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Materials and Manufacturing Processes
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Multiresponse Optimization of Abrasive Water Jet
Cutting Process Parameters Using TOPSIS Approach
a
N. Yuvaraj & M. Pradeep Kumar
a
a
Depart ment of Mechanical Engineering, CEG, Anna Universit y, Chennai, Tamil Nadu, India
Accept ed aut hor version post ed online: 16 Dec 2014. Published online: 16 Dec 2014.
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To cite this article: N. Yuvaraj & M. Pradeep Kumar (2015) Mult iresponse Opt imizat ion of Abrasive Wat er Jet
Cut t ing Process Paramet ers Using TOPSIS Approach, Mat erials and Manuf act uring Processes, 30: 7, 882-889, DOI:
10. 1080/ 10426914. 2014. 994763
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Materials and Manufacturing Processes, 30: 882–889, 2015
Copyright # Taylor & Francis Group, LLC
ISSN: 1042-6914 print=1532-2475 online
DOI: 10.1080/10426914.2014.994763
Multiresponse Optimization of Abrasive Water Jet Cutting
Process Parameters Using TOPSIS Approach
N. Yuvaraj and M. Pradeep Kumar
Downloaded by [Anna University] at 02:35 03 June 2015
Department of Mechanical Engineering, CEG, Anna University, Chennai, Tamil Nadu, India
This paper describes how optimization studies were carried out on an abrasive water jet (AWJ) cutting process with multiresponse
characteristics based on Multi Criteria Decision Making Methodology (MCDM) using the Technique for Order Preference by Similarity Ideal
Solution (TOPSIS) approach. The process parameters water jet pressure, traverse rate, abrasive flow rate, and standoff distance are optimized
with multiresponse characteristics, including the depth of penetration (DOP), cutting rate (CR), surface roughness (Ra), taper cut ratio (TCR),
and top kerf width (TKW). The optimized results obtained from this approach indicate that higher DOP and CR and lower Ra, TCR, and
TKW were achieved with combinations of the AWJ cutting process parameters, such as water jet pressure of 300 MPa, traverse rate of
120 mm/min, abrasive flow rate of 360 g/min, and standoff distance of 1 mm. The experimental results indicate that the multiresponse characteristics of the AA5083-H32 unit used during the AWJ cutting process can be enhanced through the TOPSIS method. Analysis of variance
was carried out to determine the significant factors for the AWJ cutting process.
Keywords Aluminium alloy; AWJ cutting; Multiresponse; Optimization; TOPSIS.
taper cut ratio (TCR), top kerf width (TKW), and
surface roughness (Ra) by the combined effect of the
multi-criteria decision-making methodology (MCDM)
and analysis of variance (ANOVA).
The chemical composition of AA5083-H32 is 94.24%
Al, 4.73% Mg, 0.65% Mn, 0.054% Si, 0.060% Cr,
0.055% Ti, 0.005% Cu, and 0.15% Fe; this aluminium
alloy was used as the workpiece material and its main
properties are shown in Table 1. It is a work-hardened
alloy that is stabilized at low-temperature heat to
quarter hard in the 5xxx series and offers high strength,
hardness, excellent weldability, enhanced corrosion
resistance, etc.; it is widely used in the manufacture of
various components with marine, automotive, aerospace, and railway applications. [5]. It is enriched with
magnesium which enhances its strength through work
hardening or strain hardening. Due to its poor machinability, it undergoes partial tempering which slightly
reduces its strength but improves ductility [6]. However,
machining is difficult by conventional and other nontraditional machining processes because of high tool wear,
heat-affected zone, material distortion, high cutting
force, and reduction in fatigue life. Because this alloy
cannot operate above 65 C and it performs better
under low temperatures [7, 8], researchers have stated
their preference for the AWJ cutting process to machine
this type of aluminium alloy. Few researchers have
attempted to investigating abrasive contamination
in AA5083-H32 and therefore no specific machinability
data are available on these alloys in regard to the
AWJ cutting process. This study represents the first
attempt to investigate multiresponse optimization of
AWJ cutting process parameters in AA5083-H32 alloy
using the Technique for Order Preference by similarity
INTRODUCTION
Abrasive water jet (AWJ) cutting is a successful
modern machining technique which is widely applied
in the cutting of hard or complex-to-cut materials, such
as titanium, stainless steel, and aluminium alloys and it
has also been used in the aircraft and automobile Industries. In AWJ cutting, the material can be cut through by
erosive action due to abrasive particles mixing with
high-pressure water, which acts as a cutting tool, and
material removal takes places through the cutting and
deformation wear mode [1, 2]. The AWJ cutting process
offers a wide range of benefits, such as reduced
heat-affected zone, minimal cutting forces, and no
contact tool that might break during machining [3].
