*Corr. Author’s Address: Le Quy Don Technical University, 236 Hoang Quoc Viet, Ha Noi, Vietnam, thaileminh@lqdtu.edu.vn 167
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179 Received for review: 2021-01-23
© 2020 Journal of Mechanical Engineering. All rights reserved.  Received revised form: 2021-02-21
DOI:10.5545/sv-jme.2021.7106 Original Scientific Paper Accepted for publication: 2021-03-22
Optimization of the Internal Roller Burnishing Process  
for Energy Reduction and Surface Properties 
Nguyen, T.-N. – Le, M.-T.
Trung-Thanh Nguyen
1
 – Minh-Thai Le
2,*
1 
Le Quy Don Technical University, Faculty of Mechanical Engineering, Vietnam 
2 
Le Quy Don Technical University, Faculty of Special Equipments, Vietnam
Improving the surface quality after burnishing operation has been the subject of various published investigations. Unfortunately, the trade-off 
analysis between the energy consumption and surface characteristics of the internal burnishing has been not addressed due to the expensive 
cost and huge efforts required. The objective of the present work is to optimize burnishing factors, including the spindle speed, burnishing 
feed, depth of penetration, and the number of rollers for minimizing the energy consumed in the burnishing time, as well as surface roughness 
and maximizing Rockwell hardness. An adaptive neuro-based-fuzzy inference system (ANFIS) was used to develop burnishing objectives in 
terms of machining parameters. The optimization outcomes were selected using an evolution algorithm, specifically the non-dominated sorting 
particle swarm optimization (NSPSO). The results of the proposed ANFIS models are significant and can be employed to predict response 
values in industrial applications. The optimization technique comprising the ANFIS and NOPSO is a powerful approach to model burnishing 
performances and select optimal parameters as compared to the trial and error method as well as operator experience. Finally, the optimal 
solution can help to achieve the improvements in the energy consumed by 16.3 %, surface roughness by 24.3 %, and Rockwell hardness by 
4.0 %, as compared to the common values 
Keywords: roller burnishing; energy reduction; roughness; Rockwell hardness; optimization
Highlights
• 	 Optimizing machining parameters for the internal roller burnishing process of the hardened steel 40X.
• 	 Considering the spindle speed, burnishing feed, burnishing depth, and number of the rollers.
• 	 Evaluating energy consumption, surface roughness, and Rockwell hardness.
• 	 Development of the correlations using ANFIS models.
• 	 Determination of optimal parameters using NSPSO.
0  INTRODUCTION
The burnishing operation is an effective solution to 
boost the surface properties of the machined parts. The 
outstanding characteristics of the burnished surface, 
such as reduced roughness, increased hardness, and 
enhanced compressive stress, can be obtained with the 
aid of the burnishing process. The optimal factors of 
different burnishing operations have been selected for 
improving machining responses. El-Taweel and El-
Axir [1] revealed that the burnishing performances, 
such as the surface roughness and micro-hardness, 
were primarily affected by the force, feed, speed, 
and the number of passes, respectively. A roughness 
of 0.055 μm and hardness of 46.69 HRC for the 
burnished T215Cr12 material were obtained with 
the aid of the response surface method [2]. Babu et 
al. [3] stated that the burnishing depth significantly 
increased the micro-hardness, while the average 
roughness was primarily influenced by the burnishing 
force for the burnishing processes of the EN steels, 
aluminium alloy, and alpha-beta brass. Tadic et al. [4] 
emphasized that a small burnishing force significantly 
contributed to a lower roughness. Cobanoglu and 
Ozturk [5] indicated that the average roughness and 
micro-hardness were enhanced by 100.0 % and 55.50 
%, as compared to the initial values for the burnished 
AISI 1040 steel. John and Vinayagam [6] revealed that 
the optimum values of the roughness and hardness of 
the burnished Al 63400 were 0.032 µm and 91.63 HV , 
respectively.
Revankar et al. [7] presented that the 
