This document discusses optimizing process parameters for plasma arc cutting of stainless steel. 30 experiments were conducted varying feed rate, current, voltage, and torch height. Responses like kerf, chamfer, dross, surface roughness, and material removal rate were measured. The experimental data was analyzed using response surface methodology, grey relational analysis, and principal component analysis to develop models relating the responses to the parameters. The results showed that the process parameters significantly affected the grey relational grade and interactions between parameters were also important. This hybrid optimization method provided an effective way to optimize plasma arc cutting for improved cut quality and precision.

1. ORIGINAL ARTICLE
Effect of process parameters on cut quality of stainless steel
of plasma arc cutting using hybrid approach
K. P. Maity & Dilip Kumar Bagal
Received: 10 August 2013 /Accepted: 27 October 2014 /Published online: 5 December 2014
# Springer-Verlag London 2014
Abstract An optimization concept of the various ma-
chining parameters for the plasma arc cutting procedures
on AISI 316 stainless steel conducting a hybrid optimi-
zation method has been carried out. A new composition
of response surface methodology and grey relational
analysis coupled with principal component analysis has
been proposed to evaluate and estimate the effect of
machining parameters on the responses. The major re-
sponses selected for these analyses are kerf, chamfer,
dross, surface roughness and material removal rate, and
the corresponding machining parameters concentrated
for this study are feed rate, current, voltage and torch
height. Thirty experiments were conducted on AISI 316
stainless steel workpiece materials based on a face-
centered central composite design. The experimental
results obtained are applied in grey relational analysis,
and the weights of the responses were evaluated by the
principal component analysis and further evaluated
using response surface method. The results show that
the grey relational grade was significantly affected by
the machining parameters directly as well as with some
interactions. This method is straightforward with easy
operability, and the results have also been established
by running confirmation tests. The premise attributes
beneficial knowledge for managing the machining pa-
rameters to enhance the preciseness of machined parts
by plasma arc cutting.
Keywords Grey relational grade . Plasma arc cutting .
Principalcomponentanalysis .Responsesurfacemethodology
Abbreviations
AISI American Iron and Steel Institute
CNC Computer numerical control
HV Vickers hardness
ANN Artificial neural network
QstE High-strength steel grade
Hardox Abrasion-resistant steel grade
MRR Material removal rate
SR Surface roughness
Ra Central line average roughness
EN European standard steel number
ISO International Organization for Standardization
LB Lower-the-better
HB Higher-the-better
NB Nominal-the-best
P Probability value
ANOVA Analysis of variance
PAC Plasma arc cutting
A Feed rate (mm/min)
B Current (ampere)
C Voltage (volt)
D Torch height (mm)
CCD Central composite design
F Statistic test value
Hα Hypothesis
3D Three-dimensional
RSM Response surface methodology
GRA Grey relational analysis
PCA Principal component analysis
Nomenclature
L18 Orthogonal array of 18 runs
L30 Orthogonal array of 30 runs
K. P. Maity (*) :D. K. Bagal
Department of Mechanical Engineering, NIT Rourkela,
Rourkela 769008, Odisha, India
e-mail: kpmaity@gmail.com
D. K. Bagal
e-mail: dilipbagal90@gmail.com
Int J Adv Manuf Technol (2015) 78:161–175
DOI 10.1007/s00170-014-6552-6

2. Y Response
Xi Singular term of input variable
Xii Square term of input variable
XiXj Interaction term of input variable
βo Regression coefficient of constant term
βi Regression coefficient of singular
βii Regression coefficients of square
βij Regression coefficients of interaction
ϵ Regression error coefficient
Xi*(k) Normalized value of the kth element
kth Element number
ith Sequence number
X0b(k) Desired value
max Xi*(k) Largest value of Xi(k)
min Xi*(k) Smallest value of Xi(k)
Xi(k) Sequence
X0(k) Reference sequence
ζ Distinguishing coefficient
βk Weighting value of the kth performance
Cov(xi(j)) Covariance of sequence
σxi(j) Standard deviation of sequence xi(j)
σxi(l) Standard deviation of sequence xi(l)
λ Eigenvalue
λk Eigenvalue
Vik Eigenvector
Ym1 First principal component
Ym2 Second principal component
1 Introduction
Modern industry depends on the manipulation of heavy metal
and alloys. Different cutting methods are used to form into
specified pieces for making infrastructure and machine tools.
Plasma arc cutting was developed in the mid 1950s and was
primarily used to cut stainless steel and aluminium alloys.
Plasma is the fourth and the most highly energized state of
matter. In fact, plasma looks and behaves like a high temper-
ature gas but with a capability to conduct electricity [1]. The
basic principle is that the arc formed between the electrode
and the work piece is constricted by a fine bore, copper nozzle.
This increases the temperature and velocity of the plasma
emanating from the nozzle. The temperature of the plasma is
in excess of 20,000 °C, and the velocity can approach the
speed of sound. When used for cutting, the plasma gas flow is
increased so that the deeply penetrating plasma jet cuts
through the material and molten material is removed in the
efflux plasma [2].
Plasma arc cutting involves a large number of process
parameters. It requires optimization of the process parameters
for smooth operation of plasma arc cutting process. A number
of investigators have carried out the research in this direction
[3]. Bhuvenesh et al. investigated the surface roughness and
material removal rate of AISI-1017 mild steel using manual
plasma arc cutting machining by Taguchi methodology [4].
They observed that the relationship between average material
removal rate and average surface roughness is inversely pro-
portional to each other. Kechagias and Billis modeled a para-
metric design of computer numerical control (CNC)-con-
trolled plasma arc cutting process of St. 37 carbon steel and
AISI steel plates by using robust design of orthogonal array
L18 (21
×37
) [5, 6]. Arc ampere is the most significant factor.
The standoff distance is the most significant parameter. The
plate thickness is the least significant parameter in plasma arc
cutting process.