The cutting parameters of AWJ can be characterized
as hydraulic, cutting, mixing, abrasive, etc. [2]. In contrast, use of AWJ makes it difficult to analyze multiresponse parameters, such as depth of penetration,
cutting rate, taper cut, kerf width, and roughness [1,
4]. In order to obtain a smooth surface finish, reduction
of taper, and higher depth of penetration, the selection
of process parameters is of paramount importance
for manufacturing industries. These industries require
a better cut quality of the product under optimum
conditions, which must be met by decision-making
methodologies. This study examines product cut quality
based on depth of penetration (DOP), cutting rate (CR),
Received September 4, 2014; Accepted November 30, 2014
Address correspondence to N. Yuvaraj, Department of Mechanical
Engineering, CEG, Anna University, Chennai, Tamil Nadu 600025,
India; E-mail: yuvaceg09@gmail.com or yuvabitt09@gmail.com
Color versions of one or more of the figures in the article can be
found online at www.tandfonline.com/lmmp.
882
MULTIRESPONSE OPTIMIZATION OF ABRASIVE WATER JET CUTTING PROCESS PARAMETERS
TABLE 1.—Main properties of aluminium alloy AA5083-H32.
Property
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Hardness (Brinell scale)
Density
Ultimate tensile strength
Yield strength
Modulus of elasticity
Shear strength
Thermal conductivity
Melting point
Value
87 HB
2.66 g=cm3
320 MPa
250 MPa
70.3 GPa
195 MPa
117 W=m-k
638 C
Ideal Solution (TOPSIS) approach with Simos’
weighting criteria method.
In earlier studies on optimization, the Taguchi method
was a tool frequently used for improving quality and
productivity at low cost. It is used to optimize a single
response characteristic. However, it requires further
research efforts to investigate multiresponse characteristics [9]. For AWJ cutting, DOP and CR are ‘‘the larger
the better’’ performance characteristics, while Ra, TCR,
and TKW are ‘‘the smaller the better’’ performance
characteristics. Hence, multiresponse optimization is
much more difficult than the optimization of a single
response characteristic [10]. The selection of optimal
process parameters for multiresponse characteristics in
the AWJ machining process involves a problematic criterion which necessitates the establishment of adequate
MCDM. In MCDM involving engineering problems
there are several decision-making methods available,
such as grey relational analysis, TOPSIS, Elimination
and Et choice Translating reality I, II, III, VIKOR,
and Analytic Hierarchy Process. Several researchers
used these techniques in the selection of the nontraditional machining process [11], green manufacturing
[12], and selection of warehouse location [13]. However,
it was found that few researchers had applied these techniques for the selection of manufacturing process and
very little is known about the selection of the process
parameters. Furthermore, there are no reports in the
literature on the optimization of AWJ cutting process
parameters with MCDM. Therefore, in this work we
aimed to investigate AWJ cutting parameters by varying
the level of the water jet pressure (P), traverse rate (TR),
abrasive flow rate (AFR), and standoff distance (SOD)
and, while machining the AA5083-H32 aluminium alloy,
the output parameters DOP, CR, TCR, TKW, and Ra
were considered together as a multi-objective problem.
From the literature, it is also observed that researchers
have developed MCDMs, such as Grey, Electre I, II,
TOPSIS, FUZZY TOPSIS, and ELECTRE for solving
multi-objective problems. Among these decision-making
techniques, TOPSIS was found to be the most successful
in the selection of parameters [10] and machining processes
[11, 14, 15]. Behzadian et al. [16] conducted review studies
on the TOPSIS method associated with multiple fields,
such as water resource management, human resource
management, and supply chain management. They found
only a few research studies on the selection of optimal
883
parameters for machining processes. Lan [17] optimized
turning process parameters by combining the TOPSIS
and Taguchi methods. Their results indicated that this
combination produced a satisfactory performance for
computer numerical control (CNC) turning operations.
