Int J Adv Manuf Technol (2009) 45:1096–1103
DOI 10.1007/s00170-009-2046-3
ORIGINAL ARTICLE
Estimation of heat source model parameters for twin-wire
submerged arc welding
Abhay Sharma & Ajay Kumar Chaudhary &
Navneet Arora & Bhanu K. Mishra
Received: 7 October 2008 / Accepted: 31 March 2009 / Published online: 24 April 2009
# Springer-Verlag London Limited 2009
Abstract Heat source models are mathematical expressions that represent the generation term in the fundamental
heat transfer equation. Investigators have successfully
demonstrated different heat source models for single-wire
welding. The present investigation estimates the double
ellipsoidal heat source model parameters for twin-wire
application. The heat source model parameters have been
estimated for varying set of welding conditions. It has been
found that the heat source model parameters for twin-wire
welding are different from the single-wire welding. Moreover, the heat source model parameters also depend upon
process parameters. Effects of welding current, electrode
polarity and wire diameter on the size of heat source model
have been presented. Flux consumption is also found to
play a significant role in deciding the heat source model
parameters.
A. Sharma (*)
Institute of Petroleum Technology Gandhinagar,
Raisan Village,
Gandhinagar 382 007 Gujarat, India
e-mail: abhay.sharma@iptg.ac.in
A. K. Chaudhary
Noida Institute of Engineering and Technology,
Greater Noida Phase-II,
201 305 Uttar Pradesh, India
e-mail: ajayagrohi@yahoo.co.in
N. Arora : B. K. Mishra
Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India
N. Arora
e-mail: arorafme@iitr.ernet.in
B. K. Mishra
e-mail: bhanufme@iitr.ernet.in
Keywords Twin-wire welding . Heat source model .
Thermal cycle . Flux consumption
1 Introduction
Simulating the thermal input from the arc to the work-piece
is one of the most important issues in the modelling of
welding processes. The interaction of a heat source with a
weld pool is a complex phenomenon and theoretical
investigation by mathematical modelling provides an
opportunity to understand the complex phenomenon that
occurs during welding. The basic theory of heat flow
developed by Fourier and applied to moving heat sources
by Rosenthal [1] in the late 1930s to 1940s is one of the
first analytical methods to calculate the thermal history of
welds. The fundamental equation of heat transfer in a solid
given by Fourier is as follows:
@H
@
@
@
@
@
@
¼ Qg þ
k
k
k
þ
þ
@t
@x
@x
@y
@y
@z
@z
ð1Þ
where H and k represent enthalpy and thermal conductivity,
respectively. The heat generation is represented by Qg.
During the investigation by Rosenthal [1], heat generation
has been considered from a point source. The infinite
temperature at heat source and temperature independent
material thermal properties assumed in the Rosenthal’s
model increase the error as the heat source is approached.
To overcome these limitations several researchers have
used distributed heat source models. These heat sources,
expressed in various mathematical forms, are used for heat
generation term (Qg) in Eq. 1. Investigators have used
different heat sources like two dimensional disc model [2],
Gaussian heat distribution [3], split heat source [4],
Int J Adv Manuf Technol (2009) 45:1096–1103
1097
constant heat input [5], arc heat flux [6, 7], double
ellipsoidal [8–11] etc. The resulting heat transfer equations
have been solved using different numerical techniques like
finite element method (FEM) and finite difference method.
