M. F. ERINOSHO, E. T. AKINLABI: CENTRAL COMPOSITE DESIGN ON THE VOLUME OF LASER METAL ...
419–426
CENTRAL COMPOSITE DESIGN ON THE VOLUME OF LASER
METAL DEPOSITED Ti6Al4V AND Cu
CENTRALNO NA^RTOVANJE KOMPOZITA NA OSNOVI
KOLI^INE LASERSKO NANE[ENE KOVINE Ti6Al4V IN Cu
Mutiu F. Erinosho, Esther Titilayo Akinlabi
University of Johannesburg, Department of Mechanical Engineering Science, Auckland Park Kingsway Campus, 2006 Johannesburg,
South Africa
mferinosho@uj.ac.za, mutiuerinosho1@gmail.com
Prejem rokopisa – received: 2016-01-20; sprejem za objavo – accepted for publication: 2016-05-18
doi:10.17222/mit.2016.019
The laser technology process is a pulsating practice in the field of engineering and in all paces of lifespan; since it can travel a
longer distance and be focused on a very small bright spot that exceeds the illumination of the sun. This present study reports on
the modeling and the prediction of the volume of laser-deposited composites using the central composite design (CCD). Four
input factors were put into consideration, which is the laser power, the scanning speed, the powder flow rate and the gas flow
rate. Titanium alloy (Ti6Al4V) and copper (Cu) powders were coaxially deposited to form the bulk of a single clad. The factors
considered determine the energy density and the melt pool delivered into the substrate and as such, influence the volume of the
deposited composite (VDC) that was employed in the response surface methodology (RSM) design. This has been used to
predict the actual process parameters for the optimum process setting.
Keywords: laser metal deposition, response surface methodology, central composite design, volume of deposited composite
Postopek laserske tehnologije se uporablja na podro~ju tehnike in na vseh korakih `ivljenjske dobe materialov; saj lahko
premaguje velike razdalje in je v obliki zelo majhne svelte to~ke, ki presega sevanje sonca. [tudija predstavlja modeliranje in
napovedovanje koli~ine lasersko nane{enega kompozita, z uporabo centralnega na~rtovanja kompozita (angl. CCD). Obravna-
vani so bili {tirje vplivni dejavniki: mo~ laserja, hitrost skeniranja, hitrost toka prahu in hitrost toka plina. Titanova zlitina
(Ti6Al4V) in baker (Cu) sta bila koaksialno nane{ena in sta tvorila enoten nanos. Obravnavani dejavniki so dolo~ali gostoto
energije in obseg taline nane{ene na podlago in kot taki vplivali na volumen nane{enega kompozita (angl. VDC), ki je bil
uporabljen pri na~rtovanju metodologije odgovora povr{ine (angl. RSM). To je bilo uporabljeno za napovedovanje dejanskih
procesnih parametrov pri optimiranju nastavitev procesa.
Klju~ne besede: nana{anje kovine z laserjem, metodologija odgovora povr{ine, centralno na~rtovanje kompozita, volumen
nane{enega kompozita
1 INTRODUCTION
The word laser is an acronym for "Light Amplifi-
cation by Stimulated Emission of Radiation". In terms of
wavelength, a laser device produces intense beams of
low-divergence light for electromagnetic radiation
ranging from 1 nm to 1000 μm. It is less than 500 nm for
ultraviolet and less than 800 nm in visible spectrum, and
200 nm to 400 nm for ultraviolet light. In comparison
with photon energy, the wavelength of laser light is of a
pure monochromatic type.1 The laser metal-deposition
process produces a metallurgical bonding, which is
formed permanently between the clad and the substrate.
