P. PAENGCHIT, C. SAIKAEW: USING MANOVA TO INVESTIGATE THE MACHINING PERFORMANCE ...
25–32
USING MANOVA TO INVESTIGATE THE MACHINING
PERFORMANCE OF Al
2
O
3
+ TiC INSERT DURING THE TURNING
OF AISI 4140
UPORABA METODE MANOVA ZA OCENO U^INKOVITOSTI
REZALNIH PLO[^IC IZ Al
2
O
3
+ TiC MED STRU@ENJEM JEKLA
AISI 4140
Phacharadit Paengchit, Charnnarong Saikaew
*
Department of Industrial Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen 40002 Thailand
Prejem rokopisa – received: 2018-07-10; sprejem za objavo – accepted for publication: 2018-09-06
doi:10.17222/mit.2018.139
A hard-turning experiment using Al2O3 + TiC mixed ceramic inserts for machining AISI 4140 chromium molybdenum steel for
automotive-industry applications was investigated. The turning experiments were carried out with varying feed rates ranging
from 0.06 to 0.1 mm/rev under dry conditions. A one-way multivariate analysis of variance (MANOVA) showed that the average
surface roughness and flank wear were significantly affected by the factor feed rate at a level of significance equal to 0.05. The
feed rate of 0.08 mm/rev was an appropriate operating condition for turning the AISI 4140 steel with the Al2O3 + TiC insert,
based on the results of the Bonferroni 95 % simultaneous confidence intervals for pairwise comparisons in treatment means.
Keywords: feed rate, surface roughness, multivariate analysis, Bonferroni
Avtorji so raziskovali uporabnost kerami~nih rezalnih plo{~ic (vlo`kov) iz me{anice Al2O3 + TiC za mehansko obdelavo Cr-Mo
jekla AISI 4140, uporabljanega v avtomobilski industriji. Preizkuse stru`enja so izvajali pri razli~nih hitrostih odvzema
materiala od 0,06 do 0,1 mm/vrtljaj v suhih pogojih (brez mazanja). Enosmerna ve~variantna analiza variance (MANOVA;
angl.: one-way multivariate analysis of variance) je pokazala, da sta povpre~na povr{inska hrapavost in bo~na obraba plo{~ic
mo~no odvisni od hitrosti odvzema materiala na nivoju signifikance 0,05. Hitrost odvzema 0,08 mm/vrtljaj predstavlja
najprimernej{e pogoje obratovanja za stru`enje jekla AISI 4140 s preiskovanimi rezalnimi plo{~icami iz Al2O3 + TiC, ki je
ugotovljena na osnovi rezultatov Bonferronijeve analize 95 % isto~asnih intervalov zaupanja za primerjavo v parih.
Klju~ne besede: hitrost odvzema, povr{inska hrapavost, ve~variantna analiza, Bonferroni
1 INTRODUCTION
Turning is an important machining process in a
variety of industries, including automotive, electronics
and aerospace. In the automotive industry, this operation
has been employed in the manufacturing of gears, bear-
ings, shafts, cams and other mechanical components.
1
The tough requirements for the surface quality and
accuracy characteristics of machined parts using com-
puter numerical control (CNC) lathes have considerably
increased production costs. Hard turning provides
relatively high accuracy for a variety of parts. However,
problems arise with the quality of the surface finish
under different cutting conditions and with different
cutting tools.
2
Finding the optimal operating conditions
for the process factors is an important engineering task
for improving product quality and reducing production
costs.
3
Normally, analysis of variance (ANOVA) is a
statistical approach that is widely used to investigate the
effects of one or at least two factors on a dependent
variable or a response. There are many research works
that apply the approach of ANOVA for performance
evaluations of machining and the machinability of
hardened AISI 4140 steel using an Al
2
O
3
+ TiCN mixed
ceramic insert in a dry environment,
4
hardened AISI
4340 steel using TiN/MT-TiCn/Al
2
O
3
on a cemented
carbide substrate,
5
turbine blade steels (ST 174PH, ST
12TE and ST T1/13W) using a carbide tools insert (TiN,
TiCN, and TiC coated) with ISO code CNMG 120408M
in the presence of coolant (water oil emulsion),
6
hard-
ened and tempered AISI 52100 bearing rings using the
commercial-grade TiN-coated low content CBN inserts
7
and commercially pure titanium grade-2 employing
cryogenically treated inserts and untreated ones.
