*Corr. Author’s Address: Kano University of Science and Technology/Near East University, Wudil. Kano/Nicosia, Nigeria/Cyprus, musaibrahim@kustwudil.edu.ng 359
Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 359-367 Received for review: 2021-11-11
© 2022 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2022-03-14
DOI:10.5545/sv-jme.2021.7466 Original Scientific Paper Accepted for publication: 2022-03-28
Multi-Response Optimization of the Tribological Behaviour  
of PTFE-Based Composites via Taguchi Grey Relational Analysis 
Ibrahim, M.A. – Çamur, H. – Savaş, M.A. – Sabo, A.K.
Musa Alhaji Ibrahim
1, 2,*
 – Hüseyin Çamur
2 
– Mahmut A. Savaş
2
 – Alhassan Kawu Sabo
3
1 
Kano University of Science and Technology, Faculty of Engineering, Nigeria 
2 
Near East University, Faculty of Engineering, Cyprus 
3 
Kano University of Science and Technology, Physical Planning and Development Unit, Nigeria
Polymer-based composites find applications in several areas because of their exceptional properties. This article deals with Taguchi grey 
relational optimization method of abrasive parameters (load (L), grit size (G) and sliding distance (D)) and their influence on abrasive 
performance of reinforced polytetrafluoroethylene (PTFE) composites. A Taguchi L
9
 orthogonal array was designed, and nine experimental 
tests were conducted based on the Taguchi designed experiments. A pin-on-disc tribology machine was used for the experiments. The 
coefficient of friction (µ) and abrasive specific wear rate (A
w
) were recorded for each experiment. An analysis of variance (ANOVA) was 
performed to establish the significance and percentage contribution of each parameter affecting the abrasive wear performance. Results 
from the Taguchi-grey-relational method showed that the optimal combination of parameters was achieved at load of 10 N, grit size of 1000 
mesh, and sliding distance of 350 m (coded as L3G1D3). ANOVA findings revealed that a grit size with 67.69 % as the most influential on 
the abrasive performance of polymer-based composites. Validation tests performed using the optimal combination parameter showed an 
enhancement of 55.22 % in grey relational grade.
Keywords: PTFE, carbon fibre, bronze fibre, abrasive, Taguchi, grey relational analysis
Highlights
• 	 Optimization of abrasive tribological performance of PTFE based composites has been performed. 
• 	 Influence of load, grit size and sliding distance on coefficient of friction (µ) and specific abrasive wear rate (Aw) were studied. 
• 	 Optimization of multiple responses of µ and Aw via Taguchi-grey relational method is presented. 
• 	 Analysis of variance performed to find the most significant parameter on Taguchi grey relational grade.
• 	 Optimal parameters found to be load and sliding distance at their third levels while grit size at its first level.
• 	 According to the order of significance and percentage, the contribution on and to grey relational grades in abrasive performance 
is enumerated as grit size, load, and sliding distance.
0  INTRODUCTION
Polymer matrix composites (PMCs) are used in the 
automotive and aerospace sectors because of their 
high strength and stiffness [1]. Polytetrafluoroethylene 
(PTFE) is a commonly used matrix due to its 
antifriction property, water and chemical resistance, 
thermal stability, and low cost [2] to [4]. However, 
PTFE shows poor wear properties. It is reinforced 
with fibres including glass, carbon, aramid and bronze 
fibres to improve the wear properties [5]. PTFE and 
its composites are exposed to abrasive action and used 
in highly abrasive environments. The wear rate and 
coefficient of friction (µ) of PMCs are not inherent 
material properties and strongly rely on the system 
where the system will operate [6] and [7]. 
Experimental studies showed that reinforcing 
matrices with fibres improve their wear rate. Suresha 
and Kumar [8] reinforced PA66/PP with nano-clay and 
short carbon fibres. Improvement in wear rate of the 
P66/PP matrix was observed. In their study of abrasive 
property of different polymers, Shipway and Ngao [9] 
showed that polymers exhibited different behaviours 
and concluded that the abrasive wear of polymer 
depends on the type of the polymer. Ravi Kumar et 
al. [10] studied the abrasive wear rate of glass and 
carbon fabric reinforced vinyl/ester composites. The 
results showed that vinyl/ester reinforced with carbon 
had lower abrasion compared to glass reinforced 
vinyl/ester composite and that increasing the distance 
decreased the abrasion. Liu et al. [11] studied abrasive 
performance of a filled UHMWPE matrix and found 
that the applied load was most significant process 
variable. Yousif et al. [12] studied the abrasion 
resistance of betelnut-filled epoxy composite. It was 
revealed that rougher particles and high velocity 
generated high µ and wear rate, respectively. Harsha 
and Tewari [13] studied the influence of glass fibre at 
different loadings, sliding distance, load, and grit size 
on polysulfone. The results revealed a deterioration in 
abrasive performance of the polysulfone. Moreover, 
decreasing and increasing trends of tribological 
behaviour were observed due to varying load, 
distance, speed and grit size. 
The single response optimization Taguchi method 
has been used for the tribological performance of 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 359-367
360 Ibrahim,	M.A .	–	Çamur ,	H.	–	Sa v aş,	M.A .	–	Sabo ,	A .K.
PMCs. Thakur and Chauchan [14] studied the wear 
and friction behaviour of submicron size cenosphere 
particle-reinforced vinyl ester composites using 
Taguchi L
27
. Load, roughness, filler size, speed, and 
distance (each at three levels) were considered as 
parameters controlling the tribological behaviour 
of the vinyl ester composite. Different optimal 
combinations of parameters for desired µ and A
w
 were 
found for the two responses. ANOV A showed that 
load at 68.33 % and 63.89 % was the most significant 
factor controlling the µ and A
w
. Pogosian, Cho, and 
Bahadur [15] used the Taguchi method to optimize 
polyphenylene sulphide reinforced with MoS
2
, 
Al
2
O
3 
particles. The optimal Taguchi combination 
of parameters was found to be PPS+17 % V ol. MoS
2
 
