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Transcript of Utility 6
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ORIGINAL ARTICLE
Multi-response optimization of low-pressure cold-sprayed
coatings through Taguchi method and utility concept
Tarun Goyal & R. S. Walia & T. S. Sidhu
Received: 2 August 2011 /Accepted: 5 March 2012# Springer-Verlag London Limited 2012
Abstract Cold spray process is a relatively new coating
deposition thermal spray process, and a lot of research is being carried out throughout the world towards the optimi-
zation of the process with an aim towards the performance
improvement of the process. For optimization of process
paramete rs, most of the exis ting approache s for multi-
response optimization of process parameters focus upon
the subjective and practical knowledge available about the
process. Keeping in view these limitations, an approach
based on a utility theory and Taguchi quality loss function
has been applied to low-pressure cold spray process to
deposit copper coatings, for simultaneous optimization of
more than one response characteristics. In the present paper,
three potential response parameters, i.e., coating thickness,
coating density, and surface roughness have been selected.
Utility values based upon these response parameters have
been analyzed for optimization by using Taguchi approach.
Keywords Cold spray . Taguchi . Utility . Surface
roughness . Coating thickness . Coating density
Abbreviations
CS Cold sprayTQLF Taguchi quality loss function
LPCS Low-pressure cold spray
CT Coating thickness
CD Coating density
SR Surface roughness
RSM Response surface methodology
GDA Generalized distance approach
MSE Mean squared error
AFM Abrasive flow machining
MAFM Magnetically assisted abrasive flow machining
CFAAFM Centrifugal force-assisted abrasive flow
machining
DOF Degrees of freedom
OA Orthogonal array
ANOVA Analysis of variance
CI Confidence interval
CE Conformation experiment
1 Introduction and literature review
1.1 Multi-response optimization
In the modern competitive nonconventional manufacturing
scenario, it is most vital to optimize the parameters of a
process to exploit its full utility. Practically, it is seen that
one particular setting of input parameters for a response
characteristics may not be suitable for other characteristics
of the process/product. In most of the manufacturing pro-
cesses, more than one quality characteristic has to be con-
sidered for optimization of process parameters making it
necessary that several response characteristics have to
be simultaneously optimized. Therefore, in the situations
T. Goyal (*) : R. S. Walia
PEC University of Technology,
Sector-12,
Chandigarh, India 160012e-mail: [email protected]
T. Goyal
e-mail: [email protected]
R. S. Walia
e-mail: [email protected]
T. S. Sidhu
SBSCET,
Ferozepur, Punjab, India 152004
e-mail: [email protected]
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DOI 10.1007/s00170-012-4049-8
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involving many measurable response characteristics of a
product/p rocess , an optimization strate gy is required
that can provide a unified criterion to represent the
overall optimal setting of process parameters with re-
spect to all the responses. These types of optimization
problems need to be handled by multi-response optimi-
zation techniques. In the past, the applications of Taguchi
method and RSM have been mainly dealt with single response problems [1 – 4], and only very few applications are reported
for multi-response optimization problems [5, 6].
In the graphical approach for multi-response optimization
[7, 8], a region is examined where the contours of responses
overlap and a condition is identified, which is reasonably
good for all the responses. However, for more than three
responses, this technique is not very successful. Dual re-
sponse approach [9] is applicable where both parametric
mean and variance are of importance. A primary response
function is optimized subject to the condition that a second-
ary response function assumes desirable values. Desirability
function approach was introduced by Harrington [10] andfurther applied by Derringer and Suich [11]. The individual
desirabilities are combined into a single function, which is a
measure of overall desirability of multi-response system.
This method seems to be more complex from computational
aspect than dual response approach method. Khuri and
Conlon [12] introduced GDA. In this approach, the devia-
tions from the ideal optimum are measured as a distance
function, and this function is minimized to get compromise
conditions favorable to all the responses. The advantage of
this approach is that it takes into account the correlations
among the responses and their individual variances. Lin
and Tu [13] used MSE as an objective function to be mini-
mized. Kim and Lin [14] used a fuzzy modeling approach in
which the simultaneous optimization of degree of satisfaction
with respect to both mean and the standard deviation is
achieved.
Although Taguchi's robust design concept has been ex-
tensively studied for the purpose of optimizing process
parameters in most of the industrial processes, the investi-
gations have mainly focused on the optimization of process
parameters in context to a single quality criterion, which is
most critical. In other approach, Byrne and Taguchi [15]
quality characteristics were individually optimized and then
the results were computed subjectively to select the best
levels. Logothetis and Haigh [16] employed multiple regres-
sions and a linear programming approach for multi-response
optimization of five responses by the Taguchi method.