Goldak et al. [9] used FEM with double ellipsoidal heat
source for 2-D analysis where as Robert et al. [12] used
semi-discrete technique with hemispherical heat source for
3-D analysis. The Goldak’s double ellipsoidal heat source
model [9], which is considered as a versatile model for
various applications, is based on combination of two
ellipsoids. These ellipsoids are geometrically different and
having different heat density distribution as well. This
model has been shown in Fig. 1. The front half is
quadrant of one ellipsoidal source while the rear half is of
another having semi-axis bf and br, respectively. The power
density function has been assumed as Gaussian distribution
such that the power density falls to 5% of that at the centre
of the heat source. The volumetric integration of power
density gives the total power of the heat source Qp. Thus,
the heat density in the front at any point (x, y, z) at time t
due to a heat source having power Qp moving at speed v in
y direction becomes as follows:
pffiffiffi
3ðy vt Þ2
3x2
3z2
6 3Qp
2
2
a
Qg ðx; y; z; t Þ ¼ ff pffiffiffiffiffiffiffiffiffiffiffiffi e e bf e c2
ð2Þ
p pabf c
The term ff represents the fraction of heat supplied to the
front of the arc. In Eq. 2, the parameters a, b and c that are
expansion of heat source in lateral, longitudinal and depth
directions respectively may have different values in front and
rear quadrants. Indeed, in welding dissimilar metals, it may
be necessary to use four octants, each with independent
values of a, b and c. In case of similar metal, a and c are
considered same and different b values are used in front and
rear directions. Thus, br and fr replaces bf and ff respectively
for the rear half. Physically, these parameters are the radial
dimensions of the molten weld pool in front, behind, to the
sides and underneath the arc. The model parameters can be
independently fixed so as the model can represent the heat
source for different welding process. If the cross-section of
the weld pool is known from the experiment, these data may
be used to fix the heat source dimensions. In the previous
investigation into single-wire submerged arc welding [9],
quarter of weld width and twice of weld width have been
prescribed for front and rear directions where as dimension
in the transverse direction has been considered equal to half
of weld width. Investigators have used the double ellipsoidal
model for simulation of thermal history in welded joints
produced by different welding processes. De et al. [13] used
double ellipsoidal model for representation of heat source in
LASER welding. Hongyuan et al. [14] modified the double
ellipsoidal model for the situation where, under an external
disturbance, the arc's backbone is not perpendicular to the
work surface. Slovacel et al. [15] used double ellipsoidal
model for numerical simulation of manual metal arc welding
and gas tungsten arc welding. In the recent past, Kermanpur
et al. [16] investigated surface and volumetric heat sources
for thermal simulation of gas tungsten arc welding. They
showed that a fully volumetric arc heat input represents the
best match to the welding of the thin-walled pipes.
Twin-wire application, as shown in Fig. 2, is slightly
different from the single-wire. In case of twin-wire, two
wires are fed through a common contact tube and power is
supplied through single power source. During twin-wire
welding, arcs pull together causing backward blow at the
leading arc and forward blow at the trailing arc. That means
the arcs are affected by each other. This phenomenon may
affect the heat distribution pattern. In addition, twin-wire is
meant for higher deposition and shallow penetration. Thus,
the model parameters as indicated before may change. The
moot point is whether the model parameters (a, b and c)
suggested for single-wire application is applicable for twinwire application. In the present investigation, this point has
been studied by experimental measurement of thermal
cycles and subsequent computation of the model parameters. In what follows, the experimental work regarding the
present investigation has been described. It is followed by
Qg
x
Contact
Tube
a
y
Drive
Rolls
c
br
bf
z
Fig. 1 Double ellipsoidal heat source
Fig. 2 Schematic diagram of twin-wire welding
Power
Source
1098
Int J Adv Manuf Technol (2009) 45:1096–1103
description of heat source model for twin-wire welding.
The results of computational exercise have then been
presented and discussed. The paper has then been concluded with the generalised conclusions arrived at.
Welding direction
15
The experimental work in the present investigation consists
of measurement of transient temperature during the welding
using twin-wire submerged arc welding. The specimens
used for measurement of transient temperature were
rectangular piece of mild steel of size 300×200×25 mm.
AWS/SFA A5.17 EH 14 grade filler wire was used along
with basic flux. A submerged arc welding unit LE-18
(Messer-Griesheim) was used to deposit bead-on-plate
welds. Axis-to-axis distance between wires has been kept
as 9 mm. The flux had been baked for 2 h at 200°C before
welding. Bead-on-plate welds were deposited using two
wire diameters of 2 and 3.2 mm. Total 12 welds were
deposited following the welding parameters given in
Table 1. Thermocouple of type R (Pt–Pt and 13% Rh) with
a diameter of 0.25 mm has been used for measuring the
temperature variation during the welding. The thermocouples have been attached to the plates at three points situated
within the body of the work-piece at centreline directly
below the welding arc. The schematic diagram of the
placement of thermocouples inside the plate has been
shown in Fig. 3. These points were situated at different
depths. A PC-based data acquisition system was used to
sample the signal from the thermocouples. A picture of the
experimental setup for temperature measurement is shown
in Fig. 4. Some of the representative thermal cycles are
shown in Figs. 5 and 6. Based on the experimental
Table 1 Experimental conditions
C
Top view
5 mm
32
32
32
32
32
32
32
32
32
32
32
32
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
2–2
2–2
2–2
2–2
2–2
2–2
3.2–3.2
3.2–3.2
3.2–3.2
3.2–3.2
3.2–3.2
3.2–3.2
7 mm
9 mm
Front View
Fig. 3 Thermocouple placement
observations, heat source model parameters for twin-wire
submerged arc welding have been estimated as given in the
following section.
