary (Marangoni) '

61

a) Signif icant surface velocity increase

b) Surface veloci ty approaches

elect rode feed veloci ty

c) Surface f luid part icle travels

irdd/2 due to T/dx,steady

state

d) Surface f luid part icle travels

rrdd/2in f low induced d ur ing

typical droplet per iod

5 0 - 7 0


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0 . 8

-

H

0 . 6 -

r-

fig. 6 - Approxim ate .,

ax/a/

temperature

variation for steel

electrodes as

predicted by

one-dimensional

analysis based on

constant properties,

toi 200+ A.

CONTACT TIP

0 . 4

0 . 2 -

ARC

Fig. 7 Typical temperature distribution in the

electrode

as

predicted by the PHO ENICS code,

a = 0.3, 1= 280 A.

Melt ing

Interface

t i m e s e x p l a i n w h y s u r f a c e w a v e s a r e o b

s e r v e d i n t h e g l o b u l a r m o d e b u t f e w s u c h

w a ve s a r e se e n i n sp r a y t r a n s f e r . T h e n a t

u r a l f r e q u e n c y o f t h e f u n d a m e n t a l m o d e

f o r su r f a ce o sc i l l a t i o n o f a sp h e r e o f l i q u i d

su r r o u n d e d b y a n in f i n i t e r e g i o n o f ga s

( R e f s . 2 9 , 3 0 ) ca n b e a p p r o x i m a t e d a s

f

2

= 16o- / (7 r

2

p d

3

) . A t i m e sca l e t o co r r e

sp on d to a s ign i f i can t su r face o sc i l l a t i on

m i g h t b e t a ke n a s a b o u t o n e - e i g h t h o f t h e

p e r i o d d u r i n g t h e cyc l e o f o sc i l l a t i o n .

L a ck i n g a t r a n s i e n t so l u t i o n f o r t h e r m o

ca p i l l a r y f l o w i n a su i t a b l e a x i sym m e t r i c

g e o m e t r y , w e d e v e l o p e d s e v e r a l a p p r o x

i m a t e e s t i m a t e s in a n e f f o r t t o d e d u c e o r -

d e r s - o f - m a g n i t u d e f o r t h e r m o c a p i l l a r y

t i m e sca l es . T h e f o u r a p p r o x i m a t i o n s

w e r e :

1) T im e fo r s ign i f ican t ve lo c i t y i ncreas e

a f t e r i m p o s i n g a t e m p e r a t u r e d i f f e r e n c e

on a t h in l i qu id l ayer (Re f . 31 ) , 0 ~ 0.1

M

as 0.1 h

2

/ u .

2 ) T i m e f r o m i m p o s i t i o n o f t e m p e r a t u r e

d i f f e r e n c e o n t h i n li q u i d l a ye r u n t il i n d u ce d

s u r f a c e v e l o c i t y b e c o m e s c o m p a r a b l e t o

e l e c t r o d e f e e d v e l o c i t y .

3 ) R e s i d e n c e t i m e f o r su r f a ce p a r t i c l e

( t i m e t o t r a ve r se h a l f c i r cu m f e r e n ce ) a t

s t e a d y c o n d i t i o n s b a s e d o n a x i a l t e m p e r

a t u r e g r a d i e n t .

4 ) R e s i d e n c e ti m e c o r r e s p o n d i n g t o

f l o w i n d u c e d d u r i n g a t y p i c a l d r o p l e t p e

r i o d , s ta r t i ng f rom res t (Re f . 22)Fig . 4 .

Est imates a re i nc luded in Tab le 2 . Fur ther

d e t a i ls a r e i n t h e r e p o r t b y M c E l i g o t a n d

Uhlman ( R e f. 2 4 ) . T h e se f o u r d i f f e r e n t a p

p r o a c h e s g^ve a r a n g e g r e a t e r t h a n a n o r

d e r o f m a g n i t u d e f o r t h e p o ss i b l e t h e r

m o ca p i l l a r y t i m e sca l e s .

The resu l t s o f t he t ime sca le es t imat ion

fo r 1.6-mm (Vi6-in.) d i a m e t e r s t e e l a r e

p r e se n t e d i n T a b l e 2 . I t m u s t b e e m p h a

s i z e d t h a t t h e s e a re m e r e l y o r d e r - o f - m a g -

n i t u d e e s t i m a t e s f o r g u i d a n ce . I n g e n e r a l ,

w h e n t h e r e s p o n s e f o r o n e p h e n o m e n o n

is m u ch q u i cke r t h a n a n o t h e r , t h e fi r s t ca n

b e t r e a t e d a s q u a s i - s t e a d y r e l a t i ve t o t h e

s e c o n d .

W h e n t i m e sca le s a r e o f t h e sa m e

o r d e r , b o t h p h e n o m e n a m u s t b e c o n s i d

e red in t he t rans ien t ana lys i s . F rom the

co m p a r i s o n , w e se e t h a t v i s co u s d i f f u s i o n

is t o o s l o w t o b e i m p o r t a n t e x ce p t a s i n

v o l v e d i n t h e t h e r m o c a p i l l a r y s u r f a c e p h e

n o m e n a . T h e p r o p e r t i m e s c a le f o r t h e r

m o c a p i l l a r y co n v e c t i o n i n t h is a p p l i ca t i o n

h as n o t b e e n d e t e r m i n e d . D u e t o t h e

r a n g e o f va l u e s e s t i m a t e d , o n e ca n o n l y

s a y i t m a y b e i m p o r t a n t f o r g l o b u l a r a n d /

o r sp r a y t r a n s f e r . F o r g l o b u l a r a n d sp r a y

m o d e s , t h e r m a l c o n d u c t i o n a t t h e s u r f a c e

and sur face osc i l l a t i ons have t ime sca les

c o m p a r a b l e t o t h e i r p e r i o d s . Interaction

w i t h e l e c t r i c cu r r e n t o sc i l l a t i o n s d e p e n d s

o n t h e p o w e r s u p p l y f r e q u e n c y ( a n d

w h e t h e r i t is s t a b i l i ze d e f f e c t i ve l y ) .