Phadke [17] presented a case of products with multiple
responses such as surface defects and thickness in the ex-
ample of polysilicon deposition. In this approach, pure
engineering judgment and practical experience have been
used for obtaining optimization. Shiau [18] solved the multi-
response problem by assigning the weights to signal-to-noise
(S/N) ratio of each quality characteristic and then summing up
the weighted S/N ratios for the measurement of overall per-
formance of a process. Tai et al. [19] employed empirical loss
functions for a multi-response problem involving six param-
eters and nine responses for the surface mount process. A
single response was obtained by combining the quality loss
of each response. In this approach, the empirical loss functions
for the process under study have to be studied in advance.Tong and Su [6] proposed a procedure to determine multi-
response S/N ratio through the integration of the quality loss
for all the responses, but they pointed out that the calculation
of weight ratio for the responses was difficult. They suggested
the application of fuzzy set theory for the introduction of fuzzy
data (related to weight) for multi-response optimization prob-
lems. Antony [5] introduced the application of principal com-
ponent analysis (PCA) and presented a case of multi-response
optimization of submerged arc-welding process parameters.
PCA seems to be a symmetric as well as practical approach for
Taguchi-based optimization. This is a data reduction tech-
nique used to identify a small set of quality characteristicsinto a linear combination of uncorrelated components. The
reason why the design of experiments is selected rather than
the other approaches to conduct experiment is that it has a
systematic planning of experiments, provides robustness and
immune to uncontrollable factors in the manufacturing state,
and helps to reduce the large number of experimental trials
when the number of process parameters increases.
The traditional Taguchi method is widely used for opti-
mizing the process parameters of a single response problem.
Optimization of a single response results in non-optimum
values for remaining responses. But, the performance of the
manufactured products is often evaluated by several quality
characteristics/responses. Keeping in mind that traditional
Taguchi approach fails to solve a multi-response optimiza-
tion problem, utility concept has been coupled with the
Taguchi method in the present investigation to overcome
this shortcoming. Thus, using the utility theory, the multi-
objective optimization problem has been converted into an
equivalent single objective optimization situation in which
overall utility degree serves as the representative single
objective function for optimization which has been solved
by Taguchi method. While deriving this equivalent objective
function, different priority weightages are assigned to dif-
ferent responses, according to their relative importance. But,
there is no specific guideline available for assigning these
response weightage. It entirely depends on the decision
maker (individual's perception or human judgment). That
is why the present study assumes equal priority weightage to
all the responses.
It is the statistical measure of performance proposed by
the ratio of the mean (signal) to the standard deviation
(noise). The ratio depends on the quality characteristics of
the product/process to be optimized. The optimal setting is
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the parameter combination, which has the highest S/N ratio.
Based on the S/N analysis, the S/N ratio for each level of
process parameters is computed. Larger S/N ratio corre-
sponds to better performance characteristics, regardless of
their category of performance. It means that the level of
process parameters with the highest S/N ratio corresponds to
the optimum level of process parameters. In addition to S/N
ratio, analysis of variance (ANOVA) is used to indicate theinfluence of process parameters on performance measures.
Finally, a confirmatory experiment is conducted to verify the
optimal processing parameters obtained from the parameter
design.
Some of the researchers have efficiently utilized the
Taguchi method and utility concept for multi-response op-
timization for various processes. Similar approach was fol-
lowed by Singh [20] for the optimization of the quality
characteristics of MAFM process. Walia [21] used Taguchi
method and utility concept for multi-response optimization
in CFAAFM. As low-pressure cold spray (LPCS) is com-
paratively a newer coating tec hnique, optimi zation of parameters is a promising area, presented in the present
paper.
1.2 Low-pressure cold spray process
The basic principle of the LPCS process is to use the kinetic
energy of the spray particles, after they are carried away by a
stream of carrier gas through supersonic nozzle to achieve
supersonic velocities at the exit of the nozzle. The high-
kinetic energy of the carried away particles is used as the
basis to form the coating upon impact to stationary substrate
in this category of thermal spray coating deposition tech-
nique. As the deposition is achieved by kinetic energy rather
than thermal energy of the spray particles, a number of
temperature induced deleterious effects such as oxidation,
evaporation, melting, crystallization, residual stresses, debond-
ing, gas release, phase transformation, etc. are avoided/elimi-
nated [22]. Cold spray (CS) process has been frequently used
to deposit temperature-sensitive material such as nano-
crystalline and amorphous materials [23, 24] and oxygen-
sensitive materials such as aluminum and titanium. Bonding
in CS process is achieved by means of disruption of thin
surface films such as oxides from the surface-exposing active
material. This active material is brought into intimate contact
under high localized pressure, caused by fast moving particles
undergoing adiabatic shear instability leading to formation of
strong atomic bonds [25].
The author in previous papers [26] has shown improve-
ment in process efficiency of abrasive flow machining(AFM) when centrifugal force was applied on the abrasive
media while it abrades the workpiece. The present paper
reports the effect of process parameters of LPCS process
for deposition of copper coatings using multi-response
optimization technique. The schematic diagram of the
LPCS process is shown in Fig. 1 [27]. Cold gas dynamic
spray (or simply cold spray) is a process of applying
coatings, by exposing a metallic or dielectric substrate to
a high-velocity (300 – 1,200 m/s) jet of small (1 – 50 μ m)
particles, accelerated by a supersonic jet of compressed
gas. Unlike the other thermal spray processes, cold spray
operates with little or no heat. It is a solid state processwhere relatively cold particles are sprayed on cold substrates,
therefore named cold spray.