improvements in the surface roughness and micro-
hardness were 77.0 % and 17.0 %, as compared to 
pre-machined properties for the burnished titanium 
alloy. Amdouni et al. [8] indicated that the burnishing 
crossed path could be effectively used to decrease the 
roughness, while the successive one was an alternative 
solution to increase the hardness for the burnished 
aluminium alloy. John et al. [9] emphasized that the 
average roughness could be decreased by 94.5 %, 
and the micro-hardness could be increased by around 
41.7 % for the burnishing process of EN-9 alloy. 
Similarly, the impacts of the processing conditions 
on the average roughness bore size, and the ovality 
of the internal roller burnishing were presented by 
John et al. [10]. The findings revealed that a burnished 
hole with an acceptable accuracy was produced. 
Świrad et al. [11] stated that the raster strategy was an 
effective solution for machining curved paths, while 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
168 Nguyen, T.-N. – Le, M.-T.
the burnishing pressure had a positive impact on the 
improvement of the burnished surface. 
Huuki and Laakso [12] indicated that the 
compressive stress and average roughness could be 
improved by 90 % and 400 %, while the roundness 
was enhanced by 38 % for the ultrasonic burnishing 
of 34CrNiMo6-M steel. The regression models 
of the surface roughness and micro-hardness for 
the ultrasonic-assisted burnishing process of the 
aluminium alloy were developed by Teimouri et al. 
[13]. The authors concluded that the proposed approach 
could bring a higher value of the affected depth. Yang 
et al. [14] indicated that the cryogenic condition 
significantly contributed to a decreasing burnishing 
force and roller wear, enhancing microstructure 
and hardness, as compared to the dry one for the 
burnishing of the Co–Cr–Mo biomaterial. Tang [15] 
agreed that the surface roughness, microstructure, 
and corrosion resistance of the burnished titanium 
alloy were improved with cryogenic cooling. Sachin 
et al. [16] stated that cryogenic burnishing effectively 
improved surface properties. A new burnishing 
process was developed to produce the drill shank for 
minimizing machining costs, resources, and energy 
[17]. The author stated that the proposed process 
can replace conventional operations, including 
heat treatment and grinding. Maximov et al. [18] 
emphasized that diamond burnishing is an effective 
approach to enhance the fatigue limits and decrease 
the surface roughness.   
Fig. 1.  The power used for the burnishing process
Unfortunately, the influences of machining 
parameters on the energy consumed for the internal 
burnishing operation have not been analysed. 
Furthermore, the relation between the energy 
reduction and surface properties for the burnishing 
process has not considered. 
1  METHODS
1.1  Optimizing Objectives
Fig. 1 presents the graph of the power used for 
the burnishing process. The energy components 
include the start-up energy (E
s
), standby energy (E
b
), 
transition energy (E
t
), air-burnishing energy (E
a
), and 
the burnishing energy (E
be
).
The start-up state refers to the shortest period 
for turning on the machine tool. The standby state 
presents the stable period, which starts from turning 
on the machine tool and stops by the spindle rotation. 
During this time, the lowest amount of energy is 
consumed. The spindle acceleration/deceleration state 
refers to the short period for increasing and decreasing 
the spindle speed. The air-burnishing energy state 
presents the steady period with spindle rotation but no 
material burnishing. The burnishing state refers to the 
steady period for material burnishing.
Practically, the start-up energy, standby energy, 
transition energy, and air-burnishing energy are less 
dependent on the variety of machining parameters; 
hence, the energy consumed in the burnishing state 
is considered to be an optimization objective. The 
energy consumed in the burnishing time is calculated 
as:
 EP t
be mb
 , (1)
where P
m
 is the power consumed in the burnishing 
time; and t
b
 is the burnishing time.
Fig. 2.  Optimization approach