8
There are many different models for multivariate
analysis, such as factor analysis, principal component
analysis (PCA), multiple discriminant analysis and
cluster analysis. Factor analysis and principal component
analysis are used to analyse the inter-relationships
among a large number of variables and to obtain a way
of condensing the information contained in a number of
original variables into a smaller set of variables with a
minimal loss of information.
9
Multiple discriminant
analysis is used to identify the group to which an object
belongs to a particular class or group based on many
metric independent variables, such as distinguishing a
Materiali in tehnologije / Materials and technology 53 (2019) 1, 25–32 25
UDK 666.3:669.1:621.941:519.233.4 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 53(1)25(2019)
*Corresponding author e-mail:
*
charn_sa@kku.ac.th

ductile material from a brittle material based on the
different manufacturing processes and heat-treatment
methods. Cluster analysis classifies objects such as
materials so that each object is similar to others in the
cluster based on a set of variables representing the
characteristics used to compare the objects in the cluster
analysis. Since each technique provides different benefits
depending on the applications and purposes, it is
ultimately the responsibility of the users to employ the
various techniques properly.
The method of multivariate analysis of variance
(MANOVA) is an extension of ANOVA used to accom-
modate more than one response.
9,10
It is a dependence
multivariate statistical technique that measures the
differences for two or more metric responses simult-
aneously based on a set of factor levels. This method is
useful if there is a high correlation between the
responses. There are some advantages of employing
MANOVA in a mutivariate analysis compared to
multiple univariate ANOVA. MANOVA is appropriate to
maintain control over the experimental error rate (the
combined or overall error rate that results from per-
forming multiple t-tests or F-tests that are related). The
method of MANOVA can provide insights into not only
the nature and predictive power of the factors, but also
the interrelationships and differences seen in the set of
responses. MANOVA can distinguish among the res-
ponses better than a multiple univariate test. On the other
hand, the multiple univariate test ignores the correlations
among the responses and in the presence of multi-
collinearity among the responses that may go undetected
by examining each response separately.
9
Previously, some researchers employed the approach
of MANOVA for data analysis in various applications
such as the analysis of solder-joint defect data,
11
multi-
electrode array electrophysiology data,
12
and the mecha-
nical properties of lightweight aggregate concrete data.
13
However, there are a few research works that employ
MANOVA for an assessment of machining data such as
surface roughness, run-out and diameter deviations data
when turning AISI 1045 medium-carbon steel with
coated tungsten-carbide tools,
14
the data set of machining
time, tool wear, the crater size of the machined area and
surface micro-hardness during the micro-scale wire-
EDM cutting of Ti-6Al-4V,
15
and the data set of surface
roughness (R
a
, R
z
, R
max
, R
t
) in the grinding process.
16
This study aimed to investigate the machining per-
formance of the Al
2
O
3
+ TiC inserts while turning AISI
4140 steel with different feed rates based on the machin-
ability characteristics of surface roughness (R
a
)a n d
tool-flank wear (V
b
) by systematically applying one-way
MANOVA and the Bonferroni 95 % simultaneous con-
fidence intervals.
2 MATERIALS AND METHODOLOGY
2.1 Materials and procedure
The workpiece material used in this work was AISI
4140 chromium molybdenum steel bar with an average
hardness of 58 HRC used for making gears, shafts,
bearings, cams and other automotive parts. The chemical
compositions in w/% of AISI 4140 consist of 0.4677 %
C, 0.257 % Si, 0.6714 % Mn, 0.0146 % P, 0.0117 % S,
1.0547 % Cr, 0.2011 % Mo, 0.0042 % V, 0.012 % Al and
0.19 % Cu.
In this work, a seven-step approach that involved
planning and carrying out the experiments was specified,
as follows:
1. Setting the objective: The main objective was to
obtain an approximate operating condition for a
turning operation to minimize R
a
and V
b
.
2. Identifying the important process factors and res-
ponses: This work investigated an important factor,
feed rate, during the turning operation for AISI 4140,
whereas the responses were R
a
and V
b
.
3. Determining the levels of the process factor: The
levels of feed rate included 0.06, 0.08 and 0.10
mm/rev, while the cutting speed and depth of cut
were kept constant at 220 m/min and 0.1 mm,
respectively. The ranges of the factor were based on
the experimenter’s experiences.
4. Developing the design matrix based on full-factorial
design: The full-factorial design with three levels was
used to investigate the effect of the process factor on
R
a
and V
b
. Each operating condition was carried out
with three replicates. A completely randomized
experiment was run in order to investigate the effect
of the feed rate on R
a
and V
b
.