3 Heat source model
Due to close proximity of two wires during twin-wire
application, they associate with a single weld pool and
somehow act as a single elongated heat source [17]. Hence,
a double ellipsoidal heat source, which has been found
applicable in the case of single-wire application, may also
be applied in this case. However, geometric parameters of
the model would change. It is evident from the experimentally measured thermal cycles, as shown in Figs. 5 and 6,
that the peak temperature is a momentary affair. The peak
temperature mainly depends upon the amount of heat
supplied to the work-piece at the very moment the arc acts
over the point of consideration. It means that the peak
temperature of any point is not affected by the pre- or the
Polarity
Extension Wire
S. No. Current Voltage Speed
diameter
(cm/min) (mm)
in (A) (V)
(mm)
400
500
600
400
500
600
600
700
800
600
700
800
B
160 mm
200 mm
240 mm
2 Experimental
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
A
DCEP
DCEP
DCEP
DCEN
DCEN
DCEN
DCEP
DCEP
DCEP
DCEN
DCEN
DCEN
Fig. 4 Experimental setup
Int J Adv Manuf Technol (2009) 45:1096–1103
1099
800
B
600
Temperature in ˚C
ensures heat flux continuity at control volume interface,
which is required for physical significance of discretization.
The semi-discrete form of heat diffusion equation for 3-D
heat transfer condition in steady state without any radiation
yields the following:
A
700
C
500
400
300
(
200
100
295
281
267
253
239
225
211
197
183
169
155
141
127
99
113
85
71
57
43
29
1
15
0
Time in sec.
post-heating of the point when arc remains far from the
point. Thus, the problem of model parameter identification
can be simplified by steady-state heat transfer at the
particular moment. An appropriate estimation of heat
source parameters should result in appropriate prediction
of peak temperatures at different points situated within the
body of the work-piece. The heat conduction equation has
been solved using control volume method in form of semidiscrete technique as given by Robert et al. [12]. In this
technique, the body under consideration is discretized in
small control volumes. The associated nodes are located at
the geometric centre of the control volume for interior
nodes. For control volumes that include geometric boundary of the work-piece, the associated nodes are considered
on the surfaces. The thermal conductivity at the interface
can be determined as the harmonic mean value as follows:
1
K ðT1 Þ
2
þ K ð1T2 Þ
ð3Þ
where K (T1, T2) is the thermal conductivity at the interface
between nodes 1 and 2. As pointed by Patankar [18], this
Temperature in ˚C
1800
1600
A
1400
B
1200
C
1000
800
600
400
200
13
6
15
1
16
6
18
1
19
6
21
1
22
6
24
1
25
6
27
1
28
6
1
12
6
10
91
76
61
31
46
1
16
0
Time in sec.
Fig. 6 Weld thermal cycle (3.2–3.2 mm wire, DCEN at 800 A)
Ki
1;j;k
Ki;j
1;k
Ki
ðTi
1;j;k
ðTi;j
1;k
Ki;j
Ki;j;k
1
Ti;j;k Þ
1;j;k þKi;j;k
ðTi;j;k
Ki;j;k
Ti;j;k Þ
1;k þKi;j;k
1
Ti;j;k Þ
1 þKi;j;k
þ Qg
¼0
Fig. 5 Weld thermal cycle (3.2–3.2 mm wire DCEN, 600 A)
K ðT1 ; T2 Þ ¼
8
Kiþ1;j;k ðTiþ1;k Ti;j;k Þ
>
)>
> Kiþ1;j;k þKi;j;k þ
<
2Ki;j;k
Ki;jþ1;k ðTi;jþ1;k Ti;j;k Þ
þ Ki;jþ1;k þKi;j;k
þ
ðΔxÞ2 >
>
>
: þ Ki;j;kþ1 ðTi;j;kþ1 Ti;j;k Þ þ
Ki;j;kþ1 þKi;j;k
9
>
>
>
=
>
>
>
;
ð4Þ
The task of solving heat conduction equation under
varying model parameters has been completed through a
code written in MATLAB software. For each welding
condition, more than 10,000 combinations of parameters
have been attempted which took more than 8 h of CPU
time. The initial solution of the above equation resulted in
certain amount of error in different cases. The error
indicates the effect of flux during submerged arc welding.
