### Mathematical Modeling of Melting Rates for Submerged Arc Welding

```Mathematical Modeling of Melting Rates
for Submerged Arc Welding
Models of melting rates take into account the effects of
welding variables
BY R. S. CHANDEL
ABSTRACT. The effects of welding current, arc voltage, wire diameter, electrode extension (EE), electrode polarity,
power source type and flux classification
on melting rates (MR) have been evaluated for the submerged arc welding process. The results show that for a given
heat input, greater melting rates are
obtained when higher current, longer
electrode extension, smaller diameter
electrodes and electrode negative polarity are used. Arc voltage, power source
type and flux classification do not have
any significant influence on melting rates.
Mathematical models to correlate process variables and melting rates have
been computed from the data.
Introduction
Researchers and welding engineers
have been trying to increase productivity
by increasing melting rates since the
inception of the submerged arc welding
process. Historically, welding current has
been found to have the greatest influence on the melting rate and weld bead
geometry (Refs. 1-4). However, it is also
recognized that when welding current is
increased to enhance the melting rate,
there is a corresponding increase in heat
input, which may influence the weld
metal toughness. Alternatively, travel
speed can be increased to maintain the
same heat input; however, this can
increase the propensity for defects such
as centerline cracking and incomplete
penetration (Ref. 5). However, melting
rate can be increased for a given heat
input and welding current by using electrode negative polarity, longer electrode
extension, and smaller diameter electrodes (Refs. 6-9). In order to predict and
control the melting rate, the quantitative
effect of all the variables must be known.
Wilson and Jackson (Ref. 9) formulated
R. S. CHANDEL is with Physical Metallurgy
Mineral and Energy Technology, Ottawa, Canada.
the following mathematical relationship
between welding variables and melting
rate in Imperial units, which are converted here to the following SI units:
MR (kg/h) =
9.45 +
10001
2
0.042 D + 2.906 X 10~4
(1)
MR (for DCEN)
0.042d 2 + 2.906 X 10~4 —2 1 22 1
d
J
+ [ 3 . 0 7 1 X 10- 4 (l) 1 - 5 1 3 ]
MR (for AC) =
IL 122 -,
D
2
J
8
10001
0.042d 2 + 2.906 X 10" 4 —2 ' ^ 1
d
J
+ [ 4.5 X 10~5 (I) 1686 + 3.565 1
KEY W O R D S
SAW Electrode Melting
Melting Rate Models
Mathematical Modelling
SAW Heat Input
SAW Process Variables
Heat vs. Weld Current
Electrode Polarity
Electrode Extension
Melt Rate Equation
SAW Polarity Effects
2 721
+ [ 3.485 X 10" (I)
Such a relationship is very useful, as it
enables the preselection of welding variables for a particular melting rate. However, it has some drawbacks, as it does
not take into account the effect of voltage, polarity, the type of power source
and flux basicity.
Robinson (Ref. 10) observed that Equation 1 was not valid for alternating current (AC) or direct current electrode
negative (DCEN), so he modified it to
take the effect of electrode polarity into
consideration. His modified equations,
originally in Imperial units, are converted
to SI units as follows:
MR (for DCEP) =
1000
0.042d2 + 2.906 X 10
where I = welding current (A)
D = wire diameter (mm)
L = electrode extension (mm)
(2)
(3)
10001
[
(4)
. IL
d2
-I
+ 3.565 ]
where MR = melting rate
(kg/h)
I = welding current
(A)
d = electrode diameter
(mm)
L = electrode extension
(mm)
Martin (Ref. 11) and Jackson (Ref. 12)
had observed that arc voltage also has an
influence on the melting rate. Robinson
(Ref. 10) reported that for direct current
electrode negative, an increase in arc
voltage resulted in a decrease in melting
rate. However, neither Wilson's nor Robinson's equations reflect this. Mantal (Ref.