Gullu and Atici investigated the consequence of plasma arc
parameters on the structure variation of AISI-304 and St. 52
steel plates by Panasonic digital PRIOR optic microscope and
Vicker hardness measurement device for heat affected zone
and hardness, respectively. It was evident from the statistical
analysis that the cutting speed was the most significant factor
which affects the surface roughness [7]. After cutting, it is
seen that hardness increases in the areas near the surface of
part i.e. around 250–350 HVand decreases towards the core of
the material [8]. Özek et al. performed a Fuzzy model for
predicting surface roughness in plasma cutting of AISI-4140
steel plate [7]. Radovanovic and Madic modeled a parametric
design of plasma arc cutting process by using ANN to predict
surface roughness. It is observed that surface roughness in-
creases with increase in cutting speed, but decreases with
increase in cutting arc current. Good surface finish can be
achieved in plasma arc cutting process of 8-mm thick plate
when cutting current and cutting speeds are set nearer to their
high and low level of the experimental range, respectively
[9–11].
The proficiency of a manufacturing practice to produce a
desired quality of cut and material removal rate depends on
various parameters. The factors that bias output responses are
machining parameters, tool and workpiece material properties
and cutting conditions. Therefore, it is important for the re-
searchers to model and appraise the relationship among
roughness and the parameters affecting its value. The deter-
mination of this correlation remains an open field of research,
mainly on account of the advances in machining and material
technology and the feasible modeling techniques. In machin-
ability review investigations, statistical design of experiments
is used quite extensively. Statistical design of experiments
assign to the process of planning the experiments so that the
adequate data can be examined by statistical methods,
resulting in precise and objective conclusions [12].
Nemchinsky and Severance discussed the fundamentals of
plasma arc cutting process with physical reasoning [13].
Salonitis and Vatousianos recently carried out an experimental
investigation of the plasma arc cutting process [14].
Yun and Na carried out an experiment about the real
time control of plasma arc cutting process by using
162 Int J Adv Manuf Technol (2015) 78:161–175

3. intensity measurements of ejected plasma gas. They
observed that the amount of the attached dross substan-
tially reduced by a simple controlled speed [15]. Zhang
and Zhang gave the various aspects of keyhole through-
out the plasma arc cutting process. Their experimental
results revealed that once the keyhole is established, the
width of the keyhole does not change with the changes
in the welding current and the welding speed, but it
does change with the changes in the flow rate of the
plasma gas and the diameter of the orifice [16]. Xu
et al. carried out an experiment to reduce the kerf width
and to improve the kerf quality by using the hydro-
magnetically confined plasma arc on engineering ceram-
ic plates. They concluded that for a given diameter of
nozzle, a high-quality cut can be produced by using a
lower arc current than it is usually required in conven-
tional plasma arc cutting process, while ensuring a fine
arc shape and capability of cutting simply by employing
hydro-magnetic constriction [17].
Asiabanpour et al. optimized the quality of 18 parts
manufactured by the automated plasma cutting process
by using response surface method and desirability func-
tions. They concluded that the high value of current and
pressure is necessary for quality cut due to plasma arc
cutting process [18]. Similarly, Ferreira et al. optimized
the input parameters of plasma arc cutting process using
QstE-380 and Hardox 450 alloy steel plate by using
response surface method. They observed that there is
increase in cutting speed to 65 % from 35 % with
reduction in cost around 28 % [19]. Hatala et al. de-
scribed the effect of technological factors on roughness
parameters Ra and heat-affected zone of the steel sur-
face European Standard Steel Number (EN) Internation-
al Organization for Standardization (ISO) S355 by using
planned experiment and regression model analysis. They
concluded that for achieving higher quality of cut sur-
face, it is recommended to use higher pressures of
plasma gas and appropriate feed rate of plasma torch.
For getting lower heat-affected zone value, the cutting
speed and power should be controlled [20].
It is evident from the literature review that most of
the investigators have investigated material removal rate
and surface roughness by simple Taguchi method and
response surface method [21, 22]. In general, plasma arc
cutting process involves a large number of response
parameters. In the present investigation, a number of
response parameters have been optimized with respect
to the number of process parameters using response
surface methodology combined with grey relational
analysis and principal component analysis. The quality
of cut and material removal rate is taken as the re-
sponses [23]. The feed rate, current, voltage and torch
height are acquired as the process parameters.
2 Experimental details
The whole experiment of plasma arc cutting process is carried
out by the MESSER Company built CNC plasma machine
named as BURNY 1250, where the cutting process is con-
ducted in Hypertherm environment. The parameters of oxy-
gen supply, fuel gas supply and power supply are fixed at
20 MPa, 1.2 MPa and 400 VDC, respectively. The material of
AISI 316 stainless steel is taken for experimentation whose
thickness is 120 mm. The values of process parameters are
given in Table 1. Feed rate, current, voltage and torch height
are taken as the input process parameters. The quality of cut
and material removal rate are measured as the major
responses, and the corresponding data are tabulated in
Appendix 1. Surface roughness is measured using Talysurf.
Material removal rate is calculated by weight measurement.
The value of dross and chamfer is calculated by the help of
Vernier caliper and protractor.