+10 % V ol. PTFE, speed 1.5 ms
–1
 and roughness 
0.1 µm for minimum wear rate. ANOV A indicated 
that MoS
2
 exhibited the greatest effect on wear rate 
of the composites. Chang et al. [16] optimized load, 
distance, counterface roughness, and amount of fibre 
as parameters influencing the abrasive wear of kenaf-
reinforced polyester composite via Taguchi L
9
(3
4
). 
The results showed that the optimal combination 
for minimum wear was obtained at a load of 30 
N, composition B, and distance 2,500 m and that 
applied load was the most influential parameter on 
wear rate. Şahin [1] optimized control the factors of 
abrasive wear of glass- and carbon-reinforced PTFE 
composites through the Taguchi method. Load, grit 
size, distance, and compressive strength were the 
investigated parameters. For minimum volume loss, it 
was found that a load of 5 N, a grit size of 1200 mesh, 
a distance of 45 m, and a compressive strength of 9.8 
MPa were the optimal parameters. 
To study multiple responses related to tribological 
behaviours of composites, several decision-making 
methods, including data envelopment analysis (DEA), 
analytic hierarchy process (AHP), and grey relational 
analysis (GRA) have been proposed. Of these, 
GRA, introduced by Deng in 1989 [17], is the most 
commonly used when the nature of the information is 
uncertain and incomplete. Ramesh and Suresha [18] 
integrated Taguchi with the grey relational method to 
establish the optimal levels of abrasive performance 
of carbon-epoxy hybrid composites. It was found that 
grit size and filler loading were the most influential 
parameters. Based on the Taguchi-grey relational 
analysis, Subbaya et al. [19] investigated the wear 
assessment of SiC-filled epoxy composites; the 
results showed that the optimal combination for 
minimum wear was obtained at filler content of 
10 wt. %, grit size of 320 mesh, load of 10 N, and 
distance of 75 m. Filler with 70.09 % was the found 
to be most significant parameter influencing the GRG. 
Dharmalingam et al. [20] combined Taguchi with 
GRA to determine the optimal parameter settings of 
multiple responses of abrasive wear aluminium hybrid 
metal composites. The optimal parameters were found 
to be load of 20 N, sliding speed of 1.5 m/s, and the 
amount of molybdenum disulphide at 2 wt.%. An 
integrated Taguchi with GRA has been adopted for 
optimization of μ and wear rate of co-long composite 
by Sylajakumar et al. [21] combined Taguchi with 
GRA. Using this method, optimal parameter settings 
of were found to be an applied load of 60 N, a 
sliding speed of 1 ms
-1
, and a sliding distance of 
1000 m. Validation testing showed an improvement 
of 35.25 % in GRA. Savaran and Thanigaivelan [22] 
coupled Taguchi-particle component analysis and 
GRA to optimize the dimple geometry of stainless 
steel (SS36L). The results indicated that optimum 
parameter values for the highest GRG peak value 
of 0.2642 were an average power of 12 W, a pulse 
duration of 1500 ns, and a frequency of 15 Hz.
Even though the Taguchi approach is simple, 
efficient, and economical, it is limited to optimizing 
a response at a time. The need for a method 
that can optimize multiple responses cannot be 
overemphasized. Therefore, this study is aimed at 
optimizing multiple responses of the coefficient of 
friction ( μ) and specific abrasive wear rate (A
w
) of 
reinforced PTFE composites using a Taguchi-GRA 
method. Moreover, abrasive wear performance should 
be optimized to prevent detrimental consequences on 
output performance.
1  EXPERIMENTAL
1.1  Materials
In this study, PTFE reinforced with carbon 25 % wt. 
and bronze 40 % wt. has been used. The materials 
fabricated by compression moulding process were 
supplied by Polymer Chemical Industry Ltd, Turkey 
in the form of square plates (100 mm × 100 mm × 6 
mm). Selected properties of the materials are shown 
in Table 1. All samples have been cut from the same 
lot to minimize variations in the production technique.
Table 1.  Selected properties of materials used 
Materials Code ρ [gcm
–3
] σ [kgcm
–2
]
Polytetrafluoroethylene PTFE 2.10 380
Carbon-filled composite CF25 2.05 210
Bronze-filled composites BF40 3.05 280

