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Abstract— Multi criteria decision making method is most effective approach to find the optimum solution of any non-conventional process. Wire cut electrical discharge machining process use to cut difficult materials for complicated parts. Taguchi design of experiment L 27 orthogonal array were used to plan the experiment considering the wire material, pulse on time, pulse off time, peak current, wire diameter, wire tension, wire feed rate as input parameters for response material removal rate, surface roughness and cutting velocity. Aluminum boron carbide use as work piece material. Multi criteria decision making method applied to experiment and finds the alternative 15 and 14 is best alternative amongst 27 experiments. Keywords: Wire cut electrical discharge machining, Orthogonal
array, Multi criteria decision making method.
1.INTRODUCTION
Now a day to manufacturing difficult parts and
complicated shape non-conventional machining process is
good option for it. Wire electrical discharge machining
process is used to manufacturing the integrated shape.
During the wire EDM process, the wire carries one side of
an electrical charge and the work piece carries the other
side of the charge. When the wire gets close to the part, the
attraction of electrical charges creates a controlled spark,
melting and vaporizing microscopic particles of material.
The spark also removes a miniscule chunk of the wire, so
after the wire travels through the work piece one time, the
machine discards the used wire and automatically
advances new wire. Kanlayasiri and Boonmung (2007)
investigation made on wire-EDMed DC53 die steel material
to study the effects of machining variables on the surface
roughness. Analysis of variance (ANOVA) technique was
used to find out which variables affecting the surface
roughness. Mathematical model was developed using
multiple regression method to formulate the pulse-on time
and pulse-peak current for the
surface roughness. Pulse-on time and pulse-peak current
were significant variables for the surface roughness of
wire-EDMed DC53 die steel [8]. Chen and Lin (2010)
analyzed the variation of cutting velocity and work piece
surface finish depending on wire electrical dis charge
machining (WEDM) process parameters during
manufacture of pure tungsten profiles. It uses the
integrating approach of back-propagation neural network
and simulated annealing algorithm to determine an
optimal parameter setting of the WEDM process [5].
Chakraborty et al. (2011) was found that all
decision-making problems cases the results obtained
using the MOORA method. Almost corroborate with those
resultant by the past researchers which verify the
flexibil ity, potentiality, and applicability of MOORA
method while solving different complex decision-making
problems in current day manufacturing environment [4].
Rao and Navas (2013) investigation has been made by
integrated approach, principal component analysis (PCA),
coupled with Taguchi’s robust theory for simultaneous
optimization of correlated multiple responses of wire
electrical discharge machining process for machining SiCP
reinforced ZC63 metal matrix composites. WEDM
experiments are conducted by varying the particulate size,
volume fraction, pulse-on time, pulse-off time and wire
tension. PCA is used as multi -response optimization
technique to derive the composite principal component
which acts as the overall quality index in the process.
Consequently, Taguchi’s S/N ratio analysis is applied to
optimize the CPC [14]. Darji and Rao (2014) present
intell igent and logical MCDM methods Extended TODIM,
OCRA, ARAS, EVAMIX to evaluate suitable material for
pipes. The comparison is done with the result obtained by
Use of Multi Criteria Decision Making Method for Selection of Wire Cut
Electrical Discharge Machining Process
Jaksan D Patel1, Kalpesh D Maniya2
Research Scholar, Department of Mechanical Engineering, Carusat University,Changa
Associate Professor, Department of Mechanical Engineering, C.K.Pithawala College of Engineering
&Technology, Surat
International Journal of Pure and Applied MathematicsVolume 118 No. 20 2018, 383-389ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu
383
2
the previous researchers, which is found to be the same.
The methods proposed are more specific and efficient
compared with the previous methods [6]. Patel and Patel
(2014) present a multi response optimization method using
AHP/TOPSIS method for wire electrical discharge
machining process parameter selection. An experiment is
planned by using the L27 orthogonal array. It was found that
10 number experiments give the best multi - performance
features of the WEDM process among the 27 experiments
[11].In this research we take 3 levels of each factor and
experiments perform on the ELPULS-40 DLX model WEDM
machine. Result of experiment shown in below table 1
Ex
NoWM.
