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


T. S. Sidhu

SBSCET,

Ferozepur, Punjab, India 152004


Int J Adv Manuf Technol

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


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


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)


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)


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


7/29/2019 Utility 6


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).


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.


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


7/29/2019 Utility 6


where A208.192, B308.101, C307.629, D307.905,

and E308.258, (Table 9):

T SR 08.79 (Table 2).


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.


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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Utility 6

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