*Corr. Author’s Address: Nguyen Tat Thanh University, 300A Nguyen Tat Thanh, Ho Chi Minh, Vietnam, lvan@ntt.edu.vn 155
Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168 Received for review: 2022-07-29
© 2023 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2022-12-12
DOI:10.5545/sv-jme.2022.303 Original Scientific Paper Accepted for publication: 2023-02-22
Impacts of Burnishing Variables on the Quality Indicators in a 
Single Diamond Burnishing Operation
Le, M.-T. – Van, A.-L. – Nguyen, T-.T.
Minh-Thai Le
1 
– An-Le V an
2,*
 – Trung-Thanh Nguyen
3
1
Le Quy Don Technical University, Faculty of Special Equipment, Vietnam 
2
Nguyen Tat Thanh University, Faculty of Engineering and Technology, Vietnam 
3
Le Quy Don Technical University, Faculty of Mechanical Engineering, Vietnam
Diamond burnishing is an effective solution to finish a surface. The purpose of the current work is to optimize parameter inputs, including the 
spindle speed (S), depth of penetration (D), feed rate (f), and diameter of tool-tip (DT) for improving the Vickers hardness (VH) and decreasing 
the average roughness (Ra) of a new diamond burnishing process. A set of burnishing experiments is executed under a new cooling lubrication 
system comprising the minimum quantity lubrication and double vortex tubes. The Bayesian regularized feed-forward neural network (BRFFNN) 
models of the performances are proposed in terms of the inputs. The criteria importance through the inter-criteria correlation (CRITIC) method 
and non-dominated sorting genetic algorithm based on the grid partitioning (NSGA-G) are applied to compute the weights of responses and 
find optimality. The optimal outcomes of the S, D, f, and DT were 370 rpm, 0.10 mm, 0.04 mm/rev, and 8 mm, respectively. The improvements 
in the Ra and VH were 40.7 % and 7.6 %, respectively, as compared to the original parameters. An effective approach combining the BRFFNN, 
CRITIC, and NSGA-G can be widely utilized to deal with complicated optimization problems. The optimizing results can be employed to enhance 
the surface properties of the burnished surface.
Keywords: single diamond burnishing; average roughness; Vickers hardness; Bayesian regularization; NSGA-G  
Highlights
• 	 A new diamond burnishing operation combining the minimum quantity lubrication (MQL) system and vortex tubes was 
developed.
• 	 Process parameters, including the spindle speed, depth of penetration, feed rate, and diameter of the tool tip were optimized. 
• 	 The average roughness and Vickers hardness of the burnished surface were enhanced. 
• 	 Optimal Bayesian regularized feed-forward neural network was proposed to present the non-linear data. 
0  INTRODUCTION
In industrial applications, the cost of lubricants 
accounts for 7 % to 17 % of the production expense. 
Moreover, the usage of the cutting fluid causes 
health risks and environmental problems; hence, the 
reduction or elimination of the lubricants is necessary. 
For this purpose, various cooling-lubrication (CL) 
approaches, including the minimum quantity 
lubrication (MQL), the Vortex tube (VT), and the 
cryogenic approach have been developed and utilized.
The deployment of the MQL system for different 
machining processes has attracted many researchers. 
Zaman and Dhar [1] stated that Ra, cutting force 
(CF), and cutting temperature (CT) were decreased 
by 5.78 %, 1.27 %, and 3.93 % at a proper parameter 
setting, respectively, for the MQL turning Ti6Al4V, 
in which the nozzle diameter, nozzle elevation angle 
(A), flow rate (Q), and air pressure were optimizing 
inputs. Tamang et al. [2] emphasized that the power 
consumption (PC), Ra, and tool wear (TW) of the 
MQL turning Inconel 825 were decreased by 16.57 %, 
8.47 %, and 10.41 %, respectively, as compared to the 
dry condition. Moreover, the Ra of 0.49 µm, the PC 
of 5.44 kW, and the TW of 110.68 µm were obtained 
at the optimal condition. Zan et al. [3] stated that CT, 
CF, and acceleration were decreased by 150 ºC, 5.6 
%, and 8.9 %, respectively using optimal values of 
the Q, nozzle distance (N), and A for the MQL milling 
Ti6Al4V . The Ra of 0.32 μm, the CT of 103.8 ºC, and 
the CF of 115.1 N for the MQL milling Inconel 690 
were obtained by means of optimal parameters of the 
S, f, depth of cut (dc), Q, and A [4]. V an and Nguyen [5] 
presented that the cylindricity, circularity, and average 
roughness of the MQL roller burnishing were reduced 
by 53.2 %, 57.8 %, and 72.9 %, respectively with the 
support of the optimal data of the nozzle diameter, A, 
Q, and air pressure. The maximum roughness and VH 
of the MQL roller burnishing were decreased by 17 
% and 14 %, respectively using the ANN and PSO 
[6]. Sachin et al. [7] developed an MQL diamond-
burnishing process, in which the optimal outcomes of 
the Ra and VH were 0.07 µm and 363 HV , respectively 
using the optimal data of the S, f, and burnishing force 
(f
b
).  
The VT has been widely utilized to enhance 
the technical performances of various machining 
processes. Mahapatro and Krishna [8] revealed that 
the CT and Ra of the VT-based turning Ti-6Al-4V 
were decreased by 35.6 % and 66.14 %, respectively, 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
156 Le, M.-T. – Van, A.-L. – Nguyen, T-.T.
while the CF was increased by 18.6 %, as compared 
to the dry cutting. Singh et al. [9] emphasized that 
the VT caused 45 % to 56 % lower carbon emission 
for the turning Ti-3Al-2.5V in comparison with the 
dry condition. Gupta et al. [10] proposed an effective 
system VTMQL comprising the nitrogen, VT, and 
MQL to increase the machinability in the turning 
of AA 7075-T6 alloy, in which the TW and Ra were 
decreased by 118 % and 77 %, respectively. Similarly, 
Mia et al. [11] revealed that the VTMQL caused 
reductions in the TW and Ra around 72 % and 75 %, 
respectively, for the precision turning of Al 6061-T6. 
The CF and Ra of the VTMQL-based drilling Hardox 
500 steel were decreased by 36.8 % and 46.7 %, 
respectively, as compared to the MQL, while the TW 
decreased around 4.5 times in comparison with the 
dry condition [12].
The cryogenic method has been considered for 
different machining processes. Sharma et al. [13] 
stated that the CF of 44.49 N, the CT of 24.99 ºC 
and the machining time of 37.09 s were obtained at 
the optimal data for the cryogenic turning AISI D3 
using the Taguchi method. The specific cutting energy 
(SCE), Ra, and TW for the cryogenic turning Ti-6Al-
4V were decreased by 30.5 %, 22.8 %, and 4.3 %, 
respectively, as compared to the dry condition [14]. 
The S of 78 m/min, the f of 0.16 mm/rev, and SNMM 
tool insert could be applied to decrease the Ra (1.05 
μm) and the CF (315 N) for the cryogenic turning Ti-
6Al-4V [15]. The optimal values of the S, f, and f
b
 of 
the cryogenic diamond burnishing operation were 73 
m/min, 0.048 mm/rev, and 150 N, respectively for 
decreasing the Ra and improving the VH [16]. Sachin 
et al. [17] stated that Ra of 0.2 µm and the VH of 398 
HV for the diamond burnishing operation of the 17-4 
hardened stainless could be obtained using optimal 
outcomes.
The diamond burnishing process is one of the 
finest finishing technologies, which has been widely 
executed on different surfaces for improving the 
properties and working functionalities [18] to [20]. 
Various CL methods, including cryogenic and MQL 
conditions, have been utilized in various diamond-
burnishing operations. Unfortunately, the cryogenic 
approach requires an expensive investment, while 
the low cooling-lubrication impact is the greatest 
drawback of the MQL system when machining 
high- hardness steels due to the enormous amount of 
generated heat. Therefore, it is necessary to develop 
an efficient-economic cooling-lubrication approach 
that can effectively facilitate the diamond-burnishing 
process.
Additionally, the selection of optimal factors 
for improving the surface quality of the diamond 
burnishing under the impact of a new CL system is 
also an urgent demand.
In this paper, a new diamond burnishing operation 
comprising the MQL and double vortex tubes is 
MQL system Ranque-Hilsch 
vortex 
Air compressor
Diamond-burnishing 
tool
Double Ranque-Hilsch vortex tubes-
minimum quantity lubrication-assisted 
diamond burnishing process 
Fig. 1.  A new diamond-burnishing process