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 359-367
361 Multi-Response Optimization of the Tribological Behaviour of PTFE-Based Composites via Taguchi Grey Relational Analysis  
1.2  Abrasive Test
An abrasive test was conducted according to ASTM 
G99 on a pin-on-disc tribometer (Model: Arton 
Paar, Switzerland), shown in Fig. 1. The counterface 
material for the wear test is a steel of disc 140 mm in 
diameter and thickness of 10 mm that has been heat-
treated to obtain a surface hardness of 55 RC to 60 
RC. This is ground to a surface finish of nearly 0.12 
µm centreline average. The square samples (20 mm 
×20 mm) were cut from the plates using computer 
numerical control water machining for the pin-on-
abrasive testing. A specially designed fixture for 
holding the rectangular samples was designed and 
fabricated. The samples were inserted into the fixture 
and bolted and then loaded against SiC abrasive 
papers fixed to the hardened steel holder by means of 
liquid adhesive. Control parameters and their levels 
are shown in Table 2. The experimental design is as 
shown in Table 3 and was performed at 0.15 ms
–1
. In 
all the experiments, mass before (m
1
) and mass after 
(m
2
) was measured using digital weighing balance 
(Model: PS 1000.RS RADWAG, made in Poland) 
with 10
–3
 g precision accuracy. Testing was performed 
at room temperature (29 °C and relative humidity 
55 %). Samples were cleaned with a brush before 
and after the experiment to remove debris and then 
weighed. The specific abrasive wear rate (A
w
) was 
then computed from Eq. (1):
 A
mm
LD
w


12

, (1)
where m
1
 – m
2
 is mass loss [g], L load [N], ρ density 
[gcm
–3
] and D sliding distance [m], respectively. Two 
replicates were performed for each run and the average 
reported. The tribometer is connected to a computer 
with a data acquisition system that collects and 
transmits to software for processing and generation of 
results. The coefficient of friction ( μ) is obtained from 
this process.
Table 2.  Control parameters and their levels
Parameters Symbol Level 1 Level 2 Level 3
Load [N] L 5 8 10
Grit size (mesh) G 1000 320 220
Distance [m] D 150 250 350
Pin sample
Fixture
Counterface 
(SiC against 
rotating dics)
Load
Fig. 1.  Arton Paar Tribometer used for the experiment
1.3  Taguchi Design of Experiment (DOE)
The Taguchi design of the experiment is a tool 
which optimizes process parameters, keeping the 
process under control by managing variations while 
improving quality. In this study, based on literature, 
three parameters (i.e., load (L), grit size (G), and 
sliding distance (D)) at three levels were optimized. 
The experiment was designed based on a Taguchi L
9
 
(3
3
) orthogonal array (OA) and conducted according 
to Table 2. Although the Taguchi design is simple, 
cost-effective, and improves the process, it is limited 
to optimizing a single response. For the optimization 
purpose, Taguchi uses the signal-to-noise ratios 
(SNRs) to determine the optimum combination of 
parameters and followed Eq. (2). 
 SNRs STB
n
y
i
i
n
 








10
1
10
2
1
log, (2)
where n is repetition of number of each trial and y
i
 
outcome of the i
th
 experiment for each trial. SNR of μ 
and A
w
 were computed as per Eq. (2).
Table 3.  Taguchi L
9
 (3
3
) OA Design
Run L [N] G (mesh) D [m]
1 1 1 1
2 1 2 2
3 1 3 3
4 2 1 2
5 2 2 3
6 2 3 1
7 3 1 3
8 3 2 1
9 3 3 2

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 359-367
362 Ibrahim,	M.A .	–	Çamur ,	H.	–	Sa v aş,	M.A .	–	Sabo ,	A .K.
1.4  Grey Relational Analysis (GRA)
The Taguchi design approach is limited to single 
response optimization. For multi-objective 
optimization, GRA has been developed exploiting the 
Taguchi design to estimate the degree of correlation 
between test trials (series) via grey relational grade 
(GRG). To reduce data inconsistency, the data is 
normalized to a comparable range between 0 and1 
[22]. Different objective functions exist, such as 
larger is better and smaller is better. The objective 
of this study is to minimize wear rate. Therefore, the 
smaller is better function is chosen, and the data are 
normalized according to (Eq. (3)):
 Xk
maxk k
maxkmink
i
ii
ii
*
,  
  
  


 (3)
where Xk
i
*
 is normalized for the i
th
 experiment and  
φ
i
(k) initial sequence of the average responses.
1.5  Calculation of Grey Relational Coefficient (GRC) and 
Grade (GRG)
The next step after data normalization is the 
computation of the deviation sequence using (Eq. (4)):
 
oi i
kX kX k      0
**
, (4)
where Δ
oi
(k) stands for deviation, 
Xk
0
*
 denotes 
normalized data and Xk
i
*
 refers to comparability 
sequence. GRC is thus estimated through (Eq. (5)):
 


i
minm ax
oi max
k
k
 

 