3 Analysis method
3.1 Experimental design with response surface method
As per Montgomery, response surface method is a collection
of mathematical and statistical techniques that are helpful for
modeling and analysis of problems in which response is
influenced by several input variables, and the main objective
is to find the correlation between the response and the vari-
ables inspected [23]. Response surface method has many
advantages and has effectively been applied to study and
optimize the processes. It offers enormous information from
a small number of experiments. In addition, it is possible to
detect the interaction effect of the independent parameters on
the response. The model easily clarifies the effect for binary
combination of the independent process parameters. Further-
more, the empirical model that related the response to the
independent variables is used to obtain information. Accord-
ing to Pradhan, it has been widely used in analyzing various
processes, designing the experiment, building models, evalu-
ating the effects of several factors and searching for optimum
conditions to give desirable responses and reduce the number
of experiments [24–26]. The experimental values are ana-
lyzed, and the mathematical model is then developed that
Table 1 Values of input process parameters
Process parameters Units Code L (1) L (2) L (3)
Feed rate mm/min A 920 945 970
Current A B 40.0 42.5 45.0
Voltage V C 100 120 140
Torch height mm D 2.0 2.5 3.0
Int J Adv Manuf Technol (2015) 78:161–175 163

4. illustrates the relationship between the process variable and
response. The following second-order model explains the
behavior of the system:
Y ¼ β0 þ
X
i¼1
k
βiXi þ
X
i¼1
k
βiiX2
i þ
X
i;j¼1;i≠j
k
βijXiX j þ ∈ ð1Þ
where Y is the corresponding response, Xi is the input
variables and Xii and XiXj are the squares and interaction
terms, respectively, of these input variables. The unknown
regression coefficients are β0, βi, βij and βii, and the error in
the model is depicted as ϵ [25]. The response surface method
design of matrix form is given in Appendix 1. The output
responses of plasma arc cutting as per response surface meth-
od are given in Appendix 2.
3.2 Data preprocessing
According to Fung, data preprocessing is the method of trans-
ferring the original sequence to a comparable sequence, where
the original data normalize to a range of 0 and 1 [28]. Gener-
ally, three different kinds of data normalizations are carried
out to render the data, whether the lower-the-better (LB), the
higher-the-better (HB) or nominal-the-best (NB). For ‘higher-
the-better’, characteristics such as productivity or material
removal rate, the original sequence can be HB and should be
normalized as follows [27]:
Xi
Ã
kð Þ ¼
Xi kð Þ−minXi kð Þ
maxXi kð Þ−minXi kð Þ
ð2Þ
However, if the expectancy is as small as possible for the
quality of cut such as mean surface roughness, chamfer, dross
and kerf, then the original sequence should be normalized as
‘lower-the-better’:
Xi
Ã
kð Þ ¼
maxXi kð Þ−Xi kð Þ
maxXi kð Þ−minXi kð Þ
ð3Þ
Conversely, if a specific target value is to be achieved, then
the original sequence will be normalized by the following
equation of NB:
Xi
Ã
kð Þ ¼ 1−
Xi kð Þ−minX0b kð Þj j
maxXi kð Þ−X0b kð Þ
ð4Þ
where i=1,2,…,n; k=1,2,…,p; Xi*(k) is the normalized
value of the kth element in the ith sequence; X0b(k) is the
desired value of the kth quality characteristic; max Xi*(k) is the
largest value of Xi(k); min Xi*(k) is the smallest value of Xi(k);
n is the number of experiments; and p is the number of quality
characteristics [28]. According to the type of characteristic,
type of responses normalize the Appendix 2 as per above
equation and the outcomes are tabulated in Appendix 3. As
the responses are of LB and HB types, there is no use of
Eq. (4) in the present calculation.
3.3 Grey relational coefficient and grey relational grade
After normalizing the data, usually grey relational coefficient
is calculated to display the relationship between the optimal
and actual normalized experimental results. The grey relation-
al coefficient can be expressed as [29–31]:
γi kð Þ ¼ γ X0 kð Þð − Xi kð Þð Þ ¼
Δmin þ ζΔmax
Δ0;i kð Þ þ ζΔmax
i ¼ 1; 2; 3; …; n; k ¼ 1; 2; 3; …; p
ð5Þ
where is Δ0,i(k)=|X0(k)−Xi(k)| the difference of the abso-
lute value called deviation sequence of the reference sequence
X0(k) and comparability Xi(k). ζ is the distinguishing coeffi-
cient or identification coefficient in which the value range is 0
≤ ζ ≤1. In general, it is set to 0.5 as optimistic value in normal
distribution; hence, same is adopted in this study. The aim of
defining the grey relational coefficient is to express the rela-
tional degree between the reference sequence X0(k) and the
comparability sequences Xi(k), where i=1,2,…,m and k=
1,2,…,n with m=30 and n=3 in this study [32]. The computed
deviation sequences of the normalized values are tabulated in
Appendix 4.
The grey relational grade is a weighting sum of the grey
relational coefficients and it is defined as [31]:
γ x0; xið Þ ¼
X
k¼1
n
βk x0; xið Þ ð6Þ
where βk represents the weighting value of the kth perfor-
mance characteristic and [32]
Xk¼1
n
βk ¼ 1 ð7Þ
3.4 Principal component analysis
Principal component analysis is a mathematical approach that
converts a set of observations of probably correlated variables
into a set of values of uncorrelated variables. It was invented
very early and later mostly used as a tool in investigative data
analysis and for the formation of predictive models. Principal
component analysis can be done by eigenvalue decomposition
of a data covariance matrix or singular value decomposition of a
data matrix. It is used for identifying patterns in data and
expressing the data in such a way as to highlight their similarities
and differences [33]. The main advantage of principal compo-
nent analysis is that once the patterns in data have been identi-
fied, the data can be compressed, i.e. by reducing the number of
164 Int J Adv Manuf Technol (2015) 78:161–175

5. dimensions, without much loss of information. The explicit
goals of principal component analysis are the following:
1. To extract the most significant information from the data,
2. To squeeze the size of the data set by keeping only the
significant,
3. To simplify the explanation of the data set, and
4. To analyze the structure of the observations and the
variables.
The procedure is described as follows [33]:
1. The original multiple quality characteristic array
X ¼
x1 1ð Þ x1 2ð Þ … … x1 nð Þ
x2 1ð Þ x2 2ð Þ … … x2 nð Þ
: : … … :
: : … … :
xm 1ð Þ xm 2ð Þ … … xm nð Þ
2
6
6
6
6
4
3
7
7
7
7
5
ð8Þ
i=1,2,…,m; j=1,2,…,n [34]
where m is the number of experiment and n is the
number of the response. In the present work, x is the grey
relational coefficient of each response and m=30
and n=3.