As soon as the arc acts at any point, the temperature reaches
to the peak temperature. Simultaneously, flux also melts
and in turn the entire heat supplied by the arc is not used for
creation of peak temperature. However, the heat obtained
by the flux is subsequently supplied to the work-piece in
the later stages, but this heat is not available for peak
temperature generation. Thus, peak temperature-based heat
conduction analysis might result in some error in prediction. It has been found that if one more variable in the heat
source model is added, the error goes considerably down.
This variable named as ‘flux compensation factor ( 8 )’ is
found to be different for different welding cases. This factor
signifies the fraction of heat available to the work-piece for
melting and generating peak temperature at the very
moment the arc acts on the point of consideration.
Pertaining to this factor, the modified heat source equation
for front direction is as follows:
Qg ðx; y; z; t Þ ¼ ff
pffiffiffi
8 6 3Qp
pffiffiffiffiffiffiffiffiffiffiffiffi e
p pabf c
3x2
a2
e
3ðy vt Þ2
b2
f
e
3z2
c2
ð5Þ
The origin of the moving coordinate system has been
located on the top surface of the work-piece at the midpoint
in between the leading and the trailing wires. As shown earlier,
12 different welding conditions were applied to measure the
temperature distribution at three different points. The heat
conduction equation has been solved for all these cases by
varying model parameters and the root-mean-square error
in % (% RMSE) in the peak temperatures at three different
1100
Int J Adv Manuf Technol (2009) 45:1096–1103
Table 2 Calculated model
parameters
Wire diameter (mm)
2–2
Polarity
DCEN
DCEP
3.2–3.2
DCEN
DCEP
a half of weld width, c depth
of penetration
points has been computed. Based on these results, final
model parameters have been found. The model expansion in
transverse direction, i.e., a has been considered constant as
half weld width. The value of ff and fr has been taken as 0.6
and 1.4, respectively as mentioned in the literature [12].
This consideration is based upon previous investigation into
simulation of behaviour of leading and trailing arcs in twinwire welding [19] that indicated that leading and trailing
arcs share 30% and 70%, respectively of the total heat.
Model parameters in the other directions, namely, br, bf and
c along with the flux compensation factor ( 8 ) are varied at
regular intervals and the resulting % RMSE has been
computed. This has been repeated for all the 12 conditions.
The best model parameters and related error for each case
have been given in the Table 2. The overall performance of
the considered approach for heat source model develop-
Current (A)
400
500
600
400
500
600
600
700
800
600
700
800
Model parameters in mm
8
a
bf
br
c
13.21
15.01
16.71
17.79
19.61
20.73
19.37
19.83
20.18
18.31
19.10
19.18
6.6
9.3
20.0
6.6
9.0
25.0
4.8
4.9
5.0
4.5
4.7
4.7
26
75
83
35
98
103
38
89
90
36
38
76
4.8
5.0
5.2
5.1
5.7
7.5
8.0
8.9
9.4
9.6
10.1
10.9
0.38
0.51
0.60
0.60
0.65
0.72
0.49
0.71
0.77
0.61
0.89
0.93
% RMSE
14.7
10.7
3.5
11.1
10.9
7.9
16.5
8.0
6.2
5.8
9.4
1.5
ment and subsequently prediction of peak temperature is
well-evidenced from Fig. 7. It can be seen that predicted
peak temperatures are in good agreement with the actual
peak temperatures. It is evident from the Table 2 that the
model is self-validating and in most of the cases % RMSE
is less than 10%. In some of the cases, particularly lower
currents, it is higher than 10%. Nevertheless, this is quite a
satisfactory result as error up to 100°C is acceptable for
welding thermal modelling [11]. Obviously, at lower
current when the temperatures are lower, the amount of
acceptable % error also increases. Thus, the estimated
parameters can be considered as representative of heat
source model for twin-wire welding. The subsequent
section further discusses the outcomes of the present
investigation.