, (5)
where ξ
i
(k) is a GRC of each response calculated 
as a function of D
min
 and D
max
 the lowest and the 
highest deviations of each target factor, respectively. 
Differentiating or identification coefficient is 
symbolized by ζ and is demarcated within the range 
of z ∈[0,1]. This is usually set at one half to assign 
equivalent weights to every variable. As indicated in 
(Eq. (6)), GRG is then determined by taking mean of 
GRG of each response:
 
i
i
n
i
n
k  


1
1
, (6)
where γ
i
 is a GRG obtained for i
th
 test run, and n 
summation count of performance attributes. As soon 
as optimal level of variables is established via GRG, 
the last phase is to predict and confirm the quality 
attributes by (Eq. (7)):
  
predictedm
i
q
m
 


1
0
. (7)
1.6  Analysis of Variance (ANOVA)
ANOV A is traditionally utilized to determine the 
significance of parameters on responses. Generally, 
Taguchi-GRA in combination with ANOV A is used to 
ascertain the percentage contribution of each factor to 
responses. The parameter with the largest percentage 
contribution is the most significant parameter and vice 
versa.
3  RESULTS AND DICUSSION
The results of the experiment based on Table 3 with 
corresponding SNRs of µ and A
w
 are presented in 
Table 4; these results are used for the Taguchi GRA. 
From Table 4, it was seen that run 4 produced the 
largest value of SNRs, signifying that BF40 composite 
is the most resistant material in the study. 
3.1  Effect of Load on µ and A
w
 
Fig. 2 shows the changes in A
w
 of reinforced PTFE 
composites as a function of load, grit size and 
distance. It is seen that A
w 
decreased with increasing 
applied load. The decrease in A
w
 of the PTFE based 
composites is because as the load increases the contact 
between samples, and the SiC counterface increases. 
This decreases the contact pressure, which allows 
particles of samples cooperating with the interface 
to share the stress. Additionally, a uniform, thin, and 
adherent transfer film in-between the samples and 
the counterface, which prevented direct contact with 
SiC counterface is another reason for the lower A
w
. 
However, at lower load A
w
 was high. This is related to 
high contact pressure in-between and the ineffective 
tribo-layer between samples and counterface leading 
to direct contact of the samples with the counter 
surface. Fig. 3 presents the variation in µ of PTFE 
based composites as a function L, G, D and S. It is 
observed in Fig. 3 that µ shows increasing and 
decreasing trends as the load increased from 5 N to 8 
N and from 8 N to 10 N, respectively. The low µ due 
to increasing the load is related to formation of layers 
by the fibres at the counterface and their viscoelastic 
properties. These layers act as lubricants between 
samples and SiC surface. High µ occurred, owing to 
destruction of these tribo-layers. These findings were 
in agreement with literature data [22] to [24]. 
3.2 Effect of Grit Size on µ and A
w
 
As seen in Fig. 2, increasing grit size causes a 
decrease in A
w
. The minimum A
w
 at higher G is due to 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 359-367
363 Multi-Response Optimization of the Tribological Behaviour of PTFE-Based Composites via Taguchi Grey Relational Analysis  
deposition of debris from the samples and formation 
of transfer film between samples and counterface. This 
resulted in reduction of cutting efficiency of the SiC 
particles leading to lower A
w
 loss. At smaller grit size, 
say 220 mesh, the particles are rough and penetrated 
deeply into samples. This caused large plastic 
deformation, leading to removal of more materials by 
micro-ploughing action. As seen in Fig. 3, µ exhibited 
a linear decreasing trend with an increase in grit size. 
µ is related to smoothness and roughness of surfaces. 
The high µ at smaller grit size is related to roughness 
of the SiC particle, which offered significant 
resistance. However, decrease in µ when the grit size 
is large is attributed to smoothness of the SiC particles 
leading to the formation of protective layer (lubricant) 
at the contact surface, preventing direct contact of 
the samples with the abrasive surfaces. This finding 
agrees with the finding of [1] when bronze and carbon 
filled PTFE was studied.
3.3 Effect of Sliding Distance on µ and A
w
 
As seen in Fig. 2 A
w
 linearly decreases when the 
sliding distance increases. Also, µ follows the same 
trend as A
w
 (Fig. 3). In other words, both µ and A
w
 
reduced due to increasing sliding distance. This 
could be explained on the basis that the sliding 
distance acts as lubrication to the contact surfaces 
thereby separating the pin samples from the abrasive 
counterface. More so, the lower wear rate of the 
reinforced PTFE composites could be linked to pull 
out or fracture of abrasive particles owing to the 
presence of fibres. Also, wear debris is transferred 
from the matrix leading to reduced wear rate. Similar 
findings were reported by [25] and [26] when nylon 6 
was reinforced with glass fibre at varied proportions.
3.4 Main Effect and Percentage Contribution of Factors on 
µ and A
w
 