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
169 Optimization of the Internal Roller Burnishing Process for Energy Reduction and Surface Properties  
A decreased surface roughness has a 
significant contribution to the functional performance 
of mechanical parts and production costs. In the 
roughness criteria, average roughness (R
a
) is 
considered to be a serious index of the product quality, 
which indicates the average of the absolute value 
along the sampling length. Maximum profile peak 
height (R
p
) and Maximum profile valley depth (R
v
) 
are the highest and lowest points along the sampling 
length, respectively. Practically, a decreased R
a
 leads 
to a reduction in the R
p
 and R
v
. 
The surface roughness (R
a
) is calculated as:
 R
R
a
ai
i


1
5
5
, (2)
where R
ai
 presents the average roughness at the 
burnished surface.
The Rockwell hardness (RH) is calculated as:
 RH
RH
ai
i


1
5
5
, (3)
where RH
ai
 is the Rockwell hardness after the 
burnishing operation at the measured position.
Burnishing factors are presented in Table 1. These 
ranges are determined based on the characteristics of 
the burnishing tool, workpiece, and machine tool. 
These values are verified with the handbooks and 
aforementioned works.
Table 1.  Burnishing parameters
Symbol Parameters 1 2 3
S Spindle speed [rpm] 1000 1500 2000
f Feed rate [mm/min] 200 400 600
D Burnishing depth [mm] 0.04 0.08 0.12
N Number of rollers 2 3 4
1.2  Optimization Procedure
Fig. 2 presents the optimization approach, which is 
expressed as follows:
Step 1: The internal burnishing experiments using 
the Box-Behnken method (BBM) [19]. The BMM is 
an alternative design of the experimental method, in 
which a two-level factorial design is combined. Three 
required levels of each factor are “–1”, “0”, and “1”, 
which presents the low, middle, and high ranges. 
The design points are placed on the middle points of 
the edge and the centre of the block. The BBD does 
not contain parametric combinations at their highest 
or lowest levels (at the vertices of the cube). This 
prevents the experiments from being performed under 
extreme conditions, which may cause unsatisfactory 
results. In other words, the extreme situations of the 
responses are avoided. In the BBM, the number of 
experiments is significantly decreased, which reduces 
experimental costs. 
The number of experiments (NE) in the Box-
Behnken method is calculated as:
 NE kk C
p
  21 () , (4)
where k and C
p
 present the number of factors and the 
number of centre points, respectively.
Step 2: The ANFIS approach describes the 
impacts of input process parameters on the total 
energy consumed, surface roughness, and Rockwell 
hardness. The designed ANFIS model using five-
layer feed-forward neural networks for the burnishing 
responses is expressed as follows (Fig. 3) [20] and 
[21]:
Layer 1: In this layer, the membership functions 
are assigned to the inputs. The outcome of this layer 
is expressed as:
 LA M
ii
Ax 11
 
i( )
. (5)
Fig. 3.  The typical structure of the ANFIS model
Layer 2: This layer is applied to collect the inputs 
from the respective fuzzification nodes and determine 
the firing strength of the rule. The output is expressed 
as:
 
LA xy
i
iA iB i 2
    () () .
 (6)
Layer 3: This layer is used to determine the ratio 
of the firing strength of a given rule to the total of 
firing strengths of all rules. The output is expressed 
as:

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
170 Nguyen, T.-N. – Le, M.-T.
 LA
i
i
i
i
i
n 3
1






. (7)
Layer 4: This layer is employed to defuzzify the 
received inputs and assign the consequent parameters 
of the rules. The output is expressed as:
 LA ya xb x
i
ii ii ii 4
   () .    c (8)
Layer 5: This layer is used to determine the 
overall output of all incoming signals. The output is 
expressed as:
 LA f
f
i
ii
i
ii
i
i
5






. (9)
Step 3: The NOPSO is applied to select optimal 
factors.
NSPSO is an effective optimization algorithm to 
improve working efficiency and select non-dominated 
solutions [22]. Furthermore, NOPSO propels the 
population towards the Pareto-optimal front. Three 
niching approaches, including the crowding distance, 
niche count, and max-min operations, are applied to 
enhance the diversity of the Pareto front. The principal 
working of the NOPSO is shown in Fig. 4.
Step 4: The DA is applied to identify optimal 
values of process parameters and responses, in which 
each burnishing response is transformed into the 
function of the desirability (di) [23]. The desirability 
values are computed for three cases, including the 
maximum, minimum, and constrained objectives. 
Step 5: The comparison of optimal results 
generated by two optimization approaches is 
evaluated. 
Fig. 4.  The principal working of the NOPSO
2  EXPERIMENTAL
The round bar of a material labelled 40X steel is 
employed to produce machining specimens. The 
length of 50 mm, the internal diameter of 15 mm, and 
the diameter of 50 mm are used for all specimens. The 
average values of the surface roughness and Rockwell 
hardness of the pre-machined surface are 2.06 µm and 
23.2 HRC, respectively.  
a)            b)           c) 
Fig. 5.  a) Setting the origin of the workpiece; b) measuring roughness; and c) measuring hardness