Gauri et al. [18] proposed the selection of optimal
machining parameters for an ultrasonic process using
the TOPSIS approach. It was observed that for primary
component analysis, TOPSIS performed better than grey
relational analysis. Durai Prabhakaran et al. [19] used the
TOPSIS technique for the selection of a composite
product system, observing that this technique met the
challenges of composite industry through customization
and reliability of these techniques. Rao [20] investigated
the machinability of work material by their proposed
model of the TOPSIS–AHP method. They observed that
the combined effect of TOPSIS and AHP selected the
best tool–work combinations for machining operations.
This method uses the concept of an ideal solution which
is nearest to the choice of attributes [21]. In general,
obtaining the ideal solution is a difficult task in real-time
problems, so that this method adopts two different kinds
of ideal solution, based on the best or worst performance
of the alternatives associated with multiple criteria. The
ranking-based approach [22] is used to select the best
and worst alternatives from positive (as near as possible
to the ideal solution) and negative (as distant as possible
from the ideal solution) ideal solutions. The advantages
of the TOPSIS system include an easily understandable,
simple computation technique which has ease of
implementation [11]. Maity and Chakraborty [23] studied
the selection of abrasive material for grinding wheels
using a fuzzy TOPSIS method. They found this method
capable of make the best decision based on selection
criteria and their interrelationships.
Recently, many computational techniques have evolved
for optimizing machining process parameters such as
Response Surface Methodology [24], Genetic Algorithm
[24], Particle Swarm Optimization (PSO) [25–28] and
Neural Networks [26]. Some research related to optimization of machining processes parameters using evolutionary
algorithms such as PSO and neural networks is briefly presented below. Vázquez et al. [25] used the PSO technique
for selection of micromachining parameters in the fabrication of medical devices. They observed that accuracy
and surface roughness were improved through optimal
process parameters using this evolutionary algorithm.
Ciurana et al. [26] used neural network modeling and
PSO in pulsed laser micromachining for hardened AISI
H13 steel. They investigated the neural network model
for prediction of experimental work, and multi-objective
process parameters were carried out by PSO. It was
observed that the neural network and PSO are suitable
for setting optimal process parameters. Ulutan and Özel
[27] predicted cutting forces and residual stress values on
nickel alloy during turning operations. They conducted
physics-based simulations along with PSO for predicting
values which help minimize tensile residual stress and
improve compressive residual stress on the turned surface
through the selection of optimal process parameters.
884
N. YUVARAJ AND M. PRADEEP KUMAR
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FIGURE 1.—Decision model of the AWJ cutting process parameter
selection.
Pawar et al. [28] carried out PSO for optimization of
grinding parameters for maximization of production rate
and surface finish. However, it was observed that these
optimization techniques require a coding system (algorithm) to resolve MCDM problems, and were time consuming. Among these methods, TOPSIS was found to be more
efficient in solving MCDM problems because it offers a
simple computational technique, less computational time,
and values are close to the ideal solution. So, researchers
have a keen interest in using the TOPSIS method to
optimize the selection of process parameters and determine
the optimal solution.
The TOPSIS method requires precise input data in
solving multi-criteria problems to assign weights to the
criteria, which emphasizes the relative importance of
multi-criteria (output responses) in real-time problems
[29, 30]. To use the weighting criterion, Simos’ procedure
was carried out. In this study, each response was designated by a gaming card with output responses arranged
from the least to the most important. According to the
importance of the output responses, the decision maker
classifies the parameter responses from the least to the
most important (e.g., DOP, CR, TCR, TKW, Ra). The
details and steps of Simos’ procedure are given in Ozcan
et al. [13] with reference to Figueira and Roy [31]. This procedure is a key tool for analyzing real-time problems and is
adopted by decision makers for various reasons, such as
robustness, and it has to produce results more rapidly than
the other weighting computational techniques. Ozcan et al.
also carried out Simos’ procedure through data collection,
computation of normalized weights, and minimization of
errors through rounding off the normalized values.
Figure 1 represents the decision model of the AWJ
cutting process parameter selection problem. In this
figure, each output response is related to four different
process parameters of the AWJ cutting, and these
responses are taken to optimize the cutting parameters
using the TOPSIS method.
