Resistance spot welding (RSW) is a very popular technique for joining two or more than two sheets of metal in production industries. This research mainly focuses on the grey relational analysis with Taguchi method for optimizing heat affected zone (HAZ) with tensile shear strength. (HAZ) developed nearby weld nugget diameter. Increase of (HAZ) may cause the changes in microstructure properties, appearance and chemical composition of materials. To avoid such type of defects must be eliminating. By grey relational analysis it can be possible to eliminate such type of defects.

1. http://www.iaeme.com/IJMET/index.asp 23 editor@iaeme.com
International Journal of Mechanical Engineering and Technology (IJMET)
Volume 6, Issue 11, Nov 2015, pp. 23-32, Article ID: IJMET_06_11_003
Available online at
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=6&IType=11
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
GREY RELATIONAL ANALYSIS TO
OPTIMIZE WELDING PARAMETERS FOR
DISSIMILAR SHEETS OF MATERIAL IN
RESISTANCE SPOT WELDING
Ramkrishna Parihar
M-Tech scholar, Department of Mechanical Engineering,
Medi-caps Institute of Technology & Management, Indore (MP), India
Sanjay Jathar
Prof., Department of Mechanical Engineering,
Medi-caps Institute of Technology & Management, Indore (MP), India
ABSTRACT
Resistance spot welding (RSW) is a very popular technique for joining two
or more than two sheets of metal in production industries. This research
mainly focuses on the grey relational analysis with Taguchi method for
optimizing heat affected zone (HAZ) with tensile shear strength. (HAZ)
developed nearby weld nugget diameter. Increase of (HAZ) may cause the
changes in microstructure properties, appearance and chemical composition
of materials. To avoid such type of defects must be eliminating. By grey
relational analysis it can be possible to eliminate such type of defects. Both
characteristics (HAZ) and tensile shear strength are analysed by grey
relational based Taguchi method. In this research main aim is to decrease
(HAZ) and to increase tensile shear strength for weld quality. For
experimentation dissimilar sheets of material AISI304 and mild steel were
selected. There are four inputs welding parameter weld time, hold time, weld
current and electrode force were selected at their three respective level.
Orthogonal array L27 is designed for parameter on basis Taguchi method [3].
ANOVA table are calculated for significant parameter affects weld
performance of weld joint on base of grey relational method. Grey relational
grade have been determine to find out optimal value. Ultimately confirmation
test shows improvement in grey relational grade. Improvement in grey
relational grade indicates quality characteristics of weld joint.
Key words: ANOVA, dissimilar materials, grey relational analysis, (HAZ),
tensile shear strength.
Cite this Article: Parihar, R. and Jathar, S. Grey Relational Analysis to
Optimize Welding Parameters for Dissimilar Sheets of Material in Resistance

2. Ramkrishna Parihar and Sanjay Jathar
http://www.iaeme.com/IJMET/index.asp 24 editor@iaeme.com
Spot Welding. International Journal of Mechanical Engineering and
Technology, 6(11), 2015, pp. 23-32.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=6&IType=11
1. INRODUCTION
The resistance spot welding process was first used about an hundred years ago. Now
days it is regularly using in manufacturing industries. Resistance spot welding is a
thermoelectric process. In which two or more sheets of metal are joined in one or
more spots by resistance to flow of current through object that are hold by two
electrodes under particular force. The spot welds are controlled by the combination of
heat, time pressure. The process is generally used copper electrode to impact the
pressure on work piece due to resistance of electric current to the work piece. Heat is
developed at the faying surface of wok piece. It results in melting the surface of work
piece & to become spot weld together at the metal sheets. “Figure 1” shows the
schematic diagram of welding process. The resistance spot welding (RSW) plays a
very important role for its high speed & suitable for automotive industries. There are
about a 4000–5000 spot weld in automobile vehicles. RSW is significantly plays
important role in manufacturing cars, mechanical assemblies, railway structures & in
many more structural bodies.
The quality of spot weld is best judged by weld joint strength, weld nugget
diameter & heat affected zone (HAZ). “Figure 1” shows the spot welding process.
Figure 1 Spot welding process
Aravintham arumugam, et al. [1] have studied that the parameter optimization
when spot welding steels with dissimilar thickness & type using grey based Taguchi
method the three characteristics that were optimized are weld strength, weld nugget &
weld indentation. By ANOVA calculation it is found that weld current is most
significant parameter.
Ahilan, et al. [2] have studied multi response optimization of CNC turning
parameters using grey relational grade is obtained by S/N ratio. Based on grey
relational table significant contributions of controlling parameters are estimated using
analysis of variance (ANOVA)
There are two main of this experiments. The first one is that analysis of (HAZ) &
tensile shear strength together to determine weld performance. Second aim is that to
design significant parameter that affect experiment process.
2. GREY RELATIONAL METHOD
Following steps are important in grey relational analysis.
 Normalize all experimental turns’ value.