To determine the optimal combination of parameters 
for minimum µ and A
w
, the SNRs computed were 
obtained using Eq. (2). The largest SNRs give the 
desired value. SNRs’ mean response table for µ is 
provided in Table 4, and the main effect plot depicted 
in Fig. 4. From Fig. 4, the optimum predicted 
maximum SNRs for L, G and D are obtained at 10 
N, 1000 mesh, and 350 m, respectively. In Table 5, 
the desired corresponding level values are bolded to 
facilitate understanding. The optimum combination 
of process parameters for desired µ is coded as 
L3G1D3. To estimate the significance (contribution) 
of each parameter on the µ, ANOV A (Table 6) was 
executed. As observed from Table 6, grit size with 
the percentage contribution of 69.34 %, shows the 
greatest effect on µ, followed by load with 14.62 % 
and the distance with 9.10 %. More so, it can be seen 
that the error is less than 10 %. Similarly, the same 
optimal combination of parameters was obtained for 
A
w
 (L1G1D3) for the lowest Aw using the main effect 
plot (Fig. 5). From the ANOV A results (Table 8), it 
can be implied that the grit size is the most significant 
parameter (42.65 %), followed by load (15.05 %), and 
distance shows the least significance (7.50 %) on A
w
.
Table 4.  Taguchi L
9
 (3
4
) OA results with SNRs 
Run µ
µ  
SNRs [dB]
A
w  
[mm
3
N
–1
m
–1
]
A
w
 
SNRs [dB]
1 0.11 19.54 8.5714E-07 121.34
2 0.28 10.96 2.4390E-06 112.26
3 0.53 5.47 1.7237E-06 115.27
4 0.22 13.07 5.1639E-07 125.74
5 0.30 10.34 4.0816E-07 127.78
6 0.56 5.08 3.5366E-06 109.03
7 0.03 29.50 4.1115E-07 127.72
8 0.28 11.04 1.2568E-06 118.01
9 0.40 7.90 9.8095E-07 120.17
Fig. 2.  Effect of process variables on A
w
Fig. 3.  Effect of process variables on µ

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 359-367
364 Ibrahim,	M.A .	–	Çamur ,	H.	–	Sa v aş,	M.A .	–	Sabo ,	A .K.
Fig. 4.  Main effect plot for SNRs of µ
Fig. 5.  Main effect plot for SNRs of A
w
Table 5.  Response table for SNRs of μ (STB)
Factors L1 L2 L3 Delta Rank
L [N] 11.83 9.45 16.15 6.65 2
G [mesh] 6.15 10.78 20.54 14.39 1
D [m] 11.73 10.65 15.10 4.46 3
Table 6.  ANOVA for μ
Source DF SSS AMS Contribution [%]
L [N] 2 68.3 34.15 14.62
G [mesh] 2 323.81 161.9 69.34
D [m] 2 32.41 16.2 6.94
Error 2 42.5 21.25 9.10
Total 8 467.01 100.00
Table 7.  Response table for SNRs of A
w
 (STB)
Factors L1 L2 L3 Delta Rank
L [N] 116.30 120.90 122.00 5.7 3
G [mesh] 114.80 119.40 124.90 10.10 1
D [m] 116.10 119.40 123.60 7.50 2
Table 8.  ANOVA for A
w
Source DF SSS AMS Contribution [%]
L [N] 2 54.31 27.15 15.05
G [mesh] 2 153.9 76.95 42.64
D [m] 2 84.59 42.01 23.4
Error 2 68.59 34.29 19.00
Total 8 360.81 100.00
3.5  Optimization via GRA
Principally, GRA is used to unravel real problems 
comprising a bounded amount of data. It is commonly 
employed to approximate the properties of indefinite 
systems having no black and white solutions. In a grey 
system, black signifies being without information 
whereas white connotes being with information. 
This technique is largely utilized to maximize or 
minimize problems involving multiples parameters 
and responses [27] and [28]. The data in Table 3 are 
pre-processed in the range of 0 to 1 according to Eq. 
(3). Thereafter, post-data processing was performed to 
obtain the deviation sequences using Eq. (4). Table 9 
reveals the results of the post-data processing models. 
GRC for µ and A
w
 was computed using Eq. (5). 
Eventually, the mean of GRC is calculated to establish 
the GRG. As enumerated in Table 10, the calculated 
values of GRG were employed to produce equivalent 
SNR. A larger magnitude of SNR is useful, provided 
that the tests are close to the normalized magnitudes 
of GRG. Fig. 6 depicts the plot of GRG against SNRs. 
It indicates that seventh experimental run possesses 
the highest SNR. Correspondingly, the first rank was 
assigned to the seventh run. The straggling disposition 
of the GRG, below the plot of SNR in Fig. 6 adds to 
the discussion above.
Once the ranks are obtained, the GRG response 
table was developed. Each factor of GRG at the chosen 
level was selected and the average computed to obtain 
the mean GRG for different parameters. To obtain 
mean GRG values, of each parameter from Table 9, 
for instance, parameter L at L1 in the 1
st
, 2
nd
 and 3
rd
 
runs. The corresponding GRG values from Table 9 
was used for computation as depicted in Eq. (8). 
 L
1
0 7737 0 4735 0 4435
3
0 5336 