MATERIALS AND METHODS
The experimental setup used for this study is shown in
Fig. 2. The experiments were conducted using a water jet
injection-type AWJ machining center (S 3015, Germany;
FIGURE 2.—Experimental setup.
maximum pressure: 620 MPa, traverse speed: 10 m=min,
cutting head movement in x- and y-axes: 3 m 1.5 m,
water discharge: 3.2 l=min. L27 orthogonal array was
used to conduct the experimental run, and each process
parameter was allocated to a separate column. All
experiments were conducted on AA5083-H32 (120 mm
(length) 50 mm (width) 64.065 mm (thickness)), with
the jet traversing a predetermined length of the workpiece. For each set of process parameters the jet produced a different penetration depth into the target
material. Penetration depth was determined through
measuring the length of cut (L) on the workpiece surface,
as shown in Fig. 3. The list of AWJ process parameters
and their levels are shown in Table 2. The experimental
design of the AWJ cutting process parameters is given
in Table 3. The other AWJ cutting process parameters
were maintained at a constant level (impact angle: 90 ,
garnet mesh size: 80, tungsten carbide nozzle diameter:
1.1 mm, sapphire orifice diameter: 0.35 mm, and jet
FIGURE 3.—Lengths of cut (L) on the workpiece surface (front view).
885
MULTIRESPONSE OPTIMIZATION OF ABRASIVE WATER JET CUTTING PROCESS PARAMETERS
and the computational steps of this procedure are shown
in Table 4. By using this procedure, the weighting of the
criteria is calculated as follows.
TABLE 2.—Input process parameters and their levels.
Level
Symbol
A
B
C
D
Factor
Level 1 Level 2 Level 3
Water jet pressure (P) (MPa)
Traverse rate (TR) (mm=min)
Abrasive mass flow rate (AFR) (g=min)
Standoff distance (SOD) (mm)
250
120
240
1
275
150
300
2
300
180
360
3
traverse length: 60 mm. The output responses considered
in this study were DOP, CR, TCR, Ra, and TKW.
These response parameters were used to evaluate the
performance of the AWJ cutting process by varying the
levels of input process parameters.
DOP (mm) was measured by a dial gauge of accuracy
0.05 mm. CR (mm2=s) was measured using the following
equation [2]:
Downloaded by [Anna University] at 02:35 03 June 2015
CR ¼ DOP TR
ð1Þ
TKW (mm) was measured by micro-hardness testing
microscope of accuracy 0.01 mm. TCR was determined
by the ratio of top cut width (bT) to bottom cut width
(bB). A Surftronic-3þ Hobson was used to measure
workpiece roughness (mm), with a traverse length of
4 mm and cut-off length of 0.8 mm.
In this paper, the key subjective input weights of the
output responses were determined by Simos’ procedure
. Definite set of criteria ¼ [DOP, TR, TCR, TKW,
and Ra]
. Criteria (output responses) were arranged by
decision makers according to their importance,
from least to most important (e.g., TKW, TCR,
Ra, CR, and DOP).
In this study, TCR and Ra are considered as equal
weights, as are DOP and CR. Nevertheless, because the
decision makers needed to develop the importance of
the DOP and CR criteria they put white cards between
two successive criteria in the criteria set. In this procedure, white cards play an important role by assigning
the weight of criteria from least to most important, the
cards representing the relative importance of two successive
criteria. This step gives more weightage or importance to
the criteria selected. The optimization steps of TOPSIS
were calculated using the following procedure [29].
Step 1. The TOPSIS method is a best-ranking
method which selects alternatives that eliminate the
units of all criteria, and it takes a normalized value.
Table 3 also shows the normalized performance matrix
(rij) obtained using the following equation:
TABLE 3.—Design of experiment and normalized values of output response parameters.