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
157 Impacts of Burnishing Variables on the Quality Indicators in a Single Diamond Burnishing Operation
Development of the optimal 
BRNN model for DRDB responses
Investigation of the impacts of 
DRDB parameters
Start
Execution of DRDB experiments
Yes
No
Satisfy?
End
Determination of the weights of responses 
using the CRITIC method
Determination of the best optimal point 
using NSGA-G algorithm
Operating parameters of 
BRNN model
Training process of BRNN model
Calculating mean square error
Calculating absolute error?
Yes
No
Satisfy?
Lowest mean square 
error?
The optimal BRNN model
No
Yes
1
st
Stage
2
nd
Stage
Fig. 2. The optimizing procedure
first introduced. Then, we present the optimization 
approach and experiment. Next, the obtained results 
are discussed. Finally, conclusions are drawn, and 
future research is suggested. 
1  NEW DIAMOND-BURNISHING PROCESS
The concept of the diamond burnishing operation with 
a new CL system is shown in Fig. 1. The compressed 
air is produced by the pneumatic pump and stored in 
the accumulator. The pressure value is detected and 
assigned using the pneumatic regulator valve. The 
lubricant is pumped by means of the electrical device, 
while the flow rate is adjusted using the frequency 
generator. The compressed air is transferred from the 
MQL system to the double vortex tubes for decreasing 
the working temperature. The cold mixture is 
produced and transferred into the burnishing regions.
Table 1.  Optimizing parameters of a new diamond burnishing 
process 
Symbol Parameters 1 2 3
S Spindle speed [rpm] 185 370 630
D Depth of penetration [mm] 0.06 0.08 0.10
f Feed rate [mm/rev] 0.04 0.06 0.08
DT Tool-tip Diameter [mm] 6 8 10
2  OPTIMIZATION APPROACH
The burnishing parameters, including the spindle 
speed (S), depth of penetration (D), feed rate (f), and 
tool-tip diameter (DT) are presented in Table 1. The 
ranges of the S, D, and f are determined based on the 
characteristics of the machine tool, while the DT value 
is selected using the characteristics of the burnishing 
tool. Consequently, the optimizing issue is expressed 
as:
Minimize the Ra and maximize the VH.
Constraints: 150 rpm ≤ S ≤ 630 rpm; 0.06 mm ≤ 
D ≤ 0.10 mm; 0.04 mm/rev ≤ f ≤ 0.08 mm/rev; 8 mm 
≤ DT ≤ 10 mm.
The optimizing approach is expressed in Fig. 2.
Step 1: The experimental data are observed using 
the Taguchi method.
The Ra value is calculated as:
 Ra
Ra
i
n
n
i