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
171 Optimization of the Internal Roller Burnishing Process for Energy Reduction and Surface Properties  
The burnishing trails are done with the support 
of a CNC milling machine. The burnishing tool is 
clamped on the machine spindle using the straight 
shank (Fig. 5a). The linear movement of the burnishing 
tool is performed with the aid of the Z-axis.
A KEW 6305 power meter is employed to 
measure power consumption. A reading error of ±0.3 
% and full scale error of ±0.2 % are used to enhance 
the measure accuracy. Moreover, the display update 
period of 1 second is applied to visualize the capture 
data. A Mitutoyo SJ-301 tester is used to measure the 
surface roughness. The length of 4 mm is measured 
for each segment (Fig. 5b). The resolution of 0.1 µm 
is employed to improve the accuracy of the measuring 
data.
A ERGOTEST DIGI-25R tester is used to 
measure the Rockwell hardness. The pressed load 
of 150 kf and dwell time of 5 seconds are used for 
all hardness tests (Fig. 5c). The resolution of 0.1 
Rockwell is applied to capture the experimental data.
Table 2.  Experimental data for the internal burnishing process
No. S [rpm] F [mm/min] D [mm] N E
be
 [kJ] R
a
 [µm] RH [HRC]
Experimental data  
for developing  
ANFIS model
1 1000 400 0.08 4.00 16.97 0.37 38.2
2 2000 400 0.08 2.00 18.59 0.63 37.8
3 1000 400 0.08 2.00 16.08 0.39 33.5
4 1500 400 0.04 4.00 17.16 0.37 39.1
5 1500 400 0.08 3.00 17.47 0.37 42.7
6 1000 600 0.08 3.00 11.73 0.58 37.1
7 2000 600 0.08 3.00 13.09 0.68 42.7
8 1500 200 0.08 2.00 32.59 0.31 34.3
9 1500 400 0.08 3.00 17.49 0.36 42.4
10 2000 400 0.08 4.00 18.69 0.43 43.5
11 2000 200 0.08 3.00 35.24 0.46 37.3
12 1500 600 0.12 3.00 13.01 0.52 41.0
13 2000 400 0.12 3.00 19.79 0.53 41.1
14 1500 200 0.12 3.00 34.86 0.34 36.4
15 1500 400 0.04 2.00 15.91 0.47 34.7
16 2000 400 0.04 3.00 17.33 0.58 36.8
17 1000 200 0.08 3.00 31.33 0.33 32.6
18 1500 200 0.08 4.00 33.56 0.21 38.7
19 1500 600 0.08 4.00 12.65 0.46 43.6
20 1500 400 0.12 2.00 18.46 0.42 39.3
21 1500 400 0.12 4.00 18.53 0.32 44.1
22 1000 400 0.04 3.00 15.81 0.51 31.8
23 1500 200 0.04 3.00 30.91 0.39 33.2
24 1000 400 0.12 3.00 16.99 0.46 36.2
25 1500 600 0.04 3.00 11.74 0.57 36.6
26 1500 600 0.08 2.00 12.09 0.56 39.2
Experimental data  
for testing accuracy  
of the ANFIS model
27 1200 200 0.06 2 30.58 0.34 30.4
28 1400 300 0.06 2 22.47 0.37 35.2
29 1600 400 0.08 3 17.72 0.38 42.9
30 1800 500 0.08 3 14.15 0.49 43.5
31 1800 500 0.10 4 14.64 0.37 45.6
32 2000 600 0.10 4 13.22 0.52 44.2
33 2000 600 0.12 4 13.39 0.46 43.9
34 1300 450 0.07 3 14.64 0.41 40.7
35 1700 550 0.09 4 13.25 0.39 45.4
36 1900 550 0.11 3 13.84 0.52 42.9
37 1100 350 0.05 3 18.64 0.42 34.6
38 1700 450 0.09 4 16.07 0.33 45.5
39 1900 550 0.05 4 12.95 0.53 41.2