13) reported that for arc welding the
melting rate for AC is the geometric
mean of the melting rates for DCEN and
DCEP. Lesnewich (Ref. 14) also compared
the melting rates for AC, DCEN and DCEP
and observed that the melting rate during
AC is the arithmetic mean of melting rates
during DCEN and DCEP. Robinson's
experimental results and theoretical calculations show that for welding currents
of up to 750 A, direct current electrode
positive (DCEP) gives higher melting rates
than DCEN. Thus, in the light of this
controversy, the validity of Robinson's
(Ref. 10) equations becomes questionable.
There have been a few other attempts
to formulate mathematical relationships
between welding variables and melting
rates (Refs. 15-18). However, most of
these models are useful only for particu-
WELDING RESEARCH SUPPLEMENT 1135-s
Table 1—Welding Variables and Melting Rates for DC Welds
Melting rate (kg/h)
Constant voltage
Wire dia.
(mm)
E.E.W
(mm)
Current
(A)
Voltage
(A)
4.00
25.4
400
400
400
600
600
600
800
800
800
1000
1000
(a)
Flux A
DCEP
DCEN
4.91
4.9
4.9
13.74
13.74
6.30
6.30
6.30
10.94
10.94
10.94
15.13
15.13
15.13
18.59
18.59
18.59
1000
32
35
38
32
35
38
32
35
38
32
35
38
4.0
76.2
400
400
400
600
600
600
800
800
800
1000
1000
1000
32
35
38
32
35
38
32
35
38
32
35
38
5.22
5.22
5.23
9.4
9.4
9.4
16.40
16.40
16.40
20.61
20.61
20.61
6.44
6.44
6.44
12.43
12.43
12.43
18.13
18.13
18.13
25.47
25.47
25.47
2.4
25.4
300
300
300
400
400
400
475
475
475
550
550
550
\$2
35
38
32
35
38
32
35
38
32
35
38
3.71
3.71
3.71
4.93
4.93
4.93
6.20
6.20
6.20
7.80
7.80
7.80
4.88
4.88
4.88
7.05
7.05
7.05
8.75
8.75
8.75
10.61
10.61
10.61
7.16
7.16
7.16
10.18
10.20
10.17
13.74
Constant current
Flux
DCEP
Flux A
DCEN
DCEP
Flux B
DCEN
DCEP
DCEN
Electrode extension
lar situations and are thus not applicable
to shop floor welding. Therefore, the aim
of this work was twofold: 1) to study the
effect of welding current, arc voltage,
electrode diameter, electrode extension,
electrode polarity, type of power source,
and flux classification on the melting rate
for submerged arc welding, and 2) to
develop mathematical models to correlate the melting rates with the welding
variables.
Experimental Work
The base material used for the experimental work was a 19-mm (0.75-in.) thick
ASTM A36 steel plate. This plate was cut
into 600- X 150-mm (24- X 6-in.) pieces,
and both surfaces were cleaned (sand
blasted) to remove dirt and oxides. AWS
EL12 electrodes of 2.4-, 3.2- and 4-mm
(%2-, Va- and %2-in.) diameter were used,
along with Fluxes A and B. Flux A was a
fused acid flux with a basicity index of 1,
while Flux B was an agglomerated basic
flux with a basicity index of 3.
136-s I MAY 1987
DC 1500 and AC square wave 1000
power sources were used. The DC 1500
can be operated on both constant current and constant voltage modes, while
the AC square wave 1000 is designed for
the constant vcltage mode only. The
experimental work was designed to
study the effect of welding current, voltage, electrode extension, electrode diameter, polarity, type of power source, and
flux classification on melting rate. The
welding current and arc voltage were
recorded on a chart recorder for each
deposit, while the corresponding wire
feed speed (which was converted into
melting rate) was read from a digital wire
feed tachometer. A total of 336 welds
were made, and their welding variables
and corresponding melting rates are given in Table 1.
Results
The results of the investigation are
given in Figs. 1-4 and Tables 1 and 2.