1
, (1)
where Ra
i
 denotes the average roughness at the i
th
 
measured location.
The VH value is calculated as:
 VH
VH
i
i
n
n



1
, (2)
where VH
i
 is the Vickers hardness at the i
th
 position.

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
158 Le, M.-T. – Van, A.-L. – Nguyen, T-.T.
Step 2: The Ra and VH models are developed 
using the BRFFNN approach [21].
The input parameters are considered as 
probability density functions to the hidden layer, 
which is expressed as:
 P
PDwM Pw M
PD M

(, ,) (, )
(, ,)
,


 (3)
where D and M presents the obtained data and the 
forward multi-layer perceptron, respectively. w and 
P(w|α,M) are the vector and prior knowledge of 
network weights, respectively. When the Gaussian 
function is employed, the likelihood-P (D|w, β, M) is 
expressed as:
 PDwM e
n
d
d
(, ,) ,
/






1
2
 (4)
where d
d
 is the sum of squared deviations for data. 
The normalized factor P (D|α, β, M) is expressed 
as:
 PD Me
N
d
w
(, ,) ,
/






1
2
 (5)
where d
w
 is the sum of squared errors for the weights. 
The probability density function can be expressed 
as:
 P
Z
e
F
dd
dw


1
(,)
.
()


 (6)
The highest posterior probability density function 
causes maximum regularized objective function  
(  f = βd
d
+αd
w
). 
To observe the optimal architecture of the 
BRFFNN model, the operating factors, including 
the number of neurons in each layer, performance 
function, transfer function, number of hidden layers, 
and learning functions are optimized and selected. 
The numerical experiments of each ANN model are 
executed to calculate the mean square error (MSE), 
which is expressed as:
 MSE
N
yy
ap
i
N

 

1
2
1
, (7)
where y
a
 and y
p
 are the actual and predictive values, 
respectively. N denotes the number of testing points.
The best BRFFNN architecture is chosen with the 
lowest MSE value.
Step 3: The weights of the machining responses 
are calculated using the criteria importance through 
the intercriteria correlation (CRITIC) method. 
The normalized burnishing response (x
ij
) is 
computed as: 
 x
xx
xx
ij
ij j
word
j
best
j
word



. (8)
The standard deviation (s
j
) of each response is 
calculated as:
 s
xx
m
j
ij m i
m

 


()
.
1
2
1
 (9)
Determination of symmetric matrix of n×n with 
element r
jk
, which is linear correlation coefficient 
between the vectors x
j
 and x
k
.
Computation of measure of the conflict (I
j
):
 Ir
jj k
k
m
 

() . 1
1
 (10)
Determination of the quantity of the information 
(C
j
):
 Cs r
jj jk
k
m
 

() . 1
1
 (11)
The computed (w
i
) of burnishing response is 
calculated as:
 w
C
C
i
j
j
k
n



1
. (12)
Step 4: The optimal data of the burnishing 
parameters and responses are selected using the non-
dominated sorting genetic algorithm based on the grid 
partitioning (NSGA-G) [22]. The operation steps of 
the NSGA-G are expressed in Fig. 3.
Randomly initialize parent
population P
0
Set maximum number of
iterations (t
max
)
Calculate the individual target 
values of the population P
t
Non-inferior sorting
Acquire sub-population Q
t
by genetic operation
Calculate R
t
= P
t
U Q
t 
and run 
the non-inferior ranking
Start
Comparing solutions among all 
members
Select N individuals as a new
parent population P
t+1
End
t > t
max
Yes
No
Generation of different groups 
for Min and Max Points 
Finding nearest smaller and bigger 
grid points  for each solution
Fig. 3. The working principle of the NSGA-G
The random initialization of parent population: 
the parent population is executed based on the 
definition of the optimizing issue.

