*Corr. Author’s Address: Changchun University, School of Mechanical and Vehicle Engineering, China, 210101011@mails.ccu.edu.cn 494
Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506 Received for review: 2024-01-10
© 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2024-06-20
DOI:10.5545/sv-jme.2024.918 Original Scientific Paper Accepted for publication: 2024-07-08
Study on the Properties of Sinusoidal Micro-Textured Ball End 
Milling Cutter for Milling Titanium Alloy
Li, Q. – Wang, B. – Ma, C. – Guan, Q. – Shi, H. – Xiao, K. – Zhang, S.
Qinghua Li – Baizhong Wang – Chunlu Ma – Qingyu Guan – Hu Shi – Kai Xiao – Shihong Zhang*
Changchun University, School of Mechanical and Vehicle Engineering, China
To improve the cutting performance when cutting hard alloys and achieve reasonable optimization of micro-texture parameters, this paper 
proposes a sinusoidal micro-textured tool, with four parameters set as micro-textured spacing, period, width, and amplitude. Establish three-
dimensional models of non-micro-textured and micro-textured milling tools and simulate the milling process using finite element simulation. 
Study the effects of milling force and milling temperature on tool performance. Prepare micro-textured milling tools for orthogonal experiments, 
analyse the effects of milling force and the surface roughness of a titanium alloy workpiece, and study the impact of different micro-textured 
parameters on milling tool performance. Obtain the parameters that have the greatest impact on milling tool performance, and then use 
genetic algorithm to optimize three sets of parameter combinations. Use the optimized parameters to prepare milling tools for comparative 
experiments, and then determine the optimal parameter combination. The research results indicate that micro-textured tools can effectively 
improve the milling performance of the tool, and the spacing between sinusoidal micro-textures has the greatest effect on improving the 
milling performance of the tool. When the period of sinusoidal micro-texture is 2.87 and the amplitude is 25.13 μm, width is 79.89 μm, and 
spacing is 134.54 μm, the milling performance of the tool is optimal.
Keywords: Sinusoidal micro-texture, milling performance of milling tools, milling force, milling temperature, surface roughness of the 
titanium alloy workpiece, parameter optimization, titanium alloy
Highlights
• Calculate the micro-textured placement area on the front face of the milling cutter blade through calculation.
• Propose a sinusoidal micro-texture. 
• Verification of milling performance of ball end milling cutters with sinusoidal micro-texture through finite element simulation.
• Obtaining differences in milling performance of cutting tools with different micro-texture factors under different parameters 
through orthogonal experiments.
• By using algorithms to optimize orthogonal experimental data, the optimal parameters of sinusoidal micro-textured factors 
were obtained.
0  INTRODUCTION
Titanium alloy, as a new generation of high-
temperature structural material, has advantages such 
as high strength, corrosion resistance, light of weight, 
and excellent high-temperature resistance. With the 
rapid development of the automotive manufacturing 
and aerospace industries, titanium alloys have been 
promoted towards high temperature resistance, 
long service life, and high performance [1] and [2]. 
However, at present, titanium alloy materials still have 
problems such as poor machinability, high cutting 
force per unit area, easy wear of tools, and high cutting 
temperature [3] to [5]. Scholars at home and abroad 
have found that new tools with micro-textures have 
better cutting performance than other tools [6]. Ali 
et al. [7]  conducted numerical studies on the cutting 
process of AISI630 stainless steel using different 
micro-groove tools, demonstrating that micro-texture 
can extend the tool’s service life. Patel et al. [8] studied 
the effects of micro-textured parameters on stress and 
tool wear during titanium alloy cutting. They found 
that micro-textured width, depth, and edge distance 
have a significant impact on cutting force; The depth 
of micro-texture and the distance from the main 
cutting edge have a significant impact on the cutting 
temperature. Pan et al. [9] investigated the effect of 
cutting speed on the surface quality of micro-textured 
PCBN tool dry turning hardened bearing steel GCr15. 
The research results indicate that the effect of cutting 
speed on surface roughness varies depending on the 
type of micro-texture, and a microporous texture can 
minimize the surface roughness of the workpiece. 
Zhang et al. [10] investigated the influence of cutting 
edge types and micro-textured parameters on the 
cutting performance of ball end milling cutters, 
established a mathematical model, and used a genetic 
algorithm to optimize the micro-texture and blunt 
round edge feature parameters of the rear cutting 
surface. Finally, the blunt round edge radius was 
0.04 mm, and the micro texture diameter was 40μm. 
Spacing of 175 μm. The distance from the blade is 120 
μm. Depth of 80 μm is the most effective positional 
parameter. Sahu and Jha [11]  studied the hybrid 
manufacturing of AISI316L. The research results 
indicate that different structural characteristics lead 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
495 Study on the Properties of Sinusoidal Micro-Textured Ball End Milling Cutter for Milling Titanium Alloy
to differences in the machinability of materials. Yang, 
et al. [12] studied the effect of micro-texture on the 
milling performance of ball end milling cutters and 
the anti-wear and friction reduction performance of 
surface micro-texture. The research results found that 
under dry cutting conditions, micro-texture can reduce 
milling force, lower milling temperature, reduce tool 
front face wear, and extend tool life during the milling 
process of ball end milling cutters.
Sinusoidal micro-textures can optimize the 
mechanical properties of materials by adjusting their 
shape, size, and distribution parameters. At the same 
time, they can increase the interface area and stress 
distribution of the material, thereby improving its 
strength and toughness, making the material more 
durable and reliable. 
Therefore, in order to solve the problems of 
large milling force, high milling temperature and low 
surface quality of a titanium alloy workpiece when 
milling titanium alloy with a ball end milling cutter 
and improve the milling performance of milling 
tools, this article is based on sinusoidal micro-texture. 
Orthogonal experiments are used to simulate the 
milling process using finite element simulation. The 
influence of micro-texture on the milling performance 
of the tool is studied through changes in force and 
temperature. Then the sinusoidal micro-texture was 
prepared on the rank tool surface by laser processing 
technology, and the micro-textured parameters that 
have the greatest impact on the milling performance of 
the tool are determined through experiments. Finally, 
a mathematical model is established, optimizing the 
parameter size based on genetic algorithm to obtain 
the optimal parameter combination.
1  FINITE ELEMENT SIMULATION
Ti6A14V titanium alloy is widely used in the 
manufacturing industry due to its excellent processing 
performance, but its processing efficiency is low and 
it wears easily, making it a difficult material [13] to 
machine. This article uses finite element simulation 
software (Abaqus2021) to simulate the milling of 
Ti6A14V titanium alloy with a hard alloy ball end 
milling cutter. The milling performance of the tool is 
comprehensively evaluated using milling force and 
milling temperature as evaluation criteria, and the 
influence of micro-texture on the milling performance 
of the tool is explored.
1.1  Distribution of Micro-Textured Positions
The position of micro-texture plays a crucial role 
in the entire cutting process, and the reasonable 
distribution of micro-texture can effectively improve 
cutting performance. In order to fully participate in 
milling, the micro-texture is set within the milling 
area of the tool. The milling area of the tool is related 
to the angle between the workpiece and the plane, 
the milling depth, and the size of the tool radius. The 
distribution area of micro-texture is shown in Fig. 1.
Where a
p 
is the milling depth, θ is the inclination 
angle, R
1
 is the maximum milling radius, R
2
 is the 
minimum milling radius, points A and B are the 
contact points between the tool and the workpiece, 
and V
0 
is the tool speed. Determine the milling area by 
calculating the maximum and minimum milling radii, 
expressed as:
Fig. 1.  Distribution map of micro-textured areas on the front face of ball end milling cutter blades