dw Ton Toff IP Wt Wf MRRSR
C V
1 Copper 0.2 108 50 100 4 3 60.28 3.1 3.51
2 Copper 0.2 108 50 150 7 6 55.85 3 3.54
3 Copper 0.2 108 50 200 10 9 53.05 3 3.34
4 Copper 0.25 118 55 100 4 3 89.2 4.1 4.26
5 Copper 0.25 118 55 150 7 6 80.87 4 4.57
6 Copper 0.25 118 55 200 10 9 79.5 4 4.32
7 Copper 0.3 128 60 100 4 3 124.5 4.4 3.97
8 Copper 0.3 128 60 150 7 6 120.9 4.3 4.6
9 Copper 0.3 128 60 200 10 9 115.2 4.3 3.79
10 Brass 0.2 118 60 100 7 9 69.83 3.6 3.92
11 Brass 0.2 118 60 150 10 3 67.09 3.6 4.09
12 Brass 0.2 118 60 200 4 6 65.17 4 3.83
13 Brass 0.25 128 50 100 7 9 112.7 4.3 6.97
14 Brass 0.25 128 50 150 10 3 106.2 4.3 6.93
15 Brass 0.25 128 50 200 4 6 110.7 4.7 6.94
16 Brass 0.3 108 55 100 7 9 78.86 3.4 3.05
17 Brass 0.3 108 55 150 10 3 75.45 3.5 2.95
18 Brass 0.3 108 55 200 4 6 71.68 4 3
19 Moly. 0.2 128 55 100 10 6 87.6 3.4 4.38
20 Moly. 0.2 128 55 150 4 9 92.47 3.9 4.37
21 Moly. 0.2 128 55 200 7 3 77.12 4.1 4.16
22 Moly. 0.25 108 60 100 10 6 60.68 3.1 1.73
23 Moly. 0.25 108 60 150 4 9 65.62 3.4 1.83
24 Moly. 0.25 108 60 200 7 3 60.63 3.3 1.73
25 Moly. 0.3 118 50 100 10 6 110.2 4 5.95
26 Moly. 0.3 118 50 150 4 9 105.2 4.2 5.91
27 Moly. 0.3 118 50 200 7 3 102.7 4.3 5.35
Table 1: Result of Experiment
2. MULTI CRITERIA DECISION MAKING METHOD
Multi Cri terion Decis ion Making (MCDM) refers to making
decis ions in the Presence of multiple, usual ly confl icting
cri teria . Depending on whether the problem is a selection
problem or a des ign problem, the problems of MCDM can
be broadly class i fied into two categories :
1) Multiple Attribute Decis ion Making (MADM)
2) Multiple Objective Decis ions Making (MODM)
MODM methods have decis ion variable va lues which are
determined in a continuous or integer domain with ei ther
an infini tive or a large number of choices , the best of which
should satis fy the decis ion maker’s constra ints an d
preference priori ties . MADM methods on the other hand
are genera l ly discrete, have a l imited number of
predetermined a l ternatives . MADM is an approach of
problem solving that i s employed to solve problems
involving selection from among a fini te number of
a l ternatives .
Analytic hierarchy process (AHP) i s a methodologica l
approach which impl ies s tructuring cri teria of multiple
options into a system hierarchy, including relative va lues
of a l l cri teria , comparing a l ternatives for each particular
cri terion and defining the average importance of
a l ternatives . In that way a bas is i s created to make
appropriate decis ions . AHP is a s tructured technique which
i s used in complex decis ion-making. The goal i s to s ingle
out and offer one out of severa l poss ible decis io ns . Whi le
doing so one does not ins is t on the exclus ively «correct»
decis ion, but one chooses one which through this method
proves to be the most adequate or the most useful one for
the user. The AHP is an effective decis ion making method
to solve multi -dimens ional and complex problems. AHP
method is based on three main principles : s tructure of the
model ; comparative judgment of the cri teria and/or
a l ternatives ; synthes is of the priori ties . Steps of the AHP
method as fol lows:
Step 1: Developing the Hierarchica l Structure. A decis ion
problem is s tructured as a hierarchy s tructure With the AHP,
the goal , decis ion cri teria and a l ternatives are arranged in
a hierarchica l s tructure s imi lar to a fami ly tree.
Figure 1: A Hierarchy of the Decision Making Problem
Selection
B1 B2 BM
A1 A2 An
Goal
Criteria
Alternative
International Journal of Pure and Applied Mathematics Special Issue
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Step 2: Perform the Pa ir Wise Comparisons .