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
172 Nguyen, T.-N. – Le, M.-T.
Table 3.  Comparative errors for the burnishing responses
No. E
be
 [kJ] R
a
 [µm] RH [HRC]
27 Exp. ANFIS Err. [%] Exp. ANFIS Err. [%] Exp. ANFIS Err. [%]
28 30.58 30.14 1.44 0.34 0.33 2.94 30.4 30.8 1.30
29 22.47 22.78 1.38 0.37 0.38 2.63 35.2 34.7 1.42
30 17.72 17.56 0.90 0.38 0.36 5.26 42.9 42.1 1.86
31 14.15 14.47 2.26 0.49 0.48 2.04 43.5 42.9 1.38
32 14.64 14.42 1.50 0.37 0.36 2.70 45.6 45.2 0.88
33 13.22 13.44 1.64 0.52 0.53 1.89 44.2 42.8 3.17
34 13.39 13.63 1.79 0.46 0.45 2.17 43.9 44.5 1.35
35 14.64 14.49 1.02 0.41 0.43 4.65 40.7 41.5 1.93
36 13.25 13.48 1.74 0.39 0.38 2.56 45.4 45.9 1.10
37 13.84 13.62 1.59 0.52 0.51 1.92 42.9 42.4 1.17
38 18.64 18.35 1.56 0.42 0.41 2.38 34.6 34.1 1.45
39 16.07 16.33 1.62 0.33 0.32 3.03 45.5 44.9 1.32
Exp.: Experimental value; Err.: Error
3  RESULTS AND DISCUSSIONS
3.1  ANFIS Models for Burnishing Responses
The experimental data of the internal roller burnishing 
operation are presented in Table 2. The experimental 
outcome from 1 to 26 are employed to develop ANFIS 
models, while the data from 27 to 39 are applied 
in order to evaluate the precision of the ANFIS 
correlations.
The 2-2-2-2 structure of the ANFIS model is 
applied to present the relationship between burnishing 
parameters and the energy consumed. The 3-3-3-
3 structures of the ANFIS model are used to render 
the relationships between burnishing parameters and 
the surface roughness and Rockwell hardness. The 
membership function labelled gaussmf can bring 
minimal errors. 
The comparisons between the predicted and 
experimental values of the E
be
, R
a
, and RH models are 
presented in Table 3. The small errors revealed that 
the ANFIS models can produce acceptable accuracy.
3.2  ANOVA Results for the Burnishing Responses
The ANOV A results for the E
be
, R
a
, and RH are shown 
in Tables 4, 5, and 6, respectively. The R
2
 values of 
the E
be
, R
a
, and RH are 0.9883, 0.9874, and 0.9885, 
indicating the adequacy of the proposed models.   
For the E
be
 model, the meaningful terms are the 
single factors (S, f, D, and N), interactive factors (Sf, 
SD, fD, and DN), and the quadratic factor (f
2
). The 
contributions of the S, f, D, and N are 5.61 %, 50.44 
%, 5.20 %, and 1.56 %. The contribution of the f
2
 is 
25.49 %. The contributions of the Sf, SD, fD, and DN 
are 3.11 %, 1.57 %, 3.26 %, and 1.43 %, respectively.
For the R
a
 model, the meaningful terms are the 
single factors (S, f, D, and N), interactive factors (SN), 
and quadratic factors (S
2
, f
2
, and N
2
). The contributions 
of the S, f, D, and N are 10.88 %, 21.59 %, 14.61 %, 
and 10.07 %. The contributions of the S
2
, f
2
, and N
2
 