Figure 1 shows the effect of welding
current and wire diameter on the melting
rate. It can be seen that for a given wire
diameter, melting rate increases with
welding current. However, for a given
welding current, the melting rate is higher
when a smaller diameter electrode is
used. Figure 1 also indicates that the
difference in melting rate due to wire
diameter is greater at higher currents.
Varying the voltage between 30 and
38 V did not have any effect on the
melting rate.
The effects of polarity and electrode
extension on the melting rate are shown
in Fig. 2. For the same welding variables,
DCEN results in a higher melting rate than
DCEP When AC is used, the melting
rates are slightly higher than those of
DCEP and significantly lower than DCEN
when a 25.4-mm (1-in.) electrode extension is used. However, when a 76.2-mm
(3.0-in.) electrode extension is used, the
melting rates with AC become similar to
those of DCEP.
The effects of power source type
(constant voltage and constant current)
and flux classification on the melting rate
Table 1—Welding Variables and Melting Rates for DC Welds (continued)
Melting rate (kg/h)
Constant voltage
Wire dia.
(mm)
E.E>>
(mm)
2.4
76.2
3.2
3.2
Current
(A)
Flux A
Constant current
Flux A
FluxB
Flux B
Voltage
(A)
DCEP
DCEN
DCEP
DCEN
DCEP
DCEN
DCEP
DCEN
300
300
300
400
400
400
475
475
475
550
550
550
32
35
38
32
35
38
32
35
38
32
35
38
4.92
4.92
4.92
8.27
8.27
8.27
10.71
10.71
10.71
15.10
15.10
15.10
6.42
6.42
6.42
9.76
9.76
9.76
12.92
12.92
12.92
17.06
17.06
17.06
—
—
—
—
—
—
—
-
—
—
—
—
—
—
—
—
-
—
—
-
—
—
—
—
—
-
—
—
—
—
-
—
—
—
—
-
25.4
300
300
300
450
450
450
600
600
600
750
750
750
32
35
38
32
35
38
32
35
38
32
35
38
3.83
3.83
3.83
5.56
5.56
5.56
7.38
7.38
7.38
9.87
9.87
9.87
4.98
4.98
4.98
8.16
8.16
8.16
11.70
11.70
11.70
14.29
14.29
14.29
3.53
3.53
3.53
5.18
5.18
5.18
7.00
7.00
7.00
9.78
9.78
9.78
6.14
6.14
6.14
8.72
8.72
8.72
11.44
11.44
11.44
14.86
14.86
14.86
3.74
3.74
3.74
5.66
5.66
5.66
7.86
7.86
7.86
10.35
10.35
10.35
4.98
4.98
4.98
8.53
8.53
8.53
11.70
11.70
11.70
14.29
14.29
14.29
3.64
3.64
3.64
5.65
5.65
5.65
7.86
7.86
7.86
10.35
10.35
10.35
6.23
6.23
6.23
8.82
8.82
8.82
11.41
11.41
11.41
14.58
14.58
14.58
76.2
300
300
300
450
450
450
600
600
600
750
750
750
32
35
38
32
35
38
32
35
38
32
35
38
4.79
4.79
4.79
7.57
7.57
7.57
11.80
11.80
11.80
16.40
16.40
16.40
5.65
5.65
5.65
10.35
10.35
10.35
15.05
15.05
15.05
20.60
20.60
20.60
4.41
4.41
4.41
8.15
8.15
8.15
12.08
12.08
12.08
19.00
19.00
19.00
6.33
6.33
6.33
10.07
10.07
10.07
14.19
14.19
14.19
20.77
20.77
20.77
4.51
4.51
4.51
7.19
7.19
7.19
11.51
11.51
11.51
17.74
17.74
17.74
5.75
5.75
5.75
10.17
10.17
10.17
14.67
14.67
14.67
20.58
20.58
20.58
4.31
4.31
4.31
7.67
7.67
7.67
12.56
12.56
12.56
17.84
17.84
17.84
6.45
6.45
6.45
10.64
10.64
10.64
14.48
14.48
14.48
20.58
20.58
20.58
(a)
Electrode extension
are s h o w n in Figs. 3 and 4 , respectively.