2 Experimental procedure
2.1 Process/response parameters of LPCS process
In order to obtain low porosity, high density, and better
quality of surface coatings produced by LPCS process, the
optimal level of LPCS parameters needs to be determined.
Based on the critical review of literature, process variables
of the LPCS were grouped in the following five categories:
& Powder characteristics: density of particles, powder
flow rate, grain size, crystal structure, shape morpholo-
gy, size distribution, plastic strain, drag coefficient, ulti-
mate strength, heat transfer coefficient, and thermal
conductivity
& Substrate properties: number of passes, contact temper-
ature, substrate roughness, substrate thickness, travel
Fig. 1 Operating principle
scheme of low-pressure coldspray process
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speed, stand-off distance, thermal conductivity, electrical
resistance, and Young's modulus
& Gas properties: nature of gas, gas constant, gas flow
rate, stagnation temperature, stagnation pressure, and
specific heat index
& Nozzle parameters: jet pressure ratio, aspect ratio, nozzle
mach no., expansion ratio, total nozzle length, and nozzle
throat diameter & Impact parameters: impact duration, impact angle, impact
speed, and impact pressure
An Ishikawa cause-and-effect diagram, illustrating the
possible process parameters affecting the coating quality,
has been developed and is shown in Fig. 2. Table 1 shows
the process parameters that were identified as potentially
important in affecting the quality characteristics of the LPCS
process under consideration [28 – 30]. The process parame-
ters, their designated symbols, and ranges are also given in
Table 1. The Taguchi's mixed level design was selected as it was decided to keep two levels of powder feeding arrange-
ment. The rest four parameters were studied at three levels.
The selection of levels was made in regard to literature
review and the possibility of parameter level variation with
the available cold spray setup. Two-level parameter has 1
degree of freedom (DOF), and four 3-level parameters have
8 DOF, i.e., the total DOF required will be 9 [ 01×1+(4×
2)]. As the DOF of scheme of experiments, i.e., 9, is less
than the DOF of L18 orthogonal array (OA), the most
appropriate orthogonal array in this case is L18 (21 ×37)
OA with 17 [018−1] DOF. Standard L18 OA with the
parameters assigned by using linear graphs was used. The
unassigned columns will be treated as error. Every trial
experiment was replicated three times.
The effect of selected process parameters was studied on
the following response characteristics of LPCS process:
1. Coating thickness (CT)
2. Coating density (CD)3. Surface roughness (SR)
Coating thickness and coating density are “higher the
better ” type of quality characteristic, whereas surface rough-
ness is “smaller the better ” type. The observed values of
response parameters are given in Table 2.
2.2 Measurement/determination of response parameters
The coating thickness was measured for the samples with
the help of a digital micrometer (Mitutoyo, Japan), make for
an accuracy of 0.0001 in. The density of coatings, so pro-
duced, was calculated by noting down the weight of thesubstrate material in the unsprayed condition, weight of the
as-sprayed specimens, and the thickness of the obtained
coatings. The coating density may be given as
Coating density
¼weightof sprayed specimen À weightof uncoated specimenð Þ
volume of sprayed coating:
The weights of as-sprayed specimen and uncoated speci-
mens were measured using a digital weighing balance. The
volume of the sprayed coating is calculated by multiplying
Substrate CharacteristicsPowder Characteristics
Gas Properties Nozzle Impact Parameters
COLD
SPRAY
PROCESS
Density of particles
Powder flow rate
Grain size
Crystal structure
Shape morphology
Size distribution
Plastic strain
Drag coefficient
Ultimate strength
Heat transfer coefficent
Thermal conductivity
Stand off distance
Thermal conductivity
Electrical resistance
Substrate roughness
Powder flow rate
Travel speed
Substrate thickness
Contact temperature
No. of passes
Nature of carrier gas
Stagnation pressure
Stagnation temperature
Gas
Constant
Gas flow rate
Specific
heat
index
Jet Pressure
ratio
Impact AngleExpansion ratio
Aspect ratio
Total length
Throat
diameter
Impact pressure
Impact duration
Impact speed
Mach No.
Fig. 2 Ishikawa cause-and-effect (fish bone) diagram
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the area of the coated cross-section of the specimen with the
coating thickness obtained for the individual specimens. The
coating thickness was measured for the samples with the
help of a digital micrometer (Mitutoya, Japan), make for an
accuracy of 0.0001 in. The surface roughness was measured
from the samples with the help of a surface roughness tester
(Mitutoyo, Japan make, model SJ 400 for a resolution of
0.000125 μ m and maximum measuring range of 800 μ m).
2.3 Multi-response optimization through utility concept
and Taguchi method of LPCS process
A product or a process is normally evaluated on the basis of
certain number of quality characteristics, sometimes conflicting
in nature. Therefore, a combined measure is necessary to gauge
its overall performance, which must take into account the
relative contribution of all the quality characteristics. In the
following, a methodology based upon the utility concept and
Taguchi method is developed for determining the optimal
settings of process or parameters for multi-response/multi-char-
acteristics process or product. The multi-response optimization
of quality characteristic of LPCS has been carried out by using
this methodology in this section.