In applications, a low dilution occurs in one step, with
the minimal use of powder; and no form of additional
processing is required when this is achieved.2 The extent
of the energy density absorbed by the substrate
determines the depth of the melt pool and the volume of
the deposited alloy.3 The material flow rate also has a
large effect on the chemical and the mechanical proper-
ties of the final deposited clad during laser metal-deposi-
tion process.4,5
Design of experiment (DOE) has been widely used to
minimize the guessing of results and useful for a
laboratory experiment to yield a desirable output. It is a
problem dependent on a set of experiments; and has been
widely used in industries for the development and the
optimization of production processes.6 It is also regarded
as a systematic and rigorous approach to engineering
problem-solving that applies techniques and principles
during the collection stage of data, so as to ensure and
arrive at a generally valid, defensible, and a well-aided
engineering conclusion, which are carried out under the
constraint of a minimal expenditure of engineering runs,
time, and money.7 The first stage in DOE is the planning
of the experiment before embarking on the process of
testing and data collection. The second stage is the
screening test; and this is used to identify the important
factors that affect the process parameters under investi-
gation from all the numerous potential factors.8 Optimi-
zation is followed in order to envisage the response
values for all the likely factors within the experimental
boundary and to locate the optimal experimental point.
The next stage is done to ascertain that the approach
Materiali in tehnologije / Materials and technology 51 (2017) 3, 419–426 419
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
UDK 669.715:669.295:669.058.67 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 51(3)419(2017)
used is robust enough to accommodate small alterations
in the factor levels.6 The last stage is the verification of
the results and the best-settings validation; and this is
achieved by conducting a few follow-up experimental
runs to confirm that the process parameters are well con-
formed.8 However, the effect of a specific factor can be
evaluated at different levels of the other factors; there-
fore, the results will be reliable over the whole experi-
mental space.9 The results showed how interconnected
factors respond over a wide range of values, without
requiring all the possible values to be tested directly. The
software fits the response data to mathematical equa-
tions; which serve as models to predict what would
happen for any given combination of values.10 A full-
factorial design with CCD to investigate the effects of
pH and the buffer concentration of catholyte on the
performance of two-chamber microbial fuel cell. It was
revealed that the maximum power density did not show
good manipulation on the fuel cell at a high level of
buffer concentration.11 The relationship between a high
sharpness and the configurations of the vortex finder of a
hydrocyclone was modeled using the regression
method.12 The production of recycled titanium from acid
with the high sharpness was achieved.
A series of predictions have been made in an
experiment in order to generate the validity of the result
and to optimize the process parameters. In the literature,
there are paucities of work on the estimation of the vol-
ume of laser-deposited samples. This can be really help-
ful to determine the bulk measurement of a laser-cladded
surface. However, the aim of this work is to apply a
full-factorial design and response surface methodology
to evaluate and predict the volume of the laser-deposited
titanium and copper alloys using the central composite
design. The amount of volume generated is proportional
and dependent on the laser’s energy density and the
process parameters employed.
2 EXPERIMENTAL PART
The process model started with several input factors
such as the laser power, scanning speed, powder flow
rate and gas flow rate that are controlled and varied by
the experimenter. One or more outputs are produced as
the response, which is assumed to be continuous.7 The
established experimental data are used to derive an
empirical model containing the first- and second-order
terms linking the outputs and inputs.13 Figure 1 shows
the general model of a process or system.
The most common empirical models fit to the experi-
mental data take either a linear form or a quadratic form.
A linear model with two factors, X1 and X2, can be
written as Equation (1):
Y = 0 + 1X1+ 2X2 + 12X1X2 + Experimental error (1)
From Equation (1), Y represents the response for the
given levels of the main effects; X1 and X2 and the X1X2
term are included to account for a possible interaction
effect between X1 and X2. The constant 0 represents the
response of Y when both the main effects are 0.
A quadratic model, which is a second-order model, is
typically used in response surface DOE with suspected
curvature; and it does not include the three-way interac-
tion term, but adds three more terms to the linear model,
as illustrated in Equation (2):13
11X
2
1+22X
2
2+33X
2
3 (2)
The response surface methodology (RSM) is an
efficient statistical tool that has been used successfully in
testing the process parameters and their interactive
effects.14,15 In the RSM, the first-order design and the
second-order design were adopted; and these are suitable
for fitting and checking a first- and second-degree of
polynomial. However, in other to allow for the efficient
estimation of quadratic terms in the second-order model,
a two-level factorial array is adopted,16 as shown in
Equation (3):
y x x x xi i
i
k
ii i
i
k
ij i j
j
k
i
k
= + + +
= = ==
−
∑ ∑ ∑∑   0
1
2
1 21
1
(3)
If all the variables are assumed to be measurable, the
response surface can be expressed as shown in Equation
(4):
y f x x x x x k= ( , , , , ..., )1 2 3 4 (4)
where "y" is the independent variable of the system, and
xi is the dependent variables or factors.