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
159 Impacts of Burnishing Variables on the Quality Indicators in a Single Diamond Burnishing Operation
Non-dominance sorting of the parent population: 
the parent population (P) is divided into the number of 
the subsets (P
i
), in which the subset P
k+1 
is dominated 
by the individual P
k
. The individual P
i
 is expressed as:
 Pi ni N
ii
  
/, ,, ..., . 12 (13)
The population P
k
 is expressed as:
 Pn
ki
   All individual/ k, 1 (14)
where n
i
 is the number of individuals in the population 
for dominating generations.
The parent population with N size and offspring 
population with N members at t
th
 generation are 
produced with the aid of crossover and mutation 
operations.
Generation of different groups for Min and Max 
Points: the nearest smaller and bigger grid point for 
each solution were selected. The design space is 
divided into multi small groups.
Compare solutions in a group and selection of the 
best individual: The weak individuals are removed to 
form a new generation. The control loop is executed 
until the maximum number of generations is fit. 
3  EXPERIMENTAL SETTING
The machining specimens having the round 
cylindrical shape are made from the hardened AISI 
4340 steel. The length and diameter of each workpiece 
are 130 mm and 80 mm, respectively. The turning and 
grinding operations are applied to produce the external 
surface in each specimen. The average roughness and 
Vickers hardness of the pre-machined surface are 
approximately 2.46 µm and 420.6 HV , respectively.
The experiments are performed using a 
conventional turning machine. The dead and live 
centres are employed to hold the specimen (Fig. 4a). 
The rotational motion of the workpiece is conducted 
by means of the friction between the machining 
sample and the dead centre. 
A novel diamond-burnishing tool has been 
designed and fabricated to facilitate burnishing 
experiments, as shown in Fig. 4b. Primary 
components are the shank, tool head, stem, diamond 
tip, positioning bolts, and adjusting screws. The stem 
having the diamond tip is tightly mounted in the tool 
head. The stem is replaced after each experiment to 
eliminate the impact of the tool wear. The hardness of 
62 HRC and roughness of 0.05 μm are employed in 
the diamond tip.
The average roughness is computed from three 
different positions using the Mitutoyo SJ-301. The 
Vickers hardness is measured in three different points 
on the burnished surface using a Wilson Wolpert 
tester.
The representative values of the burnishing 
responses are presented in Fig. 5. 
4  RESULTS AND DISCUSSIONS
4.1  Impacts of Process Parameters on the Ra and VH
Table 2 presents experimental data for the diamond 
burnishing operation.
Table 2.  Experimental data for a new diamond burnishing process
No. S D f DT Ra VH
Experimental 
data for 
developing 
the BRNN 
model
1 185 0.06 0.04 6 0.46 511.5
2 370 0.06 0.06 6 0.42 478.3
3 630 0.06 0.08 6 0.44 424.6
4 370 0.06 0.04 8 0.31 488.8
5 630 0.06 0.06 8 0.32 451.6
6 185 0.06 0.08 8 0.54 480.2
7 630 0.06 0.04 10 0.23 444.4
8 185 0.06 0.06 10 0.42 484.8
9 370 0.06 0.08 10 0.41 456.2
10 370 0.08 0.04 6 0.27 497.7
11 630 0.08 0.06 6 0.29 464.8
12 185 0.08 0.08 6 0.54 474.3
13 630 0.08 0.04 8 0.18 475.7
14 185 0.08 0.06 8 0.41 496.6
15 370 0.08 0.08 8 0.38 469.9
16 185 0.08 0.04 10 0.29 485.1
17 370 0.08 0.06 10 0.27 474.3
18 630 0.08 0.08 10 0.33 446.8
19 630 0.10 0.04 6 0.14 495.7
20 185 0.10 0.06 6 0.39 497.3
21 370 0.10 0.08 6 0.37 472.4
22 185 0.10 0.04 8 0.26 503.8
23 370 0.10 0.06 8 0.24 494.8
24 630 0.10 0.08 8 0.29 470.9
25 370 0.10 0.04 10 0.13 483.1
26 630 0.10 0.06 10 0.18 475.7
27 185 0.10 0.08 10 0.36 481.8
Experimental 
data for 
testing the 
precision of 
the BRNN 
model
28 185 0.06 0.05 7 0.46 505.4
29 250 0.07 0.07 9 0.41 481.9
30 250 0.09 0.05 7 0.32 501.3
31 630 0.10 0.07 9 0.23 477.6
32 370 0.07 0.06 10 0.31 470.5
33 250 0.08 0.08 9 0.41 476.9
34 185 0.06 0.05 9 0.41 496.3
35 370 0.08 0.07 7 0.36 477.9
36 370 0.06 0.06 8 0.37 479.4