I n su m m a r y , f o r t h e g e n e r a l ca se o f

e l e c t r o d e m e l t i n g a n d d e t a c h m e n t , t h e

order-of -magnitude e s t i m a t e s o f g o v e r n

i n g p a r a m e t e r s a n d t i m e sca le s r e ve a l n o

s i g n i f i ca n t s i m p l i f i ca t i o n e xce p t t h a t b u o y

ancy f o rces a re l i ke l y t o be neg l i g ib le i n t he

d r o p l e t . F u r t h e r , s i n ce a n u m b e r o f t i m e

sca le s a r e o f t h e sa m e o r d e r - o f - m a g n i

t u d e ,

t h e f l u i d a n d h e a t t r a n s f e r p r o b l e m s

i n t h e l iq u i d d r o p l e t sh o u l d n o t b e co n s i d

e r e d t o b e q u a s i - s t e a d y p r o ce sse s . A

s t e a d y - s t a t e a n a l ys i s ( w h i ch m i g h t b e a t

t e m p t e d w i t h s o m e a v a i l a b l e c o d e s )

w o u l d b e i n a p p r o p r i a t e a n d p e r h a p s m i s

l e a d i n g .

U l t i m a t e l y , i t w i l l p r o b a b l y b e

n e ce ssa r y t o so l ve t h e t r a n s i e n t , co u p l e d

thermof lu idmechanic e q u a t i o n s f o r t h e

d r o p l e t a n d w i r e i n c o n j u n c t i o n w i t h e x

p e r i m e n t a l o b s e r v a t i o n s t o o b t a i n p r e d i c

t i o n s w i t h r e a so n a b l e d e t a i l . T h e p r e s e n t

s t u d y b e g i n s t h a t p r o ce ss , co n ce n t r a t i n g

o n t h e so l i d e l e c t r o d e .

Melt ing Exper iments

M e a s u r e m e n t s w e r e o b t a i n e d w i t h r e

s e a r c h w e l d i n g e q u i p m e n t t o o b s e r v e t h e

e l e c t r o d e s h a p e , a r c a t t a c h m e n t , d r o p l e t

s i ze ,

t r a n s f e r m o d e s a n d th e i r r e l a t i o n

s h ip s t o t y p i c a l w e l d i n g c o n t r o l p a r a m e

te rs .

T h e se e xp e r i m e n t s e s t a b l i sh e d t h e

c o n d i t i o n s f o r w h i c h n u m e r i c a l s i m u l a

t io n s w e r e l a te r c o n d u c t e d .

Appara tus

D i r e c t c u r r e n t e l e c t r o d e - p o s i t i v e

( DC E P) w e l d i n g w a s p e r f o r m e d i n t h e

c o n s t a n t c u r r e n t m o d e u s i n g a n e l e c t r o d e

f e e d m o t o r , w h i c h w a s r e g u l a t e d b y t h e

a r c vo l t a g e s i g n a l. C u r r e n t w a s co n t r o l l e d

b y a 2 0 k W a n a l o g t r a n s is t o r p o w e r s u p

p l y d e s i g n e d b y Kusko (Re f . 31) , wh ich

su p p l i e d cu r r e n t w i t h l e ss t h a n 1 % r i p p l e .

I n o r d e r t o co n t r o l va r i a t i o n s i n r e s i s t i ve

h e a t i n g o f t h e e l e c t r o d e e x t e n s i o n , a n

a l u m i n a t u b e w a s i n se r t e d i n t o t h e co n t a c t

t i p ,

l e a v i n g o n l y 5 m m ( 0 . 2 in . ) f o r e l e c t r i

ca l co n t a c t r a t h e r t h a n t h e cu s t o m a r y

co n t a c t l e n g t h va r i a t i o n o f 2 4 m m ( 1 i n .) in

t h is co m m e r c i a l e l e c t r o d e h o l d e r (R e f. 1 9 ) .

An a l ys i s o f t h e m e t a l t r a n s f e r p r o ce ss

w a s p e r f o r m e d u s in g h i g h - s p e e d v i d e o -

24-s |JANUARY 1991


6/12

pho togr aph y at 1000 fps. In contrast t o

the convent iona l h igh-speed cinematog

raphy, which uses a l ight source with

greater intensity than the arc and a strong

neutral-density filter, a laser backlit shad-

owgraphic method (Ref. 33) was used in

this study. This system excludes most of

the intense arc light and transmits most of

the laser light by placing a spatial filter at

the focal point of the objective lens. The

system setup and the equ ipment speci f i

cations are detailed by Kim (Ref. 19).

Procedures and Ranges of Variables

Measurements emphasized mild steel

(AWS ER70S-3) as the electrode materia l

but a luminum

alloys (AA1100 and

AA5356)

and t i tanium al loy (Ti-6AI-4V) were also

emp loyed to include a wider range o f

physical properties. An electrode diame

ter of

Vi6

in . (1 .6 mm ) was used th r ough

out. The shielding gases used were pure

argon, pure hel ium, their mixtures, argon-

2%

oxygen and carbon d ioxide . The ranges

of variation of welding parameters during

this study are given in Table 3. Overal l

we ld ing curren t ranged f rom 80 to 420 A

and electro de extension was set at 16, 26

-o r

36 mm (0.63, 1.02 or 1.4 in.).

Electrode extension is defined in th is

study as the distance from the end of th e

contact t ip to the l iquid-sol id interface.

With the v ideo moni to r ing techn ique, i t

cou ld be contro l led wi th in

1

mm (0.04

in.) during welding. Electrical current was

measured by an external shunt, which is

capable of measurement with in an uncer

ta inty of

1%

of full scale.