are 21.59 %, 8.60 %, and 3.65 %, respectively. The 
contribution of the SN is 8.77 %.
For the RH model, the meaningful terms are the 
single factors (S, f, D, and N) and quadratic factors 
(S
2
, f
2
, D
2
, and N
2
). The contributions of the S, f, D, 
and N are 19.98 %, 18.78 %, 16.49 %, and 14.70 %. 
The contributions of the S
2
, f
2
, D
2
, and N
2
 are 11.77 %, 
7.31 %, 9.20 %, and 1.09 %, respectively.
3.3  Parametric Influences
Fig. 6a presents the impacts of the spindle speed and 
feed rate on the energy consumed. An increment in the 
feed rate has a significant contribution to a decrement 
in the burnishing time. The higher the feed rate is, the 
faster the burnishing will be. Therefore, a higher feed 
rate causes a reduction in energy consumption. At a 
higher spindle speed, the momentum of the spindle 
system increases to satisfy a targeted setting, which 
causes increased energy consumption. Moreover, an 
increased spindle speed causes a higher power used 
of the spindle system, which increases the total power 
used in the machine tool. The similar influences of the 
feed rate and spindle speed on the energy consumption 
for the flat burnishing process were presented in the 
works of [24] and [25].
Fig. 6b presents the influences of the burnishing 
depth and number of rollers on the energy consumed. 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
173 Optimization of the Internal Roller Burnishing Process for Energy Reduction and Surface Properties  
burnishing depth and number of rollers on the energy 
used for the flat burnishing process were similarly 
described in the works of [24] and [25].
Fig. 7a presents the influences of the spindle 
speed and feed rate on the surface roughness. A higher 
temperature in the machining area is obtained with 
an increased spindle speed, which causes a reduction 
in the workpiece hardness. Therefore, the material 
is easily burnished, and the roughness is reduced. 
Unfortunately, when the speed increases from 1500 
rpm to 2000 rpm, the work-hardening behaviour 
is appeared, which causes a higher roughness. A 
higher feed rate causes a higher distance between 
two consecutive paths; hence, higher roughness is 
produced. The similar impacts of the feed rate and 
spindle speed on the surface roughness can be found 
for the external burnishings [1], [5], [6], and [9], 
flat burnishings [2], [24], and [25], and the internal 
burnishings [10], and [17]. 
Fig. 7b presents the influences of the burnishing 
depth and number of rollers on the surface roughness. 
Higher burnishing depth causes a larger degree 
of plastic deformation; hence, low roughness is 
obtained. A reduction in the roughness with an 
increased burnishing depth was also found in the 
published investigations [5], [6], [10], [17], [24], and 
[25]. A higher number of rollers leads to an increased 
frequency of engagement; hence, a higher degree of 
plastic deformation is obtained. More material is 
burnished, which causes a reduction in the roughness. 
A similar influence of the number of rollers on the 
surface roughness was presented in the works of [6], 
[10], and [25].
Fig. 8a presents the impacts of the spindle speed 
and feed rate on the Rockwell hardness. A higher 
feed rate causes an increased burnishing pressure on 
the machined surface, which increases the degree 
of the plastic deformation; hence, the Rockwell 
hardness is improved. A higher spindle speed results 
in an increased temperature in the burnishing region, 
which causes an improvement in the larger plastic 
deformation. More material is then compressed and 
burnished; hence, the Rockwell hardness is enhanced. 
A further feed rate and/or speed may cause excessive 
burnishing temperature, and the residual stress can 
be relieved; hence, the Rockwell hardness value is 
decreased. Similar impacts of the spindle speed and 
feed rate on the machined hardness were presented in 
the works of [17], [18], [24], [25], and [26].
Fig. 8b presents the impacts of the burnishing 
depth and number of rollers on the Rockwell hardness. 
An increased burnishing depth results in higher 
machining pressure, which causes a higher degree 
An increased burnishing depth leads to a higher 
machining pressure, which causes a greater resistance 
on the machined surface; hence, higher energy 
consumed is required to overcome resistance. 
Similarly, a higher number of rollers causes an 
increased burnishing pressure. Therefore, more energy 
is required to burnish the material. The impacts of the 
Table 4.  ANOVA results for the E
be
 model
So. SS MS F Value P value
Mod. 1479.343 105.667 66.370 < 0.0001
S 80.751 80.751 50.720 < 0.0001
f 726.022 726.022 456.015 < 0.0001
D 74.796 74.796 46.979 < 0.0001
N 22.490 22.490 14.126 0.0013
Sf 44.765 44.765 28.117 0.0004
SD 22.654 22.654 14.229 0.0276
fD 46.924 46.924 29.473 0.0002
DN 20.583 20.583 12.928 0.0392
f  
2
366.955 366.955 230.485 < 0.0001
Res. 17.513 1.592 904.040
Cor. 1496.857  
Mod.: Model; So.: Source; Res.: Residual; Cor.: Core total
Table 5.  ANOVA results for the R
a
 model
So. SS MS F Value P value
Mod. 0.305 0.022 61.332 < 0.0001
S 0.032 0.032 90.771 < 0.0001
f 0.064 0.064 180.181 < 0.0001
D 0.043 0.043 121.923 0.0001
N 0.030 0.030 84.036 < 0.0001
SN 0.026 0.026 73.187 0.0225
S 
2
0.064 0.064 180.181 < 0.0001
f  
2
0.025 0.025 71.769 0.0010
N 
2
0.011 0.011 30.460 0.0385
Res. 0.004 0.000 834.512
Cor. 0.309  
Table 6.  ANOVA results for the RH model
So. SS MS F Value P value
Mod. 318.318 22.737 67.460 < 0.0001
S 72.521 72.521 215.166 < 0.0001
f 68.163 68.163 202.238 < 0.0001
D 59.853 59.853 177.582 < 0.0001
N 53.341 53.341 158.260 < 0.0001
S 
2
42.727 42.727 126.770 < 0.0001
f  
2
26.550 26.550 78.774 < 0.0001
D 
2
33.401 33.401 99.100 < 0.0001
N 
2
3.973 3.973 11.787 0.0056
Res. 3.708 0.337 1076.947
Cor. 322.025  

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
174 Nguyen, T.-N. – Le, M.-T.
a)                 b) 
Fig. 6.  The influences of the burnishing parameters on the E
b
: a) E
b
 versus S and f; b) E
b
 versus D and N
a)                 b) 
Fig. 7.  The influences of the burnishing parameters on the R
a
: a) R
a
 versus S and f; b) R
a
 versus D and N
a)             b) 
Fig. 8.  The influences of the burnishing parameters on the RH: a) RH versus S and f; b) RH versus D and N