2.3.1 Utility concept
Utility can be defined as the usefulness of a product or a
process in reference to the expectations of the users. The
overall usefulness of a process/product can be represented by a unified index termed as utility which is the sum of the
individual utilities of various quality characteristics of the
process/product. The methodological basis for the utility
approach is to transform the estimated response of each
quality characteristic into a common index.
If X i is the measure of effectiveness of an attribute (or
quality characteristic), i and there are n attributes evaluating
Table 1 Process parameters and
their range
Nozzle type, converging –
diverging; carrier gas, air;
powder size, <45 μ m
Symbol Process parameter Range Level 1 Level 2 Level 3
A Feed type Gravity, argon Gravity Argon –
B Substrate material Al alloy, brass, Ni alloy Al alloy Brass Ni alloy
C Stagnation pressure 104 – 120 psi 104 112 120
D Stagnation temperature 350 – 400°C 350 375 400
E Stand-off distance 2.5 – 7.5 mm 2.5 5.0 7.5
Table 2 Experimental results of various response characteristics
Exp
no.
Coating thickness (mil), CT S/N ratio
(dB)
Coating density (kg/m3
), CD S/N ratio
(dB)
Surface roughness (μ m), SR S/N ratio
(dB)
R1 R2 R3 R1 R2 R3 R1 R2 R3
1 28 26.2 30.4 28.95 4,654.4 4,623.6 4,593.2 73.29 13.56 13.71 13.83 −22.73
2 52 51.5 52.2 34.30 3,128.5 3,157.9 3,116.9 69.92 10.87 10.91 10.36 −20.60
3 74.5 74.2 74.7 37.43 5,012.1 5,034.4 4,997.4 74.00 8.05 7.81 7.73 −17.91
4 58.4 58.2 58.7 35.33 4,638.1 4,654.1 4,614.4 73.32 9.2 10.04 10.68 −19.99
5 44.7 44.1 45.4 33.01 6,229.5 6,169.3 6,125.0 75.81 8.17 8.02 10.23 −18.95
6 25.8 24.3 25.5 28.01 9,016.9 8,992.2 9,021.0 79.09 8.7 7.5 8.6 −18.36
7 14.7 11.2 14.6 22.39 27,354.5 27,106.4 27,500.7 88.72 11.17 11.22 11.56 −21.07
8 55.1 55.6 55.5 34.86 8,948.0 8,887.9 8,877.1 78.99 6.69 6.68 7.35 −16.79
9 53.9 54.5 54.3 34.68 9,440.4 9,442.0 9,474.6 79.51 6.89 6.97 7.02 −16.85
10 68.9 64.1 69.7 36.57 3,075.1 3,111.0 3,084.0 69.79 8.31 8.26 9.59 −18.83
11 38.6 38.2 38.7 31.70 3,259.0 3,211.9 3,245.9 70.20 9.24 9.6 9.52 −19.51
12 58.2 57.5 57.9 35.24 3,422.3 3,457.9 3,437.5 70.72 8.42 8.29 8.92−
18.63
13 43.2 43.3 43.6 32.74 5,273.6 5,261.5 5,225.3 74.40 9.04 9.78 9.62 −19.54
14 28.3 27.2 25.5 28.60 5,206.4 5,299.1 5,216.8 74.38 7.19 7.79 7.82 −17.62
15 64.8 65.4 64.6 36.24 2,741.4 2,758.3 2,749.8 68.78 6.18 6.97 6.39 −16.28
16 56.9 57.1 59.5 35.23 8,615.5 8,628.4 8,671.6 78.72 7.94 8.13 8.15 −18.14
17 57.9 56.2 56.7 35.10 5,796.5 5,874.8 5,818.7 75.31 7.19 8.62 7.34 −17.77
18 17.3 19.1 16.7 24.91 30,161.0 30,513.7 30,244.6 89.63 7.94 7.11 7.84 −17.66
Total 841.2 827.9 844.2 585.4 145,973.1 146,184.4 146,014.3 1,364.67 154.75 157.41 162.55 −337.23
T CT ¼ overall mean of CT ¼ 46:54 T CD ¼ overall meanof CD ¼ 8; 114:29 T SR ¼ overall meanof SR ¼ 8:79
R1, R2, and R3 represent repetitions
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the outcome space, then the joint utility function can be
expressed [31] as:
U X 1; X 2; ::: X nð Þ ¼ f U 1 X 1ð Þ; U 2 X 2ð Þ::::U n X nð Þð Þ ð1Þ
where U i ( X i) is the utility of the ith attribute.