Melt ing rates were measured by read

ing the output vo l tage o f a tachometer,

wh ic h was in contact w i t h the m oving

e lectrode. The tachometer was care fu l ly

cal ibrated by indenting the surface of the

e lectrode once e very second w i th a so le

noid indenter tr igge red by a rotating cam .

Afterwards, the indented sections of the

e lectrode were removed and the actua l

mass of the electro de passing throug h the

system per unit t ime was measured to an

accuracy of 0.0005 g. In addit ion, the cal

ibration was performed by measuring the

mass that passed through the inde ntor for

5

s .

Experimental Results

Typical data for melt ing rates (or wire

feed speeds

V

w

)

w ith steel and a range of

shielding gases are pre sen ted in Fig. 2. The

same trends were seen at shorter and

longer ex tensions (Ref. 19). Wi th argo n, as

we ll as w ith A-2%C>2, the re is an appar ent

sl ight variation in the tren d of th e curv e, or

a transit ion at intermediate currents. With

helium and carbon dioxide as shielding

gases, th is effect was n ot evid ent; th e

slopes of the curves were continuous and

nearly constant.

For mixtures wi th an argon-r ich com

posit ion (75% A/25% He) there also is an

apparent transit ion in the melt ing rate

curve . H owe ver, as the he l ium content is

increased (50% A/50% He), the transit ion

disappears. Aluminum and t i tanium re

vealed slight transitions in their curves

when shielded with pure argon. Thus, i t

seems that the transit ion is re lated to arc

behavior with argon shielding gas.

For the same variety of welding condi

t ions, droplet sizes were determined. The

size was measu red fro m the stil l image on

the video screen once every 10 s, then

these ten samples were averaged. Figure

3 compares the results for steel with

A-2%C>2,

helium and

CO2

as the shielding

gases. Again there is a substantial differ

ence in behavior depending on shielding

gas, but no critical transition in size is ob

served.

Calculations of the related drople t

T

(K)

2100

1500

900

300

Steel

Ar-2/o0

2

=

0.25

260

amp.

0.5

2.5

detachment frequencies also fa i led to

show any sharp transi t ion . How eve r, w i th

argon, much smaller droplets are evident

at high currents.

Visualization of the electrode and

d rop

let detachment provides some insight into

the effects of argon on the metal transfer

process. Figure 4 demonstrates the effect

of e lectrical current on the size of the de

tached dro plets and the shape of the sol id

e lectrode fo r steel and argon over the

same range as Figs. 2 and 3. A co ntin uou s,

gradual va riation is seen. If one defines t he

transit ion to spray transfer as occurring

whe n the drop le t d iameter is approxi

mately equal to the wire diameter, i t is

seen in the middle sub-f igure for i

=s

253

A. This value agrees wi th the observa tions

of Figs. 3. This gradual transition contra

dicts work in the 1950s, which reported a

sharp transition (Refs. 2, 3), but is consis

ten t w i th a l l fo l low-on stud ies perfo rmed

over the past 30 years.

At low curren ts, the photographs show

large subglobular droplets and a relatively

blunt t ip to the electrode. As the current

is increased: 1) the drop lets bec om e

smaller, 2) the required wire speed in

creases and 3) the electrode tip acquires a

sharpening taper. The sequenc e is con tin

uous and gradual.

No taper was observed with shielding

by helium or CO2, but visualization

show ed a repe l led fo rm o f de tachmen t,

which led to large drop sizes. With alumi

num and argon shielding, a taper formed

16 0 0 -

1 2 0 0 -

aoo -

400 -

Sleel

Heliun

gas

380

a m p ^ ^ - ^

-~ ^ C Z -

180 amp

I ' | ' I 1

x (cm)

Fig. 8Axialtemperature distribution along electrode centerlineas predicted by thePHOENICS

code.

Fig.

9 Predictedaxial temperature distribution

with

negligible

electron condensation on side

surface a~0).

WELDING RESEARCH SUPPLEMENTI25-s


7/12

Fig.

10-Predicted

effect of electron

condensation

on side

surface

of

solid

electrode.

but was sho rter (or b lunter) than for steel.

None was seen fo r D C ope ra t ion o f t i ta

nium electrodes t o 260 A (maximum used),

but i t d id occ ur wi th pulsed currents at 500

A, so it is exp ecte d for h igher DC currents

wi th argon.

Consideration of the electron current

path yie lds further understanding. The

distr ibution of current on the surface of

the electro de is affec ted by several fac

to rs,

such as material, shielding gas and

total welding current. Precise measure

me nt of th e distr ibution is not available.

However, in Kim's study (Ref. 19), an ap

proximate method, consider ing the main

current path to be related to the bright

spots on the photographs, gave useful in

dications. These observations of anode

spot behavior were made wi th a co lor

video camera using the laser backl ight

system.

Instead of the narrow band f i l ter

used wi th th e h igh-speed video, a neutra l -

density filter was used to adjust the light

input to the camera.

Figure 5 shows obs erve d bright spots or

indicated current paths for steel and t i ta

nium alloys in globu lar trans fer a nd steel in

streaming transfer, a l l with argon . In steel,

there is no well-d efined cu rrent path in to

the consumable electrode. Rather, the arc

root appears to be diffuse. Therefore, i t

seems that the electrons condense not

only on the l iquid drop, but a lso on the

solid side surface of the electrode. Com

parab le phenomena were observed wi th

aluminum. With the t i tanium al loy there is

a sharp anode spot on the l iquid drop,

wi th a strong plasma jet emanating f rom

this spot, and most of the electrons seem

to condense on the l iquid drop at th is

spot .

W i t h CO2 shielding, most of the elec

t rons condense a t the bot tom o f the liq

u id drop. Wi th he l ium, the e lectron con

densat ion is conf ined to the lower bo t tom

but is less concentrated than with

CO2

(Ref. 19).