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
160 Le, M.-T. – Van, A.-L. – Nguyen, T-.T.
a) 
b) 
1. The shank
2. The tool head
3. The stem
4. Positioning bolts 
5. The adjusting screw
6. Diamond tip
Fig. 4.  The experimental setting; a) burnishing experiment,  
and b) diamond burnishing tool
As shown in Fig. 6a, the Ra decreases (relatively 
around 34.8 %) with an increase in the S (from 185 
rpm to 630 rpm). Higher S increases the engagement 
frequency between the diamond tip and the surface, 
which increases the number of burnishing traces. The 
irregularities of the pre- machined surface are easily 
deformed; thus, the Ra decreases. The machining 
temperature at the interfaces increases with an 
increased S, which reduces the hardness and strength 
of the workpiece; hence, the material is smoothly 
compressed. Therefore, a reduction in the Ra is 
obtained. 
As shown in Fig. 6b, an increase in the D (from 
0.06 mm to 0.10 mm) leads to a reduction in the Ra 
(relatively around 30.4 %). Higher D increases the 
machining pressure on the surface to be machined, and 
the material is compressed. The pre-machined peaks 
are flattened, and the valleys are filled up; hence, the 
Ra significantly decreases.
As shown in Fig. 6c, an increase in the f (from 
0.04 mm/rev to 0.08 mm/rev) increases the Ra 
(relatively around 24.4 %). An increased f causes a 
higher distance between the consecutive burnishing 
paths, which decreases the engagement frequency. 
The machining time available to process material 
decreases with an increased f; hence, the Ra increases.
a) 
b) 
Fig. 5.  The representative values of a new diamond-burnishing 
process; a) the SEM image of the burnished surface at the 
experimental No. 11, and b) the Vickers hardness at the 
experimental No. 11
As shown in Fig. 6d, an increase in the DT (from 
8 mm to 10 mm) decreases the Ra (relatively around 
19.6 %). An increased DT causes a higher contact 
length between the tool tip and the specimen’s surface. 
The pre-machined peaks are flattened, and the valleys 
are filled up; thus, the Ra significantly decreases.
Table 3.  Computed ANOVA results for the Ra
Source SS MS F value p-value
Model 0.209 0.015 41.916 < 0.0001
S 0.178 0.178 499.782 < 0.0001
D 0.164 0.164 458.560 < 0.0001
f 0.197 0.197 552.648 < 0.0001
DT 0.094 0.094 264.563 < 0.0001
Sf 0.013 0.013 35.166 0.0182
SDT 0.038 0.038 105.732 0.0091
S
2
0.103 0.103 288.085 < 0.0001
DT
2
0.015 0.015 42.619 0.0174
Residual 0.004 0.000 
Cor. total 0.213  
R
2
 = 0.9816; Adjusted R
2
 = 0.9724; Predicted R
2
 = 0.9682

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
161 Impacts of Burnishing Variables on the Quality Indicators in a Single Diamond Burnishing Operation
The contribution of each factor on the Ra is shown 
in Table 3. Significant parameters are all single factors 
(S, D, f, and DT), interactive factors (Sf and SDT), and 
quadratic factors (S
2
 and DT
2
). The contributions of 
the S, D, f, and DT are 21.46 %, 19.69 %, 23.73 %, 
and 11.36 %, respectively. The contributions of the 
Sf and SDT are 1.51 % and 4.54 %, respectively. The 
contributions of the S
2
 and DT
2
 are 12.37 % and 1.83 
%, respectively. The R
2
 value of 0.9816 indicates the 
Ra model is adequate.
As shown in Fig. 7a, the VH decreases (relatively 
around 12.3 %) with an increased S (from 105 
rpm to 630 rpm). An increase in the S increases the 
engagement frequency, leading to higher machining 
temperature at the burnishing area; hence, the VH 
decreases.
As shown in Fig. 7b, an increased D (from 0.06 
mm to 0.10 mm) leads to a higher VH (relatively 
around 2.5 %). An increased D increases the 
machining pressure on the surface to be machined. 
The material is compressed and higher VH is 
obtained.
As shown in Fig. 7c, an increased higher f 
(from 0.04 mm/rev to 0.08 mm/rev) decreases the 
VH (relatively around 9.8 %). A higher f causes a 
low degree of plastic deformation due to higher 
distance among the consecutive traces; hence, the VH 
decreases.
As shown in Fig. 7d, an increased DT (from 6 
mm to 10 mm) decreases the VH (relatively around 
6.1 %). At a lower DT, higher burnishing pressure 
is produced due to the low contact area between the 
tool tip and surface to be machined. More material 
is compressed and the VH increases. When the DT 
increases, the burnishing pressure decreases; hence, 
the VH decreases.
The contribution of each factor on the Vickers 
hardness is shown in Table 4. Significant parameters 
are all single factors (S, D, f, and DT), interactive 
factors (SD, Sf, SDT, DDT, and fDT), and quadratic 
factors (S
2
, D
2
, f
2
, and DT
2
). The contributions of the 
a)      b) 
c)      d) 
Fig. 6.  Parametric influences on the Ra; a) Ra vs. S, b) Ra vs. D, c) Ra vs. f, and d) Ra vs. DT

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
162 Le, M.-T. – Van, A.-L. – Nguyen, T-.T.
S, D, f, and DT are 19.51 %, 12.79 %, 16.31 %, and 
8.77 %, respectively. The contributions of the SD, Sf, 
SDT, DDT, and fDT are 10.0 %, 1.25 %, 3.75 %, 1.68 
%, and 11.19 %, respectively. The contributions of the 
S
2
, D
2
, f
2
, and DT
2 
are 1.82 %, 2.33 %, 4.44 %, and 
5.48 %, respectively. The R
2
 value of 0.9843 indicates 
the developed VH model is adequate. 
4.2  Impacts of MQL Parameters on the Ra and VH
The ranges of the flow rate (Q), nozzle distance (N), 
and nozzle elevation angle (A) are selected based on 
the characteristics of the MQL system and confirmed 
with references [1], [3], and [5]. The Box-Benkhen 
design with two replications is applied to produce the 
experimental data in terms of saving trial costs and 
human efforts, as shown in Table 5.
As shown in Fig. 8a, when the Q relatively 
increases from 40 ml/h to 120 ml/h, the Ra is relatively 
decreased by 39.5 %. A higher Q increases the number 
a)       b) 
c)           d) 
Fig. 7.  Parametric influences on the VH; a) VH vs. S, b) VH vs. D, c) VH vs. f, and d) VH vs. DT
Table 4.  Computed ANOVA results for the VH
Source SS MS F value p-value
Model 7624.43 544.60 49.26 < 0.0001
S 1856.20 1856.20 167.90 < 0.0001
D 1216.86 1216.86 110.07 < 0.0001
f 1551.75 1551.75 140.36 < 0.0001
DT 834.39 834.39 75.47 < 0.0001
SD 951.41 951.41 86.06 0.0002
Sf 118.93 118.93 10.76 0.0014
SDT 356.78 356.78 32.27 0.0006
DDT 64.70 64.70 5.85 0.0012
fDT 159.84 159.84 14.46 < 0.0001
S
2
1064.63 1064.63 96.30 0.0011
D
2
173.16 173.16 15.66 0.0008
f
2
221.68 221.68 20.05 0.0005
DT
2
422.43 422.43 38.21 0.0004
Residual 521.37 521.37 47.16
Cor. total 121.61 11.06 
R
2
 = 0.9843; Adjusted R
2
 = 0.9752; Predicted R
2
 = 0.9636