Normalized matrix value (rij)
Ex. no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
A
B
C
D
DOP
CR
TKW
TCR
Ra
250
250
250
250
250
250
250
250
250
275
275
275
275
275
275
275
275
275
300
300
300
300
300
300
300
300
300
120
120
120
150
150
150
180
180
180
120
120
120
150
150
150
180
180
180
120
120
120
150
150
150
180
180
180
240
300
360
240
300
360
240
300
360
240
300
360
240
300
360
240
300
360
240
300
360
240
300
360
240
300
360
1
2
3
2
3
1
3
1
2
1
2
3
2
3
1
3
1
2
1
2
3
2
3
1
3
1
2
0.182
0.188
0.214
0.136
0.162
0.162
0.115
0.136
0.152
0.193
0.214
0.225
0.157
0.183
0.214
0.157
0.173
0.188
0.240
0.251
0.266
0.204
0.193
0.250
0.178
0.182
0.188
0.150
0.154
0.175
0.139
0.166
0.166
0.142
0.167
0.187
0.159
0.176
0.184
0.161
0.188
0.219
0.194
0.213
0.231
0.197
0.206
0.218
0.209
0.198
0.257
0.219
0.224
0.231
0.184
0.187
0.218
0.190
0.194
0.139
0.184
0.124
0.159
0.193
0.208
0.227
0.194
0.210
0.157
0.187
0.155
0.213
0.200
0.204
0.234
0.215
0.208
0.179
0.202
0.181
0.204
0.152
0.195
0.154
0.165
0.143
0.181
0.231
0.145
0.383
0.144
0.189
0.148
0.155
0.136
0.185
0.171
0.139
0.363
0.137
0.180
0.114
0.139
0.120
0.159
0.202
0.135
0.313
0.200
0.197
0.179
0.214
0.205
0.220
0.252
0.193
0.189
0.191
0.175
0.157
0.205
0.177
0.187
0.236
0.216
0.182
0.174
0.169
0.146
0.189
0.166
0.174
0.209
0.188
0.168
886
N. YUVARAJ AND M. PRADEEP KUMAR
TABLE 4.—Computational steps of Simos’ weighting procedure.
Subset
criterion
TKW
TCR, Ra
White cards
DOP, CR
Total
Number
of criteria
Number
of position
Non-normalized
weighted matrix
Total
1
2
1
2
6
1
2,3
(4)
5,6
17
1=17 100 ¼ 5.88 6
2.5=17 100 ¼ 14.70 15
6
30
5.5=17 100 ¼ 32.35 32
64
100
Xij
ffi
rij ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pm
2
X
i¼1 ij
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TABLE 5.—Closeness coefficient values and ranking of alternatives.
Ex. no.
i ¼ 1; 2; . . . . . . 27; j ¼ 1; 2; . . . . . . 5
ð2Þ
where
i ¼ number of alternatives (experimental runs)
j ¼ number of criteria (output responses)
xij ¼ normalized value of ith experimental run
associated with jth output response.
Step 2. The weighted normalized matrix (Wij) is
obtained by the product of the normalized value and
weighted values:
Wij ¼ wj rij i ¼ 1; 2; . . . . . . 27; j ¼ 1; 2; . . . . . . 5
ð3Þ
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Dþ
i
D
i
Ci
Ranking
0.04456
0.04376
0.03220
0.05751
0.04536
0.04661
0.06504
0.05113
0.05904
0.03992
0.03337
0.02771
0.04745
0.03497
0.02393
0.04321
0.03471
0.04624
0.02194
0.02041
0.01378
0.02638
0.03025
0.00990
0.03474
0.02957
0.04022
0.041401
0.037499
0.04899
0.033531
0.040201
0.035201
0.022553
0.038606
0.02202
0.044816
0.045699
0.053411
0.037817
0.046851
0.051175
0.038535
0.04745
0.039044
0.058293
0.058259
0.069447
0.052116
0.051744
0.067331
0.042704
0.051591
0.040844
0.48160
0.46149
0.60342
0.36829
0.46987
0.43027
0.25746
0.43023
0.27166
0.52888
0.57800
0.65838
0.44351
0.57260
0.68135
0.47139
0.57750
0.45782
0.72653
0.74051
0.83444
0.66394
0.63108
0.87180
0.55141
0.63564
0.50387
17
20
10
25
19
23
2
24
26
15
11
7
22
13
5
18
12
21
4
3
2
6
9
1
14
8
16
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ffi
X27
Wij Sj
¼
i¼1
Step 3. Every response that is an ideal alternative
to the best (Sþ) and worst alternative performance
(S) was identified.
If the jth criteria have the optimal performance:
D
i
Sþ ¼
Step 5. For each alternative, closeness coefficient
(Ci) values were determined using the following
equation:
maxðSij Þj j 2 J or minðSij Þj j 2 J 0 i ¼ 1; 2;......27
ð4Þ
where
Sþ represents a positive ideal solution [0.085, 0.082,
0.00742, 0.01703, 0.022]
Similarly the S values were determined if the jth
criteria have the worst performance [0.03687, 0.04456,
0.0140, 0.0570, 0.03782]
where S represents a negative ideal solution.