3. Grey Relational Analysis to Optimize Welding Parameters for Dissimilar Sheets of Material
in Resistance Spot Welding
http://www.iaeme.com/IJMET/index.asp 25 editor@iaeme.com
 Perform operation of grey relational generating & to calculate grey relational
coefficient (GRC).
 Averaging the value of grey relational coefficient (GRC) to determine grey relational
grade (GRG).
 Perform ANOVA analysis with grey relational grade (GRG) and to find which
parameter significantly affects experimental process.
 Select optimal level of parameters to determine optimal or prediction value.
 Conduct confirmation test and validate the prediction value.
3. METHODOLOGY
A batch of 160mm×30×1mm dissimilar sheets of AISI304 & mild steel were selected.
A schematic specimen is shown in “Figure 2”. The chemical component of both steels
is shown in “Table 1” & “Table 2”. The material of electrode is of copper.
Figure 2 Specimen
Table 1 Chemical component of AISI304
Component C Cr Fe Mn Ni P S Si
Wt % Max 0.08 18–20 66.345–74 Max2 8–10.5 Max0.045 Max0.03 Max1
Table 2 Chemical component of Mild steel
Component C Si Mn S P
Wt % 0.16–0.18 0.40 max 0.70–0.90 0.040 max 0.040 max
The input parameter is selected as weld time, hold time, weld current & electrode
force. Desired output parameters are (HAZ) & tensile shear strength. The input
parameters are shown in “Table 3”.
For experimentation a pedal operated rocker arm type spot welding machine with
the attachment of spot welding timer for controlling welding time, hold time in cycles
were used. Total 27 runs are taken & three responses of each run are taken as shown
in “Figure 3”. After runs samples are go through for tensile shear test on universal
testing machine (UTM). Diameter of (HAZ) has been measured.

4. Ramkrishna Parihar and Sanjay Jathar
http://www.iaeme.com/IJMET/index.asp 26 editor@iaeme.com
Table 3 Input parameters
Level Weld time
(cycle)
Hold time
(cycle)
Weld current
(ampere)
Electrode
force
(N)
(A) (B) (C) (D)
1 10 10 2044 19.81
2 30 30 2628 39.65
3 50 50 3650 59.48
Figure 3 Samples of runs
3.1. Grey based Taguchi method
A grey based Taguchi method approach is used for experimental analysis. Average
shear strength & (HAZ) value of each runs are illustrated in “Table 4.”
3.2. Normalized experiment results
Following equation (1) & (2) are used when a larger quality characteristics results are
desired (larger the better) & when smaller quality characteristics results are desired
(smaller the better).
Table 4 Average shear strength & (HAZ) & normalized value of each runs
Experiment
no.
Weld
time
(cycle)
Hold
time
(cycle)
Weld
current
(ampere)
Electrode
force
(N)
Average
Tensile
shear
strength
(KN)
Average
(HAZ)
(mm)
Normalized
value
Tensile
shear
strength
Normalized
value (HAZ)
(A) (B) (C) (D)
1 1 1 1 1 2.1 2.43 0.04 1
2 1 1 2 2 2.0 2.56 0 0.97
3 1 1 3 3 2.4 3.36 0.16 0.82
4 1 2 1 2 2.4 3.03 0.16 0.89
5 1 2 2 3 2.3 3.46 0.12 0.81
6 1 2 3 1 2.9 3.7 0.36 0.76
7 1 3 1 3 2.5 3.26 0.2 0.84
8 1 3 2 1 2.0 2.83 0 0.92

