GMAW Forces at Droplet
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Transcript of 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 -
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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).
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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)
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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\ } \
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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
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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
-
8/11/2019 GMAW Forces at Droplet
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 )