4 Results and discussion
1800
Predicted peak temperature in °C
1600
1400
1200
1000
800
600
400
200
0
0
200
400
600
800
1000 1200 1400 1600 1800
Actual peak temperature in °C
Fig. 7 Comparison of actual and predicted peak temperatures
The significant outcome of the present investigation is the
difference between the model parameters of single and
twin-wire welding heat source model. During previous
investigation with single-wire welding [9], under given
welding condition (single weld), values of model parameters a, bf and br, have been suggested equal to half of weld
width, quarter of weld width and twice of weld width,
respectively. Thus, the model parameters in this particular
case follow the relation bf/a = 0.5 and br/a = 4. However,
these relations represent a particular welding condition. It is
evident form Table 2 that under varying welding conditions
the same ratios do not hold good. The ratios bf/a and br/a
are found varying between 0.24 to 1.20 and 1.96 to 4.99,
respectively. Thus, difference between the model parameters of single and twin-wire welding along with dependence
of model parameters on welding conditions is established.
Int J Adv Manuf Technol (2009) 45:1096–1103
Distance along the depth direction in mm
-80
0
-70
Distance along the longitudinal direction in mm
-60
-50
-40
-30
-20
-10
1101
0
10
2
Reference Plane
4
6
8
10
DCEP 600 A
DCEP 700 A
DCEP 800 A
12
Fig. 8 Effect of current on heat source (3.2–3.2 mm wire combination
DCEP)
The heat source model parameters under different welding conditions indicate expansion of heat in different
directions. It is evident from Fig. 8 that the depth of heat
source increases with the current. On the other hand,
change in expansion of heat source in the front direction is
not that much significant and it remains almost constant.
However, the expansion in the rear direction is greatly
affected by the current and a drastic increase is evidenced
with increase in the current. These outcomes can be
justified on the basis of physics of the process. It is well
known that increment in the current increases the current
density in the welding wire, which facilitates the increment
in the penetration. In turn, the heat source attains larger
depth with increase in the current. The expansion of heat
source in the front direction can be attributed to two factors.
In the front portion of the arc, metal remains in comparatively cold condition, which concentrates the arc. The
second reason is due to the mechanism of twin-wire
welding. Due to same polarity, the arcs are subject to arc
Distance along the depth direction in mm
-80
0
-70
Distance along the longitudinal direction in mm
-60
-50
-40
-30
-20
-10
0
10
2
Reference Plane
4
6
8
10
DCEP 600 A
DCEN 600 A
12
Fig. 9 Effect of polarity on heat source (3.2–3.2 mm wire combination)
blow in the inward direction. This further contracts the arc
and results in lesser expansion. The model parameter in the
rear direction is largely affected by current. The reason
behind this outcome is the fact that higher current melts
more metal, as well as the amount of heat supplied to the
work-piece also increases. This results in more molten
metal available beneath the arc and the size of weld puddle
increases. This behaviour can be justified on the basis of
fluid flow patterns during submerged arc welding, which
has been studied by Mori and Horii [20]. According to
them, a depression is formed at the forward edge of the
weld pool and metal that is melted at the front of the pool
flows rearward underneath and either side of the depression. This eventually results in higher expansion of the heat
source in the rear direction.
Figure 9 shows the effect of polarity on heat source for
3.2–3.2 mm wire combination. It is evident that expansion
in the depth direction is more in the case of direct current
electrode positive (DCEP). This is due to the fact that
DCEP produces more penetration, while in case of direct
current electrode negative (DCEN) more filler material is
melted and lesser penetration is achieved. As discussed
earlier, the expansion of heat source in the front direction is
not much affected by the welding conditions and the same
is true for different polarities also. However, the expansion
in the rear direction is affected by the polarity. The reason
being that the DCEN melts more material that has the
tendency to flow in the rear direction; in turn heat source is
larger in the rear direction for the case of DCEN. However, a
different observation is observed in case of the DCEN with
smaller wire diameter (2–2 mm). It is evident from Table 2
that the size of heat source in all the three directions, i.e.,
front, rear and depth directions are smaller with DCEN. The
DCEN and smaller wire diameter both yield more melting
of filler wire. It seems that the excess molten metal hinders
the heat flow to the base metal. Moreover, the flow of
molten metal in the rear direction is also hampered. Thus,
the dimension of heat source in the rear direction is found
smaller with DCEN in case of 2–2 mm wire combination.
Figure 10 describes the effect of wire diameter on heat
source. It is evident that smaller wire diameter produces
less expansion of the heat source in the depth direction;
where as in the front and rear directions, small wire
diameter gives more expansion. The smaller wire diameter
results in more melting of the filler material that flows in
the either direction of the arc. Thus, the expansion in the
front and rear direction with small wire diameter is found
more. On the other hand, due to more melting of filler wire
less energy is provided to the base metal, thus, less
penetration is observed with smaller wire diameter. In turn,
the expansion in the depth direction with small wire
diameter (2–2 mm) is found lesser compared to larger wire
diameter (3.2–3.2 mm).