The overall utility function is the sum of individual utilities
if the attributes are independent and is given as follows:
U X 1; X 2; ::: X nð Þ ¼Xn
i¼1
U i X ið Þ: ð2Þ
The attributes may be assigned with weights depending
upon the relative importance or priorities of the character-
istics. The overall utility function after assigning weights to
the attributes can be expressed as:
U X 1; X 2; ::: X nð Þ ¼Xn
i¼1
W iU i X ið Þ ð3Þ
where W i is the weight assigned to the attribute i; the sum of
the weights for all the attributes must be equal to 1.
Table 3 Optimal setting and
values of process parameters
(individual quality
characteristics optimization)
Response
characteristics
Optimal level of process
parameters
Significant process
parameters
Predicted optimal value of
quality characteristics
CT A2, B1, C3, D3, E2 A, B, C, D, E 72.36 mil
CD A1, B3, C3, D2, E1 A, B, C, D, E 27,584.59 kg/m3
SR A2, B3, C3, D3, E3 A, B, C, D, E 4.92 μ m
Determine optimal values of individual response characteristics using Taguchi
parameter design approach
Construct preference scales for each response characteristics using Equation 4
Assign the weight to various quality characteristics based upon the importance
and their use keeping in view that the total sum of weights is equal to 1
Determine Utility values corresponding to each trial condition of the experiment
using Equation 5
Use these values as a response of the trial conditions of the selected OA
Analyze the results using Taguchi method
Find the optimal settings of the process parameters for optimal Utility
Predict the values of response characteristics based upon the optimal significant
parameters determined by the previous step
Perform confirmation experiment at the optimal settings and compare predicted
optimal values of the response characteristics with experimental values
Fig. 3 Methodology for multi-
response optimization by utility
concept and Taguchi method
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2.3.2 Determination of utility value
A preference scale for each quality characteristic is con-
structed for determining its utility value. Two arbitrary nu-
merical values (preference number) 0 and 9 are assigned to
the just acceptable and the best value of the quality charac-
teristic, respectively. The preference number ( P i) can be
expressed on a logarithmic scale as follows [32, 33]:
P i ¼ A Â logX i
X 0
i
ð4Þ
where
X i value of any quality characteristic or attribute i
X 0
ijust acceptable value of quality characteristic or
attribute i
A constant
The value of A can be found by the condition that if X i0
X * (where X* is the optimal or best value, obtained from theconformation experiments run at optimal parameter settings
for the individual response characteristic given in Table 3),
then Pi09. Further details regarding the determination of X*
have been presented in the author's previous publications
[28 – 30]. Therefore, A ¼ 9log X
Ã
X 0i
:
The overall utility can be calculated as follows:
U ¼Xn
i¼1
W i P i ð5Þ
subject to the condition:Pni¼1
W i ¼ 1:
Among various quality characteristics type, viz., smaller
the better, higher the better, and nominal the better sug-
gested by Taguchi, the utility function would be higher the
better type. Therefore, if the utility function is maximized,
the quality characteristics considered for its evaluation will
automatically be optimized (maximized or minimized as the
case may be). The stepwise procedure for carrying out
Table 5 Average and main effects (raw data: CT, CD, and SR)
Process parameter
designation
Average utility
values
Main effects Difference
L1 L2 L3 L2 – L1 L3 – L2 (L3 – L2) –
(L2 – L1)
A 4.46 4.80 – 0.33 – 0.33
B 3.89 4.50 5.49 0.61 0.99 0.38
C 4.03 4.60 5.25 0.57 0.64 0.07
D 4.59 4.26 5.04 −0.34 0.78 1.12
E 3.83 4.91 5.15 1.08 0.24 −0.84
L1, L2, and L3 represent average values of raw data of corresponding
parameters at levels 1, 2, and 3, respectively. L2 – L1 is the average
main effect when the corresponding parameter changes from level 1 to
level 2. L3 – L2 is the average main effect when the corresponding
parameter changes from level 2 to level 3
A powder feed arrangement, B substrate material, C air stagnation
pressure, D air stagnation temperature, E stand-off distance
Table 6 Average S/N values and main effects (raw data: CT, CD, and SR)
Process parameter
designation
S/N average values Main
effects (dB)
Difference
L1 L2 L3 L2 – L1 L3 – L2 (L3 – L2) –
(L2 – L1)
A 12.58 13.45 – 0.87 – 0.87
B 11.46 13.00 14.59 1.53 1.58 0.05C 11.74 12.98 14.31 1.24 1.32 0.08
D 12.72 12.40 13.92 −0.31 1.51 1.82
E 11.29 13.63 14.12 2.34 0.48 −1.86
L1, L2, and L3 represent average values of S/N data of corresponding
parameters at levels 1, 2, and 3, respectively. L2 – L1 is the average
main effect when the corresponding parameter changes from level 1 to
level 2. L3 – L2 is the average main effect when the corresponding
parameter changes from level 2 to level 3
A powder feed arrangement, B substrate material, C air stagnation
pressure, D air stagnation temperature, E stand-off distance
Table 4 Calculated utility data based on responses CT, CD, and SR
Trial number Utility values S/N ratio (dB)
R1 R2 R3
1 2.28 2.14 2.34 07.03
2 3.39 3.38 3.53 10.70
3 5.43 5.52 5.55 14.80
4 4.56 4.31 4.13 12.71
5 4.86 4.87 4.21 13.28
6 4.28 4.60 4.29 12.83
7 3.70 3.24 2.99 10.29
8 6.23 6.24 5.96 15.76
9 6.18 6.16 6.14 15.79
10 4.59 4.50 4.20 12.90
11 3.43 3.29 3.35 10.5112 4.42 4.46 4.25 12.81
13 4.30 4.07 4.12 12.38
14 4.26 3.99 3.86 12.10
15 5.19 5.87 5.29 14.68
16 5.74 5.68 5.74 15.15
17 6.19 5.99 5.85 15.57
18 5.46 5.95 5.44 14.96
R1, R2, and R3 0 repetitions of experiments against each of the trial
conditions
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multi-response optimization with the utility concept and
Taguchi method is illustrated in a block diagram (Fig. 3).