In this s tep, comparison matrices are formed and pair wise
comparisons are conducted. Decis ion cri teria are compared
in the corresponding level us ing fundamental comparison
sca le. The tabl e below shows the comparison sca le used
by AHP.
1
1
1
1
1
1
3
2
1
1
321
33231
22321
11312
MMM
M
M
M
MxM
aaa
aaa
aaa
aaa
BM
B
B
B
A
Where a ij denotes the comparative importance of attribute i
with respect to attribute j and Bi denoted the cri teria in the
matrix, a ij = 1, when i = j and a ji =1/a ij.
Sca
le
Importance Meaning of attributes
1 equal
importance
Two attributes are equal ly
important
3 moderate
importance
One attribute i s moderately
important over the other
5 s trong
importance
One attribute i s s trongly
important over the other
7 very
importance
One attribute i s very important
over the other
9 Absolute
importance
One attribute i s absolutely
important over the other 2,4,6,8, compromise importance between 1,3,5,7 and 9
Table 2: Sca le of Relative Importance
Step 3: Determination of Relative Normal ized
Weight. A relative normal ized we ight at each level
of hierarchy s tructure i s ca lculated us ing Equation.1
and Equation.2.
Step 4: Cons is tency Test.
If the judgment matrix or comparison matrix i s
incons is tent then judgment shoul d be reviewed and
improved i t to obta in the cons is tent matrix. Hence,
cons is tency test wi l l be carried out us ing fol lowing
s teps .
Calculate matrices
A3 = A1 x A2 and A4 = A3 /A2, Where; A1= [a ij] M×M
A2 = [W1, W2, …..,Wj]T
Calculate Eigen va lue ƛmax(average of matrix
A4)
Calculate the cons is tency index:
CI = (ƛmax- M) / (M - 1)
Calculate the cons is tency ratio: CR = CI/RI,
select va lue of random index (RI) according
to number of attributes used in
decis ion-making.
If CR < 0.1, considered as acceptable decision, otherwise
judgment of the analyst about the problem under study.
Step 5: Creating the Decis ion Matrix.
The method s tarts with a decis ion matrix of responses of
di fferent a l ternatives to eva luation cri teria .
1
1
1
1
1
1
3
2
1
1
321
33231
22321
11312
MMM
M
M
M
MxM
aaa
aaa
aaa
aaa
BM
B
B
B
A
Where a ij i s the performance measure of i th a l ternative on
jth
attribute, m is the number of a l ternatives , and n i s the
number of attributes .
3. ILLUSTRATION OF EXAMPLE USING AHP -SAW METHOD
Step 1: A WEDM process parameters selection problem can
be decomposed proce dure described in the hierarchy
s tructure shown in Figure 1.
Figure 1: A Hierarchy of WEDM Process Parameters Selection
Problem
International Journal of Pure and Applied Mathematics Special Issue
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Step 2: A relative importance of between attributes i s
ass igned with respect to the goal . The judgments are
entered us ing Sca l e of Relative Importance of the AHP
method as shown in Table 3.
Table No 3: Pa ir Wise Comparison Matrix for Di fferent
Cri teria
Step 3: A Relative Normal ized Weight of Attributes Is
Ca lculated Us ing Eq. (1) and Eq. (2)
GM1 = (1×1×1)1/3 = 1
GM2 = (1×1×1)1/3 = 1
GM3 = (1×1×1)1/3 = 1
W1 =1/ (1+1+1) = 0.3333
W2 =1/ (1+1+1) = 0.3333
W3 =1/ (1+1+1) = 0.3333
Tabl
e 4: Relative Normal ized Weight of Attribute
Step 4: Cons is tency Test.
If the judgment matrix or comparison matrix i s incons is tent
then judgment should be reviewed and improved i t to
obta in the cons is tent matrix.
A3 = A1*A2 Where, A1= [a i j]M*M A2 = [W1, W2... Wj]T
A3 = A1 * A 2 = * =
A4 = A3 /A2 = / =
λmax = Average of matrix A4 = 3.0003
Calculate the cons is tency index: CI = (max - m) / (m
- 1)
CI = (3.0003 - 3) / (3 -
1)
= 0.0001
RI i s 0.52, Select in the Random Index table
Table 5.: Random Index (RI) for Di fferent Matrix Order
Here,
CR = CI/RI= 0.0001/0.0000=0
If CR < 0.1, considered as acceptable decision,
otherwise judgment of the analyst about the problem
under study.