5. Grey Relational Analysis to Optimize Welding Parameters for Dissimilar Sheets of Material
in Resistance Spot Welding
http://www.iaeme.com/IJMET/index.asp 27 editor@iaeme.com
Experiment
no.
Weld
time
(cycle)
Hold
time
(cycle)
Weld
current
(ampere)
Electrode
force
(N)
Average
Tensile
shear
strength
(KN)
Average
(HAZ)
(mm)
Normalized
value
Tensile
shear
strength
Normalized
value (HAZ)
(A) (B) (C) (D)
9 1 3 3 2 3.4 3.86 0.56 0.73
10 2 1 1 1 3.4 5.76 0.56 0.39
11 2 1 2 2 3.9 5.76 0.76 0.39
12 2 1 3 3 4.1 5.73 0.84 0.39
13 2 2 1 2 3.5 5.43 0.6 0.45
14 2 2 2 3 3.5 5.3 0.6 0.47
15 2 2 3 1 4.2 5.73 0.88 0.39
16 2 3 1 3 3.3 5.3 0.52 0.47
17 2 3 2 1 3.4 5.56 0.56 0.42
18 2 3 3 2 3.9 5.83 0.76 0.37
19 3 1 1 1 3.6 6.53 0.64 0.25
20 3 1 2 2 3.4 6.73 0.56 0.21
21 3 1 3 3 4.0 7.7 0.8 0.03
22 3 2 1 2 4.4 6.8 0.96 0.20
23 3 2 2 3 4.2 6.83 0.88 0.19
24 3 2 3 1 4.5 7.76 1 0.02
25 3 3 1 3 4.2 7.2 0.88 0.12
26 3 3 2 1 4.3 7.1 0.92 0.14
27 3 3 3 2 4.4 7.9 0.96 0
“ ” (1)
“ ” (2)
Where no. of runs) & no. of responses)
3.4. Deviation sequence
Deviation sequence value of each are calculated & illustrated in “Table 5”
Table 5 Deviation sequence value
Expt. no. Tensile shear strength (HAZ)
Reference sequence 1 1
1 0.96 0
2 1 0.03
3 0.84 0.18
4 0.84 0.11
5 0.88 0.19
6 0.64 0.24

6. Ramkrishna Parihar and Sanjay Jathar
http://www.iaeme.com/IJMET/index.asp 28 editor@iaeme.com
Expt. no. Tensile shear strength (HAZ)
7 0.8 0.16
8 1 0.08
9 0.44 0.27
10 0.44 0.61
11 0.24 0.61
12 0.16 0.61
13 0.4 0.55
14 0.4 0.53
15 0.12 0.61
16 0.48 0.53
17 0.44 0.58
18 0.24 0.63
19 0.36 0.75
20 0.44 0.79
21 0.2 0.97
22 0.04 0.8
23 0.12 0.81
24 0 0.98
25 0.12 0.88
26 0.08 0.86
27 0.04 1
Where is the deviation sequence of the reference sequence and the
comparability sequence) i.e.
(3)
3.5. Determination of grey relational coefficient (GRC) & Grey relational
grade (GRG)
Following formula (4) are used for grey relational coefficient (GRC)
(4)
Where distinguishing coefficient is was given a value 0.5.
Calculation of (GRC), (GRG) & rank of (GRG) are given in “TABLE-6”
Table 6 The calculated (GRC) & (GRG) and its order in the Optimization process
Exp. No.
GRC of tensile
shear strength
GRC of (HAZ) GRG RANKS
1 0.3424 1 0.6712 1
2 0.3333 0.9433 0.6383 4
3 0.3731 0.7352 0.5541 18
4 0.3731 0.8196 0.5963 10
5 0.3623 0.7246 0.5434 19
6 0.4385 0.6756 0.5570 17