2. Correlation coefficient array
The correlation coefficient array is evaluated as
follows:
Rjl ¼
Cov xi jð Þ; xi lð Þð Þ
σxi jð Þ Â σxi lð Þ
j ¼ 1; 2; 3; …; m
l ¼ 1; 2; 3; …; n
ð9Þ
where Cov(xi(j)), xi(l) is the covariance of se-
quences xi(l) and xi(l), σxi(j) is the standard devia-
tion of sequence xi(j) and σxi(l) is the standard
deviation of sequence xi(l).
3. Determining the eigenvalues and eigenvectors
The eigenvalues and eigenvectors are determined from
the correlation coefficient array:
R−λkImð ÞVik ¼ 0 ð10Þ
where λ is the eigenvalue ∑
k¼1
n
λk ¼ n; k ¼ 1; 2; 3; …;
n and Vik=[ak1,ak2,ak3,…,akm]T
is the eigenvectors cor-
responding to the eigenvalue λk. The eigenvalues and its
variation are shown in (Table 2 as per Eq. 10 ).
4. Principal components
The uncorrelated principal component is formulated as:
Ymk ¼
X
i¼1
n
xm ið Þ⋅Vik ð11Þ
where Ym1 is called the first principal component, Ym2
is called the second principal component and so on. The
principal components are aligned in descending order
with respect to variance, and therefore, the first principal
component Ym1 accounts for most variance in the data.
The eigenvectors and its contributions are displayed in
Appendix 5. By using Eq. 5, the grey relational
coefficients are computed and the results are written
in Appendix 6. The total average of the grey relational
grade value for all the 30 experiments is computed and
listed in Appendix 6. The optimization design is accom-
plished relating to a single grey relational grade instead of
complex multi-response characteristic. Fundamentally,
the larger the grey relational grade, the better is the mul-
tiple performance characteristics. Thus, the overall grey
relational grade of each combination is ranked as per
value [35–37]. The regression coefficient values, standard
deviations, T values and probability (p) values are given
in Appendix 7. Regression analysis is performed to find
out the relationship between the input factors and the
response grey relational grade. Here, 0.80 is the maximum
value of overall grey relational grade, and hence, it is
ranked as 1. The analysis of parameters is carried out by
using analysis of variance (ANOVA), and the data are
shown in (Table 3).
Once the optimal level of the cutting parameters is recog-
nized, which is acquired from the analysis, it is customary to
validate the responses. The confirmation experiments are per-
formed to assist the verification of the plasma arc cutting
process at its optimum condition of input parameters. The
results of the confirmation runs for the responses are tabulated
in Appendix 3. The following equations of plasma arc cutting
(PAC) output responses are given below:
Mean material removal rate ¼ 6921:73 þ 0:0311833
à Feed Rate − 39:8295
 Current − 2:71381
 Voltage − 71:8525
 Torch Height; ð12Þ
Table 2 The eigenvalues and explained variation for principal
components
Principal components Eigenvalue Explained variations (%)
First 1.31 26.20
Second 1.28 25.70
Third 1.00 20.00
Fourth 0.82 16.40
Fifth 0.59 12.70
Int J Adv Manuf Technol (2015) 78:161–175 165

6. Mean surface roughness ¼ 9:1349 þ 0:0503167
 Feed Rate − 1:52617
 Current− 0:171021
 Voltage þ 4:2075
 Torch Height;
Chamfer ¼ 1:82142 − 0:00045
 Feed Rate − 0:00683333
 Current − 0:00139583  Voltage
þ 0:220833 Â Torch Height;
Dross ¼ 46:2527 − 0:0262 Ã Feed Rate − 0:381667
 Current − 0:020625  Voltage þ 1:08833
 Torch Height;
Table 3 The ANOVA table
*p≤0.05
Sources DF Seq. SS Adj. SS Adj. MS F P Percent contribution
Regression 14 0.30 0.30 0.02 1.07 0.45 49.90
Linear 4 0.13 0.12 0.03 1.52 0.25 22.65
A 1 0.02 0.02 0.02 0.88 0.36 3.51
B 1 0.02 0.03 0.03 1.46 0.25 3.39
C 1 0.01 0.00 0.00 0.02 0.89 1.05
D 1 0.09 0.09 0.09 4.62 0.05* 14.70
Square 4 0.06 0.06 0.01 0.71 0.60 9.53
A×A 1 0.00 0.01 0.01 0.45 0.51 0.50
B×B 1 0.03 0.04 0.04 1.98 0.18 5.48
C×C 1 0.00 0.00 0.00 0.03 0.86 0.00
D×D 1 0.02 0.02 0.02 1.06 0.32 3.55
Interaction 6 0.11 0.11 0.02 0.88 0.53 17.71
A×B 1 0.01 0.01 0.01 0.34 0.57 1.12
A×C 1 0.00 0.00 0.00 0.04 0.84 0.15
A×D 1 0.09 0.09 0.09 4.53 0.05* 15.13
B×C 1 0.00 0.00 0.00 0.02 0.89 0.00
B×D 1 0.00 0.00 0.00 0.02 0.90 0.00
C×D 1 0.01 0.01 0.01 0.36 0.56 1.19
Residual error 15 0.30 0.30 0.02 5.10
Lack-of-fit 10 0.20 0.20 0.02 0.98 0.54 33.22
Pure error 5 0.10 0.10 0.02 16.89
Total 29 0.60
166 Int J Adv Manuf Technol (2015) 78:161–175
4%4%
1%
16%
1%
0%
17%
0%
0%
1%
56%
% Contibution of parameters on overall grey grades
FEED RATE CURRENT
VOLTAGE TORCH HEIGHT
FEED RATE*CURRENT FEED RATE*VOLTAGE
FEED RATE*TORCH HEIGHT CURRENT*VOLTAGE
CURRENT*TORCH HEIGHT VOLTAGE*TORCH HEIGHT