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
163 Impacts of Burnishing Variables on the Quality Indicators in a Single Diamond Burnishing Operation
of oil droplets entering the burnishing zone, which 
enhances the cooling-lubrication efficiency. The 
friction at the interfaces decreases and the burnished 
surface is wetted and protected; hence, the Ra 
significantly decreases.
Table 5.  The impacts of MQL parameters on the Ra and VH
No. Q [ml/h] N [mm] A [deg] Ra [μm] VH [HV]
1 40 30 60 0.41 451.8
2 80 40 60 0.33 459.2
3 120 30 30 0.29 491.2
4 80 40 30 0.33 457.1
5 120 30 60 0.28 492.8
6 80 30 45 0.31 485.2
7 40 30 30 0.43 450.4
8 40 40 45 0.37 448.4
9 80 30 45 0.31 484.2
10 80 20 60 0.46 492.9
11 120 20 45 0.35 513.8
12 120 40 45 0.21 478.6
13 80 30 45 0.31 486.8
14 40 20 45 0.49 468.2
15 80 20 30 0.47 491.8
As shown in Fig. 8b, when the N relatively 
increases from 20 mm to 40 mm, the Ra is relatively 
increased by 30.9 %. At a low distance, a high 
proportion of the mixture is effectively transferred 
into the burnishing zones, resulting in low friction 
at the interfaces. The cooling-lubrication efficiency 
improves; thus, the Ra decreases. When the distance 
increases, a low proportion of the mixture enters into 
the burnishing zones, resulting in a lower cooling-
lubrication efficiency; hence, the Ra increases.
As shown in Fig. 8c, a higher A causes a reduced 
Ra value, while a further angle causes a negative 
impact. When the angle increases from 30 deg to 45 
deg, the Ra is relatively decreased by 13.8 %. When 
the angle increases from 45 deg to 60 deg, the Ra is 
relatively increased by 12.9 %. An increased angle 
leads to a decreased Ra due to a reduction in friction 
with the aid of proper positions of nozzles. However, 
a further increased angle causes a higher frictional 
impact at the interfaces and the Ra slightly increases.
As shown in Fig. 9a, when the Q relatively 
increases from 40 ml/h to 120 ml/h, the VH is 
enhanced by 10.8 %. An increased Q leads to a higher 
amount of lubricant; thus, the burnished surface is 
wetted and protected. The friction at the interface 
decreases, leading to a reduction in the machining 
temperature. The diminishing of the residual stress is 
then prevented; thus, a higher VH is achieved.
a) 
b) 
c) 
Fig. 8.  Impacts of MQL parameters on the Ra;  
a) Ra vs. Q, b) Ra vs. N, and c) Ra vs. A
As shown in Fig. 9, when the N relatively 
increases from 20 mm to 40 mm, the VH is relatively 
decreased by 6.2 %. At a low distance, a higher 
amount of lubricant enters into the burnishing zone, 
which wets and protects the burnished surface. The 
machining temperature at the interfaces decreases, 
which diminishes the residual stress; hence, the VH 
enhances. At a low distance, the temperature at the 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
164 Le, M.-T. – Van, A.-L. – Nguyen, T-.T.
interfaces increases, leading to diminishing residual 
stress; hence, the VH decreases.
a) 
b) 
c) 
Fig. 9.  Impacts of MQL parameters on the VH; a) VH vs. Q, b) VH 
vs. N, and c) VH vs. A
As shown in Fig. 9c, the contradictory trends of 
the VH are observed under the variety of the elevation 
angle. When the angle increases from 30 deg to 45 
deg, the VH is relatively improved by 1.7 %. When the 
elevation angle increases from 45 deg to 60 deg, the 
VH is relatively reduced by 1.5 %. An increased angle 
causes an accurate penetration of the mixture, leading 
to a reduction in the machining temperature; thus, 
a higher VH is obtained. A further increased angle 
leads to an improper cooling-lubrication efficiency, 
resulting in a higher burnishing temperature and the 
residual stress is relieved; hence, the VH decreases.
4.3  Optimal BRNN Model
The operating parameters of the BRFFNN model, 
including the HN, PM, TF, HL, and LF are shown 
in Table 6. The computational trials of the BRFFNN 
are performed based on the parameter combination 
entitled Taguchi L
18
. The obtained results of the MSE 
values are shown in Table 7. As a result, the optimal 
data of the HN, PM, TF, HL, and LF are 19, MSEREG, 
logsig, 3, and LearnGDM, respectively. The schematic 
of the developed BRNN model is presented in Fig. 10.
To confirm the precision of the developed ANN 
model, the comparisons between the experimental and 
predictive results are conducted. Table 8 indicates the 
comparative values at different points. As a result, the 
computed deviations of the Ra and VH lie from -313 
% to 4.35 % and -0.52 % to 0.65 %, respectively. The 
small errors revealed that the proposed models ensure 
the prediction accuracy.
Output 
layer
Input
layer
S
f
DT
D
Hidden layers
Ra
VH
19 Neurons 19 Neurons 19 Neurons
Fig. 10.  The schematic of the developed BRNN model
The regression plots of the BRFFNN are depicted 
in Fig. 11, in which the R values of the training, testing, 
and all stages are 0.97364, 0.96032, and 0.96536, 
respectively. Consequently, the developed BRFFNN 
model can accurately approximate experimental data.