x x x x x k1 2 3 4, , , , ..., are the input factors, which influ-
ence the response y; 0, ii ij are the unknown
parameters.17–19
2.1 Design of experiment
The RSM was implemented in order to analyze the
experimental variables, and to provide an average res-
ponse to the values of the quantitative variables
analyzed. The factors from the volume of the deposited
Ti6Al4V/Cu composite (VDC) were employed for the
RSM design; and these have been used to predict the
M. F. ERINOSHO, E. T. AKINLABI: CENTRAL COMPOSITE DESIGN ON THE VOLUME OF LASER METAL ...
420 Materiali in tehnologije / Materials and technology 51 (2017) 3, 419–426
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 1: General model of a process or system9
Slika 1: Splo{ni model procesa ali sistema9
actual process parameters that produced the optimum
process set-up. Figure 2 displays a schematic view of a
deposited composite showing the track length, track
width and the height of the deposit. The schematic is a
sample image of the laser-deposited Ti6Al4V/Cu
composite, as deposited on the substrate.
The volume of the laser-deposited composite is gene-
rated using Equation (5). The full geometry can be
obtained elsewhere.20
( )V L R h L R
R h
R
R h
W
( , , ) cos=
−⎛
⎝
⎜ ⎞
⎠
⎟ − − ⎛⎝
⎜ ⎞
⎠
⎟⎡
⎣⎢
⎤
⎦⎥
−2 1
2
(5)
where L designates the length of the deposit track; W is
the deposit width; h is the height of the deposit; R is the
radius of the circle and V represents the volume of the
deposited composite.
The process parameters were controlled to give
reasonable volumes of the deposited samples. The
polynomial function is introduced in the RSM design to
provide a depiction of how the response is affected by a
number of variables over a unit of experimental interest.
The input parameters are the laser power, scanning
speed, powder flow rate and the gas flow rate, respec-
tively. In the settings, the low level and high level of the
factors are the inputs, as shown in Table 1.
Table 1: Input parametric factors for the RMS design
Tabela 1: Vhodni parametri dejavnikov za na~rtovanje RMS
Factor Name Level Low Level High Level
A Laser power 1.60 0.80 1.60
B Scanningspeed 0.60 0.30 0.90
C Powderflow rate 2.40 2.40 2.50
D Gas flowrate 2.95 2.90 3.00
The VDC is studied by using the central composite
design (CCD). This is appropriate to fit the quadratic
M. F. ERINOSHO, E. T. AKINLABI: CENTRAL COMPOSITE DESIGN ON THE VOLUME OF LASER METAL ...
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MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 2: Schematic view of a laser-deposited sample20
Slika 2: Shematski prikaz lasersko deponiranega vzorca20
Table 2: Point-type design layout
Tabela 2: Postavitev to~kaste vrste na~rtovanja
Number of
run
Standard
order Block Space type
Laser power
(kW)
Scanning
speed
(m/min)
Powder flow
rate (min-1)
Gas flow
rate (l/min)
Volume of deposited
composite (mm3)
1 18 Day 1 Center 1.40 0.40 2.45 2.95 100.54
2 20 Day 1 Center 1.40 0.40 2.45 2.95 100.54
3 11 Day 1 Factorial 1.20 0.50 2.40 3.00 78.68
4 9 Day 1 Factorial 1.20 0.30 2.40 3.00 91.9
5 6 Day 1 Factorial 1.60 0.30 2.50 2.90 147.88
6 13 Day 1 Factorial 1.20 0.30 2.50 3.00 91.90
7 1 Day 1 Factorial 1.20 0.30 2.40 2.90 91.90
8 19 Day 1 Center 1.40 0.40 2.45 2.95 100.54
9 5 Day 1 Factorial 1.20 0.30 2.50 2.90 120.29
10 12 Day 1 Factorial 1.60 0.50 2.40 3.00 104.48
11 3 Day 1 Factorial 1.20 0.50 2.40 2.90 78.68
12 16 Day 1 Factorial 1.60 0.50 2.50 3.00 104.48
13 10 Day 1 Factorial 1.60 0.30 2.40 3.00 111.65
14 17 Day 1 Center 1.40 0.40 2.45 2.95 100.54
15 14 Day 1 Factorial 1.60 0.30 2.50 3.00 147.88
16 4 Day 1 Factorial 1.60 0.50 2.40 2.90 104.48
17 2 Day 1 Factorial 1.60 0.30 2.40 2.90 111.65