Step 4. In this step, the performance of the criteria
was measured as the best alternative distance (Dþ
ij ) from
the Sþ values and the worst alternative distance (D
ij )
from the S values. The values of Dþ
and
D
were
ij
ij
determined using the equations below (5, 6). Table 5
shows the performance of each alternative under the best
and worst conditions.
Dþ
i
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ffi
X27
þ
¼
Wij Sj
i¼1
ð5Þ
ð6Þ
where i ¼ 1,2,3. . .,27
Ci ¼
D
i
þ
D
i þ Di
i ¼ 1; 2; . . . . . . : 27; 0 Ci 1
ð7Þ
The best alternative was chosen according to preference
ranking ordered by the Ci value, which is very close to
the ideal solution.
RESULTS AND DISCUSSION
Table 5 also indicates the closeness coefficient values
of each experimental run using L27 orthogonal array.
Among the values of the 27 closeness coefficients, experiment no. 24 showed the best multiresponse characteristics because it represents the maximum closeness
coefficient; the values recorded in each experiment are
shown in Fig. 4. A higher closeness coefficient
means that the corresponding experiment is closer to
the ideal value; experiment no. 24 yielded optimal
process parameters for the multi-criteria output responses
of the AWJ cutting process.
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MULTIRESPONSE OPTIMIZATION OF ABRASIVE WATER JET CUTTING PROCESS PARAMETERS
FIGURE 4.—Effect of process parameters in each experiment.
FIGURE 5.—Mean response values of AWJ process parameters.
Table 6 shows the closeness coefficient values of the
process parameters at the factor level. The values were
determined by the closeness coefficient value of each
level of the cutting parameter in the L27 orthogonal
array, and their mean. These represent the optimal level
of process parameter by factor level. From the mean
responses shown in Fig. 5, it is observed that the optimal
parameter setting is maintained at P 300 MPa, TR
120 mm=min, AFR 360 mm=min, and SOD 1 mm, thus
distinguishing between maximum and minimum values
of closeness coefficient. P is the most effective process
parameter and its maximum–minimum value is higher
than that of the other input parameters. Higher P values
result in maximum DOP and CR and minimum TKW,
TCR, and Ra.
ANOVA was conducted to determine the significant
level of each input process parameter affecting the
multi-performance characteristics of AWJ. Results
show that the F-ratio indicates the significant process
parameters of the AWJ cutting process, determining
whether the statistical test is significant at the confidence
level selected. Significance level is based on the critical
value: if it exceeds the critical value the test is significant,
otherwise it is not [32].
In the present study, ANOVA was carried out at
a confidence level of 95% and significance level of 5%.
Table 7 shows the results of ANOVA for the effects of
input and interaction parameters on multiresponse
parameters. It was found that P and TR are the most
significant and significant factors, respectively, in the
assessment of DOP, CR, TKW, TCR, and Ra, because
higher pressure resulted in increased DOP and CR and
decreased TCR, TKW and Ra, regardless of the material
used. Higher pressure results in the production of
high kinetic energy by the abrasive particles impacting
on the workpiece surface, thereby enhancing cutting
of the material with better surface quality, high jet
penetration, and minimization of kerf width and taper
cut. At lower TR there is a possibility of increasing
the number of abrasive particles, which impacts on the
workpiece per unit time and hence an improved surface
finish, penetration depth, CR, kerf width, and taper cut
are obtained [2, 33]. The other input process parameters
and interaction parameters were found to be less significant due to failure of the statistical test.
Table 7 also indicates the influence of input process
parameters on AWJ cutting. The most influential
parameter was P (54.03%), followed by TR (20.93%),
SOD (7.46%), AFR (6.86%), P TR (2.68%), P
AFR (1.40%), and P SOD (0.66%). The influence of
each process parameter on multiresponse characteristics
is shown in Fig. 6. From Table 7 it is observed that P
plays a crucial role in affecting multiresponse characteristics while SOD and AFR contribute to the cutting
quality of the machined surface along with P and TR.
Lower SOD produced a narrow abrasive water jet
diameter resulting in reduced kerf width [33] while
increased AFR, along with higher P and lower TR,
resulted in enhanced quality of the machined surface
due to the additional particles created which serve to
smoothen the workpiece surface [2].