T h e results indicate that p o w e r source
t y p e a n d flux classification d i d n o t have
any significant effect on melting rates.
Table 2—Welding Variables and Melting Rates for AC Welds
Melting rate (kg/h)
Mathematical Model
The above results have shown that the
melting rate during submerged arc welding is affected by welding current, electrode diameter, electrode extension and
electrode polarity. To present the above
results in a meaningful mathematical
expression, some fundamental concepts
of melting during arc welding have to be
considered. It is well understood that the
total melting is composed of melting due
to arc energy and melting due to resistance heating ()oule heating effect) (Refs.
9, 10 and 15-18). Arc heat is proportional
to welding current, while the Joule heating effect is proportional to the (current)2
and electrode extension, and inversely
proportional to (electrode diameter) 2 . An
equation to correlate melting rate and
welding variables and incorporating arc
Flux A
Wire dia
Current
(A)
Voltage
(V)
25.4 mm
E.E>>
450
450
550
550
650
650
750
750
32
36
32
36
32
36
32
36
5.44
5.46
7.05
7.00
8.50
8.50
10.57
10.53
400
400
500
500
600
600
700
700
30
34
30
34
30
34
30
34
4.74
4.75
5.99
6.00
8.52
8.51
10.80
10.76
4.00
3.2
Flux B
76.2 mm
25.4 mrr
76.2 mm
E.E.<*>
E.E.<a>
E.E.<a>
5.93
5.96
8.14
8.14
10.25
10.05
13.41
13.38
—
—
—
—
-
—
—
—
—
—
—
-
5.5
5.5
8.14
8.17
11.24
11.24
15.37
15.37
5.26
5.26
6.70
6.71
8.64
8.64
10.52
10.50
6.33
6.34
8.6
8.5
11.72
11.71
15.83
15.83
""Electrode extension.
WELDING RESEARCH SUPPLEMENT 1137-s
POLARITY- DCEP
WIRE DIA.-3.2mm
O
DCEP
A
DCEN
0
2.4mm WIRE
A
3.2mm WIRE
D
—
AC
25.4mm EE
D
4.0mm WIRE
—
76.2mm EE
<
rr
<
cr
o
z
CD
z
I-
_l
LU
300
400
500
600
700
S00
900
300
1000
400
WELDING CURRENT (A)
500
600
700
BOO
900
1000
WELDING CURRENT (A)
Fig. 1-Effect of welding current and wire diameter on the melting rate
(Flux A, 25.4-mm electrode extension)
Fig. 2 —Effect of electrode polarity
melting rate (Flux A)
cr
CD
<
rr
CD
z
z
<
and electrode
extension on the
_i
w
r
300
400
500
600
700
800
900
1000
WELDING CURRENT (A)
Fig. 3 —Effect of power source
25.4-mm electrode extension)
138-s | MAY 1987
type on the melting rate (Flux A,
300
400
500
600
700
800
900
1000
WELDING CURRENT (A)
Fig. 4 —Effect of flux type on the melting rate (25.4-mm
extension)
electrode
20
-
IB
-
1G
-
CD
Z
12
-
Kj
10
O)
where R is the coefficient of multiple
correlation and SE is the standard error.
The validity of the above equations
can be judged from their high coefficients
of correlation (>0.99) and Fig. 5, which
shows the relationship between measured and computed melting rates. Compared with other equations referred to
earlier (Refs. 9,10), these equations are
simpler, maintain mathematical uniformity
and show a better relationship between
measured and calculated melting rates —
Fig. 6. The important feature of the
above equations is that the coefficients
for the second term, l 2 L/d 2 , are similar for
electrode negative and electrode positive, which agrees with the findings of
Demyantsevich (Ref. 18) and Chandel
and Malik (Ref. 19). This implies that
resistance heating is not influenced by the
polarity during direct current arc welding.