Residual Error
Fig. 1 3D pie chart of percentage contribution of input variables on
overall grey relational grades
ð13Þ
ð14Þ
ð15Þ

7. Int J Adv Manuf Technol (2015) 78:161–175 167
3210-1-2-3
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Residual
Percent
Normal Probability Plot
(response is Overall Grey Relational Grade)
0.70.60.50.40.3
2
1
0
-1
-2
Fitted Value
StandardizedResidual
Versus Fits
(response is Overall Grey Relational Grade)
(a) (b)
0.20.10.0-0.1-0.2
10
8
6
4
2
0
Standardized Residual
Frequency
Histogram
(response is Overall Grey Relational Grade)
30282624222018161412108642
2
1
0
-1
-2
Observation Order
StandardizedResidual
Versus Order
(response is Overall Grey Relational Grade)
(c) (d)
Fig. 2 Plot of residuals of overall grey relational grade
995970945920895
0.7
0.6
0.5
0.4
0.3
47.545.042.540.037.5
16014012010080
0.7
0.6
0.5
0.4
0.3
3.53.02.52.01.5
Feed Rate
Mean
Current
Voltage Torch Height
Main Effects Plot for Overall Grey Relational GradeFig. 3 Main effect plot of overall
grey relational grade

8. Kerf ¼ 10:436 − 0:00596667
 Feed Rate − 0:0693333
 Current − 0:00075  Voltage þ 0:435
 Torch Height; ð16Þ
4 Results and discussions
Cutting the stainless steel plates is still more defying than that
of other steel metals due to the difference in the physical,
mechanical and metallurgical properties of the metals to be
cut. Proper choice of mechanism and process variables are,
168 Int J Adv Manuf Technol (2015) 78:161–175
Feed Rate
Current
990980970960950940930920910900
47
46
45
44
43
42
41
40
39
38
Voltage 120
Torch Height 2.5
Hold Values
–
–
–
0.5
0.5 0.6
0.6 0.7
0.7 0.8
0.8
Grade
Relational
Grey
Overall
Contour Plot of Overall Grey Relational Grade vs Current, Feed Rate
Feed Rate
Voltage
990980970960950940930920910900
160
150
140
130
120
110
100
90
80
Current 42.5
Torch Height 2.5
Hold Values
–
–
–
–
–
–
0.450
0.450 0.475
0.475 0.500
0.500 0.525
0.525 0.550
0.550 0.575
0.575 0.600
0.600
Grade
Relational
Overall Grey
Contour Plot of Overall Grey Relational Grade vs Voltage, Feed Rate
(a) (b)
Feed Rate
TorchHeight
990980970960950940930920910900
3.5
3.0
2.5
2.0
1.5
Current 42.5
Voltage 120
Hold Values
–
–
–
–
0.2
0.2 0.4
0.4 0.6
0.6 0.8
0.8 1.0
1.0
Grade
Relational
Grey
Overall
Contour Plot of Overall Grey Relational vs Torch Height, Feed Rate
Current
Voltage
47464544434241403938
160
150
140
130
120
110
100
90
80
Feed Rate 945
Torch Height 2.5
Hold Values
–
–
–
–
–
0.45
0.45 0.50
0.50 0.55
0.55 0.60
0.60 0.65
0.65 0.70
0.70
Grade
Relational
Overall Grey
Contour Plot of Overall Grey Relational Grade vs Voltage, Current
(c) (d)
Current
TorchHeight
47464544434241403938
3.5
3.0
2.5
2.0
1.5
Feed Rate 945
Voltage 120
Hold Values
–
–
–
–
0.5
0.5 0.6
0.6 0.7
0.7 0.8
0.8 0.9
0.9
Grade
Relational
Grey
Overall
Contour Plot of Overall Grey Relational Grade vs Torch Height, Current
Voltage
TorchHeight
1601501401301201101009080
3.5
3.0
2.5
2.0
1.5
Feed Rate 945
Current 42.5
Hold Values
–
–
–
0.4
0.4 0.5
0.5 0.6
0.6 0.7
0.7
Grade
Relational
Grey
Overall
Contour Plot of Overall Grey Relational Grade vs Torch Height, Voltage
(e) (f)
Fig. 4 Contour plot of interaction terms vs. overall grey relational grade

9. therefore, obligatory to make the cuts with good quality.
Therefore, plasma arc cutting of stainless steel metals has
increasing demand due to the higher penetration rates and
with the benefits of high cutting speed providing higher
productivity. This paper demonstrated a bid for devel-
opment of mathematical models of the plasma arc cut-
ting process based on response surface methodology.
Parameter design of response surface methodology be-
ing simple and cheap is adopted for in-depth study to
understand process parameters and their interaction ef-
fects on responses like accuracy of dimensions in dif-
ferent directions of PAC built parts with minimum ex-
perimental runs [38]. To maintain a high production rate
and admissible quality of cut devices, the machining
process parameters of PAC must be optimized [39].
From the design of experiments and due to a broad range of
input process parameters, the present work is contoured to
four factors, three levels and an L30 orthogonal array design
matrix to simplify the present dilemma. In this present study,
30 experiments are carried out based on response surface
method with a face-centered central composite design
(CCD). Here, the MINITAB version 16 software is used to
optimize the experimental data, and this software is a well-
efficient statistical tool which helps to analyze the influence of
input parameters on output responses of whole experimental
design.