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
175 Optimization of the Internal Roller Burnishing Process for Energy Reduction and Surface Properties  
of work-hardening; hence, the Rockwell hardness is 
enhanced. However, a further burnishing depth leads 
to higher burnishing temperature and the residual 
stress can be relieved; hence, the Rockwell hardness 
is decreased. As the number of rollers increases, 
more material is compressed and burnished. A higher 
degree of plastic deformation is generated; hence, 
higher Rockwell hardness is obtained. An increased 
hardness with higher burnishing depth and the number 
of rollers can be found in the works of [17], [18], [24], 
[25], and [26].
Fig. 9.  Surface morphology after burnishing process
The surface morphology after the burnishing 
operation is presented in Fig. 9 with the aid of a Nano 
Nova 450˝scanning electron microscope. It can be 
stated that a smooth surface can be achieved using the 
burnishing process. The pre-machined defects, such as 
grooves, cracks, and waviness, were filled.
3.4 Optimization Outcomes Generated by NOPSO
The single optimization is executed to find the best 
outcome for each response, as shown in Table 7. 
The Pareto graphs produced by NSPSO are shown 
in Fig. 10. The global relation between the energy 
consumption and average roughness is depicted in Fig. 
10a, while the trade-off analysis between the energy 
consumption and Rockwell hardness is presented in 
Fig. 10b.  
It can be stated that machining performances have 
contradictory trends. The minimization of the average 
roughness may lead to increased energy consumed and 
decreased Rockwell hardness. Three typical solutions, 
including points 1, 2, and 3, are chosen to evaluate the 
burnishing performances (Table 8).
For the first point, the average roughness 
increases, while the energy consumed and Rockwell 
hardness decreases; hence, this solution does not 
satisfy the optimization requirement. For the second 
point, the energy consumed increases, while the 
average roughness and Rockwell hardness decrease; 
hence, this point cannot consider as a proper solution. 
For the third solution, the energy consumed and 
average roughness simultaneously are decreased, 
while the Rockwell hardness increases, as compared 
to the initial values. Consequently, the third point 
can be selected as an appropriate solution to enhance 
burnishing performances.
Based on the optimization requirement, the third 
point is selected as the optimal point. As a result, 
the optimum values of the spindle speed, feed rate, 
burnishing depth, and the number of rollers are 1513 
rpm, 490 mm/min, 0.11 mm, and 4, respectively. 
The reductions in E
be
 and R
a
 are 16.3 % and 24.3 %, 
a)    b)  
Fig. 10.  Pareto graphs: a) E
b
 versus R
a
; b) E
b
 versus RH

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
176 Nguyen, T.-N. – Le, M.-T.
respectively, while the RH is enhanced by 4.0 %, as 
compared to the initial values. 
3.5  Optimization Outcomes Generated by DA
The mathematical models of the E
be
, R
a
, and RH are 
expressed using Eqs. (10) to (12), respectively.
ES fD
NS f
be

 
44 70623 0 00374 0 13858 63 7
1 47729 0 000006 0
.. ..
.. .. .. . ,
01614
0 08356 73 50 00013
2
SD
fD DN f   (10)
RS fD
NS N
a
 
 
0 78458 0 00088 0 00013 17 5
0 19583 0 00009 00 0
.. ..
.. .0 00004
0 000001 0 01875
2
22
S
fN   .. , (11)
RH Sf
DN
 
 
33 99167 0 04038 0 05858
316 39167 6 68633 0 00001
.. .
...2 2
0 000065 1773 41146 0 88208
2
22 2
S
fD N   .. . . (12)
Optimization outcomes are shown in Fig. 11. 
The optimum values of the spindle speed, feed rate, 
burnishing depth, and the number of rollers are 1427 
rpm, 468 mm/min, 0.09 mm, and 4, respectively. The 
reductions in the E
be
 and R
a
 are 14.4 % and 2.7 %, 
respectively, while the RH is enhanced by 2.8 %, as 
compared to the initial values. 
3.6  Evaluation of Optimization Outcomes
As given in Table 8, the ANFIS-NOPSO provides the 
improvements in the E
be
, R
a
, and RH are 16.3 %, 24.3 
%, and 4.0 %, respectively. As shown in Table 9, the 
reductions in the E
be
 and R
a
 are 14.4 % and 2.7 %, 
respectively, while the RH is enhanced by 2.8 % at the 
optimal solution produced by the RSM-DA. It can be 
stated that the ANFIS-NOPSO is more efficient than 
the RSM-DA regarding the optimization issues for the 
burnishing operation.
3.7  Scientific and Industrial Contributions
The optimal values of process parameters and 
burnishing responses are only determined using the 
optimization technique. The ANFIS-NOPSO is more 
efficient than the RSM-DA in resolving the complex 
optimizing issue.
The proposed optimization approach using ANFIS 
and NOPSO can be applied to solve optimization 
problems for different burnishing operations with 
different materials.  
The scientific findings can be effectively applied 
in future works for optimization of the burnishing 
operation or development of the expert system in 
terms of the burnishing process.
The ANFIS models of the energy consumed, 
surface roughness, and Rockwell hardness have 
been developed in terms of machining factors. These 
models have an industrial interest, which can be 
applied to forecast the burnishing performances for 
hardened 40X steel.
The optimal outcomes generated by the ANFIS-
NOPSO can be employed to improve the technical 
parameters for the internal burnishing operation of 
hardened 40X steel.
Table 7.  Optimization results for each response
Scenarios
Optimization parameters Responses
S [rpm] f [mm/min] D [mm] N E
be 
[kJ] R
a
 [µm] RH [HRC]
For minimizing Eb 1000 600 0.04 2 11.09
For minimizing Ra 1484 200 0.12 4 0.16
For maximizing RH 1545 480 0.10 4 45.6
Table 8.  Optimization results for the burnishing responses using ANFIS-NOPSO
Method
Optimization parameters Responses
S [rpm] f [mm/min] D [mm] N E
be
 [kJ] R
a
 [µm] RH [HRC]
Initial values 1500 400 0.08 3 17.47 0.37 42.7
Point 1 1024 573 0.04 2 11.16 0.60 29.5
Point 2 1470 224 0.12 4 32.23 0.17 39.1
Point 3 1513 490 0.11 4 14.63 0.28 44.4
Improvement [%] -16.3 -24.3 4.0