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
165 Impacts of Burnishing Variables on the Quality Indicators in a Single Diamond Burnishing Operation
Table 6.  Operating parameters of the BRNN model
Symbol Parameters Classifications
HN
Number of 
hidden neurons
15 to 20
PM
Performance 
function
Mean squared error: MSE; 
Mean squared error with regularization: 
MSEREG; 
Sum squared error: SSE
TF
Transfer 
function
Log sigmoid: logsig; 
Linear: purelin; 
Hyperbolic tangent sigmoid: tansig
HL
Number of 
hidden layers
1; 2; 3
LF
Learning 
function
Gradient descent with momentum weight 
and bias learning function: LearnGDM; 
Gradient descent weight and bias 
learning function: LearnGD
Table 7.  Computing the MSE values
No. HN PM TF HL LF MSE
1 15 MSE logsig 1 LearnGDM 0.004236
2 15 MSEREG purelin 2 LearnGD 0.002298
3 15 SSE tansig 3 LearnGDM 0.001948
4 16 MSE logsig 2 LearnGD 0.001481
5 16 MSEREG purelin 3 LearnGDM 0.000929
6 16 SSE tansig 1 LearnGDM 0.001025
7 17 MSE purelin 1 LearnGDM 0.000622
8 17 MSEREG tansig 2 LearnGDM 0.00106
9 17 SSE logsig 3 LearnGD 0.001016
10 18 MSE tansig 3 LearnGD 0.001477
11 18 MSEREG logsig 1 LearnGDM 0.000653
12 18 SSE purelin 2 LearnGDM 0.006799
13 19 MSE purelin 3 LearnGDM 0.000606
14 19 MSEREG tansig 1 LearnGD 0.000632
15 19 SSE logsig 2 LearnGDM 0.00066
16 20 MSE tansig 2 LearnGDM 0.006992
17 20 MSEREG logsig 3 LearnGDM 0.001112
18 20 SSE purelin 1 LearnGD 0.007437
Table 8.  Investigation of the precision of the developed BRNN 
model
No.
Ra VH
Experiment BRFFNN
Error 
[%]
Experiment BRFFNN
Error
[%]
28 0.46 0.47 -2.17 505.4 504.6 0.16
29 0.41 0.42 -2.44 481.9 480.6 0.27
30 0.32 0.33 -3.13 501.3 503.9 -0.52
31 0.23 0.22 4.35 477.6 479.9 -0.48
32 0.31 0.32 -3.23 470.5 468.4 0.45
33 0.41 0.42 -2.44 476.9 473.8 0.65
34 0.41 0.42 -2.44 496.3 498.7 -0.48
35 0.36 0.35 2.78 477.9 475.8 0.44
a) 
b) 
c) 
Fig. 11.  Regression plots for the BRNN model; a) training stage, b) 
testing stage, and c) all stages
4.4  Optimizing outcomes
The computed weights of the Ra and VH are 0.53 and 
0.47, respectively. To prove the effectiveness of the 
NSGA-G, the optimal data produced by NSGA-II are 
generated and compared. Fig. 12 presents the Pareto 
front produced by the NSGA-G. The computational 
times of the NSGA-G and NSGA-II are 80.8 s and 
126.4 s, respectively. The number of feasible designs 
produced by the NSGA-G and NSGA-II are 801 
points and 408 points, respectively. The optimal data 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
166 Le, M.-T. – Van, A.-L. – Nguyen, T-.T.
produced by the NSGA-G of the S, D, f, and DT 
were 370 rpm, 0.10 mm, 0.04 mm/rev, and 8 mm, 
respectively (Table 9). The optimal data produced by 
the NSGA-II of the S, D, f, and DT were 352 rpm, 
0.10 mm, 0.04 mm/rev, and 7 mm, respectively. It 
can be stated that the NSGA-G provides a lower 
computational time, produces a higher number of 
feasible points, and better optimal results, as compared 
to the NSGA-II. Consequently, the VH is improved 
by 7.6 %, while the Ra is decreased by 40.7 % at the 
optimal solution, as compared to initial values.
Fig. 12.  The Pareto front produced by the NSGA-G
4.5  Scientific and Industrial Contributions
As a result, the average roughness and Vickers 
hardness of a new diamond burnishing process have 
been enhanced with the aid of optimum factors. The 
academic remarks are expressed as:
The proposed technique combining the ANN, 
CRITIC, and NSGA-G can be effectively utilized 
to find optimizing values of parameter inputs 
and responses for other diamond burnishing and 
machining processes.
The correlations developed by the BRFFNN 
approach can be applied to describe the complex data 
of the machining process.
The obtained data can be used in the practical 
diamond burnishing process to decrease the average 
roughness and enhance the Vickers hardness.
The industrial remarks are expressed as:
• A new diamond burnishing process comprising 
the MQL and double vortex tubes can be directly 
utilized in industrial applications for improving 
the surface properties of the external surface.
• The Pareto graphs can be applied to select 
optimal values of parameter inputs and responses 
for different burnishing aims. 
• The CL efficiency of different machining 
operations (turning, milling, and grinding) can be 
enhanced with using the proposed system.
• The Ra and VH models developed BRFFNN approach 
can be precisely utilized to calculate the machining 
targets for different deployments.
4.6  Evaluation of the total diamond burnishing cost 
The total diamond burnishing cost (TDC) is a 
summarization of the operation cost, lighting cost, 
depreciation cost, energy cost, tool cost, fluid cost, 
and cleaning cost. The TDC model is expressed as:
 