Int J Adv Manuf Technol (2015) 78:161–175 169
48
440.4
0.6
40900
0.8
950 1000
Current
GRG
Feed Rate
Voltage 120
Torch Height 2.5
Hold Values
Surface Plot of Overall GRG vs Current, Feed Rate
1600.45
120
0.50
0.55
900
0.60
80950 1000
GRG
Voltage
Feed Rate
Current 42.5
Torch Height 2.5
Hold Values
Surface Plot of Overall GRG vs Voltage, Feed Rate
3.6
3.0
0.3
2.4
0.6
90
0.9
1.8
950 1000
GRG
Torch Height
Feed Rate
Current 42.5
Voltage 120
Hold Values
Surface Plot of Overall GRG vs Torch Height, Feed Rate
160
120
0.5
0.6
40
0.7
8044 48
GRG
Voltage
Current
Feed Rate 945
Torch Height 2.5
Hold Values
Surface Plot of Overall GRG vs Voltage, Current
(a) (b)
(c) (d)
(e) (f)
3.6
3.00.4 2.4
0.6
0.8
40 1.8
44 48
GRG
Torch Height
Current
Feed Rate 945
Voltage 120
Hold Values
Surface Plot of Overall GRG vs Torch Height, Current
3.6
3.00.4
2.4
0.5
0.6
80
0.7
1.8120
160
GRG
Torch Height
Voltage
Feed Rate 945
Current 42.5
Hold Values
Surface Plot of Overall GRG vs Torch Height, Voltage
Fig. 5 Surface plot of interaction terms vs. overall grey relational grade

10. The regression analysis is carried out to inspect how much
is the goodness of relationship in between process variables
and the overall grey relational grade in the experiment. From
Appendix 7, it can be concluded that the torch height and the
interaction of feed rate and torch height are the most influenc-
ing character as the P value comes 0.05. The ANOVA analysis
is applied to test the adequacy of the design by observing the P
value for the F statistic under the 95 % confidence interval.
According to the null hypothesis, if the value of P is less than
or equal to 0.05, then it is concluded that the Hα is very much
exact and the treatments have statistically significant effect on
experiment. From the last column of Appendix 2, it is seen
that the torch height is the most significant term due to its
maximum percentage contribution, i.e. 14.70 % followed by
feed rate with 3.51 % and current and voltage with 3.39 and
1.05 %, respectively. Similarly, analysis is carried out to
determine the percentage contribution of the square and the
interaction terms of input process parameters from this table.
Again, from this column of Appendix 7, it can be predicted
that the residual error of experiment has only 5.10 % contri-
bution to the experiment. Then, the percentage of contribution
of lack-of-fit and pure error is listed as 33.22 and 16.89 %,
respectively, which shows the deficiency in fitting the data.
From the 3D pie chart of Fig. 1, it is indicated that
the torch height has the highest impact on experimental
results. The residual plots of input variable of plasma
arc cutting process have been plotted in Fig. 3. From
Fig. 2a of normal probability plot, it can be understood
that all the data follow a normal distribution as all the
points were placed near the straight line. It can be seen
that the process parameters of plasma arc cutting pro-
cess have a fruitful significance on experiment as there
is a large angled slope of straight line in the graph. The
fitted value vs. standardized residual of overall grey
relational grade is plotted in Fig. 2b where a random
distribution is observed for the model. Here, the stan-
dardized residual distribution pursues that the indepen-
dent patterns are normally placed on each side of the
reference line. Now, from the histogram plot of stan-
dardized residuals in Fig. 2c, it is inferred that all the
columns are performed in a normal distribution with its
mean and standard deviation. Figure 2d shows that the
plot in between the observed run order and the stan-
dardized residuals in which it can be visually under-
stood that the maximum and minimum influence of
process parameters on responses occurred at the 17th
and 25th run order, respectively.
The main effect plot of overall grey relational grade
is presented in Fig. 3. This obtains the optimal para-
metric setting of process parameters in plasma arc cut-
ting machining operation. From the main effect plot, it
is concluded that the optimistic overall grey relational
grade can be achieved with feed rate=970 mm/min,
current=47.5 A, voltage=140 V and torch height=
1.5 mm respectively.
The counter plots of interaction terms at their average
level vs. overall grey relational grade are found in Fig. 4.
Mainly, the shapes of counter plots might be elliptical or
saddle form which indicates that the combination of each
variable is significant except voltage vs. current plot be-
cause of the lowest value of overall grey relational grade
obtained in the middle region of current, which can be
seen in Fig. 4d.
Similarly, the 3D surface plot of the abovementioned inter-
action terms can be exerted in Fig. 5. It is to be noted that all
other terms are taken into account at their average value.
Finally, the confirmation test has been carried out at the
optimum condition of plasma arc cutting process parameters
which is to confirm the feasibility of the correct optimal
setting on responses of the experiment. The outcomes of the
confirmation test for the mean material removal rate and the
quality of cut values are computed in Table 4. Here, the
distance between nozzle of torch and workpiece is the crucial
factor in this experiment. From the ANOVA analysis, it is
evident that the interaction of feed rate and torch height is also
influenced to the abovementioned outputs.
From the above descriptive analysis, evidently, the best
design is becoming one primary challenge of technology
market. In this paper, the optimal values of process parameters
have been numerically found out using the quadratic model of
response surface methodology (RSM). Since time and cost are
comprised while operating the experimental runs, it is relevant
to reduce the number of runs while not compromising the
desired goals [40].