As a conseq uence of the abo ve obs er

vations, the fo l lowing hypotheses of taper

form ation is pro pos ed (Ref. 19): W he n the

shielding gas is argon, a port ion of the

electrons cond ense o n the cyl indrical side

surface of the,sol id electrode and l iberate

heat of condensation at th is location.

When this energy generation rate is high

enough on the surface, the electrode sur

face wil l melt an d the l iquid metal f i lm wil l

be swep t

downward

b y

gravitational

a n d /

or other forces. When this melt ing occurs

ove r a sufficient length of the cyl inder, a

taper wil l develop at the end of the elec

t rode.

W het her th is hypothesis is quanti

tat ively consistent with the thermal phe

nome na in the sol id electrode is a question

that is examined analytically in the later

sections.

Prel iminary Analyses for Sol id

E lec t rode

As an introduction to the next section,

and to provide further insight, th is section

provides discussion of a limiting closed

form analysis. By treating the materia l

properties as constant and the electrical

and therma l f ie lds as steady, one may ap

proximate the thermal behavior in the

solid electrode by two l imit ing cases: 1)

resist ive heating without heat transfer

through the side surface i.e.,one -d imen

sional), and 2) heating at the side surface

without axial conduction. The f irst corre

sponds to the observa t ions whe re no sig

nif icant current path to the side of the

e lectrode was apparent , and the second

represents the situation hypothesized

above as leading to taper formation.

Closed form analyses are possible for

both cases.

The steady idealization implies that the

dimensions of interest are large relative to

the penetra t ion depth ( ie . , dept h to wh ich

the thermal oscillation is significant) for

thermal conduct ion a t the drop le t de tach

ment f requencies and/or tha t the pred ic

t ions represent effective temporal aver

ages.

This penetration depth can be esti

mated f rom the t ransien t conduct ion

solutio n for a cosinusoidally oscillating

surface temperature on a semi-inf in ite

solid (Ref. 34, Equation 6.12a). For the n-

th harmonic about the mean it takes the

fo rm

1

(3)

' Tmean =

T

0

e x p 1 ~ I ^p

2-irn nit \

Vi

The dept h at whic h the am plitude is a

fraction 1/u of the surface amplitude is

then

Ax = fin v ^aP/ mr) 4)

From the f irst harmo nic an d a 5% criterio n,

one may estimate th is penetration depth

to be about 0 .1d

w

for spray transfer and

0 .6d

w

for globular transfer for steel in the

present experiments. There may be a bit

mo re variation du e to the actual size of the

drops, bu t i t wou ld be countered by the

convect ive w ire mot ion in the oppos i te

direction to the thermal disturbance.

The treatment of heating of the side

surfaces by electron condensation in

volves the solution of Equation 1 as a par

t ia l d ifferentia l equation. With suitable

idealizations the pro blem m ay be attack ed

wi th superposi t ion techn iques employed

for convection heat transfer in the en

trance of a heated tube (Ref. 18) or t ran

sient conduction in a rod (Ref. 34). Appli

cation of such an analysis to the moving

e lectrode prob lem is under d eve lopm ent

b y

Uhlman

(Ref. 35), but i t is considered

beyond the scope of the present paper.

Thus, we wil l concentrate on the f irst

(one-dimensional) situation for prel imi

nary, closed form analysis.

The one-dimensional idealization corre

sponds to condit ions where al l heating by

electron condensation occurs at the t ip,

and there is no significant heat loss (or

gain) at the cylindrical surface of the elec

trode. In th is situation, the governing en

ergy Equation 1 may be re duce d and

nondimensionalized to an ordinary differ

entia l equation.

d

2

T

dT

_

dF

df -

q c

(5)

whe re z = L x is measured f rom the

mo lten t ip so u =

V

w

and the non-

dimensional variables are

T = (T

m

- T) / (T

m

- T

r

)

z =

(VwZ/a)

= zPe /D

and

- q

c

' D

2

q

k(T

m

- T

r

)P e

2

'

16 i

2

p

e

TT

2

kD

2

(T

m

- T

r

)P e

2

(6)

Appropr ia te boundary cond i t ions are

T =

O

at z =

O

T = 1 at z = L = LPe /D (7)

26 s

|J A N U A R Y 1 9 9 1


8/12

of this mathem atical pro ble m

qc taken constant may be wr i t ten

T(z) =

( 1 - q

G

L )

N]

qc z (8)

con

up

nst the m ot io n, and the secon d

the c onseque nce of resist ive heat ing by

In a previous sec

we saw that for steel electrodes we

Pe < 40 and in the exp er

was abo ut 10 to 20 so the de

inator is near unity, giving the app rox

T(z) ~ (1 - q

c

L) [ 1 - e x p - z ] +

q

G

z

T =

T - T

r

Tm

-

T

r

(1 - qcL) [1

1 - q

c

z

(9)

_to zero approaching the con

Equat ion 9 is presen ted for typical con

Fig.6. The parameters em ployed

this_

calcula tion are L/D = 15, Pe = 10

nd

qc

corresponding to sl ight ly more

1.6-mm

(Vi6-in.) diameter

es negligible b eyo nd z > 5 or

ber ex pec ted, this is only of the order

The fract ion of the total temperature

se fro m

T

r

t o

T

m

due to conduc t ion f rom

qcL). The n ondime nsional quant ity

~

200 A at 1000 K with

steel, typical values would be of

q

G

=s0.5/Pe

2

. How eve r, i t must

be_considered qua litat ive. The q uan

p

e

in

T

r

and T

m

so the slope of the

T

m

is approached .

Effects of choice of other materials may

as steel, Pe will b e less by a factor of

timesjurther.

For the same elec

qc decreases both due to

3H_

_ti_

(

_

dH\ } \


9/12

Equat ion 10 and conversion to tempera

ture via the pro per ty relat ion T(H) can ac

count for the heat of fusion and phase

transformat ion e.g., y toa) in addit ion to

the varying specific heat of the

solid.

