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ExperimentalInvestigationandMultiObjectiveOptimizationofWEDMofDuplexSteelusingGreyCoupledFuzzy
ARTICLE·AUGUST2015
2AUTHORS:
BalaNarasimha
NationalInstituteofTechnologyKarnataka
4PUBLICATIONS0CITATIONS
SEEPROFILE
VamsikrishnaMamidi
MadanapalleInstituteofTechnology&Science
9PUBLICATIONS1CITATION
SEEPROFILE
Availablefrom:BalaNarasimha
Retrievedon:21August2015
Experimental Investigation and Multi Objective
Optimization of WEDM of Duplex Steel using Grey
Coupled Fuzzy
Bala G Narasimha S. V. College of Engineering
Tirupati, India
Vamsi M Krishna MadanapalleInstitute of
Technology and Science
Madanapalle, India,
Rajesh Nagadolla S. V. College of Engineering
Tirupati, India
Abstract:In this study, Grey coupled fuzzy logic methodology is
used for multi response optimization of Wire Electrical
Discharge Machining parameters, which converts the multi
responses into a single MPCI. Based on MPCI, optimal
combination of parameters are determined. L9 orthogonal array
is used for plan of experiments. Maximum Material removal rate
and Minimum surface roughness were chosen as the objectives.
The attractive combination of high corrosion resistance, good
mechanical strength and relatively low cost makes duplex
stainless steels (DSSs) as one of the fastest growing groups of
stainless steels. In this study Duplex steel is considered as the
target material for Wire Electrical discharge Machining. A Multi
- performance characteristic index (MPCI) was used for
optimization. The process parameters viz., pulse on time, pulse
off time, wire feed, wire tension were optimized with
consideration of MPCI. The confirmation run, results shows that
the better quality is achieved by the optimal combination of process parameters.
Keywords: Duplex Steel, Multi objective optimization, Grey
relational analysis, Fuzzy logic
I. INTRODUCTION
Duplex stainless steels are named as “Duplex” because, it is of two-phase microstructure consisting of grains of austenitic and ferritic stainless steel, possessing high corrosion resistance and excellent mechanical properties [1]. At present, these steels are used in various industries like power plants, water purification and marine etc. Wire Electrical Discharge Machining (WEDM) is a unconventional manufacturing process, used to machine very hard materials with high precision. The unique feature of WEDM is that it utilizes thermal energy to machine electrically conductive parts, which makes advantage in the manufacture of parts with complex shapes and hard material [2]. WEDM has been widely used in many industries, which requires high precision and quality [3]. The research in WEDM processing has been focused on rapid machining with best quality. Manufacturing industries applies various methodologies to identify the effect of machining parameters on material removal rate and surface roughness, which are the most important objectives in the manufacturing.
To achieve best quality and good functionality, it is important to select the suitable, optimal process parameters and its levels
[4]. Generally, Taguchi method is used to optimize the single response characteristics of process parameters to achieve high quality [e.g., 5-6], which is not suitable for present scenario in industries. At present, handling multi-response characteristics are an interesting and challenging research. Grey relational analysis is used to determine the optimal parameters by converting multi responses into single response (grey relational grade) [e.g., 7 - 8]. Zadeh [9] initiated Fuzzy logic theory, which is used to deal with uncertain and vague information, using fuzzy sets such as „low‟, „medium‟ and „high‟. Fuzzy theory proves an effective way of solving the problem, which attracts the many researchers in various fields. To improve system performance, few researchers investigated grey relational analysis coupled with fuzzy logic [10-11] and identified improvement in the results. ANOVA is carried out to determine the percentage of contribution of each factor on the response of the system.
II. EXPERIMENTAL SETUP/OUTPUT MESUREMENT
In the present study, Duplex steel is used as target material.
Experiments were performed using Electronica Maxicut Wire
EDM. A 0.25 mm diameter, brass wire was used as an
electrode and distilled water is used as dielectric fluid. A
small gap of 0.025 mm to 0.05 mm is maintained in between
the wire and work-piece. The dimensions of the work piece
for experimentation is 10 * 10 * 13 mm. The process
parameters were being set in the WEDM control panel and the
experiments were conducted as per the design of experiments
shown in Table 2. The time required for metal removal from
work piece is determined by using stopwatch and the surface
roughness is determined by using talysurf instrument and the
results were tabulated in Table 2. In this study four process
parameters with three levels are chosen for machining. The
parameters and its levels are shown in Table 1. L9 (33-1 = 9
runs) orthogonal array of experiments was chosen for
experimentation, instead of L 27 array (33 = 27 runs) to reduce
the experimentation cost.