7. Grey Relational Analysis to Optimize Welding Parameters for Dissimilar Sheets of Material
in Resistance Spot Welding
http://www.iaeme.com/IJMET/index.asp 29 editor@iaeme.com
Exp. No.
GRC of tensile
shear strength
GRC of (HAZ) GRG RANKS
7 0.3846 0.7575 0.5710 13
8 0.3333 0.8620 0.5976 9
9 0.5319 0.6493 0.5906 11
10 0.5319 0.4504 0.4911 24
11 0.6756 0.4504 0.563 14
12 0.7575 0.4504 0.6039 8
13 0.5555 0.4761 0.5158 22
14 0.5555 0.4854 0.5204 21
15 0.8064 0.4504 0.6284 6
16 0.5555 0.4854 0.5204 21
17 0.5319 0.4629 0.4974 23
18 0.6756 0.4424 0.559 16
19 0.5813 0.4 0.4906 25
20 0.5319 0.3875 0.4597 26
21 0.7142 0.3401 0.5271 20
22 0.9259 0.3846 0.6552 3
23 0.8064 0.316 0.5612 15
24 1 0.3378 0.6689 2
25 0.8064 0.3623 0.5843 12
26 0.8620 0.3676 0.6148 7
27 0.9259 0.3333 0.6296 5
Response table for GRG are shown in “TABLE-7”.
Table 7 Response table for the grey relational grade
Level A B C D
1 0.5910 0.5554 0.5662 0.5796
2 0.5443 0.5829 0.5550 0.5786
3 0.5768 0.5738 0.5909 0.5539
Delta 0.0467 0.0275 0.0359 0.0257
Rank 1 3 2 4

8. Ramkrishna Parihar and Sanjay Jathar
http://www.iaeme.com/IJMET/index.asp 30 editor@iaeme.com
Figure 4 Graph for GRG with levels of parameter
4. ANALYSIS OF VARIANCE (ANOVA)
ANOVA is a statistical analysis tool for data analysis. It includes design parameters
that affect significantly output characteristics. In ANOVA method, sum of square
(SS), mean square (MS) & F-test values are calculated for deciding significant factors
which affecting the process & also percentage contribution contributed by parameters
are calculated. ANOVA table for grey relational grade are described in “TABLE-8”,
Table 8- ANOVA table for grey relational grade
Source DOF SS MS F-value % C
A 2 0.0103 0.0051 1.5 12.103
B 2 0.0035 0.00175 0.51 4.112
C 2 0.0060 0.003 0.88 7.050
D 2 0.0034 0.0017 0.5 3.995
Error 18 0.0618 0.0034 72.620
Total 26 0.0851 100
5. RESULTS & DISCUSSIONS
Above the “Figure 4” shows the Graph for GRG with levels of parameter. Larger
value of GRG represents better quality characteristics for both (HAZ) & tensile shear
strength. According to GRG graph the levels of parameters to be set for determine
optimum value of desired weld quality characteristics is A1B2C3D1.
Most significant parameter according to ANOVA table is weld time which affect
the performance of tensile shear strength & heat affected zone (HAZ). After weld
time the significant parameter are weld current, hold time, & electrode force. Hold
time & electrode force are less effective parameters. The percentage contributed by
weld time, weld current, hold time, & electrode force are 12.103%, 7.050%,4.112%,
& 3.995%.
1 2 3
A 0.591 0.5443 0.5768
B 0.5554 0.5829 0.5738
C 0.5662 0.555 0.5909
D 0.5796 0.5786 0.5539
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.6
GRD
LEVELS OFPARAMETER