18 7 Day 1 Factorial 1.20 0.50 2.50 2.90 78.68
19 8 Day 1 Factorial 1.60 0.50 2.50 2.90 104.48
20 15 Day 1 Factorial 1.20 0.50 2.50 3.00 78.68
21 29 Day 2 Center 1.40 0.40 2.45 2.95 100.54
22 23 Day 2 Axial 1.40 0.20 2.45 2.95 102.76
23 22 Day 2 Axial 1.80 0.40 2.45 2.95 120.76
24 21 Day 2 Axial 1.00 0.40 2.45 2.95 69.38
25 30 Day 2 Center 1.40 0.40 2.45 2.95 100.54
26 28 Day 2 Axial 1.40 0.40 2.45 3.05 100.54
27 26 Day 2 Axial 1.40 0.40 2.55 2.95 100.54
28 27 Day 2 Axial 1.40 0.40 2.45 2.85 100.54
29 24 Day 2 Axial 1.40 0.60 2.45 2.95 97.36
30 25 Day 2 Axial 1.40 0.40 2.35 2.95 98.58
surface. The numerical factors were selected based on
the number of factors. The numbers of factors involved
are: the laser power, the scanning speed, the powder flow
rate, and the gas flow rate. From the CCD formed, a full
factorial type was proposed. The number of blockings
selected was designated to be run for 2 d, that is d 1 and
d 2 are proposed for the experiment. In total, 30 runs
were involved for the experiment within the two days.
This displays the graphical illustration of the blocks’
interpretation in Table 2; and the orientation would be
much more productive to the impact of the control
factors in response to the surface graphics.
The quadratic model used was not aliased, which
means there are no fewer independent points in the
design model; therefore, the parameters used can be
estimated independently. Aliases are calculated, based on
the responses selected, and taking into consideration the
degree of freedom for the evaluation.
Table 3 illustrates the power at a 5 % alpha level to
detect the signal or noise level in this model. The
standard error estimates the standard deviation of the
parameters; and it is used to calculate a confidence
interval around the parameters.
The smaller the standard deviation, the better is the
result. In this design, the Variance Inflation Factor (VIF)
measures how much the variance of that parameters or
model coefficient is inflated by the lack of orthogonality
in the design. The VIF in this design follows between 1.0
and 1.05, which is almost ideal. The VIF above 10
indicates some cause for alarm; and this shows that the
coefficients are poorly estimated – due to multi-colli-
nearity. The ideal Ri-squared is 0.0, which makes the
model a good one. A high Ri-squared specifies that the
terms are correlated with each other; and this could
possibly lead to poor models. In this design model, the
minimum, average and maximum variance mean are
0.159, 0.193 and 0.588, respectively. The average
leverage for the 30 runs in the experiment is 0.5333.
3 RESULTS AND DISCUSSION
3.1 Analyses of the responses on the volume of the
deposited composites within the CCD
The results of the responses are numerically analyzed
after the design evaluation. The resulting values of the
VDC were input, based on the output from the number of
runs within the design configurations. The design experts
offer a full array of response transformation. The res-
ponses of the VDC range from the minimum value 69.38
mm3 and the maximum value 120.29 mm3. The ratio
between the maximum and the minimum values is 1.73.
This obtained ratio is less than 3; and the power trans-
formation would consequently have little effect.
In the analysis of the results, a model for the fit
summary is suggested. The Sequential Model is formed
with the combination of the source, sum of squares,
degree of freedom (df), mean square, F value and the
p-value. A small F value and a high p-value, which is
greater than 0.1, are good for the model. The lowest F
value is 0.14; and the highest p-value is 0.9634. These
two values fall within the quadratic versus 2 factors
interaction (2FI) of the Sequential Model.