A - Pulse-on (μs), B - Pulse-off (μs), C - Wire tension (N), D -
Wire feed (m/min), X - MRR (mm3/sec), Y – Surface
Roughness (μm).
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TABLE1 PROCESS PARAMETERS AND LEVELS
Process
parameters
Levels
Level – 1 Level – 2 Level - 3
Pulse-on
(μs) 3 6 9
Pulse-off
(μs) 3 6 9
Wire tension
(N) 1 2 3
Wire feed
(m/min) 7 8 9
TABLE2 DESIGN OF EXPERIMENTS AND RESPONSES
Expt.
No A B C D X Y
1 3 3 1 7 18.57 2.65
2 3 6 2 8 19.70 2.90
3 3 9 3 9 20.00 2.65
4 6 3 2 9 26.00 2.83
5 6 6 3 7 28.89 2.97
6 6 9 1 8 28.89 2.76
7 9 3 3 8 20.00 3.00
8 9 6 1 9 26.00 2.94
9 9 9 2 7 32.50 2.85
III. GREY RELATIONAL ANALYSIS
In 1989, Deng proposed Grey relational analysis for solving
complicated interrelationships between the multiple response
characteristics problems. In grey relational analysis, the
system has information in the form of black and white. If the
system is grey, some information is known and some
information is unknown, i.e., relationships among factors in
the system are uncertain. If the system is white, the
relationships between factors are certain. In the grey relational
analysis, grey relational grade is used to optimize multi-
response system. The grey relational analysis includes the
following steps:
Conduct the experiments as per design of experiments.
Transform the experimental results into signal-to-noise
ratio.
Normalize the values of signal-to-noise ratio.
Perform grey relational generating and calculate grey
relational coefficient.
Calculate the grey relational grade by averaging the grey
relational coefficient.
A. Normalization
Convert the original sequences to a set of comparable
sequences by normalizing the data. Depending upon the
response characteristic, three main categories for normalizing
the data is as follows:
Larger the better‟
ai ∗ k =
b i ∗ k −min b i
∗ k
max b i ∗ k −min b i
∗ k (1)
„Smaller the better‟
ai ∗ k =
max b i ∗ k −b i
∗ k
max b i ∗ k −min b i
∗ k (2)
„Nominal the better‟
𝑎𝑖 ∗ 𝑘 = 1 −
𝑏𝑖 ∗ 𝑘 −𝑂𝑉
max {𝑚𝑎𝑥 𝑏𝑖 ∗ 𝑘 −𝑂𝑉 ,𝑂𝑉−𝑚𝑖𝑛 𝑏𝑖
∗ 𝑘 }(3)
Where 𝑏𝑖 ∗ 𝑘 is the experimental result in ith, 𝑎𝑖
∗ 𝑘 is the
normalized result in the ith experiment and OV is the
optimum value. The original reference sequence𝑎0(∗)
(k) = 1
and normalized data ai(∗)
(k) (comparability sequence) where i
= 1,2,….,m; k =1,2,.....,n respectively, where m is the number of experiments and n is the total number of observations of data.
B. Grey relational coefficient and grey relational grade:
Grey relation coefficient (αij ) is calculated for each of the
performance characteristics, which expresses the relationship between ideal and actual normalized experimental results, as shown in “Eq.(4).”
αij =∆min +ξ∆max
∆oi k +ξ∆max (4)
i =1,2,….,m; k =1,2,.....,n respectively, where m is the number of experiments and n is the total number of observations of data. Where ∆oi k is the deviation sequence of the reference
sequence a0 ∗ k and comparability sequence ai
∗ k .
i.e.; ∆𝑜𝑖 𝑘 = |𝑎0 ∗ 𝑘 − 𝑎𝑖
∗ 𝑘 |, and
∆min = 𝑚𝑖𝑛|𝑎0 ∗ 𝑘 − 𝑎𝑖
∗ 𝑘 |,
∆max = 𝑚𝑎𝑥|𝑎0 ∗ 𝑘 − 𝑎𝑖
∗ 𝑘 |
„𝜉‟ is the distinguishing coefficient and the value lies between 0 and 1 i.e. 0 ≤ 𝜉 ≥ 1. The distinguishing coefficient 𝜉 value generally chosen to be 0.5. Grey relational grade can be calculated by taking the average of is the weighted grey relational coefficient and defined as follows:
Ʃ𝛽𝑘𝛾(𝑥0 ∗ 𝑘 , 𝑥𝑖
∗ 𝑘 ) = 1 (5)
International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.71 (2015) © Research India Publications; http://www.ripublication.com/ijaer.htm
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where𝛽𝑘 is the weighting factor of each response. In the present study, all process parameters influence the responses, so equal weights are assigned to parameters.