9. Grey Relational Analysis to Optimize Welding Parameters for Dissimilar Sheets of Material
in Resistance Spot Welding
http://www.iaeme.com/IJMET/index.asp 31 editor@iaeme.com
6. CONFIRMATION TEST
Confirmation test is very important in design of parameters. The aim of confirmation
test is to validate the optimal value during analysis is A1B2C3D1. The confirmation
test is done by the specific combination of parameters with their levels which were
predicted as A1B2C3D1. In this experimental procedure the optimal value has been
predicted & new experiment is designed to conducting new experiments to get best
weld performance for quality characteristics. The predictions for optimum value for
GRG are.
Predicted mean =
= 0.6436
Comparison result of initial welding parameter, predicted and experimental
parameter are shown in “TABLE-9”. The improvement in Taguchi based grey
relational grade is 0.0832.So by grey based Taguchi method it is possible to increase
in tensile shear strength & decrease (HAZ) characteristics. Results of confirmation
test are illustrated in “TABLE-9”.
Table 9 Results of confirmation test
Initial welding process
parameters
Optimum welding parameter
Prediction Experimental
Levels A1B3C3D1 A1B2C3D1 A1B2C3D1
Tensile shear strength(KN)
2.9
- 3
(HAZ) (mm) 3.719 - 3.706
Taguchi based grey relational
grade 0.5569
0.6436 0.6401
Improvement of Taguchi
based grey relational grade
0.0867 0.0832
7. CONCLUSION
This research paper deals with optimization & the affect of factors on heat affected
zone (HAZ) & tensile shear strength. ANOVA table determines significant welding
parameters. According to ANOVA table welding time are highly affects tensile shear
strength & (HAZ) where as welding current are second higher parameter that affects
desired weld quality characteristics. Hold time and electrode force are less affective
parameters. GRG determines the optimum combination of parameters with their
levels or maximizing tensile shear strength & minimizing (HAZ). By conducting
confirmation test & its results it is possible to increase tensile shear strength & heat
affected zone. The experimental results validate Taguchi method for quality
engineering to best performance & optimization of welding parameters in resistance
spot welding.
REFERENCES
[1] Arumugam, A. and Amizi Nor, M. Spot Welding Parameter Optimization To
Improve Weld Characteristics For Dissimilar Metals. International journal of
scientific & technology research, 4(01), 2015, pp. 75–80.

10. Ramkrishna Parihar and Sanjay Jathar
http://www.iaeme.com/IJMET/index.asp 32 editor@iaeme.com
[2] Ahilan, C., Kumaran, S. and Shivkumaran, N. Application Of Taguchi Method In
Multi-response Optimization Of Turning Process. Advance In Production
Engineering & Management, 5(3), 2010, pp. 171–180.
[3] Ross, P. J. Taguchi techniques for quality engineering, 2nd Ed. Tata McGraw
Hill, 2005.
[4] Hasani, H., Tabatabaei, S. A. and Amiri, G. Grey Relational Analysis to
Determine the OptimumProcess Parameters for Open-End Spinning Yarns.
Journal of Engineered Fibers and Fabrics, 7(2), 2012, pp. 80–86
[5] Datta, S., Bandyopadhyay, A. and Kumar Pal, P. Grey based Taguchi
method for optimization of bead geometry in submerged arc bead on plate
welding. International Journal of Advanced Manufacturing Technology,
39, 2008, pp. 1136‐1143.
[6] Niranjan Kumar, S. and Vijayakumar, Y. Application of Taguchi method for
optimization of resistance spot welding of austenitic stainless steel AISI 301L,
Innovative Systems Design and Engineering, 3(12), 2012, pp 49–61.
[7] Juang, S. C. and Tarng, Y. S. Process Parameter Selection for
Optimization the Weld Pool Geometry in the Tungsten Inert Gas Welding
of Stainless Steel. Journal of Material Processing Technology, 122, 2002,
pp. 33–37.
[8] Jagannatha, N., Hiremath, S. S. and Sadashivappa, K. Analysis and
parametric optimization of abrasive hot air jet machining for glass using
Taguchi method and utility concept. International Journal of Mechanical
and materials engineering, 7(1.9.15), 2012, pp. 9–15.
[9] Aslanlar, S. The effect of nucleus size on mechanical properties in electrical
resistance spot welding of sheets used in automotive industry. Journal of
Materials and Design, 27, 2006, pp. 125–131.
[10] Sun, D. Q., Lang, B., Sun, D. X. and Li, J. B. Microstructures and
mechanical properties of resistance spot welded magnesium alloy
joints. Materials Science and Engineering A, 2007, pp. 460–461, 494–498.
[11] Gurav, B. D. and Ambekar, S. D. Optimization of the Welding Parameters in
Resistance Spot Welding. International Journal of Mechanical Engineering and
Technology, 4(5), 2013, pp. 31–36.