However, this coefficient is smaller for
AC, which indicates that melting due to
resistance heating is smaller during AC
welding. This discrepancy in the resistance heating during AC and DC welding
is difficult to explain at this stage, and it is
recommended that further work be carried out. The regression coefficient for
the first term, i.e., arc heat, is highest
when the electrode is negative and lowest when the electrode is positive,
because during arc welding, more heat is
liberated at the cathode, which for electrode negative is the electrode tip. The
value of this coefficient for AC is higher
than when the electrode is positive, but
smaller than when the electrode is negative.
u
I-
i
a
HI
B
-
6
-
4
-
o
I-H
a
0-
4
6
10
8
12
14
16
OBSERVED MELTING RATE
IB
20
(kg/h)
Fig. 5 — Relationship between measured and calculated melting rates
MR (for AC) = 0.01523 I +
J2L
1.6882 X I O " 6 —2 - 2 . 3 9 6
d
(R = 0.991, SE = 0.435)
energy and Joule heating effect was conceived in the following form:
l2L
MR = Al + B —2 + C
d
MR (for DCEN) = 0.016178 I +
J2L
2.087 X 10" 6 —2 - 0.643
d
(R = 0.996, SE = 0.5)
where A, B and C are constants which
depend upon the polarity and electrode
material and I, L and d are welding
current, electrode extension and electrode diameter, respectively.
In order to compute the values of A, B
and C, multiple regression analyses of the
experimental data were carried out and
the following equations were obtained:
(R = 0.993, SE = 0.56)
20
20
O)
O
A
18
<p/
THIS WORK
ROBINSON
18
tu
<
16
tr
z
14
AA
12
10
A
0
6
<
4
Q
LU
I-
A
8
§
_J
UJ
Z
/o
-
•
uJ
CD
ry
_J
UJ
<
/
-
A
CJ
_l
<
*
DCEN
A
6
i
8
1
10
16
12
1
1
14
16
MEASURED MELTING RATE
A
•
-
a
ROBINSON
UILSON
O
•
14
A
12
-
10
-
a
-
G
-
_l
A
/
/
T H I S WORK
O
JC
UJ
CD
The effect of current, wire diameter,
electrode extension and polarity on the
melting rates can be explained by the
equations above. As explained earlier,
the total melting is composed of melting
due to arc heat and resistance heat. Thus,
MR for (DCEP) = 0.01037 I +
J2L
2.2426 X 10" 6 — - 0 . 4 6 2
d^
4
'
/
•
A
{ya
A
AO'
- So
1
1
i
i
l
l
1
1
1
1
'
IB
20
4
E
S
10
12
1+
16
IS
20
(kg/h)
DCEP
MEASURED MELTING RATE (kg/h)
Fig. 6 — Comparison of various mathematical models to calculate melting rates
WELDINC RESEARCH SUPPLEMENT 1139-s
with an increase in welding current, there
is a linear increase in arc heat, while the
resistance heat increases exponentially.
The rate of increase in arc heat and
resistance heat with current also depends
upon the coefficients. Thus, for the same
increase in welding current, there is a
larger increase in melting from arc heat
when DCEN is used.
Conclusions
1. Submerged arc welding variables
such as current, polarity, wire diameter
and electrode extension have an influence on the melting rate.
2. For a given wire diameter, electrode polarity and electrode extension,
there is an increase in melting rate with an
increase in welding current.
3. For a given welding current, higher
melting rates are obtained when longer
electrode extension and electrode negative and smaller wire diameter electrodes
are used. For the same welding variables,
melting rate for AC is slightly higher than
that for DC electrode positive.
4. Arc voltage and power source type
do not show any significant effect on
melting rate.
References
1. Apps, R. L., Gourd, L M., and Nelson, K.
A. 1963. Welding and Metal Fabrication
31:453.
2. Metals Handbook, Vol. 6, 9th edition.
1982. American Society for Metals, Metals
Park, Ohio.
3. McGlone, |. C, and Chadwick, D. B.
1978. The submerged arc butt welding of mild
steel: part 2. The Welding Institute, Abington,
Cambridge, England, Report R/RB/PE 26/78.