However, the velocity and boundaries of

the solut ion region were kept f ixed so

convect ion and f ree sur face phenome na

in the molten l iquid were not t rea ted. Fur

ther, since the main interest in the present

study focused o n the solid region, most of

the simulat ions neglected the treatment of

melt ing and phase transformat ion. The

effect of phase transformat ion was tested

with comparat ive calculat ions and was

found negligible.

Calculations we re essentially simulations

of individual melting experiments. Elec

trode diameter was taken as Vie in (1.6

mm) and propert ies were for the mater ial

used, usually steel. The electrode exten

sion L, electrode feed spee d V

w

and elec

tr ical current i were as measured in the

specif ic experiment. The quant it ies q

to

tai

an d q

s

were est imated f rom the exper i

mental measurements via Equations 16

and 14, respect ively. The resist ive energy

generat ion rate q

G

was evaluated via

integrat ion and Equat ions 11, 12 and 17

during the iterat ive solut ion.

A f ixed numerical gr id was employed.

Twe nty nodes were d is t r ibuted uni formly

in the radial direct ion between the cen

terline and the surface and 80 in the axial

d irect ion ,

also equidistant. The solutions

we re obta ined via a t ransient approac h t o

steady state. At each step, the enthalpy

distr ibut ion was determined via the en

ergy equat ion and the local temperatures

and other proper t ies were then deter

mined from the property relat ionships. I t

erat ions cont inued unt i l they converged

with in

0 .001%

of the temperature at suc

cessive time steps.

Inlet temp eratu re at the contact t ip was

takenasthe measured room temperature,

about 300 K. An approximate calculat ion

by Kim (Ref. 19) demonstrated that the

convect ive and radiat ive heat losses from

the electrode would be less than one per

cent of the energy rate required for melt

ing.

In other preliminary calculat ions, nu

merical solut ions with surface heat ing

q

s

set to zero w ere com pared to the one-d i

mensional analytic solution that applies if

propert ies are constant. The axial temp er

ature distr ibut ion predicted numerically

wi th a l lowance for proper ty var ia t ion,

agreed reasonably.

The effect of shielding gas was intro

duced via the parameter

a,

which is the

fract ion of energy received via electron

condensat ion on the electrode side sur

face relat ive to the total electron conden

sation. Based on the experimental obser

vat ions of the arc and electrode, the

val

ues shown in Table 4 were chosen.

(Practical thermal f ield solutions presented

later suggesta var ies fro m 0.1 to 0.25 for

steel with argon.) Variat ion of the Gaus

sian distr ibut ion parameter was examined

(Ref. 1 9), bu t a value a= 0.35 cm (0.14 in.)

was employed unless st ipulated other

wise.This value w as based o n estimates of

the radial distribution of current density in

a welding plasma (Ref. 41).

In the regions where predicted temper

atures exceeded the melt ing temperature,

the velocity was st il l taken as the w ire feed

speed V

w

. Thus, possible relat ive mot ion

of the molten l iquid was neglected and no

liquid f i lm f low was simulated along the

tapering interface observed in some ex

periments.

Typical predict ions are demon strated in

Fig.

7. Steel is simulated wi th argon s hield

ing,

electrode extension of 2.6 cm (1.02

in.),wi re fee d speed of 6.6 cm /s (2.6 in. /s)

and electr ical current of 280 A. The non-

dimens ional ve locity is Pe= 14. The value

a - 0.3 is used for the electron con den

sation parameter in this case. Selected

isotherms are plot ted across a vert ical

centerplane of the electrode via an as

sumpt ion of symmetry . Mot ion is

ver t i

cally do w nw ar d as in the experimen t. The

crosshatching represents the region w he re

the temperature is predic ted to exceed

the melt ing temperature.

It is evident that outer surface heating

and thermal conduct ion in the solid initi

ated the growth of a thermal boundary

layer f rom the surface above the 600 K

iso therm.

As a consequence of the in-

Table

3The

Com bination of W elding Parameters Used in Experiments

Argon

Mild

steel

Aluminium

(1100,

5356)

TE6AI-4V

Shielding

Gas

Hel ium

X

co

2

X

X

Elect rode

Extension

(mm)

16,26,36

16,26,36

16,26,36

Arc

Length

(mm)

1 4 - A r

6 - H e

8 - C 0

2

1 4 - A r

1 4 - A r

Weld ing

Current

(amp)

180-420

8 0 - 2 2 0

120-260

(a ) We ld ing was performed

creased tem pera ture near the surface, the

electrical resistivity (and therefore

q c '

)

is increased the re, raising the temp erature

further. This thermal bo und ary appears to

have penetrated almost to the center l ine

by the second isotherm at 1000 K. For

comparable laminar f low in tubes, ful ly

established Nusselt numbers are expe cted

to require a nondimensional distance

L

+

= (x/r

w

)/Pe = 0.1 or so without axial

conduction (Ref. 18). For the conditions of

this simulat ion that cr iter ion corresponds

to 0.7 diameters, but the distance for the

temperature prof i le to become approx i

mately invar iant would be longer.

Below the melt ing isotherm(~1900 K),

the steel is predicted to be molten. In

pract ice, the l iqu id mot ion wo uld depe nd

on gravity and electromagnet ic forces

(accelerating forces) in relation to the

elect rode feed speed (momentum). At

low V

w

, one would expect a l iquid f i lm to

form at the surface when T(x,r

w

) = T

m

and to run down the solid surface, form

ing a taper and droplet as in the spray

transfer experiments. At high V

w

( there

fo re ,

high current) there may be insuff i

cient t ime for the liquid film to clear so the

molten region may cont inue to move in

sol id body m ot i on as some cases of

streaming transfer appear. The present

simulat ion does not discr iminate between

these tw o cases. Instead , it represe nts a

form of average cylindr ical equivalent to

the solid-plus-liquid regions of the elec

trode with their interface fal l ing in the in

ter ior.