Simple Additive Weighting (SAW) method
This i s a lso ca l led the weighted sum method and is the
s implest and s ti l l the widest used MADM method. Here,
each attribute i s given a weight and the sum of a l l weights
must be 1. Each a l ternative i s assessed with regard to every
attribute. The overa l l or compos ite performance score of an
a l ternative i s given by Equation.
(3)
Where, (mi j) represe nts the normal ized va lue and Pi i s the
overa l l or compos ite score of the a l ternative Ai . The
a l ternative with the highest va lue of Pi i s cons idered as
the best a l ternative.
Alternat
ive
al+b4c
MRR
(mm³/min)
SR
(μm)
CV
(mm/min)
A1 60.28 3.094 3.51
A2 55.85 2.978 3.54
A3 53.05 2.983 3.34
A4 89.2 4.061 4.26
A5 80.87 4.049 4.57
A6 79.5 3.988 4.32
A7 124.5 4.443 3.97
A8 120.87 4.252 4.6
A9 115.15 4.274 3.79
A10 69.83 3.649 3.92
A11 67.09 3.574 4.09
Attribute B1 B2 B3
B1 1 1 1
B2 1 1 1
B3 1 1 1
Attribute Weight Wj
(B1)= Materia l Removal Rate W1 = 0.3333
(B2)= Surface Roughness W2 = 0.3333
(B3)= Cutting Veloci ty W3 = 0.3333
Attrib
ute
1 2 3 4 5 6 7 8 9 10
RI 0 0 0.52 0.8
9
1.1
1
1.2
5
1.3
5
1.
4
1.4
5
1.4
9
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A12 65.17 4.034 3.83
A13 112.67 4.289 6.97
A14 106.17 4.262 6.93
A15 110.67 4.682 6.94
A16 78.86 3.375 3.05
A17 75.45 3.484 2.95
A18 71.68 4.032 3
A19 87.6 3.427 4.38
A20 92.47 3.876 4.37
A21 77.12 4.099 4.16
A22 60.68 3.124 1.73
A23 65.62 3.422 1.83
A24 60.63 3.275 1.73
A25 110.15 4.009 5.95
A26 105.16 4.241 5.91
A27 102.73 4.333 5.35
Table 6: Decis ion Matrix
Alternative
MRR SR CV (mm/min)
Pi RANK (mm³/min)
(μm)
A1 0.484 0.6608 0.504 0.544 22
A2 0.449 0.6361 0.508 0.526 23
A3 0.426 0.6371 0.479 0.509 24
A4 0.717 0.8674 0.611 0.724 11
A5 0.65 0.8648 0.656 0.716 12
A6 0.639 0.8518 0.62 0.696 13
A7 1 0.949 0.57 0.831 7
A8 0.971 0.9082 0.66 0.838 6
A9 0.925 0.9129 0.544 0.786 9
A10 0.561 0.7794 0.562 0.628 17
A11 0.539 0.7633 0.587 0.623 18
A12 0.524 0.8616 0.55 0.638 16
A13 0.905 0.9161 1 0.931 2
A14 0.853 0.9103 0.994 0.91 3
A15 0.889 1 0.996 0.952 1
A16 0.633 0.7208 0.438 0.591 20
A17 0.606 0.7441 0.423 0.585 21
A18 0.576 0.8612 0.43 0.616 19
A19 0.704 0.732 0.628 0.681 15
A20 0.743 0.8279 0.627 0.725 10
A21 0.619 0.8755 0.597 0.69 14
A22 0.487 0.6672 0.248 0.463 27
A23 0.527 0.7309 0.263 0.502 25
A24 0.487 0.6995 0.248 0.473 26
A25 0.885 0.8563 0.854 0.856 5
A26 0.845 0.9058 0.848 0.858 4
A27 0.825 0.9255 0.768 0.831 8
Table 7: Normal ize Decis ion Matrix and ranking of
a l ternative
4.CONCLUSION
Result obta ined for WEDM process parameter for
a luminum boron carbide us ing multi cri te ria decis ion
making method is presented in table no 7.Inthis table
ranking of a l l 27 a l ternatives i s carried out based on the
weighted assessment va lue. It i s clearly observed that
experiments or a l ternative number 15 gives the best multi
performance features of WEDM process among the 27
experiments .
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