However, the model may fit the design points at some
point; but it may not be a very good predictor at the other
points. Extra design points need to be added, to check
the model fit; and these should be beyond those for
determining the model coefficients. The variation bet-
ween the model prediction and the extra points can be
compared with the experimental or pure error, to test the
lack of fit. The experimental error, or the pure error, is
the normal variation within the response when there is a
replicate of the experiment. Only one experiment was
M. F. ERINOSHO, E. T. AKINLABI: CENTRAL COMPOSITE DESIGN ON THE VOLUME OF LASER METAL ...
422 Materiali in tehnologije / Materials and technology 51 (2017) 3, 419–426
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Table 3: Power at 5 % alpha level to detect the signal for various standard-deviation values
Tabela 3: Mo~ na 5 % vsebnosti alfa za zaznavanje signala pri razli~nih standardnih vrednostih odstopanj
Term Standard error VIF Ri-squared 0.5 Standarddeviation
1 Standard
deviation
2 Standard
deviation
Day 1 0.19 1.00 0.0000
Day 2
A 0.20 1.00 0.0000 20.8 % 62.5 % 99.5 %
B 0.20 1.00 0.0000 20.8 % 62.5 % 99.5 %
C 0.20 1.00 0.0000 20.8 % 62.5 % 99.5 %
D 0.20 1.00 0.0000 20.8 % 62.5 % 99.5 %
AB 0.25 1.00 0.0000 15.4 % 46.1 % 96.0 %
AC 0.25 1.00 0.0000 15.4 % 46.1 % 96.0 %
AD 0.25 1.00 0.0000 15.4 % 46.1 % 96.0 %
BC 0.25 1.00 0.0000 15.4 % 46.1 % 96.0 %
BD 0.25 1.00 0.0000 15.4 % 46.1 % 96.0 %
CD 0.25 1.00 0.0000 15.4 % 46.1 % 96.0 %
A^2 0.19 1.05 0.0476 68.3 % 99.8 % 99.9 %
B^2 0.19 1.05 0.0476 68.3 % 99.8 % 99.9 %
C^2 0.19 1.05 0.0476 68.3 % 99.8 % 99.9 %
D^2 0.19 1.05 0.0476 68.3 % 99.8 % 99.9 %
run in the design space; and the pure error is negligible;
since the value of the sum of the square and mean square
in the lack of fit test table is zero. The lack of fit tests
table compares the residual error with the pure error
from replicated design points. Since the pure error is
zero, the F value and the Prob > F were not revealed by
the model (Table 4). The model has an insignificant lack
of fit, which shows that it is a good predictor, and a
better forecaster of the responses; and this follows the
statistical and numerical output.
3.2 Analysis of variance results
The Analysis of Variance (ANOVA) is the statistical
approach that partitions the total variation of a dataset
into its component parts for the purpose of testing an
assumption on the parameters of the certain selected
model. The ANOVA is constructed totally on the basis
that the factors are fixed, and the design is crossed.
Table 4 depicts the ANOVA for the response surface
quadratic model used. The quadratic model is a poly-
nomial model containing the linear and two-factor terms.
The sources in the response surface quadratic model
include the block, the model, the factors, the residuals,
and the lack of fit.
Table 4: Analysis of variance for the response surface quadratic
model
Tabela 4: Analiza variance odziva povr{insko kvadratnega modela
Source Sum ofsquares Df
Mean
square F Value
p-value
Prob > F
Block 74.57 1 74.57
Model 7528.41 14 537.74 6.92 0.0004
A-Laser
power 4505.93 1 4505.93 58.01 < 0.0001
B-Scanning
speed 1554.46 1 1554.46 20.01 0.0005
C-Powder
flow rate 457.36 1 457.36 5.89 0.0293
D-Gas flow
rate 33.58 1 33.58 0.43 0.5215
AB 24.68 1 24.68 0.32 0.5819
AC 121.39 1 121.39 1.56 0.2317
AD 50.37 1 50.37 0.65 0.4341
BC 635.67 1 635.67 8.18 0.0126
BD 50.37 1 50.37 0.65 0.4341
CD 50.37 1 50.37 0.65 0.4341
A^2 12.76 1 12.76 0.16 0.6914
B^2 9.24 1 9.24 0.12 0.7352
C^2 5.60 1 5.60 0.072 0.7923
D^2 13.32 1 13.32 0.17 0.6851
Residual 1087.38 14 77.67
Lack of fit 1087.38 10 108.74
Pure error 0.000 4 0.000
Cor total 8690.36 29
From the source, the "F-value" of the Model is 6.92;
and this infers that the model is significant. There is only
a 0.04 % chance that an "F-value" this large could occur
due to noise. The values of "Prob > F" less than 0.0500
indicate that the model terms are significant. In other
words and as indicated, A, B, C and BC are the signi-
ficant model terms. Other values greater than 0.1000,
indicate that the model terms are not significant.
