ARTIFICIAL NEURAL NETWORKS FOR PREDICTION OF
DEPTH OF PENETRATION IN MIG
WELDING.
Abstract
Depth of penetration is one of
important physical characteristic of a weldment. This paper was done on the
basis of prediction that there is a relationship between welding parameters and
depth of penetration in gas metal arc welding. Dimensionless model and artificial
neural network were used as methods for predicting the depth of penetration.
The dimensionless model and the artificial neural network were formed, and the
analytical expression for depth of penetration was taken from the research done
by P.E Murray and A.Scotti for dimensionless model, and the training data or
test data which were used in the formation process of the artificial neural
network, were used to perform the prediction of the depth of penetration was
taken from experiment done by above researchers. Back-propagation neural
networks are used to associate the welding process variables with the features
of the penetration. These networks have achieved good agreement with the
training data and have yielded satisfactory generalization.
Therefore
it is concluded that the error rate predicted by the artificial neural network
was smaller than that predicted by the dimensionless model, in terms of the
depth of the penetration.
MIG
Welding Process:
MIG
(Metal Inert Gas) or as it even is called GMAW (Gas Metal Arc Welding) uses an aluminum
alloy wire as a combined electrode and filler material. Since all welding
parameters are controlled by the welding machine, the process is also called
semi-automatic welding.
Penetration
The Welding Encyclopedia refers to two types of penetrations—‘‘weld
penetration’’ also called ‘fusion’ and ‘‘heat penetration.’’ In fusion welding
the depth of weld penetration or fusion is generally recognized as the distance
below the original surface of the work to which the molten metal progresses.
The HAZ refers to the parent metal metallurgically affected by the heat of
welding, but not melted.
The
other factors which influence the penetration are heat conductivity,
arc-length, and arc-force. Summarizing, it can be stated that the penetration
affect the weldment characteristics and are dependent on a number of welding
variables like arc-length, arc-travel rate, electrode feed rate, arc-power,
arc-voltage and arc-current.
. Dimensionless
Model :
Theoretical models of heat transfer to the weld pool have been used to
predict the size and shape of the cross-sectional area of fused metal. These
models assume steady state energy transfer to the base metal by conduction
only, and the geometrical idealization of a planar base metal is used to obtain
analytical solutions to the energy equation.
The model is based on the assumption that the depth of the weld pool,
the heat transfer from the arc, and the mass transfer due to droplets impinging
on the weld pool may be correlated by a dimensionless relation. Therefore a
characteristic thermal length scale α/S is introduced, where α is the thermal
diffusivity of the base metal and S is the travel speed. A characteristic
length scale for mass transfer is also introduced, which is the radius of
droplets impinging on the pool. Using these characteristic length scales, three
important dimensionless variables are defined.
1.The
dimensionless depth of penetration is
…………………(1)
Where d is the depth of
penetration
2.The
dimensionless mass transfer number is
……………………(2)
Where M is the melting rate of
the electrode,
μ
is the viscosity of the pool and
r is the radius of droplets impinging on the pool.
3.The
dimensionless heat transfer number is
………………...(3)
where V is the arc voltage
I is the current,
and
ΔH is the change in
enthalpy of the base metal that is heated from
the initial temperature to the melting temperature.
Although the
current and electrode extension are measured in the experiment , the melting
rate is obtained directly from the relation M=ρπR2U, where ρ is the
electrode density, R is the electrode radius ,and U is the speed of the
electrode .The mass of a droplet detaching from the electrode is obtained from
the following relation
…………………..(4)
Where m
is the average mass and
n
is the measured frequency of detaching droplets.
Assuming a
spherical droplet ,the radius is related to the mass according to
m=1.333
ρ π r3………...(5)
Where r
is the radius of the droplets.
An accurate
computation may be obtained by defining the efficiency of penetration
…………………(6)
To establish
mathematical and physical bases for a correlation between A, B, and δ, a
general relationship is considered given by
δ =F
(ABn)…………….(7)
Where F (ABn)
is an arbitary function of the variable ABn and n is a positive
constant. This implies that δ satisfies
the following equation.
……(8)
Hence the
exponent n satisfies the following
relation
Where the
subscript denotes the variables that is held constant in the evaluation of the
derivative .Experimental data on the variation in δ with respect to variations
in A and B may be used to determine the exponent empirically. Using the
experimental data it was found from above equation that n=1/2 . Hence δ is a
function of AB1/2. Furthermore, it was found from linear regression
that the correlation between AB1/2 and δ may be accurately
represented by the following relationship
δ= η
(AB1/2) 1/3…………….(10)
Where η is a
positive constant.