3 Results and discussions
3.1 Multi-response optimization for LPCS response
parameters
Based upon the methodology developed in the previous
sections, following case has been considered to obtain the
optimal settings of the process parameters of LPCS for
predicting the optimal values of combined responses. All
the three quality characteristics, i.e., CT, CD, and SR, have
been included in utility response [28 – 30].
Taguchi L18 OA [34] has been adopted for conducting the
experiments. Powder feeding arrangement (A), substrate ma-
terial (B), air stagnation pressure (C), air stagnation tempera-
ture (D), and stand-off distance (E) were selected as input
parameters. Response parameters (quality characteristics) werecoating thickness, coating density, and surface roughness,
when they are optimized individually; the summary of results
is produced in Table 3. The following is thestepwise procedure
for transforming experimental data into utility data.
(i)
(ii)
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
12
12.2
12.4
12.6
12.8
13
13.2
13.4
13.6
(Argon)(Gravity)
U t i l i t y ( c t g . t h
i c k n e s s , d e n s i t y , s u r f a c e r o u g h n e s s )
S /
N r
a t i o
Powder feeding arrangement
S/N ratio
Utility
3.50
4.00
4.50
5.00
5.50
6.00
10.5
11
11.5
12
12.5
13
13.5
14
14.5
15
(B36) (B435)(B221)
U t i l l i t y ( c t g . t
h i c k n e
s s , d e n s i t y , s u r f a c e r o u g h n e s s )
S / N r
a t i o
Substrate material (ASTM No.)
S/N ratio
Utility
(iv)3.80
4.00
4.20
4.40
4.60
4.80
5.00
5.20
11.5
12
12.5
13
13.5
14
14.5
350 375 400
U t i l i t y ( c t g . t h
i c k n e s s , d e
n s i t y , s u r f a c e r o u g h n e s s )
S / N
r a t i o
Air temperature (0C)
S/N ratio
Utility
(iii)
3.50
3.70
3.90
4.10
4.30
4.50
4.70
4.90
5.10
5.30
5.50
11
11.5
12
12.5
13
13.5
14
14.5
104 112 120
U t i l i t y ( c t g . t
h i c k n
e s s , d e n s i t y , s u r f a c e r o u g h n e s s )
S / N r
a t i o
Air pressure (psi)
S/N ratio
Utility
(v)
(vi)
3.00
3.50
4.00
4.50
5.00
5.50
10
10.5
11
11.5
12
12.5
13
13.5
14
14.5
2.5 5 7.5
U t i l i t y ( c t g . t h
i c k n e s s , d e n s i t y , s u r f a c e r o u g h n e s s )
S / N r
a t i o
Stand-off distance (mm)
S/N ratio
Utility
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
9
10
11
12
13
14
15
16
0 36 72
U t i l i t y ( c t g . t h i c k n e s s , d e n s i t y , s u r f a c e r o u g h n e s s )
S / N r
a t i o
Interaction b/w powder feeding arrangement and substratematerial
S/N ratio (A1)
S/N ratio (A2)
Utility (A1)
Utility (A2)
Fig. 4 i Effect of powder feeding arrangement on utility value (U CT,
CD, SR ) and S/N ratio (main effects). ii Effect of substrate material on
utility value (U CT, CD, SR ) and S/N ratio (main effects). iii Effect of air
stagnation pressure on utility value (U CT, CD, SR ) and S/N ratio (main
effects). iv Effect of air stagnation temperature on utility value (U CT,
CD, SR ) and S/N ratio (main effects). v Effect of stand-off distance on
utility value (U CT, CD, SR ) and S/N ratio (main effects). vi Interaction
between powder feeding arrangement and substrate material in terms
of utility value (U CT, CD, SR ) and S/N ratio (main effects)
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3.1.1 Construction of preference scales
1. Preference scale for CT ( P CT):
X* Optimal value of CT072.36 (refer to Table 3)
X 0
iJust acceptable value of CT011 (all the observed
values of CT are greater than 11)
The following equation is obtained from Eq. 4:
P CT ¼ 11:00 Â logX CT
11
ð6Þ
2. Preference scale for CD ( P CD):
X* Optimal value of CD027,584.59 (refer to Table 3)
X 0
iJust acceptable value of CD02,700 (all the observed
values of CD are greater than 2,700)
The following equation is obtained from Eq. 4:
P CD ¼ 8:91 Â logX
CD2; 700
ð7Þ
3. Preference scale for SR ( P SR ):
X* Optimal value of SR 04.92 (refer to Table 3)
X 0
iJust acceptable value of SR 014 (all the observed
values of SR are lesser than 14)
The following equation is obtained from Eq. 4:
P SR ¼ À19:81 Â logX SR
14
ð8Þ
3.1.2 Calculation of utility value
It is known that LPCS is thermal spray coating deposition
process and the higher thickness and density of the coating
are required so as to enable the coating to prevent interaction
of the bulk phase with environmental degradation. Similar-
ly, surface roughness of the coating is expected to be min-
imum so as to have a smooth surface finish. Equal weights
(one third each) have been assigned to the selected quality
characteristics assuming all the quality characteristics are
equally important. However, these weights can be varied
depending upon the case or user requirements, if any.