TABLE3 S/N RATIOS, NORMALIZED AND GREY
RELATIONAL COEFFICIENTS
Expt
No
S/N ratios Normalized
values
Grey Relational
Coefficients
MRR SR MRR SR MRR SR
1. 25.376 -8.464 0.000 0.006 0.333 0.335
2. 25.888 -9.233 0.105 0.712 0.358 0.635
3. 26.020 -8.458 0.132 0.000 0.366 0.333
4. 28.299 -9.035 0.601 0.531 0.556 0.516
5. 29.214 -9.458 0.789 0.919 0.704 0.862
6. 29.214 -8.811 0.789 0.325 0.704 0.426
7. 26.020 -9.545 0.132 1.000 0.366 1.000
8. 28.299 -9.378 0.601 0.846 0.556 0.765
9. 30.237 -9.081 1.000 0.573 1.000 0.540
IV. DETERMINATION OF OVERALL FUZZY
GRADE
Fuzzy logic is one of the powerful artificial intelligence
techniques, resolves problem which consists huge uncertain
information. It is highly suitable for defining the relationship
between system input and desired outputs in linguistic form. A
fuzzy logic unit comprises a fuzzifier, membership functions,
a fuzzy rule base, an inference engine and a defuzzifier as
shown in Fig.1. At first, using membership functions the
inputs are fuzzified by the fuzzifier, and then fuzzy value is
generated by the inference engine based on fuzzy rules and
lastly the fuzzy value into a fuzzy grade by the defuzzifier.
The structure built for this study is a two inputs and one
output as shown in Fig. 2.
Fig. 1. Fuzzy Logic model
Fig. 2. Fuzzy Structure
In this study, grey relation coefficient of Material removal rate
(MRR) and surface roughness(SR) has been taken as fuzzy
inputs using triangular membership functions form and grey
relation fuzzy grade (MPCI) as output for finding out optimal
process parameters. The input and output „fuzzy set‟ has been
defined in the range between 0 and 1. The desired output is
targeted on maximizing grey relation fuzzy grade. The fuzzy
inputs are uniformly assigned into five fuzzy subsets – very
low (VL), low (L), medium (M), High (H) and very High
(VH) grade, as shown in Fig. 3.
Fig. 3. Fuzzy input – MRR & SR
Unlike the input variables, the output variable is assigned into
relatively nine subsets i.e., very very low (VVL), very low
(VL), Low (L), medium low (ML), medium (M), medium
high (MH), high (H), very high (VH), very very high (VVH),
as shown in Fig.4.
Fig. 4. Fuzzy output – MPCI
The relationship between the two fuzzy inputs are defined in
the form of if-then fuzzy rules as listed in Table 4.
International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.71 (2015) © Research India Publications; http://www.ripublication.com/ijaer.htm
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TABLE4 FUZZY RULES
Rules Grey relational coefficients of MRR
VL L M H VH
Grey
rela
tio
na
l
co
eff
icie
nts
of
SR
VL VVL VL L ML M
L VL L ML M MH
M L ML M MH H
H ML M MH H VH
VH M MH H VH VVH
In this study, Mamdani max-min compositional operation is
adopted for fuzzy reasoning. A typical linguistic fuzzy rule
called Mamdani is described as
Rule 1: if x1is A1and x2 is B1 then y is C1 else
Rule 2: if x1is A2 and x2 is B2 then y is C2 else
---------------------------------------------------------
Rule n: : if x1 is An and x2 is Bn then y is Cn
In above, Ai, Bi, are fuzzy subsets defined by the
corresponding membership functions, i.e., μAi, μBi, and μCi.
the membership function of the output of fuzzy reasoning can
be expressed as
𝜇𝑐0 𝑦 = 𝜇𝐴1
𝑥1 ˄ 𝜇𝐵1 𝑥2 ˄ 𝜇𝐶1
𝑦1 ˅
𝜇𝐴𝑛 𝑥1 ˄ 𝜇𝐵𝑛
𝑥2 ˄ 𝜇𝐶𝑛 𝑦1 (6)
where „˄‟ is the minimum operation and „˅‟ is the maximum operation. In this study, Fuzzy grade 𝑦0, is computed using Center-of-gravity defuzzication method, transforms the fuzzy inference output 𝜇𝑐0
into a fuzzy grade 𝑦0, i.e.
