use of multi criteria decision making method for …surface roughness and cutting velocity. aluminum...

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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

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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


385

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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


386

5

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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use of multi criteria decision making method for …surface roughness and cutting velocity. aluminum...

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