1102
Int J Adv Manuf Technol (2009) 45:1096–1103
Distance along the longitudinal direction in mm
Distance along the depth direction in mm
-90
0
-80
-70
-60
-50
-40
1
-30
-20
-10
0
10
20
Reference Plane
2
3
4
5
6
2-2 mm DCEN 600 A
7
3.2 3.2 mm DCEN 600 A
8
9
Fig. 10 Depth of heat source at different wire combinations
One of the important outcomes of this study is role of
flux in producing peak temperatures. Figure 11 depicts the
flux compensation factor ( 8 ) for different welding conditions. This factor signifies the instantaneous amount of
the heat available to the work-piece, while the flux has
consumed the remaining part. It is evident that increment in
current increases the factor at either polarities and at both
wire combinations. This is due to increase in current which
results in increase in the total amount of the heat. At the
same time, the width of weld bead remains almost same and
penetration increases. The net effect is in the form of more
availability of heat to the work-piece and in turn 8
increases. It is to be further noted that this factor has
higher value at DCEP. This is due to the reason that DCEP
melts less filler metal that keeps the surface area of the weld
bead smaller and in turn less flux is consumed due to lesser
area of contact. In addition, DCEP produces deeper
penetration that provides more heat to the work-piece. As
defined earlier, the flux compensation factor ( 8 ) signifies
1
5 Conclusions
0.9
Flux Compensation Factor
the fraction of heat available to the work-piece for melting
and generating peak temperature, thus, flux compensation
factor ( 8 ) achieves higher value with DCEP.
It can be found in literature that the flux consumption
depends upon heat input, electrode polarity and wire
diameter [21]. The same reasons are also responsible for
alteration in heat transfer pattern. Thus, in order to assess
the effect of flux consumption on the heat transfer pattern,
effect of wire diameter and heat input must be secluded. It
is evident that for the same wire diameter and current value
(as shown in Fig. 11), 8 is found higher for DCEP. It is also
known that DCEP consumes less flux. Thus, more heat is
supplied to the work-piece and 8 has been found higher in
case of DCEP. In case of smaller wire diameter the 8 for
the same current value (600 A) is found to be more than the
other case. It seems that larger wire diameter increases the
spread of the arc in lateral directions in turn more flux is
consumed. Thus, lesser heat is available to the work-piece;
eventually, 8 achieves higher value at smaller wire
diameter.
The discussion above lead to an important outcome that
heat conduction equation solution for a given welding
condition depends upon the surroundings. This becomes
more important in case of submerged arc welding as flux is
a good consumer of heat. Flux consumption is known to be
a function of process parameters [21]. Thus, heat transfer
model should be constructed keeping process conditions
and the surrounding effects in consideration. Moreover,
twin-wire welding results in more deposition of material
that affects the flux consumption and heat distribution
pattern as well. Thus, heat distribution pattern in a workpiece during the twin-wire welding becomes more dependent on the surroundings. The present investigation
attempted to capture the same. The developed approach
would also be useful in the future research in heat transfer
modelling of other welding process.
DCEN
DCEP
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
400
500
600
Wire diameter 2-2 mm
600
700
800
Wire diameter 3.2-3.2 mm
Process Condition
Fig. 11 Effect of welding conditions on flux compensation factor
1. The peak temperature-based approach for estimation of
heat source model parameters is elaborative and tries to
identify heat source model parameters according to the
welding conditions.
2. Heat source model parameters for twin-wire welding
are quite different from the single-wire heat source
model. Due to mutual interaction between two wires,
more melting and less penetration previous heat source
model parameters for single-wire welding requires to be
modified for twin-wire welding.
3. Effect of flux consumption on the heat transfer pattern
can be quantified by appropriate compensation in the
heat source model.
Int J Adv Manuf Technol (2009) 45:1096–1103
4. Static analysis considering stationary heat source is a
simple and less time-consuming approach towards the
identification of heat source parameters. This approach is
quiet successful in understanding the mechanism of
process variations like twin-wire submerged arc welding.
Acknowledgement This work has been carried out as a part of a
research project funded by Department of Science and Technology,
Government of India under the project number SR/S3/MERC-21/
2005. The authors would like to thank All India Council for Technical
Education (AICTE), Government of India, for supporting one of the
authors (AS) during the period of this research.
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