𝑦0 = Ʃ𝑦 𝜇𝑐0
𝑦
Ʃ 𝜇𝑐0 𝑦
(7)
The fuzzy grade is the final crisp output value known as
MPCI, as shown in Table 5.
TABLE5 GREY RELATIONAL AND GREY FUZZY
GRADES
Expt. No Grey Relational
grade
Grey Fuzzy
grade (MPCI) Order
1 0.334 0.349 9
2 0.497 0.498 7
3 0.349 0.358 8
4 0.536 0.547 6
5 0.777 0.783 1
6 0.565 0.549 5
7 0.683 0.684 3
8 0.661 0.671 4
9 0.770 0.775 2
Table 5. Shows the order of grey relational and grey fuzzy
reasoning grades obtained from the FIS. On comparing the
results, there is an improvement in the values of grey fuzzy
grades, which indicates the reduction of uncertainty in data.
The larger MPCI value among all possible combinations of
the process parameters indicates the optimal combination of
parameters and confirmed that the experiment number 9 has
the optimal combination of process parameters for machining.
The averages of MPCIs for each level of the machining
factors are then computed and tabulated in Table 6. The
darkened number in each column of factors indicates the best
level for each factor. The delta, indicates the difference
between maximum and minimum, of MPCIs. Rank 1
represents the largest delta among their levels and have more
influence on the machining process.
TABLE6 RESPONSE TABLE FOR GREY-FUZZY GRADE
LEVEL PULSE
ON
PULSE
OFF
WIRE
TENSION
WIRE
FEED
1 -8.047 -5.897 -5.940 -4.519
2 -4.209 -3.903 -4.503 -4.853
3 -2.991 -5.448 -4.805 -5.874
DELTA 5.056 1.994 1.437 1.355
RANK 1 2 4 3
V. ANALYSIS OF VARIANCE (ANOVA)
ANOVA is performed to identify the contribution of process
parameters of WEDM on MPCI‟s. An ANOVA table as
shown in Table. 7 consists of degrees of freedom, sums of
squares and the percentage of contribution. From Table 7, it
shows that the process parameters Pulse on and Pulse off have
the most influence on the MPCI, which coincides with the
results of Table 7. It is observed that the Pulse On (72.73%) is
most significant factor followed by Pulse off (11.74%), Wire
feed (8.72%) and Wire tension (6.81%). The percentage of
error is 0% indicating the selection of the process parameters
are highly reliable.
TABLE7 ANALYSIS OF VARIANCE
Source DF Seq SS Adj SS Seq MS %
Contribution
Pulse on 2 0.1525 0.1525 0.07627 72.73
Pulse off 2 0.0246 0.0246 0.01231 11.74
Wire tension 2 0.0142 0.0142 0.00714 6.81
Wire feed 2 0.0182 0.0182 0.00914 8.72
Error 0 -- -- -- --
Total 8 0.2097 -- -- 100.00
International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.71 (2015) © Research India Publications; http://www.ripublication.com/ijaer.htm
501
VI. CONFIRMATION TEST
TABLE8 CONFIRMATION TEST RESULTS
Type Optimal /
Predicted
Optimal/
Experimental % Error
Level combination A3B2C2D1 A3B2C2D1 --
MRR (mm3/sec) 29.2038 29.1967 0.024
SR
(μm) 2.94 2.93 0.34
Grey fuzzy grade
(MPCI) 0.789 0.787 0.25
From the table 8. It shows that A3B2C2D1 is an optimal
parameter combination of the machining process obtained by
grey coupled fuzzy logic. The confirmation experiment is
carried out to validate the optimal level of parameters for
maximum Metal removal rate and minimum surface
roughness. After confirmation test, it is clear that the MRR
and SR increased greatly with the optimal parameters and the
fuzzy grade is increased by 43.8%.
VII. CONCLUSION
In this paper, Grey coupled fuzzy logic analysis is
applied for optimizing the process parameters of WEDM
process, which minimizes the uncertainty and
improvement in Fuzzy grade (MPCI).
The optimal combination of parameters are: pulse on --
9 μs, pulse off – 6 μs, wire tension – 2 N and wire feed –
7 m/min.
From the ANOVA, it shows that Pulse on and Pulse off
are the predominant factors for machining.
Increase of MPCI from 0.349 to 0.787 confirms the
improvement in performance characteristics at optimal
level of process parameters.
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