Using equation
(6) in equation (10) yields the final that is given in dimensionless variables
D=
η A1/3 B2/3…………….(11)
Using the
definition of A, B and D in equation (11) yields the final result is given in dimensionless variables
EXPERIMENTAL :
Horizontal bead on plate welds were made on 0.25 and 0.5 in (1in=25.4mm)
thickness stainless steel type ASTM304 using an automated gas metal arc welding
apparatus. A Miller Maxtron 450 power supply was used in the constant voltage
mode. The shielding gas was a mixture consisting of 98%Ar and 2% O2
and the flow rate of gas was fixed at 35 standard cubic feet per hour
(1cu.ft-0.028 m3). The electrodes were stainless steel type AWS
ER308L with diameters equal to 0.89 and 1.14 mm. An experiment was designed to
vary all the important processing variables that affect the depth of
penetration, which include voltage, current, rate of deposition , electrode
size ,travel speed, arc length and mode
of mass transfer. All the data obtained
from this experiment are given in table-1
Table 1: Experimental data
for gas metal arc welding of stainless steel using shielding gas consisting of
98Ar-2O2
|
R, mm
|
S, mm s-1
|
U, mm s-1
|
V, V
|
I, A
|
ν, s-1
|
L, mm
|
d, mm
|
|
0.445
|
4
|
96.7
|
17.6
|
96.0
|
36
|
3.1
|
1.9
|
|
0.445
|
4
|
157.1
|
19.2
|
132.4
|
65
|
3.1
|
2.0
|
|
0.572
|
7
|
102.3
|
21.6
|
173.6
|
39
|
2.8
|
2.5
|
|
0.572
|
4
|
95.0
|
21.4
|
168.3
|
40
|
3.5
|
3.0
|
|
0.572
|
7
|
102.3
|
17.6
|
188.8
|
47
|
1.7
|
2.1
|
|
0.445
|
10
|
317.2
|
24.6
|
197.1
|
170
|
3.6
|
2.3
|
|
0.445
|
4
|
126.9
|
24.1
|
141.6
|
144
|
5.8
|
3.7
|
|
0.445
|
7
|
222.0
|
25.2
|
216.1
|
202
|
4.6
|
3.2
|
|
0.572
|
4
|
58.5
|
28.1
|
128.5
|
9
|
9.1
|
1.4
|
|
0.572
|
4
|
76.7
|
27.5
|
167.2
|
177
|
9.1
|
3.6
|
|
0.572
|
10
|
237.6
|
28.8
|
315.9
|
100
|
2.6
|
4.0
|
|
0.445
|
7
|
169.2
|
26.3
|
155.2
|
216
|
5.2
|
3.2
|
|
0.445
|
7
|
274.5
|
30.2
|
208.8
|
194
|
6.5
|
3.2
|
|
0.572
|
10
|
146.2
|
26.6
|
255.0
|
209
|
4.4
|
3.5
|
|
0.572
|
4
|
95.0
|
27.0
|
178.7
|
347
|
7.2
|
3.5
|
|
0.445
|
10
|
241.7
|
31.1
|
213.3
|
259
|
9.5
|
3.3
|
|
0.445
|
7
|
222.0
|
30.9
|
235.1
|
421
|
10.1
|
4.4
|
|
0.572
|
7
|
163.3
|
32.7
|
346.3
|
436
|
10.0
|
6.2
|
|
0.445
|
10
|
241.7
|
31.3
|
276.3
|
500
|
9.1
|
4.1
|
|
0.572
|
7
|
166.3
|
29.6
|
319.6
|
500
|
10.0
|
6.3
|
|
0.445
|
10
|
392.7
|
31.3
|
333.5
|
500
|
6.3
|
6.4
|
|
0.572
|
10
|
191.9
|
28.9
|
334.1
|
500
|
4.6
|
6.0
|
|
0.572
|
10
|
191.9
|
28.9
|
328.1
|
500
|
4.6
|
5.7
|
|
0.445
|
10
|
392.7
|
35.0
|
389.6
|
500
|
9.6
|
6.4
|
R
electrode radius; S travel speed; U electrode sped; V voltage ;I current ;v
frequency of detaching droplets; L arc length ;d depth of penetration.
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