Figure 8 presents the axial temperature

prof i le along the electrode center l ine for

approximately the same situat ion (here

a = 0.25 and i = 260 A). During the first

half of the travel, the temperature in

creases slowly due to electrical resistance

heating,

and there is a slight increase in

slope as p

e

increases with temperature.

Near x~ 1.4 cm, the hypothes ized sur

face heating begins to affect the centerline

temperature. This observat ion cor re

sponds to the propagat ion of the appar

ent thermal boundary layer as descr ibed

above .

As T approache sT

me

it,the re is also

a further increase due to thermal conduc

t ion upstream from the melt ing interface,

in accordance with Equat ion 8 or 9

eval

uate d nea r x = L i.e., near z = 0). The

upstream propagat ion could be est imated

to be the order of

x/ r

w

~ 10/Pe or 0.6

m m . The near-linear increase of T(x) to

ward the end of the electrode is l ikely to

be a fortuitous consequence of counter

ing ef fects of thermal boundary layer

g r o w t h ,

the Gaussian increase of

q

s

with x and upst ream conduct ion.

Discussion of Results

As noted ear l ier, the temperature dis

tr ibut ion in the solid elec trode is pr imarily

af fected by the resist ive heat ing, heat

transfer via the l iquid drop and electron

28 s|

J A NUA R Y 1 9 9 1


10/12

Table 4Values Assigned According to

Experimental Observations

Electrode

Steel

Steel

Titanium

(TE6AI-4V)

Alum inum

Cas

Hel ium, CO2

A r g o n - 2 % 0

2

Argon

Argon

Varied 0 1

0

0

conde nsation o n the cyl indrical side of the

e lectrode. Measurement o f these quant i

ties is impractical, if not impossible, so in

direct methods become necessary to

eval

ua te them. In th is section, the numerical

technique previously discussed is applied

to deduce quant i ta t ive ly whether e lec

tron condensation is a reasonable expla

nation for the tapering of steel e lectrodes

in argon shielding, to estimate i ts rate and,

then, to determine the relative magni

tudes of these thermal phenomena. Elec

tron condensation on the side surface is

represented by

a,

the ratio at the side to

the total condensation on the l iquid drop

le t

plus

side.

In

a sense, the numerical so

lution is used to calibrate

a

fo r the cond i

t ions of the experiments.

Effects of Side Electron Conde nsation on

Temperature Distribution

Examination of the visual observations

led to the conclusion that there was no

signif icant e lectron condensation on the

electrode side for a luminum or t i tanium

alloys or for steel shielded by helium or

carbon dioxide. Therefore, in these cases,

a

a*0 . The prob le m becomes one-d i

mensiona l in space wi th un i fo rm temper

atures in the radial d irection. The axial

tempera ture d ist r ibu t ion cou ld be pre

dicted by Equation 8 i f the properties did

not vary signif icantly with temperature.

To account fo r the prope rty var ia t ion , the

numerical solution was obtained.

Figure 9 presents the predicted results

at typical experim ental condit ions

for

these

materials an d shielding gaseswith a = 0. A

typ ica l two-d imensiona l p re d ict ion

fo r

this

case is include d asFig.10A, dem onstra t ing

the one-d imensiona l isotherms or un i fo rm

radial tem peratu re profi les. For aluminu m,

the low electrical resist ivi ty yie lds very l i t

tle resistive heating and only a slight

tem

perature increase along the electrode.

Thus, the increase to the melt ing point

must be provided almost entire ly by ther

mal conduct ion f rom the mel t ing in te r

face, comparab le t o the bracketed te rm in

Equation 8. On the other hand, the elec

trical resistivity of the titanium alloy is high

so most of the approach to melt ing is due

to resistive heatingFig.9B.

For steel e lectrodes, the thermal varia

t ion of e lectrical resist ivi ty is more signif i

cant, as demonstrated by the nonlinear

tem pera ture va riation in Fig. 9C w ith h e-

W )

liumshielding. W ith carb on dioxid e shield

ing, comparable results are predicted, but

the temperature is a bit h igher at a given

current because the electrode velocity

(melting rate) is less. An effect of electron

condensation on the cyl indrical side can

be seen by comparison to Fig. 8, which is

fo ra = 0.25, simulating argon shielding. In

the latter case, the induced tem pera ture

rise is substantial and approaches the

melt ing temperature near the end of the

e lectrode.

The pred icted e f fect o f a on the inter

na l tempe ra ture o f the e lectrode is dem

onstrated in Fig. 10 with variation from

zero to unity

i.e.,

no e lectron condensa

tion on the side to all on the side surface).

These simulations represent steel with ar

gon shielding with an electrical current of

280 A. The length shown corresponds to

the measured extension length . Wi th

a >

0, the tem pera ture p rofi le shapes are

approximately the same, appearing l ike

the results of the near analogous thermal

entry p rob lem for f low in a tube wi th a

heated sidewall (Ref. 18).

The plotted 1800 K isotherms are ap

proxima te ind ica t ions o f the pred icted lo

cations of the melt ing interface. The ex

t remes show tha t some e lectron conden

sation must occur on the side surfaces. For

a =

0(Fig. 10A), the temp eratu re

does

not

even approach the mel t ing po in t . On the

other han d, fo r

a =

1 (Fig. 10D) the m elt

ing temperature is reached across the en

t ire electrode

before

three-quarters of the

measured length ,

i.e.,

the e lectrode w ou ld

be much shorter than the simulation. A

reasonable value predicting some surface

melt ing, and therefore tapering, appears

to fall in the range of 0.1 to 0.25

for

a.