...
. . (8)
The mean of chosen GRG was computed utilizing 
technique above and put together to generate the 
response table (Table 11). The grades in the response 
table are used as a degree of correlation between the 
normalized and comparability sequence of GRA. 
Higher values of GRG show strong correlation 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 359-367
365 Multi-Response Optimization of the Tribological Behaviour of PTFE-Based Composites via Taguchi Grey Relational Analysis  
[29]. Hence, from Table 11, it is possible to achieve 
a combination of optimal parameters capable of 
maximizing the overall response. As observed in 
Table 10, the maximum GRG exists at L3, G1, and 
D3. Therefore, the optimal levels for useful abrasive 
tribological property of reinforced PTFE composites 
are L = 10 N, G at 1000 mesh and D = 350 m.
Table 9.  Reference and deviation sequences post data processing
Run
Xk
i
*
 Δ
oi
μ A
w
μ A
w
1 0.8510 0.8565 0.1490 0.1435
2 0.5234 0.3508 0.4766 0.6492
3 0.0458 0.5795 0.9542 0.4205
4 0.6399 0.9654 0.3601 0.0346
5 0.4833 1.0000 0.5167 0.0000
6 0.0000 0.0000 1.0000 1.0000
7 1.0000 0.9990 0.0000 0.0010
8 0.5282 0.7287 0.4718 0.2713
9 0.2951 0.8169 0.7049 0.1831
Table 10.  Computed GRC and GRG with SNRs
Run
Xk
i
*

γ
i
γ
i
 SNR  
[dB]
Rank
μ A
w
1 0.7704 0.7770 0.7737 -2.2285 2
2 0.5120 0.4351 0.4735 -6.4929 7
3 0.3438 0.5432 0.4435 -7.0619 8
4 0.5813 0.9353 0.7583 -2.4030 3
5 0.4918 1.0000 0.7459 -2.5465 4
6 0.3333 0.3333 0.3333 -9.5424 9
7 1.0000 0.9981 0.9990 -0.0083 1
7 0.5145 0.6483 0.5814 -4.7107 5
8 0.4150 0.7320 0.5735 -4.8297 6
9 0.7704 0.7770 0.7737 -2.2285 2
Table 11.  Response table for GRGs
Factors L1 L2 L3 Delta Rank
L [N] 0.5636 0.6125 0.7189 0.1544 3
G [mesh] 0.4501 0.6003 0.8437 0.3936 1
D [m] 0.5628 0.6018 0.7295 0.1667 2
Table 12.  ANOVA for GRG
Source DF SSS AMS Contribution [%]
L [N] 2 7.22 3.61 10.37
G [mesh] 2 47.12 23.56 67.69
D [m] 2 7.96 3.98 11.44
Error 2 7.32 7.32 10.51
Total 8 69.61 100.00
Fig. 6.  Plot of GRG versus SNRs
3.6  ANOVA for GRG
To study the significance and percentage contribution 
of each parameter on the multiple Aw of reinforced 
PTFE composites, an ANOV A was executed for GRG. 
Taking into account the responses of µ and A
w
, Table 
12 depicts that grit size has the maximum influence of 
67.69 % on the GRG, load has 12.37 %, and distance 
with lowest effect of 10.53%. 
3.7  Confirmatory Tests
When the identities of optimum levels were 
established, the concluding phase in GRA is to 
predict and validate performance enhancement of 
the responses. The prediction of GRG was conducted 
based on Eq. (8). Confirmatory tests were performed 
to validate the results of the analysis and mean of 
GRG of two trials was computed. For the optimal 
conditions, the µ and Aw were determined to be (0.04 
and 1.40×10
–7
) mm
3
N
–1
m
–1
, respectively. Moreover, 
it can be implied from Table 13 that the outcomes of 
the validation experiment are in concordance with the 
predicted results. Furthermore, an improvement of 
55.22 % in GRG is also achieved. This enhancement 
in the experimental outcomes over the initial design 
parameter asserts the validity of the Taguchi-GRA 
method for improving the abrasive wear performance 
of reinforced PTFE composites.
Table 13.  Results of the confirmatory tests
Initial design parameters
Optimal design parameters
Prediction Experiment
Setting levels L1G3D3 L3G1D3 L3G1D3
GRA 0.4435 1.0000 0.9904
Improvement in GRG [%] 55.65 55.22