4. Salter, G. R„ and Doherty,). 1981. Metal
Construction 9:20.
5. Chandel, R. S. 1981. Optimization of
groove angles. AMCA International, Report
No. 1-R78-016/7.
6. Thomas, W. |. F., and Apps, R. L. 1978.
The influence of electrode extension and cold
filler wire additions on the deposition rates and
properties of submerged arc welds. Proc. of
Int. Conf. on Advances in Welding, Harrowgate, England.
7. Reynolds, D. E. H. 1978. High deposition
rate submerged arc welding. Submerged Arc
Welding, Chapter 7, The Welding Institute,
Abington, Cambridge, England.
8. Renwick, B. G., and Patchett, B. M. 1976.
Welding lournal 55(3):69-s to 76-s.
9. Wilson,). L, Claussen, G. E., and lackson,
C. E. 1956. Welding lournal35(1): 1-s to 8-s.
10. Robinson, M. H. 1961. Welding lournal
40(11):503-s to 515-s.
11. Martin, D. C, Rieppel, P. (., and Voldrich, C. B. May 1949. Welding Research
Council Bulletin, Series No. 3.
12. lackson, C. E., and Shrubsall, A. E. 1950.
Welding lournal 29(5):231-s to 241-s.
13. Mantal, W. 1956. Schweissen und
Schneiden 8:280.
14. Lesnewich, A. 1958. Welding journal
37(8):343-s to 353-s.
15. Thorn, K., Feenstra, M., Yound, |. C,
Lawson, W. H. S., and Kerr, H. W. 1982. Metal
Construction 3:128.
16. Halmoy, E. 1979. Wire melting rate,
droplet temperature and effective anode melting potential. Proc. of Int. Conf. on Arc Physics
and Weld Pool Behavior, London, England.
17. Mazel, A. G., and Gorarev, L. A. 1970.
Welding Production 3:34.
18. Demyantsevich, V. P. 1974. Automatic
Welding 8:47.
19. Chandel, R. S., and Malik, L. M. 1985.
Relationship between wire feed speed and
submerged arc welding parameters. Proc. of
Int. Conf. on Welding for Challenging Environments, Toronto, Canada.
WRC Bulletin 319
November 1986
Sensitization of Austenitic Stainless Steels: Effect of Welding Variables on HAZ Sensitization of AISI 304
and HAZ Behavior of BWR Alternative Alloys 316NG and 347
By C. D. Lundin, C. H. Lee, R. Menon and E. E. Stansbury
The research described in this report was undertaken to derive a better understanding of t h e HAZ
sensitization response of 3 0 4 , 3 0 4 L N , 316NG and 347 austenitic stainless steels. The results are directly
applicable t o both the as-welded and long-time service behavior of these austenitic stainless steels.
Publication of this report was sponsored by the S u b c o m m i t t e e on Welding Stainless Steel of t h e High
Alloys C o m m i t t e e of the Welding Research Council. The price of WRC Bulletin 319 is \$24.00 per copy,
plus \$5.00 for postage and handling. Orders should be sent with payment to t h e Welding Research
Council, Suite 1 3 0 1 , 345 E. 4 7 t h St., New York, NY 10017.
WRC Bulletin 320
December 1986
Welding Metallurgy and Weldability of High Strength Aluminum Alloys
By S. Kou
A literature survey was conducted to gather the information available on the welding metallurgy of
high strength aluminum alloys, and its effect on their weldability. Both conventional high strength
aluminum alloys and newer products, e.g., powder metallurgy aluminum alloys, Al-Li alloys and Al-matrix
composites, are included in this report.
Publication of this report was sponsored by the Aluminum Alloys C o m m i t t e e of the Welding Research
Council. The price of WRC Bulletin 3 2 0 is \$12.00 per copy, plus \$5.00 for postage and handling. Orders
should be sent with payment to the Welding Research Council, Suite 1 3 0 1 , 345 E. 4 7 t h St., New York, NY
10017.
140-s I M A Y 1987
```