The following relation was used to calculate the utilityfunction based upon the experimental trials:
U n; r ð Þ ¼ P CT n; r ð Þ Â W CT þ P CD n; r ð Þ Â W CD þ P SR n; r ð Þ Â W SR
ð9Þ
where W CT, W CD, and W SR are the weights assigned to the
attributes (coating thickness, coating density, and surface
roughness) respectively. In this case,
W CT ¼ 13
; W CD ¼ 13
; W SR ¼ 13
n is the trial number (n01, 2, 3,…, 18) and r is the repetition
number (r 01, 2, 3). The calculated utility values are shown
in Table 4.
3.1.3 Analysis of utility data for optimal setting of process
parameters
The average and main response in terms of utility values
and S/N ratio (Tables 5 and 6) are plotted in Fig. 4. It
can be observed from Fig. 4(i – v) that the second level of
powder feed arrangement (A2), third level of substrate
material (B3), third level of air stagnation pressure (C3),
third level of air stagnation temperature (D3), and third
level stand-off distance (E3) are expected to yield max-
imum values of the utility and S/N ratio within the
experimental space.The pooled version of ANOVA for utility data and S/N
ratio are given in Tables 7 and 8, respectively. It can be
noticed from Table 7 that all the input parameters have
significant effect (at 95% confidence level) on the utility
function. Similarly, it had been found from Table 8 that all
the chosen parameters in the study have a significant effect
Table 7 Pooled ANOVA (raw data: CT, CD, and SR)
Source SS DOF V F ratio SS′ P %
A 1.491 1 1.491 5.059a 1.196 1.819
B 23.586 2 11.793 40.009a 22.997 34.968
C 13.277 2 6.638 5.059a 12.687 19.292
D 5.502 2 2.751 9.334a 4.913 7.471
E 8.936 2 4.468 15.158a 8.347 12.692
E (pooled) 12.969 44 0.294 – 15.622 24.651
Total (T ) 65.764 53 – – 65.764 100
a Significant at 95% confidence level
SS sum of squares, DOF degree of freedom, V variance, SS ′ pure sum
of squares
Table 8 S/N pooled ANOVA (raw data: CT, CD, and SR)
Source SS DOF V F ratio SS′ P %
A 3.43 1 3.43 6.01a
2.86 3.09B 29.37 2 14.68 25.72a 28.23 30.54
C 19.82 2 9.91 17.35a 18.67 20.20
D 7.71 2 3.85 6.75a 6.57 7.11
E 27.52 2 13.76 24.10a 26.38 28.54
E (pooled) 4.56 8 0.57 – 9.70 10.50
Total (T ) 92.44 17 – – 92.44 100
a Significant at 95% confidence level
SS sum of squares, DOF degree of freedom, V variance, SS ′ pure sum
of squares
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on the S/N ratio of utility function. The optimal values of
utility and thus the optimal values of response characteristics
in consideration are predicted at the above levels of significant
parameters.
3.1.4 Optimal values of quality characteristics (predicted
means)
The average values of all the response characteristics at
the optimum levels of significant parameters with re-
spect to utility function are recorded in Table 9. The
optimal values of the predicted means (μ) of different
response characteristics can be obtained from the following
equation:
μ ¼ A2 þ B3 þ C3 þ D3 þ E3 À 4T ð10Þ
where, A2 — second level of powder feed arrangement, B3 —
third level of substrate material, C3 — third level of air stagna-
tion pressure, D3 — third level of air stagnation temperature,and E3 — third level of stand-off distance.
The 95 % confidence interval of confirmation experi-
ments (CICE) can be computed [34] by using the following
equation:
CICE ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F a 1; f eð ÞV e
1
neff
þ1
R
s ð11Þ
where F α
(1, f e) 0 the F ratio at the confidence level of
(1−α ) against DOF 1 and error degree of freedom f e, R 0
sample size for conformation experiments, V e 0 error variance,
neff ¼ N
1þDOF, N 0 total number of trials, and DOF 0 total
degrees of freedom associated in the estimate of mean
response.