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 359-367
366 Ibrahim,	M.A .	–	Çamur ,	H.	–	Sa v aş,	M.A .	–	Sabo ,	A .K.
nanoplatelets by solid-state processing. Composites 
Part B: Engineering, vol. 95, p. 317-323, DOI:10.1016/j.
compositesb.2016.03.082.
[5] Friedrich, K., Zhang, Z., Schlarb, A.K. (2005). Effects of various 
fillers on the sliding wear of polymer composites. Composites 
Science and Technology, vol. 65, no. 15-16, p. 2329-2343, 
DOI:10.1016/j.compscitech.2005.05.028.
[6] Harsh, A.P., Tewari, U.S. (2007). Tribological studies on glass 
fiber reinforced polyether ketone composites. Journal of 
Reinforced Plastics Composites, vol. 23, no. 1, p. 65-82, 
DOI:10.1177/0731684404029349.
[7] Hashmi, S.A.R., Dwivedi, U.K., Chand, N. (2006). Friction and 
sliding wear of UHMWPE modified cotton fibre reinforced 
polyester composites. Tribology Letters, vol. 21, p. 79-87, 
DOI:10.1007/s11249-006-9014-y.
[8] Suresha, B., Kumar, K.N.S. (2009). Investigations on 
mechanical and two-body abrasive wear behaviour of glass/
carbon fabric reinforced vinyl ester composites. Materials 
& Design, vol. 30, no. 6, p. 2056-2060, DOI:10.1016/j.
matdes.2008.08.038.
[9] Shipway, P.H., Ngao, N.K. (2003). Microscale abrasive wear 
of polymeric materials. Wear, vol. 255, no. 1-6, p. 742-750, 
DOI:10.1016/S0043-1648(03)00106-6.
[10] Ravikumar, B.N., Suresha, B. Venkataramareddy, M. (2009). 
Effect of particulate fillers on mechanical and abrasive wear 
behaviour of polyamide 66/polypropylene nanocomposites. 
Materials & Design, vol. 30, no. 9, p. 3852-3858, 
DOI:10.1016/j.matdes.2009.01.034.
[11] Liu, C., Ren, L.Q., Arnell, R.D., Tong, J. (1999). Abrasive wear 
behavior of particle reinforced ultrahigh molecular weight 
polethylene composites. Wear, vol. 225-229, p. 199-204, 
DOI:10.1016/50043-1648(99)00011-3.
[12] Yousif, B.F., Nirmal, U., Wong, K.J. (2010). Three-body abrasion 
on wear and frictional performance of treated betelnut fibre 
reinforced epoxy (T-BFRE) composite. Materials & Design, vol. 
31, no. 9, p. 4514-4521, DOI:10.1016/j.matdes.2010.04.008.
[13] Harsha, A.P. Tewari U.S. (2002). Abrasive wear resitance of 
glass fibre reinforced polysulfone composites. Indian Journal 
of Engineering & Materials Science, vol. 9, p. 203-208.
[14] Sunil Thakur and SR Chauhan. (2014). Friction and sliding 
wear characteristics study of submicron size cenosphere 
particles filled vinylester composites using Taguchi design of 
experimental technique. Journal of Composite Materials, vol. 
48, no. 23, p. 2831-2841, DOI:10.1177/0021998313502740.
[15] Cho, MH., Bahadur, S., Pogosian, A.K. (2005). Friction and 
wear studies using Taguchi method on polyphenylene sulfide 
filled with a complex mixture of MoS2, Al2O3, and other 
compounds. Wear, vol. 258, no. 11-12, p. 1825-1835, 
DOI:10.1016/j.wear.2004.12.017.
[16] Chang, B.P., Yong, Y.F., Akil, H., Nasir, R. (2017). Optimization 
on abrasive wear performance of pultruded kenaf-reinforced 
polymer composite using Taguchi method. Key Energy 
Materials, vol. 739, p. 42-49, DOI:10.4028/www.scientific.
net/KEM.739.42.
[17] Deng, J.L. (1989). Introduction to Grey System Theory. Journal 
of Grey Systems, vol. 1, p. 1-24.
[18] Ramesh, B.N., Suresha, B. (2014). Optimization of tribological 
parameters in abrasive wear mode of carbon-epoxy 
5  CONCLUSIONS
This study presents the results of optimal parameters 
that influence the abrasive performance of reinforced 
PTFE composite involving multiple responses. 
Initially, the result of varying three factors (i.e., load, 
grit size, and sliding distance) on multiple responses 
of specific wear rate and coefficient of friction was 
investigated using a Taguchi L
9
 orthogonal array and 
grey relational analysis. As seen in the response table 
of the grey relational grades, the optimum combination 
of parameters for improved abrasive performance of 
the reinforced PTFE composites was found to be load 
at 10 N, grit size at 1000 mesh, and sliding distance 
at 350 m. Analysis of variance for grey relational 
grade showed that grit size with 67.69 % is the most 
influential parameter followed by applied load with 
12.37 %, and sliding distance indicated the least 
effect having 10.52 % on the grey relational grade. 
Finally, validation tests were conducted to validate the 
improvement 55.22 % in grey relational grade from 
0.4435 for the initial design parameters (L1G3D3) 
to 0.9903 for the optimal combination of parameters 
(L3G1D3). It is recommended that heavy conditions 
of parameters should be studied. The presented 
Taguchi-grey relational analysis results has proven 
to be capable of dealing with several responses in 
the optimization of tribological wear study of PTFE 
matrix composites.
6  ACKNOWLEDGEMENTS
The authors are grateful to Kano University of Science 
and Technology, Wudil, Kano State, Nigeria, Kano 
State Scholarship Board, Kano State, Nigeria and 
Near East University, Nicosia, Cyprus
8  REFERENCES
[1] Şahin, Y. (2015). Analysis of abrasive wear behavior of PTFE 
composite using Taguchi’s technique. Cogent Engineering, vol. 
2, no. 1, p. 1-15, DOI:10.1080/23311916.2014.1000510.
[2] Vasilev, A.P. Struchkova, T.S., Nikiforov, L.A., Okhlopkova, A.A., 
Grakovich, P.N., Shim, E.L., Cho, J.-H. (2019). Mechanical and 
tribological properties of polytetrafluoroethylene composites 
with carbon fiber and layered silicate fillers. Molecules, vol. 
24, art. ID. 224, DOI:10.3390/molecules24020224.
[3] He, R., Chang, Q., Huang, X., Bo, J. (2018). Improved 
mechanical properties of carbon fiber reinforced PTFE 
composites by growing graphene oxide on carbon fiber 
surface. Composite Interfaces, vol. 25, no. 11, p. 995-1004, 
DOI:10.1080/09276440.2018.1451677.
[4] Suh, J., Bae, D. (2016). Mechanical properties of 
polytetrafluoroethylene composites reinforced with graphene 