Effects

of Side Electron Condensation on

Energy Balance

For an assumed fraction of e lectron

condensation occurring on the side sur

face, the require d heat transfer rate to the

l iquid-sol id interface may be deduced by

an energy balance. The experimental ly

measured melt ing rate determines the to

ta l power requ i red . From p

e

(T) and the

Fig.11-Predicted

effects of electron

condensation ratio a

on thermalenergy

balance forsteel

1

electrodes with argon

shielding.

predicted T(x,r), the energy generation

rate by resist ive heating may be calcu

lated. Integration of Eq uation 14 for the

specif ied value of

a

gives

q jc ,

the total in

put due to electron condensation on the

side surface. The difference then is the

required heat transfer rate through the

l iquid drop to the l iquid-sol id interface at

the t ip,

q

L

-s = m AH -

q

c

-

q

E C

where AH represents the energy per unit

mass required to melt the electrode. Fig

ure 11 shows the pred icted e f fects on

these terms of varying

a

fo r an exper i

ment with steel at 260 A and 2.6 cm ex

tension.

The side surface contribution

qsc

in

creases directly with

a,

as expected. In

add i t ion ,

qc

increases slightly at low values

o f

a,

and since the side heating increases

the temperature local ly, the electrical re

sistance and

qc

increase. The required

heat transfer

ra t e j o

the interface q^s

drops. And fo r

a >

0.4 i t becomes nega

tive.

Thatis ,in con junct ion w i th

q

c

a value

of a ~ 0 .4 provides enough heat ing to

melt the electrode entire ly. Any higher

value is physically unrealistic for this case.

Thus^

th_e

value estimated previously,

0 .1 < a < 0 . 2 5 , is a ccep ta b le f r o m t he

energy balance viewpoint presented in

Fig.11 .

Energy Balances for Differing Materials

Energy balance analyses supplement

the qua l i ta t ive observa t ions f r om examin

ing temperature distr ibutions as in Fig. 9.

Predictions were made for the ranges of

experim ental con dit ions stu died. Side sur

face electron condensation was taken as

negligible

(a

= 0) for each m ateria l and

shielding gas, except for steel with argon

(a =

0.25). Results are summarized in Fig.

12 and generally con firm the expectations

from the temperature results.

For the aluminum alloy, the resistive

heatingqc is almos t negligible and mos t of

the requ i red thermal energy

flow is

via the

droplet to the l iquid-sol id interface

qi_-s

Fig.

12A.

For the titanium alloy, the situa-

WELDING RESEARCH SUPPLEMENT129-s


11/12

Fig. 12-Predicted

thermalenergy

balances forvarious

electrode materials.

t ion is part ly reverse d, wi th the ma jor ity of

the required energy being prov ided by

q G ~ ^ g -

12B.In both cases, the required

value of qc shows a break in its trend at

intermediate currents. This break corre

sponds to the transition in melting rates

and change from globular to spray mode

of droplet detachment. These predict ions

emphasize the importance of the droplet

behav ior in the energy rate distr ibut ion, as

well as weld quality.

With steel electrodes, the balance de

pends strongly on the shielding gas due to

its ef fect on the electron condensat ion

Figs.

12C, D. With hel ium, predic ted en

ergy balances are comparable to carbon

dioxide w ith sl ight dif ferences in the mag

nitudes (Ref. 19), and about 30% of the

required energy would be prov ided by

resistive heating and the rest via the

liquid-solid interface. With argon, predic

t ions treat inga as indepe nden t of electr i

cal current show

q

E

c

to be comparable in

magnitude to qc, while the required con

t r ibut ion of qL-s is reduced. Since a may

vary with the surface area available to the

arc at the t ip of the electrode, and there

fore with the electr ical current, the mag

nitudes in this last simulation should be

considered as illustrative rather than as an

actual calibrat ion. However, this compar

ison again demonstrates the importance

of the energy contr ibut ion of electron

conden sat ion o n the cylindr ical side of the

solid electrode, consistent with the t e m

perature predict ions and the visual obser

vations.

An alternate explanat ion for the ob

served taper was suggested by a re

viewer: the taper may be a stream of

liq

uid f rom the sol id e lect rode dr iven by

drag from the plasma jet and electromag

net ic forces. The present conduct ion

cal

culat ions coupled with the empir ical ob

servat ions demonstrate that for the con

dit ions of the experiment (moderate i and

V) a uniform melt ing fron t at the end is not

likely. Rather, the energy balance shows

side heat ing is required and the tempera

ture distr ibut ions predict that the melt ing

isotherm is two-dimensional ( tapered).

The l iquid then runs down this surface.

For very high currents and velocit ies,

orde r-of-mag nitude est imates indicate the

possibility that the effects of tapering of

the melt ing front plus high electromag

net ic forces on the l iquid can lead to a ta

pered l iquid jet below the solid electrode.

McEligot and Uhlman (Ref. 42) used ap

proximat ions to compare capil lary wave

speeds to the velocity of the l iquid f low,

and at very high currents i.e., liquid

velocit ies > capillary wave velocity), a

liq

uid je t may form and then break down

later into droplets. At the currents of the

experiments, the capillary velocity is

greater, so droplets form direct ly.

Concluding Remarks

Examination of typical t ime scales and

governing parameters, exper imenta l ob

servations and analyses and numerical

simulat ions of thermal conduct ion in mov

ing e lect rodes for GMAW have led to

new conclusions concerning the pract ical

ity of modelin g the GM A W process. These

conclusions are as fol lows:

1) Thermal con duc t ion in the solid elec

trode m ay be ap proxim ated as a quasi-

steady process except in the immediate

vicinity of the molten droplet .

2) Dime nsiona l and tim e scales analyses,

including a number of the interact ing

transient thermal phenomena involved in

droplet format ion and detachment , fou nd

no signif icant simplif icat ion t o ap ply in an

alyzing the droplet .

3) Given the transient nature of con

vect ion wi th in the droplet , the re lat ive

signif icance of so many thermal phenom

ena and the poor ly quant i f ied boundary

condit ions from experiments, accurate

solut ions within the droplet wil l be very

diff icult.

4) In orde r to invest igate the e f fects of

thermocapi l lary convect ion on droplet

format ion and detachment , one must em

ploy a transient analysis wi th pro vision for

temporal surface deformat ion. A steady-

state calculation for internal f low in a

spherical geometry (which could be at

tempted with some exist ing general pur

pose codes) would be inappropriate and

possibly misleading.