5. Carrying out the experiments of turning AISI 4140 as
per the full-factorial design: The turning operation
was performed on a Fanuc CNC lathe machine
(Takisawa: model NEX-106) under conventional dry
hard turning using a mixed ceramic cutting tool
(Al
2
O
3
+ TiC: Tungaloy, Japan) with physical and
mechanical properties of the insert cutting tool as
follows: hardness of 94 HRA, modulus of elasticity
of 400 GPa, transverse rupture strength of 0.9 GPa
P. PAENGCHIT, C. SAIKAEW: USING MANOVA TO INVESTIGATE THE MACHINING PERFORMANCE ...
26 Materiali in tehnologije / Materials and technology 53 (2019) 1, 25–32
Figure 1: Experimental setup

and surface roughness of 0.101 μm, as shown in
Figure 1.
6. Recording the responses of Ra and Vb: A sample of 9
parts and that of 9 cutting inserts were used to carry
out the turning experiments and data collections of
the R
a
and V
b
values as per the design of experiments.
The R
a
values were measured using a commercial
surface-roughness testing machine (Germany, Mahr
model: MarSurf PSl) with a cut-off length of 0.8 mm
and a sampling length of 5 mm. The R
a
measure-
ments were performed at three positions on the
machined workpiece.
7. Investigating the effect of the factor on the two
responses and determining an appropriate optimal
operating condition. One-way MANOVA and 95 %
confidence interval (C.I.) using Bonferroni were used
to determine an appropriate operating condition of
the feed rate based on R
a
and V
b
minimization.
2.2 One-way MANOVA
In this work, a one-way MANOVA was employed to
investigate the influence of the one factor (feed rate with
3 levels) on the two responses (R
a
and V
b
). A one-way
MANOVA model can be defined for one factor as:
9
y
ik i ik
=++ mte, i = 1,2,...,a; k = 1,2,...,n (1)
where y
ik
represents the p × 1 vector of the two
responses (p = 2) on the particular level ith of the factor
feed rate (i = 1 for 0.06 mm/rev, i = 2 for 0.08 mm/rev
and i = 3 for 0.1 mm/rev) with a replicate of k
th
. The
vector μ denotes the p × 1 vector of the overall mean,
whereas the vector t
i
is the p × 1 vector of the treatment
effect of factor feed rate. The vector e
ik
is the p ×1
random vector corresponding to the error and is
assumed to have a zero vector as the mean and the
variance-covariance matrix  with the assumption of  ik
NID
p
(0, ).
The hypothesis testing for the factor feed rate was
expressed as:
H
Hi l
il
0123
1
:
:, ()
mmm
mm
==
≠≠ for at least one pair
(2)
Table 1 shows the source of variation, the matrices of
the sum of squares and cross products (SS & CP) and the
degree of freedom (df) for the one-way MANOVA.
9,12
Table 1: One-way MANOVA Table
Source of
variation
SS&CP df
Feed rate
Bnyyyy
i
i
a
io io
=−−
=
∑
1
() () '
21 () a −
Error
Wy y y y
iko io iko
k
n
i
a i
=−−
= =
∑ ∑
() () '
1 1
21
1
na
i
i
a
−−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ =
∑
Total
BW yyyy
ik ik
k
n
i
a i
+= − −
= =
∑ ∑
() () '
1 1
where y is the overall mean and y
io
denotes the p ×1
mean vector of the two responses (p =2 )o nt h e
particular level ith of the factor feed rate with the
replicate of k
th
.
The statistic used to test the effect of the factor feed
rate is the Wilks’ lambda ( ) statistic test. The Wilks’ statistic is the ratio of the determinant of the
within-group sums of squares and cross- products matrix
(SS & CP) for error W to the determinant of the total
sums of squares and cross-products matrix B + W,a s
described in Equation (3).
9,17,18
Wilks's  =  =
W
BW +
(3)
where B represents the SS & CP matrix for the factor
feed rate. The Wilks’ is a value between zero and one.
The Bonferroni technique is used to construct the 100
(1– )% simultaneous confidence intervals for pairwise
comparisons in treatment means, which are defined as:
9
[]
100 1
1
1
 
  CI 
)
/() ,
ki li
pa a n a
ii
t
W
nan
−
±
−
−−
kl
n
+
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1
(4)
where() () 
ki li ki i li i
yyyy −=−−− is the difference
between the two treatment effects. W
ii
is the i
th
diagonal
element of W. The vectors of  ki
and  li
for each of the
three levels of the factor feed rate are used to estimate
the 100 (1– )% simultaneous confidence intervals.