5 Conclusion
This paper furnishes the findings of an experimental
investigation into the effect of feed rate, current, voltage
Table 4 Conformation results for mean material removal rate and the quality of cut
Best combination Experimental value Predicted value
Mean MRR
(mm2
/min)
Mean SR
(μm)
Chamfer
(mm)
Dross
(mm2
)
Kerf
(mm)
Mean MRR
(mm2
/min)
Mean SR
(μm)
Chamfer
(mm)
Dross
(mm2
)
Kerf
(mm)
A B C D
970 47.50 140 1.5 3987.47 62.94 1.48 1.72 1.95 4572.4 32.18 1.20 1.45 1.90
170 Int J Adv Manuf Technol (2015) 78:161–175

11. and torch height on the characteristic of cut when ma-
chining AISI 316 stainless steel by plasma. The specific
problems of PAC have been analyzed. Response surface
method coupled with grey relational analysis and prin-
cipal component analysis has been carried out to opti-
mize plasma arc cutting processes with multi-objective
criteria. The best possible optimum conditions of this
process are the following: 970 mm/min of feed rate,
47.5 A of current, 140 V of voltage and 1.5 mm of
torch height. Torch height as well as interaction of torch
height with feed rate is the most influencing parameters
in plasma arc cutting machining. The shortened quadrat-
ic models developed using the combinatorial plea of
RSM and grey relational analysis (GRA) with principal
component analysis (PCA) were reasonably accurate and
can be used for prediction within the limits of the
factors investigated.
Appendix 1
Appendix 2
Table 6 Output responses of plasma arc cutting process
Run order Mean material
removal rate
Mean surface
roughness
Chamfer Dross Kerf
1 4891.10 58.16 1.83 3.63 2.73
2 3992.62 46.49 1.01 0.80 3.44
3 5541.59 51.81 1.52 9.57 2.64
4 4494.18 25.82 1.42 4.26 2.70
5 5497.43 71.42 1.88 8.26 3.53
6 5082.01 41.88 1.00 7.00 3.30
7 3842.59 62.86 1.05 4.29 2.38
8 4865.14 69.52 1.64 7.63 3.41
9 5345.53 51.13 1.52 8.52 2.61
10 5678.41 32.08 1.83 0.45 2.73
11 3061.77 37.48 1.24 3.00 3.48
12 3929.05 63.29 1.47 1.74 1.93
13 3905.86 72.62 1.58 4.56 2.39
14 5670.24 52.73 1.05 5.25 2.63
15 3489.34 35.60 1.62 2.73 3.73
16 4995.12 63.60 1.10 6.34 2.53
17 5427.69 34.60 1.53 1.74 3.58
18 4223.34 56.61 1.08 6.43 2.65
19 4854.34 71.30 1.63 3.83 3.41
20 5030.29 54.97 1.38 5.27 2.64
21 4072.35 62.76 1.97 8.57 2.34
22 5448.16 34.18 1.68 4.56 2.57
23 4402.74 43.74 1.47 8.43 2.62
24 5470.08 52.35 1.64 9.03 3.73
25 4415.95 66.97 1.78 5.89 2.93
26 5520.10 26.57 1.93 8.52 2.28
27 4649.92 45.13 1.43 3.67 2.04
28 3805.88 44.59 1.67 7.27 3.16
29 5453.33 63.04 1.24 5.79 2.27
30 5538.55 61.25 1.52 8.53 3.07
Table 5 Response surface method design with input parameters
Std. order Run order Feed rate Current Voltage Torch height
18 1 945 42.5 120 2.5
7 2 920 45.0 140 2.0
20 3 945 42.5 120 2.5
3 4 920 45.0 100 2.0
9 5 920 40.0 100 3.0
5 6 920 40.0 140 2.0
2 7 970 40.0 100 2.0
11 8 920 45.0 100 3.0
19 9 945 42.5 120 2.5
4 10 970 45.0 100 2.0
17 11 945 42.5 120 2.5
8 12 970 45.0 140 2.0
13 13 920 40.0 140 3.0
16 14 970 45.0 140 3.0
15 15 920 45.0 140 3.0
12 16 970 45.0 100 3.0
14 17 970 40.0 140 3.0
6 18 970 40.0 140 2.0
10 19 970 40.0 100 3.0
1 20 920 40.0 100 2.0
29 21 945 42.5 120 2.5
30 22 945 42.5 120 2.5
25 23 945 42.5 80 2.5
23 24 945 37.5 120 2.5
Table 5 (continued)
Std. order Run order Feed rate Current Voltage Torch height
22 25 995 42.5 120 2.5
26 26 945 42.5 160 2.5
24 27 945 47.5 120 2.5
28 28 945 42.5 120 3.5
27 29 945 42.5 120 1.5
21 30 895 42.5 120 2.5
Int J Adv Manuf Technol (2015) 78:161–175 171

12. Appendix 3 Appendix 4
Table 7 Normalized values for mean material removal rate and the
quality of cut
Run order Mean material
removal rate
Mean surface
roughness
Chamfer Dross Kerf
1 0.70 0.31 0.15 0.65 0.56
2 0.36 0.56 1.00 0.96 0.16
3 0.95 0.44 0.46 0.00 0.61
4 0.55 1.00 0.57 0.58 0.58
5 0.93 0.03 0.09 0.14 0.11
6 0.77 0.66 1.00 0.28 0.24
7 0.30 0.21 0.95 0.58 0.75
8 0.69 0.07 0.34 0.21 0.18
9 0.87 0.46 0.46 0.12 0.63
10 1.00 0.87 0.15 1.00 0.56
11 0.00 0.75 0.76 0.72 0.14
12 0.33 0.20 0.52 0.86 1.00
13 0.32 0.00 0.41 0.55 0.74