5) Axial thermal conduct ion is pr imarily

important only for a distance of the order

of 5D/Pe from the t ip where it supplies

the energy necessary to supplement re

sistive (Joule) heating and brings the tem

perature to the melt ing point .

6) Thermal conduct ion simulat ions, for

steel electro des s hielded by a rgon gas, are

quant itat ively consistent with the hypo

thesis that electron condensat ion of the

cylindrical side surface provides an addi

t ional energy source to form a taper at

high electr ic currents for this combin at ion .

At 260 A, the required fract ion is about

10 -25%.

I t is hoped that the approximate analy

ses presented here wil l provide guidance

for others at tempt ing to develop more

complete models of the GMAW melt ing

process.

Acknowledgments

The authors are grateful to the Off ic e of

Naval Research and its scientif ic officers,

Drs.

Bruce A. MacD onald, Ralph W . judy

and George R. Yoder, for encourage

ment, and for f inancial support f rom the

We lding Science Program

of

their Material

Science Division. Parts of the work were

accomplished under f inancial support

f rom the Department of Energy to Pro

fessor Eagar at Massachusetts Institute of

Tech nolog y. W e also thank Mssrs. Richard

A. Morr is and Robert R. Hardy of the

David Taylor Research Center for cont in

uous interest and advice. Mrs. Eileen Des-

rosiers is also to be applauded for excel

lent typing in a very compressed and de

manding t ime scale.

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Appendix

Acs

A

s

C

P

D,d

e

11

h

C r o ss - se c t i o n a l a r e a

Su r f a ce a r e a

Sp e c i f i c h e a t a t co n s t a n t

p r e ssu r e

D i a m e t e r

E l e c t r o n ch a r g e

A c c e l e r a t i o n o f g r a v i t y

U n i t c o n v e r s i o n f a c t o r

Sp e c i f i c e n t h a l p y

C o n v e c t i v e h e a t t ra n s f e r

c o e f f i c i e n t ,

q

s

' '

/ ( T

w

Tf)

Sp e c i f i c i n t e r n a l t h e r m a l

e n e r g y

e l e c t r i ca l cu r r e n t

E l e c tr i cal cu r r e n t d e n s i t y ,

i/Acs

T h e r m a l c o n d u c t i v i t y

C h a r a c t e r i s t i c l e n g t h , a l so

l e n g t h o f e l e c t r o d e f r o m

c o n t a c t ti p t o a r c - m o l t e n

m e t a l i n t e r f a ce

M a s s f l o w r a t e ; m e l t i n g

r a t e

Pe r i o d

E n e r g y r a t e ( p o w e r ) o r

h e a t t r a n s f e r r a t e ; q c , t o

t a l res i s t i ve hea t ing ; q r ; c ,

e n e r g y a b s o r b e d o n s i d e

su r f a ce s d u e t o e l e c t r o n

q c

t

u

V

c o n d e n s a t i o n ;

qL-s,

r e

q u i r e d f r o m l i q u id d r o p t o

l i q u i d - so l i d i n t e r f a ce

E l e c t r o n ch a r g e

V o l u m e t r i c e n e r g y g e n e r

a t i on ra te ( res i s t i ve hea t

i n g p e r u n i t vo l u m e )

Sur face hea t f l ux

R a d i a l d i s t a n ce ; r

0

, o u t

s ide rad ius

A b s o l u t e t e m p e r a t u r e ;T

r

,

r e f e r e n c e o r r o o m t e m

p e r a t u r e ; T

0

,

a m p l i t u d e o f t e m p e r a t u r e

f l u c t u a t i o n s

T i m e ,

r e l a t i v e t e m p e r a

t u r e e.g., C)

V e l o c i t y c o m p o n e n t in a x

i a l d i r e c t i o n

V o l t a g e ; V

c

, a p p a r e n t

c o n d e n s a t i o n v o l t a g e ;

V

a

,

a n o d e v o l t a g e d r o p

U n i f o r m o r b u l k v e l o c i t y ;

V

w

, e l e c t r o d e ( w i r e ) f e e d

v e l o c i t y

V e l o c i t y c o m p o n e n t i n r a

d i a l d i r e c t i o n

Ax ia l d i s tance

Ax i a l d i s t a n ce , m e a su r e d

f r o m m o l t e n t i p , L - x

Nond imens iona l Parameters

Bd, Bo

Bo

d

Pr

Re

Greek Letters

Bond numbers for ther

mocapi l lary phenomena

(Lai,

Ost rach and Kamot

ani,

1985 Biot n um ber , h

Vol / IA

s

k

SO

ii

d

)

Pe Peclet

number, Pr Re = Vd/a

Prandt l number,

c

p(

u/k

Reynolds

number, 4rh/

o

M

v

P

Pe

a

Subscripts

F r a c t i o n o f t o t a l e l e c t r o n

c o n d e n s a t i o n a b s o r b e d

o n e l e c t r o d e s i d e su r f a ce ;

t h e r m a l d i f f u s i v i ty ,

k /pc

p

V o l u m e t r i c c o e f f i c i e n t o f

t h e r m a l e x p a n s i o n

T i m e sca l e ;

dj,

t h e r m a l ;

v

,

v i sco u s

V i sco s i t y

K i n e m a t i c v i s co s i t y , fi/p

D e n s i t y ; pg, l i q u i d d e n s i t y

E lec t r i ca l res i s t i v i t y

Su r f a ce t e n s i o n ; G a u ss i a n

d i s t r i b u t i o n p a r a m e t e r

W o r k f u n c t i o n o f m a t e ri a l

(vo l t s )

L i q u i d - so l i d i n t e r f a ce

Eva l u a t e d a t su r f a ce

c o n

d i t i o n s

W i r e ( e l e c t r o d e )

Documents

GMAW Forces at Droplet