The values of the R-Squared and the adjusted
R-Squared are good; since there values are close to 1.
The "Predicted R-Squared" of 0.1082 is not as close to
the "Adjusted R-Squared" of 0.7476, as one might nor-
mally expect; and the difference is more than 0.2; and
this may indicate a large block effect. The "Adequate
Precision" measures the signal-to-noise ratio21 with a
value of 11.481, which is desirable for the model; since
its ratio is greater than 4. This model can be used to steer
and pilot the design space.
The final equation, in terms of the coded factors, is
given in the following iteration, as shown in Equation
(6):
Volume of Deposited Composites =
99.98+13.70*A-8.05*B+4.37*C-1.18*D-1.24*AB+2.75
*AC+1.77*AD-6.30*BC+1.77*BD-1.77*CB-0.68*A^2
+0.58B^2+0.45*C^2+0.70*D^2 (6)
Equation (6) in the iteration of coded factors can be
used to make predictions about the response for given
levels of each factor. The coded equation is useful for
identifying the relative impact of the factors by compar-
ing the factor coefficients.
3.3 Statistical analysis and the properties of the model
The diagnosis and the statistical properties of the
model are presented by normal probability plots. The
studentized residuals are used to validate the ANOVA.
The normal plot of residuals is a plot of normal percen-
tage probability against the residuals. The data points are
linear in the error term, which signifies no problems or
difficulties in the data obtained from the probability
distribution. Figure 3 shows the plot of percentage pro-
bability versus the externally studentized residual.
M. F. ERINOSHO, E. T. AKINLABI: CENTRAL COMPOSITE DESIGN ON THE VOLUME OF LASER METAL ...
Materiali in tehnologije / Materials and technology 51 (2017) 3, 419–426 423
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 3: Plot of percentage probability versus the externally stu-
dentized residual
Slika 3: Diagram odstotka verjetnosti v primerjavi z zunanje prou~e-
vanim ostankom
The plot shows the way the actual value deviates
from the predicted value. The Design-Expert puts control
limits on the externally studentized residuals plot, in
order to identify the abnormal runs easily. The externally
studentized residual test or outlier t test is applicable
when checking whether a run is consistent with the other
runs; and is based on the assumption that the chosen
model holds. The prediction of the responses at this point
is made. In this model, there is no outlier and the res-
ponses fit the model, since the value is not greater than
3.5. This can be seen from the residual plots.
Figure 4 represents the plot of residuals versus the
experimental run order.
This plot checks for lurking and unobserved variables
that may have influenced the response during the experi-
ment. The plot shows a random scatter with a line
connecting each point. A consistent trend indicates a
time-related variable lurking in the background of the
plot. Randomization and blocking provide protection and
indemnity for the trends, in order not to tarnish the
analysis. The trend from the first run to the thirtieth runs
falls between the upper and lower red lines. This proves
the assumptions to be established, and most of the green
points are found close to the zero point of the externally
studentized residuals.
Figure 5 portrays the surface plot of the VDC at
varying laser powers and scanning speeds, as well as a
constant powder flow rate of 2.45 min–1, and a gas flow
rate of 2.95053 L/min, respectively.