3 RESULTS AND DISCUSSION
3.1 Preliminary data analysis
Table 2 shows the results of R
a
and V
b
based on the
experimental design. To determine the optimal operating
condition of the significant process factor influencing R
a
and V
b
, a numerical analysis using one-way MANOVA
was used.
Table 2: Results of R
a
and V
b
during turning AISI 4140 with Al
2
O
3
+
TiC
Feed rate (mm/rev) R a
(μm) V
b
(μm)
0.06 0.736 61
0.06 0.742 56
0.06 0.754 64
0.08 0.960 55
0.08 1.065 63
0.08 1.008 47
0.10 1.128 81
0.10 1.048 96
0.10 1.196 111
The probability plot is used to display the data points,
fitted line of the data points and the associated con-
fidence intervals (C.I.) based on parameters estimated
from the data sets along with an Anderson-Darling (AD)
goodness-of-fit statistic and the associated p-value in
P. PAENGCHIT, C. SAIKAEW: USING MANOVA TO INVESTIGATE THE MACHINING PERFORMANCE ...
Materiali in tehnologije / Materials and technology 53 (2019) 1, 25–32 27

order to examine the validity of the data set distributed as
the normal probability distribution.
9
The hypotheses for
the AD test are:
H
0
: The data follow a normal distribution
H
1
: The data do not follow a normal distribution
If the p-value is greater than the  -level, the data
follow a normal distribution.
Figures 2 and 3 depict the probability plot of the R
a
and V
b
data sets. The probability plots indicated that the
plotted points of all the data sets of R
a
and V
b
approxi-
mately formed a straight line and fell within the C.I. The
AD statistics of both data sets were small with high
p-values compared to the level of significance ( = 0.05).
These confirmed that the normal probability distribution
fitted these data sets of the R
a
and V
b
values moderately
well.
Before investigating the effect of the feed rate on the
average R
a
and V
b
values using one-way MANOVA, the
model adequacy checking is employed by examining the
residuals. A residual is defined as the difference between
an observed value and its corresponding fitted value. The
normal probability plot of the residuals is used to test the
goodness of model fit. If the residuals are normally
distributed, the points in this plot should form a straight
line.
9
Generally, the normality assumption may be inva-
lid if the points on the plot diverge from a straight line.
As the number of observations decreases, the probability
plot might illustrate considerable variation and nonline-
arity, even if the residuals are normally distributed.
Figures 4 and 5 indicate that the values of the residuals
lie moderately along the linear line, confirming a good
model adequacy. These tests indicated that the one-way
MANOVA model was effective for investigating the
effect of feed rate on the averages R
a
and V
b
.
The plot of residuals versus run order is used to
inspect the independence assumption. The observations
are not independent if the plot has a pattern such as a
P. PAENGCHIT, C. SAIKAEW: USING MANOVA TO INVESTIGATE THE MACHINING PERFORMANCE ...
28 Materiali in tehnologije / Materials and technology 53 (2019) 1, 25–32
Figure 5: Normal probability plot of residuals for the V
b
values
Figure 3: Probability plot of the V
b
values
Figure 2: Probability plot of the R
a
values Figure 4: Normal probability plot of residuals for the R
a
values

sequence of positive or negative residuals. Figures 6 and
7 illustrate the plots of residuals and the run order for the
R
a
and V
b
values, respectively. These plots did not show a
violation of the independence assumption.
A plot of residuals versus fitted value is used to test
the non-constant variance. Non-constant variance occurs
if the plot looks like an outward-opening funnel or mega-
phone. This plot should illustrate a random pattern of
residuals on both sides of 0. This plot indicates a non-
random pattern based on the reasons of a series of de-
creasing or increasing points, a predominance of nega-
tive residuals or a predominance of positive residuals,
and patterns, such as decreasing residuals with decreas-
ing fits or vice versa. Figures 8 and 9 show the plots of
residuals and the fitted R
a
and V
b
values, respectively.
The plots did not reveal any violation of the assumption
of homogeneity of variances.