TDCCN
t
CP
t
CCt
M
od b
db
eL T
db
mi sv db
l
 



() ()
(
)
3600 3600
3600
) )( )
() ()
(






 
CPt
Ct
t
FC
t
CF
t
ed bd b
Td b
T
l
db
c
3600
60
3600

h h
3600
), (15)
where C
o
, N
db
, and t
db
 are the unit operator cost, the 
number of operators, and machining time, respectively. 
C
e
 and P
L 
are the unit energy cost and lighting power, 
respectively. C
mi
, C
sv
, and t
db
 are the initial cost, 
salvage value, and useful life, respectively. C
e
, P
db
, 
and η present the unit energy cost, power used in the 
machining time, and the working efficiency of the 
machine tool, respectively. C
T
 and T
T
 are the unit cost 
Table 9.  Optimization results generated by the BRNN-CRITI-NSGAG
Method
Optimization parameters Responses
S [rpm] D [mm] f [mm/rev] DT [mm] Ra [μm] VH [HV]
Initial values 630 0.06 0.04 6 0.27 467.2
NSGA-G 630 0.10 0.05 8 0.16 502.6
NSGA-II 352 0.10 0.04 7 0.18 497.2
Improvement [%] 40.7 7.6

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)3-4, 155-168
167 Impacts of Burnishing Variables on the Quality Indicators in a Single Diamond Burnishing Operation
and useful life of the diamond tool tip, respectively. 
C
l
, F, and C
c
 present the unit cost, flow rate of the 
fluid, and the unit cost of the cleaning operation, 
respectively. Table 10 presents the experimental 
coefficients for the TDC model. The TDC value 
is decreased by 20 % at the selected optimality, as 
compared to the common values (Table 11). 
Table 10.  The experimental coefficients for estimating total 
diamond burnishing cost
C
o
 
[USD/h]
N
db
C
mu
 
[USD]
C
sv
 
[USD]
M
l
  
[h]
C
e
  
[USD/kWh]
8.2 1 61500 4000 20000 0.14
C
T
 
[USD]
t
T
 
  
[s]
F  
[ml/h]
C
l
 
[USD/l]
C
c
 
[USD/l]
13.8 3000 80 2 0.46
Table 11.  The reduction in the total diamond burnishing cost
Method
Optimization parameters Cost
S
[rpm]
D
[mm]
f 
[mm/rev]
DT 
[mm]
TDC 
[USD]
Common values 630 0.06 0.04 6 2.45
Optimal values 630 0.10 0.05 8 1.96
Reduction [%] 20.0
5  CONCLUSIONS
In this study, a new single diamond burnishing 
process was proposed and optimized to improve the 
Vickers hardness and decrease the average roughness. 
The parameter inputs were the S, D, f, and DT. The 
CRITIC method was applied to compute the weights, 
while the BRFFNN approach was utilized to develop 
the response model in terms of the optimizing factors. 
The obtained findings can be expressed as:
1. To enhance the Vickers hardness, the highest DT 
is applied, while the lowest values of the S, f, and 
DT are recommended. To decrease the average 
roughness, the highest values of the S, D, and DT 
are applied, while the lowest f is encouraged.    
2. For the Ra, the f is named as the most effective 
parameter, followed by the S, D, and DT, 
respectively. For the VH, the S is named as the 
most effective parameter, followed by the f, D, 
and DT, respectively. 
3. The optimal data of the S, D, f, and DT were 
370 rpm, 0.10 mm, 0.04 mm/rev, and 8 mm, 
respectively. The VH was improved by 7.6 % 
while the Ra was decreased by 40.7 %. The total 
diamond burnishing cost could be decreased by 
20 % at the optimal solution.   
4. This investigation considered the average 
roughness and Vickers hardness of a new 
single diamond burnishing. Further work with 
more objectives, such as the wear rate, energy 
consumption, and grain size will be addressed.
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