From the surface plot, it can be deduced that towards
the direction of the laser power, an upward tilt or
elevation of the surface plot was observed, as the laser
power increases. Their representations indicate that an
increase in the laser power leads to an increase in the
volume of the composites, as directed by the upward tilt
of the surface plot. The reverse is the case for the
scanning speed on the same surface plot. Towards the
path of the scanning speed, a downward tilt of the
surface plot was observed, which indicates that the
deposited volume decreases as the scanning speed in-
creases. This phenomenon of the decrease in the volume
with an increase in the scanning speed can be attributed
M. F. ERINOSHO, E. T. AKINLABI: CENTRAL COMPOSITE DESIGN ON THE VOLUME OF LASER METAL ...
424 Materiali in tehnologije / Materials and technology 51 (2017) 3, 419–426
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 6: a) Surface plot of the desirability at varying lasers power
and scanning speeds, b) surface plot of desirability with a standard
order of 21 and run order of 24
Slika 6: a) Za`eljena povr{ina pri razli~nih mo~eh laserja in hitrosti
skeniranja, b) za`eljena povr{ina z zahtevkom 21 in potekom 24
Figure 5: Surface plot of the volume of deposited composites at
varying laser powers between 1.2 kW and 1.6 kW, scanning speeds
between 0.3 m/min and 0.5 m/min
Slika 5: Povr{ina volumna nane{enih kompozitov pri razli~nih mo~eh
laserja med 1,2 kW in 1,6 kW, hitrost skeniranja med 0,3 m/min in 0,5
m/min
Figure 4: Plot of externally studentized residuals versus experimental
run order
Slika 4: Diagram zunanje prou~evanega ostanka v odvisnosti od
eksperimentalnega poteka
to the interaction time it takes the powders to be formed
on the surface of the substrate. In other words, the faster
the speed of the scan, the quicker the time of deposit, and
the smaller the deposited volume becomes, and vice
versa. For this plot, the powder flow rate and the gas
flow rate were kept constant.
The surface plot in Figures 6a and 6b shows a gra-
phical representation and the response optimization of
the normal desirability plot and the desirability with a
standard order of 21 and a run order of 24 at varying
laser powers between 1.2 kW and 1.6 kW, and with a
scanning speed between 0.3 m/min and 0.5 m/min.
The contours of the desirability shortened inwardly
as the laser power and the scanning speed decrease. This
occurrence improves the desirability of achieving the
optimal setting. The green and the faint red arcs drawn
on the yellow square surface give an indication of the
respective desirability. The desirability lies between the
laser power of 1.2 kW and 1.4 kW, and the scanning
speed lies between 0.3 m/min and 0.42 m/min. The 3D
surface plotted ridge and fold are where the desirability
can be maintained at a high level over a range of factor
levels. The solution is relatively robust to a laser power
between 1.6 kW and 1.8 kW, and also robust to the
scanning speed between 0.45 m/min and 0.6 m/min. The
robustness is indicated by the blue colour, and this shows
that the approach used is robust enough to create a small
alteration in the factor levels.6
3.4 Validation of the experiment
The experiment validation was established to verify
the variations between the predicted value by the soft-
ware and the actual value from the current experiment.
This is actually done to validate and confirm the reality
of the model. The actual results are almost twice the
results predicted by the software. Figure 7 presents the
plot of the actual value against the predicted value of the
volume of the deposited composites.
The plot is a linear regression curve with the indepen-
dent value of y = 6.954x – 465.89. The values of y repre-
sent the actual values resulting from the experiment
conducted on the selected parameters. The results
obtained were approximately two times the predicted
VDC. The laser system used for the trial runs and the
preliminary studies was different from the laser system
used to validate the results. The different laser-system
configurations has a strong effect on the result. Also, the
heights of the deposit undergoing validation have an
influence on the actual results, which in turn affects the
area of the segment and the volume of the composites.
4 CONCLUSION
This study discusses the application of RSM and
CCD for the modeling and optimization of the effect of
some operating variables on the volume of the deposited
composite (VDC). It was observed that the cladded
volume is directly proportional to the laser power and
inversely proportional to the scanning speed. The model
has an insignificant lack of fit, which shows that it is a
good predictor, and a better forecaster of the responses,
and this follows the statistical and numerical outputs.
The mathematical model equations were derived for both
the dependent variable (response) and the independent
variables (input factors) using design expert software 9.
The 3D response surface plots, which are simulations
from the models, were presented to describe the effect of
the process variables on the output volume. The F-value
of the model was 6.92, which inferred that the model is
significant. The value of the adjusted R-Square was
0.7476 and the adequate precision measures the
signal-to-noise ratio with a value of 11.481, which was
desirable for the model.
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