14 1.00 0.42 0.95 0.47 0.61
15 0.16 0.79 0.36 0.75 0.00
16 0.74 0.19 0.90 0.35 0.67
17 0.90 0.81 0.46 0.86 0.08
18 0.44 0.34 0.92 0.34 0.60
19 0.69 0.03 0.36 0.63 0.18
20 0.75 0.38 0.61 0.47 0.61
21 0.39 0.21 0.00 0.11 0.77
22 0.91 0.82 0.30 0.55 0.64
23 0.51 0.62 0.52 0.13 0.62
24 0.92 0.43 0.34 0.06 0.00
25 0.52 0.12 0.20 0.40 0.45
26 0.94 0.98 0.05 0.11 0.81
27 0.61 0.59 0.56 0.65 0.94
28 0.28 0.60 0.31 0.25 0.31
29 0.91 0.20 0.75 0.41 0.81
30 0.95 0.24 0.47 0.11 0.37
Table 8 The deviation sequences for mean material removal rate and the
quality of cut
Run order Mean material
removal rate
Mean surface
roughness
Chamfer Dross Kerf
1 0.30 0.69 0.85 0.35 0.44
2 0.64 0.44 0.00 0.04 0.84
3 0.05 0.56 0.54 1.00 0.39
4 0.45 0.00 0.43 0.42 0.42
5 0.07 0.97 0.91 0.86 0.89
6 0.23 0.34 0.00 0.72 0.76
7 0.70 0.79 0.05 0.42 0.25
8 0.31 0.93 0.66 0.79 0.82
9 0.13 0.54 0.54 0.88 0.37
10 0.00 0.13 0.85 0.00 0.44
11 1.00 0.25 0.24 0.28 0.86
12 0.67 0.80 0.48 0.14 0.00
13 0.68 1.00 0.59 0.45 0.26
14 0.00 0.58 0.05 0.53 0.39
15 0.84 0.21 0.64 0.25 1.00
16 0.26 0.81 0.10 0.65 0.33
17 0.10 0.19 0.54 0.14 0.92
18 0.56 0.66 0.08 0.66 0.40
19 0.31 0.97 0.64 0.37 0.82
20 0.25 0.62 0.39 0.53 0.39
21 0.61 0.79 1.00 0.89 0.23
22 0.09 0.18 0.70 0.45 0.36
23 0.49 0.38 0.48 0.87 0.38
24 0.08 0.57 0.66 0.94 1.00
25 0.48 0.88 0.80 0.60 0.55
26 0.06 0.02 0.95 0.89 0.19
27 0.39 0.41 0.44 0.35 0.06
28 0.72 0.40 0.69 0.75 0.69
29 0.09 0.80 0.25 0.59 0.19
30 0.05 0.76 0.53 0.89 0.63
172 Int J Adv Manuf Technol (2015) 78:161–175

13. Appendix 5
Appendix 6
Table 9 The eigenvectors for principal components and contribution
Outputs Eigenvectors
Principal
component
analysis
(1)
Principal component
analysis
(2)
Principal component
analysis
(3)
Principal component
analysis
(4)
Principal component
analysis
(5)
%
Mean material removal rate −0.59 0.27 0.05 0.67 −0.34 35
Mean surface roughness 0.04 0.76 −0.11 0.06 0.63 00
Chamfer 0.53 −0.23 0.41 0.66 0.25 29
Dross 0.58 0.49 −0.07 −0.01 −0.65 33
Kerf 0.16 −0.22 −0.90 0.33 0.07 03
Table 10 Grey relational coefficient, grey relational grade and rank of the mean material removal rate and the quality of cut
Sl. no. Grey relational coefficient Overall grey relational grade Rank
Material removal rate Surface roughness Chamfer Dross Kerf
1 0.62 0.42 0.37 0.59 0.53 0.53 16
2 0.44 0.53 0.99 0.93 0.37 0.74 4
3 0.91 0.47 0.48 0.33 0.56 0.49 19
4 0.52 1.00 0.54 0.54 0.54 0.57 13
5 0.88 0.34 0.36 0.37 0.36 0.41 26
6 0.69 0.59 1.00 0.41 0.40 0.66 6
7 0.42 0.39 0.91 0.54 0.67 0.59 11
8 0.62 0.35 0.43 0.39 0.38 0.42 23
9 0.80 0.48 0.48 0.36 0.57 0.50 18
10 1.00 0.79 0.37 1.00 0.53 0.75 2
11 0.33 0.67 0.68 0.64 0.37 0.46 20
12 0.43 0.38 0.51 0.78 1.00 0.58 12
13 0.42 0.33 0.46 0.53 0.66 0.43 22
14 0.99 0.47 0.90 0.49 0.56 0.80 1
15 0.37 0.71 0.44 0.67 0.33 0.41 24
16 0.66 0.38 0.84 0.44 0.60 0.66 7
17 0.84 0.73 0.48 0.78 0.35 0.74 3
18 0.47 0.43 0.86 0.43 0.56 0.55 15
19 0.61 0.34 0.44 0.57 0.38 0.56 14
20 0.67 0.45 0.56 0.49 0.56 0.62 9
21 0.45 0.39 0.33 0.36 0.69 0.20 30
22 0.85 0.74 0.42 0.53 0.58 0.61 10
23 0.51 0.57 0.51 0.36 0.57 0.39 27
24 0.86 0.47 0.43 0.35 0.33 0.45 21
25 0.51 0.36 0.38 0.46 0.47 0.39 28
Int J Adv Manuf Technol (2015) 78:161–175 173

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27 0.56 0.55 0.53 0.59 0.89 0.62 8
28 0.41 0.55 0.42 0.40 0.42 0.28 29
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30 0.90 0.40 0.48 0.36 0.44 0.52 17
Table 11 Estimated regression coefficients for grey relational grade
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Terms Coef. SE coef. T P
Constant 62.05 47.89 1.30 0.22
A −0.08 0.09 −0.94 0.36
B −0.79 0.66 −1.21 0.25
C 0.01 0.08 0.14 0.89
D −6.45 3.00 −2.15 0.05*
A×A 0.00 0.00 0.67 0.51
B×B 0.01 0.00 1.41 0.18
C×C 0.00 0.00 0.18 0.86
D×D 0.11 0.11 1.03 0.32
A×B 0.00 0.00 0.58 0.57
A×C 0.00 0.00 −0.21 0.84
A×D 0.01 0.00 2.13 0.05*
B×C −0.00 0.00 −0.14 0.89
B×D −0.00 0.03 −0.13 0.90
C×D 0.00 0.00 0.60 0.56
*p≤0.05
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