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
177 Optimization of the Internal Roller Burnishing Process for Energy Reduction and Surface Properties  
Moreover, the parametric influences can help 
machine operators deeply understand the impacts of 
burnishing factors on the process responses.
4  CONCLUSIONS
In this investigation, an attempt has been made to 
optimize the machining conditions of the roller 
burnishing operation for reducing the energy 
consumed in the burnishing state, surface roughness, 
and Rockwell hardness. The inputs considered 
are the spindle speed, burnishing feed, burnishing 
depth, and the number of rollers. The ANFIS method 
was employed to propose the predictive models of 
technical outcomes. The NSPSO was utilized to find 
optimal outcomes. The conclusion can be presented as 
bellows:
1. The minimum values of the spindle speed, 
burnishing depth, and the number of rollers can 
be applied to save the energy consumed, while 
the highest feed rate is recommended to apply. 
Higher values of the burnishing depth and 
number of rollers can be employed to decrease 
the roughness, while a minimum feed rate leads 
to a reduction in the roughness. The middle level 
of the spindle speed is used to obtain a smooth 
surface. Higher levels of process parameters are 
recommended to enhance the Rockwell hardness.
2. The ANFIS models of the energy consumption 
in the burnishing time, surface roughness, and 
Rockwell hardness can be applied to predict 
the response values with high accuracy. These 
developed models are effectively employed to 
save experimental costs and human efforts.
3. The Pareto fronts can significantly help machine 
operators to determine proper parameters for 
decreasing energy consumed as well as average 
roughness and enhancing Rockwell hardness. The 
appropriate selection of process parameters can 
decrease machining costs, time, operator skills, 
and efforts.  
4. As shown in the optimal setting generated by 
NSPSO, the optimal parameters of the S, f, D, 
and N are 1513 rpm, 490 mm/min, 0.11 mm, and 
4, respectively. The E
be
, and R
a
 are decreased by 
16.3 % and 24.3 %, while the RH is enhanced by 
4.0 %, respectively in comparison with the initial 
values. 
5. In the current investigation, the machining 
factors are optimized to decrease the energy 
consumption as well as average roughness and 
to improve the Rockwell hardness. Practically, 
the impacts of burnishing parameters on the 
residual stress, the depth of the affected layer, 
and machining costs have been not presented. 
Therefore, a holistic optimization considering 
Table 9.  Optimization results for the burnishing responses using RSM-DA
Method
Optimization parameters Responses
S [rpm] f [mm/min] D [mm] N E
be 
[kJ] R
a
 [µm] RH [HRC]
Initial values 1500 400 0.08 3 17.47 0.37 42.7
Optimal values 1427 468 0.09 4 14.96 0.36 43.9
Improvement [%] -14.4 -2.7 2.8
Fig. 11.  The optimal values generated by the DA

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)4, 167-179
178 Nguyen, T.-N. – Le, M.-T.
more burnishing performances will be addressed 
in future investigation.
5  ACKNOWLEDGEMENTS
This research is funded by Vietnam National 
Foundation for Science and Technology Development 
(NAFOSTED) under grant number 107.04-2020.02.
6  NOMENCLATURE
D Burnishing depth, [mm]
E
be
 Energy consumption in the burnishing time, [kJ]
f Feed rate, [mm/min]
MS Mean square
N Number of rollers
RH Rockwell hardness, [HRC]
S Spindle speed, [rpm]
SS Sum of squares
R
a 
Surface roughness, [μm]
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