The comparative test results for initial and optimal
selection of AWJ process parameters (predicted and
TABLE 7.—Results of ANOVA for multiresponse parameters.
Source of
process parameters
TABLE 6.—Mean response for closeness coefficient.
Average
closeness coefficient
Symbol
A
B
C
D
Process
parameter
Water jet pressure
Traverse rate
Abrasive mass flow
rate
Standoff distance
Level 1 Level 2 Level 3
Maximum.–
Minimum
0.4194 0.5522 0.6844
0.6237 0.5703 0.4619
0.4992 0.5663 0.5903
0.2650
0.1618
0.0911
0.5960 0.4988 0.5611
0.0972
P
TR
AFR
SOD
P TR
P AFR
P SOD
Error
Total
DOF
SS
MS
F
P
value
%
contribution
2
2
2
2
4
4
4
6
26
0.3160
0.1224
0.0401
0.0436
0.0157
0.0082
0.0038
0.0349
0.5849
0.1580
0.0612
0.0201
0.0218
0.0039
0.0020
0.0009
0.0058
27.15
10.51
3.45
3.75
0.68
0.35
0.17
0.001
0.011
0.101
0.088
0.633
0.834
0.948
54.03
20.93
6.86
7.46
2.68
1.40
0.66
5.98
100
Most significant parameter.
Significant parameter.
888
N. YUVARAJ AND M. PRADEEP KUMAR
FIGURE 6.—Process parameter influence, by percentage.
TABLE 8.—Initial and predicted test results.
the maximum closeness coefficient value for multiresponse optimization of AWJ cutting parameters: water
jet pressure (P): 300 MPa, traverse rate (TR):
150 mm=min, abrasive flow rate (AFR): 360 mm=min,
and standoff distance (SOD): 1 mm.
The optimum levels of input process parameter
combinations were identified according to the response
of closeness coefficient values: 300 MPa (P), 120 mm=min
(TR), 360 mm=min (AFR), and 1 mm (SOD). ANOVA
was conducted to investigate the significant parameters
for the multi-performance characteristics of AWJ. From
the above analysis, P was found to be the most significant
factor, followed by TR, SOD, and AFR. It was observed
that the proposed combination of TOPSIS and ANOVA
was more effective in solving AWJ multiresponse
problems than previously used methods.
Output response
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Condition
Initial setting
parameter
Predicted
Experimental
Setting
level
DOP
(mm)
Ci
CR
TKW
Ra
(mm2=s) (mm) TCR (mm) value
A3B3C2D1 35.017 105.05 1.172 1.34 3.52 0.6356
Optimal process parameters
A3B1C3D1
A3B1C3D1 48.17
96.34 1.23
0.8387
1.15 2.96 0.8617
Improvement in TOPSIS grade: 0.2261.
experimental conditions, respectively) are shown in
Table 8. Once the optimal level of machining parameters
was determined, confirmation tests were carried out to
validate enhancement of the multiresponse characteristic
of AWJ. Using the optimal level of AWJ cutting
parameters, predicted response value (cpredicted) can be
estimated from the following equation [9]:
Xn
ðc cm Þ
ð8Þ
Upredicted ¼ Um þ
j¼1 o
where Um is the overall mean multiresponse value, Uo is
the mean multiresponse value at the optimum level of
factors, and n is the number of input process parameters.
These test results indicate that the overall Ci value of
the optimal parameter condition (A3B1C3D1) is higher
than that of the initial setting parameter condition
(A3B3C2D1), and also that the predicted response value
is close to the experimental value.
CONCLUSION
In the present work, use of the TOPSIS method with
orthogonal array was carried out to optimize process
parameters in the abrasive water jet (AWJ) cutting
process of AA5083-H32 alloy for multiresponse characteristics. Simos’ weighting criteria method was used to
rank the output response parameters.
An optimal combination of AWJ cutting parameters
and their levels was identified in regard to achieving
better depth of penetration (DOP), cutting rate (CR),
taper cut ratio (TCR), and top kerf width (TKW) and
lower surface roughness (Ra). Experiment no. 24 yielded
ACKNOWLEDGMENTS
The authors acknowledge the experimental facilities
provided by the Director, Water Jet Germany Ltd,
Chennai.
FUNDING
The authors are grateful to the Council of Scientific
and Industrial Research (CSIR) under the Senior
Research Fellowship (SRF), Government of India,
New Delhi, for their financial support to this research
work.
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