Strojniški vestnik - Journal of Mechanical Engineering 68(2022)5, 359-367
367 Multi-Response Optimization of the Tribological Behaviour of PTFE-Based Composites via Taguchi Grey Relational Analysis  
hybrid composites. Materials & Design, vol. 59, p. 38-49, 
DOI:10.1016/j.matdes.2014.02.023.
[19] Subbaya, K.M., Suresha, B., Rajendra, N., Varadarajan, Y.S. 
(2012). Grey-based Taguchi approach for wear assessment of 
SiC filled carbon-epoxy composites. Materials & Design, vol. 
41, p. 124-130, DOI:10.1016/j.matdes.2012.04.051.
[20] Dharmalingam, S., Subramanian, R., Kök, M. (2013). 
Optimization of abrasive wear performance in aluminium 
hybrid metal matrix composites using Taguchi-grey relational 
analysis. Proceedings of the Institution of Mechanical 
Engineers, Part J: Journal of Engineering Tribology, vol. 227, 
no. 7, p. 749-760, DOI:10.1177/1350650112467945.
[21] Sylajakumari, P.A., Ramakrishnasamy, R., Palaniappan, G. 
(2018). Taguchi grey relational analysis for multi-response 
optimization of wear in co-continous composite. Materials, vol. 
11, no. 9, p. 1743, DOI:10.3390/ma11091743.
[22] Saravanan, K.G., Thanigaivelan, R. (2021). Optimisation of 
laser parameters and dimple geometry using PCA-coupled 
GRG. Strojniški vestnik - Journal of Mechanical Engineering, 
vol. 67, no. 10, p. 525-533, DOI:10.5545/sv-jme.2021.7246.
[23] Kim, J.W., Jang, H., Kim, J.W. (2014). Friction and wear 
of monolithic and glass fibre reinforced PA66 in humid 
condition. Wear, vol. 309, no. 1-2, p. 82-88, DOI:10.1016/j.
wear.2013.11.007.
[24] Chowdhury, M.A., Nuruzzaman, D.M., Roy, B.K., Samad, S. 
Sarker, R., Rezwan, A.H.M. (2013). Experimental Investigation 
of friction coefficient and wear rate of composite materials 
sliding against smooth and rough mild steel counterfaces. 
Tribology in Industry, vol. 35, no. 4, p. 286-292.
[25] Gunes, I. Uygunoğlu, T., Çelik, A.G. (2021). Tribological 
properties of fly ash blended polymer composites. Matéria, 
vol. 26, no. 1, DOI:10.1590/S1517-707620210001.1229.
[26] Deo, C., Acharya, S.K. (2010). Effects of load and sliding 
velocity on abrasive wear of Lantana camara fibre-reinforced. 
Proceedings of the Institution of Mechanical Engineers, Part J: 
Journal of Engineering Tribology, vol. 224, no. 5, p. 491-496, 
DOI:10.1243/13506501JET699.
[27] Zou, S.Y., Huang, R., Chi, M.C., Hsu, H.M. (2013). Factors 
affecting the effectiveness of inorganic silicate sealer 
materials through multi-quality characteristics. Materials, vol. 
6, no. 3, p. 1191-1204, DOI:10.3390/ma6031191.
[28] Kasemsiri, P., Dulsang, N., Pongsa, U., Hiziroglu, S., 
Chindaprasit, P. (2017). Optimization of biodegradable foam 
composites from cassava starch, oil palm fibre, chitosan and 
palm oil using Taguchi method and grey relational analysis. 
Journal of Polymers and the Environment, vol. 25, p. 378-390, 
DOI:10.1007/s10924-016-0818-z.
[29] Wojceichowski, P. Maruda, S., Krolczyk, R.W., Nieslony, G.M. 
(2018). Application of signal noise ratio and grey relational 
analysis to minimze forces and vibrations during precise 
ball end milling. Precision Engineering, vol. 51, p. 582-596, 
DOI:10.1016/j.precisioneng.2017.10.014.