Figure 10 shows the relationship between the R
a
and
V
b
values. The relationship was linear with the regression
equation of y = 0.00046x + 0.6614 and R
2
= 0.3835,
where y was the R
a
and x was the V
b
value. It indicated
that the method of MANOVA was required in order to
reduce the error rate. If ANOVA is used to investigate the
P. PAENGCHIT, C. SAIKAEW: USING MANOVA TO INVESTIGATE THE MACHINING PERFORMANCE ...
Materiali in tehnologije / Materials and technology 53 (2019) 1, 25–32 29
Figure 10: Relationship between R
a
and V
b
values
Figure 9: Plot of residuals vs fitted V
b
values
Figure 8: Plot of residuals vs fitted R
a
values
Figure 7: Plot of residuals vs run order for the V
b
values
Figure 6: Plot of residuals vs run order for the R
a
values

effect of feed rate on at least two correlated R
a
and V
b
values, the error rate will be greater than the set value of
the level of significance.
9
3.2 One-way MANOVA results
Table 3 shows the one-way MANOVA results for R
a
and V
b
during turning AISI 4140, including sources of
variation, matrices of the sum of squares and cross pro-
ducts (SS&CP) and the degree of freedom.
9
The matrix
B is the hypothesis sums of squares and cross-product
matrix for the R
a
and V
b
responses. The diagonal ele-
ments of this matrix, 0.2285 and 2981.56 were the uni-
variate ANOVA sums of squares for the model term
when the responses were R
a
and V
b
, respectively. The
off-diagonal elements of this matrix were the cross
products. The matrix W is the error sums of squares and
cross-product matrix. The diagonal elements of this
matrix, 0.0167 and 610.667 were the univariate ANOVA
error sums of squares when the responses were R
a
and
V
b
, respectively. The off-diagonal elements of this matrix
were the cross products.
Table 3: One-way MANOVA for R
a
and V
b
during turning AISI 4140
Sources of
variation
SS & CP matrix
Degree of
freedom
Feed rate
B =
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 0 2285 16 7623
16 7623 298156
..
..
4
Error
W =
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 0 0167 1516
1516 610 667
..
..
10
Total
BW +=
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 0 2452 1827833
182783 3592 227
..
..
The Wilks’ lambda ( ) statistic is used to test the
effect of the feed rate on R
a
and V
b
. The Wilks’  statistic is the ratio determinant of the error sums of
squares and cross-product matrix W to the determinant
of the total sums of squares and cross-products matrix
B + W. Hence, the Wilks’ statistic was:
Wilks's  =  =
W
BW +
=
789988
54671781
001445
.
.
. =
which corresponded to the F-distribution. The value
of F was calculated as follows:
F
na
a
i
i
a
=
−−
−
⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ −
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ =
−−
−
⎛ ⎝ ⎜ ⎞ ⎠ =
∑ 1
1
19 3 1
31
1
  ⎟ −
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1 001445
001445
.
.
=
= 18.2975
where n
i
is the number of replicates for each level of the
factor and a is the number of levels. The value of F is
used to compare to the F critical value with the degrees
of freedom as follows:
dfa na
i
i
a
=− −−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟=−− −=
=
∑ 21 2 12 31 2 9314 1 0
1
() , () , ( ),
The critical value of F
0.05,4,10
= 3.48 The F value of
18.2975 was greater than the F critical value of 3.48 with
the degrees of freedom of 4 and 10 at the level of
significance of 0.05. The hypothesis of no effect of the
factor feed rate was rejected. This implied that the feed
rate had a statistically significant effect on the averages
R
a
and V
b
at the level of significance of 0.05.
The Bonferroni 95 % simultaneous confidence inter-
vals for pairwise comparisons in treatment means from
Equation (4) were used to investigate the differences in
the averages R
a
and V
b
among each pair of feed-rate
comparisons. Table 4 provides vectors of  ki
and  li
for
each of the three levels of factor feed rate calculated for
estimating the 95 % simultaneous confidence intervals.
Table 4: Vectors  ki
and  li
Feed
rate
Difference of vectors
 ki
and
 li
0.06
 ()
..
..
 11 11 1
0 7440 0 9597
60 3333 70 4444
=−=
−
−
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ =
−
yy
0 2157
101111
.
. −
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 0.08
 ()
..
..
 21 21 1
10110 0 9597
550000 70 4444
0
=−=
−
−
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = yy
.
.
0513
154444 −
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 0.10
 ()
..
..
 31 31 1
11240 0 9597
96 0000 70 4444
0
=−=
−
−
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = yy
.