1. For CT:
μCT ¼ A2 þ B3 þ C3 þ D3 þ E3 À 4T CT ¼ 61:40
where A2047.97, B3042.60, C3049.07, D3051.24,and E3056.68 (Table 9):
T CT046.54 (Table 2).
The following values have been obtained by the
ANOVA:
N ¼ 54; f e ¼ 44; v e ¼ 2:00; neff ¼ 5:4;
R ¼ 3; F 0:05 1; 44ð Þ ¼ 4:064:
From Eq. 11, CICE0±2.05.
The predicted optimal range (for conformation
runs of three experiments) for CT is given by CICE:
59.35<μCT<63.45.
2. For CD
μCD ¼ A2 þ B3 þ C3 þ D3 þ E3 À 4T CD ¼ 12; 597:68
where A207,531.91, B3015,075.3, C309,995.41,
D306,649.71, and E305,802.51 (Table 9):
T CD08,114.29 (Table 2).
The following values have been obtained by the
ANOVA:
N ¼ 54; f e ¼ 44; v e ¼ 4; 349; 657:9; neff ¼ 5:4;
R ¼ 3; F 0:05 1; 44ð Þ ¼ 4:064:
From Eq. 11, CICE0±3,027.51.
The predicted optimal range (for conformation
runs of three experiments) for CD is given by CICE:
9,570.17<μCD <15,625.19.
3. For SR
μSR ¼ A2 þ B3 þ C3 þ D3 þ E3 À 4T SR ¼ 4:925
Table 9 Average values of various responses at optimal levels
Levels Coating thickness,
CT (mil)
Coating density,
CD (kg/m3)
Surface roughness,
SR (μ m)
A2 47.97 7,531.91 8.192
B3 42.60 15,075.35 8.101
C3 49.07 9,995.41 7.629
D3 51.24 6,649.71 7.905
E3 56.88 5,802.51 8.258
The above average values are taken from experimental data
Table 10 Observed values of
quality characteristics
(confirmation experiment)
Exp. no. CT CD SR
r 1 r 2 r 3 r 1 r 2 r 3 r 1 r 2 r 3
1 59.64 60.43 60.75 9,865.64 11,816.67 12,758.48 4.90 4.91 4.94
2 59.85 61.68 62.17 13,478.63 14,568.96 12,943.21 4.89 4.92 4.95
3 60.29 63.16 62.92 9,985.37 14,643.69 13,798.52 4.93 4.90 4.94
Overall average 61.21 12,651.02 4.92
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where A208.192, B308.101, C307.629, D307.905,
and E308.258, (Table 9):
T SR 08.79 (Table 2).
The following values have been obtained by the
ANOVA:
N ¼ 54; f e ¼ 44; v e ¼ 0:000387079; neff ¼ 5:4;
R ¼ 3; F 0:05 1; 44ð Þ ¼ 4:064:
From Eq. 11, CICE0±0.02856.
The predicted optimal range (for conformation
runs of three experiments) for SR is given by CICE:
4.89644<μSR <4.95356.
3.1.5 Confirmation experiment
For confirmation of experimental results, three experi-
ments were performed at optimal settings as suggested
by Taguchi analysis of utility data. The observed values
of various response characteristics have been given in
Table 10. It can be noticed that overall average of the
observed values of the response characteristics fall well
within the 95% CICE of the optimal range of the respective
response characteristics.
4 Conclusions
A simplified model based on the Taguchi method and utility
concept was used to analyze the multi-response optimiza-
tion of low-pressure cold spray process. Following conclu-
sions can be drawn from this study:
& All the input parameters significantly improve the utility
function and S/N ratio comprising three quality charac-
teristics (coating thickness, coating density, and surface
roughness).
& The decreasing order of percentage contribution of the
parameters to achieve a higher value of utility function
is: substrate material (34.96%), air stagnation pressure
(19.29%), stand-off distance (12.69%), air stagnation
temperature (7.47%), and powder feeding arrangement
(1.81%).
&The optimum levels of parameters for maximum utilityvalue have been obtained as second level of powder
feeding arrangement (A2), third level of substrate mate-
rial (B3), third level of air stagnation pressure (C3), third
level of air stagnation temperature (D3), and third level
of stand-off distance (E3).
& The predicted optimal range (for conformation runs of
three experiments) at 95% confidence interval for the
evaluated responses is given by:
CICE: 59.35<μCT<63.45
CICE: 9,570.17<μCD<15,625.19
CICE: 4.89644<μSR <4.95356
& The average of observed values of responses, i.e., coating
thickness, coating density, and surface roughness are
61.21 mil, 12,651.02 kg/m3, and 4.92 μ m, respectively,
as obtained from the confirmation experiments at the
optimum levels of the utility function. These values fallwell within the predicted optimal range at 95% confidence
interval of confirmation experiments for the responses.
& In this paper, three responses have been assigned equal
priority weights of one third each. This may be extended
for any number of responses and different priority weight-
age may assigned to different responses, according to their
relative importance keeping the total assigned weight to
all the responses as 1.
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