.
1643
255556
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ The 95 % simultaneous confidence interval table of
R
a
between the level of 0.06 mm/rev and 0.08 mm/rev
was calculated as:
[]
100 1
1
1
 
  CI 
)
/() ,
ki li
pa a n a
ii
t
W
nan
−
±
−
−−
kl
n
+
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1
[]
9 02157 00513
0
00 5233193
     CI−−
±
−−
..
)
.
. / () () ( ),
t
0167
93
1
3
1
3 −
+
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = –0.267±(3.863)(0.1664) = (–0.4334, –0.1006)
The 95 % simultaneous confidence interval table of
R
a
and V
b
estimated from Equation 4 is summarized in
Table 5 based on the vectors of  ki
and  li
in Table 4.
Statistically significant differences at the level of signi-
ficance of 0.05 are marked with an asterisk if each of the
95 % simultaneous confidence interval does not contain
zero. According to Table 5, no difference in R
a
existed
between the level of 0.08 and that of 0.10 mm/rev at the
level of significance of 0.05. Similarly, Table 5 shows no
difference in V
b
between the level of 0.06 and that of
0.08 mm/rev. Thus, the feed rate of 0.08 mm/rev was an
appropriate operating condition for the turning of AISI
4140 steel with an Al
2
O
3
+ TiC insert.
The results of the MANOVA could be used to prove
the possibility of applications to other machining oper-
P. PAENGCHIT, C. SAIKAEW: USING MANOVA TO INVESTIGATE THE MACHINING PERFORMANCE ...
30 Materiali in tehnologije / Materials and technology 53 (2019) 1, 25–32

ations with other workpiece materials such as milling
operations of AISI 1045 steel, AISI 52100 hardened
steel, drilling operations of aluminium 6061 by investi-
gating the effects of machining factors on multiple
correlated responses simultaneously.
Table 5: 95 % confidence interval (C.I.) for R
a
and V
b
during turning
AISI 4140
Pair 95%C .I. for R
a
95%C .I. for V
b
0.06 VS 0.08 (–0.4334, –0.1006)* (–26.487, 37.1537)
0.06 VS 0.10 (–0.5464, –0.2136)* (–67.487, –3.8463)*
0.08 VS 0.10 (–0.2794, 0.0534)( – 72.820, –9.1797)*
4 CONCLUSIONS
The following conclusions were drawn after carrying
out the experiments into the performance of an Al
2
O
3
+
TiC mixed ceramic insert when turning AISI 4140
chromium molybdenum steel.
• The feed rate had a significant effect on R
a
and V
b
at
the level of significance of 0.05 based on the results
of a one-way MANOVA.
• The feed rate of 0.08 mm/rev was an appropriate
operating condition for turning AISI 4140 steel with
an Al
2
O
3
+TiC insert based on the results of the
Bonferroni 95 % simultaneous confidence intervals
for pairwise comparisons in treatment means of R
a
and V
b
values.
The one-way MANOVA and the Bonferroni 95 %
simultaneous confidence intervals for pairwise compa-
risons in treatment means of multiple correlated res-
ponses of R
a
and V
b
were successfully used to investigate
the effect of the feed rate on the averages R
a
and V
b
and
to determine an appropriate operating condition for the
statistically significant factor feed rate at the level of
significance of 0.05. It is worth noting, however, that the
limitations of MANOVA in comparison with other
methods of multivariate data analysis techniques include
a high correlation among the responses and a sensitivity
to outliers.
9
Thus, it is eventually the responsibility of the
users to apply the MANOVA and other multivariate
data-analysis approaches properly. The further develop-
ment of investigations of the effects of other factors such
as cutting speed, depth of cut and tool geometry on other
quality characteristics such as the material removal rate
and energy consumption during the turning operation of
the AISI 4140 steel with the Al
2
O
3
+TiC insert should be
taken into consideration for identifying the significant
process factor(s) and determining the optimal operating
condition of the statistically significant factor(s) using
the MANOVA approach coupled with other multi-
objective optimization techniques, such as the response
surface methodology (RSM) using the desirability
function
19
, and the multivariate mean square error
developed by combining RSM, PCA and the concept of
mean square error that can convert the original multiple
correlated responses into a new set of uncorrelated
ones.
20
Acknowledgement
The authors gratefully acknowledge the Office of the
Higher Education Commission of Thailand and the
Faculty of Engineering, Khon Kaen University for
financial support.
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