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
496 Li, Q. – Wang, B. – Ma, C. – Guan, Q. – Shi, H. – Xiao, K. – Zhang, S.
 
1
15 , (1)
 
2

 





arccos,
Ra
R
p
 (2)
 RR
Ra
R
p
11

 





sina rccos,  (3)
 RR
21
 sin.  (4)
Given the tool radius and workpiece inclination 
angle, calculate the sizes of R
1 
and R
2
, and construct a 
rectangular micro-textured region abcd in the O
1
O
2
BA 
region.
1.2  Simulation Model Establishment
During the cutting process, micro-texture can reduce 
the contact area between the tool and chip, as well as 
reduce frictional stress and cutting temperature, and 
its effect often changes with the change of micro-
textured parameters [14] and [15]. Therefore, in order 
to explore the influence of different parameters of 
sinusoidal micro-texture on the milling performance 
of milling tools, this paper sets four parameters: 
period, width, amplitude, and micro-textured spacing 
as variables for research. The established ball end 
milling cutter model and sinusoidal micro-textured 
ball end milling cutter model are shown in Fig. 2, and 
the sinusoidal micro-textured model is shown in Fig. 
3.
Fig. 2. Three dimensional simulation models  
of non-micro-textured ball end milling cutters  
and sinusoidal micro-textured ball end milling cutters
The three-dimensional model of the ball end 
milling cutter is divided into tetrahedral grids. 
The minimum grid size of the tool is 0.01 mm, the 
maximum grid size is 0.05 mm, the minimum grid size 
of the workpiece is 0.025 mm, and the maximum grid 
size is 0.05 mm. The finite element simulation model 
of the interaction between the tool and the workpiece 
is shown in Fig. 4. The design milling amount scheme 
is: v
c
 = 120 m/min, f
z
 = 0.08 mm/z, a
p 
= 0.5 mm.
Fig. 3.  A three-dimensional model of sinusoidal micro-texture
Fig. 4.  Assembly model of tool -workpiece in finite element 
simulation
The finite element simulation analysis adopts the 
Johnson Cook constitutive model, which can meet 
the simulation material requirements under various 
conditions. It can accurately reflect the large strain 
and thermal softening effects of materials during the 
milling process  [16] to [18] .The workpiece material 
is Ti6A14V titanium alloy, and its constitutive model 
parameters are shown in Table 1. The empirical 
formula of the Johnson Cook constitutive model is:



 






























AB C
tt
tt
n p
m
m
11
0
0
0
ln


 


	

	


	

	
,(5)
among them σ is material flow stress, A material 
yield limit, B strain change coefficient, C strain rate 
reinforcement factor, m thermal softening parameters, 
n strain hardening parameters, ε equivalent plastic 
strain, p equivalent plastic strain rate, 0 reference 
value of strain rate, t deformation temperature, t
0 
room temperature, and t
m
 material melting point 
temperature.
Table 1.  Johnson Cook constitutive model parameters   
of Ti6A14V [19]
A [MPa] B [MPa] C n m t
0
 [°C] t
m
 [°C]
860 683.1 0.035 0.47 1 25 1650

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
497 Study on the Properties of Sinusoidal Micro-Textured Ball End Milling Cutter for Milling Titanium Alloy
Using the orthogonal experimental method 
for milling simulation, a four factor, three level 
orthogonal experiment is designed. The period of the 
sinusoidal micro-texture is 2 to 4, the width of the 
micro texture is 0.02 mm to 0.08 mm, the amplitude 
of the micro texture is 0.1 mm to 0.2 mm, and the 
spacing between the micro-textures is 0.1 mm to 0.2 
mm. The factor and level table are shown in Table 
2, and the orthogonal experimental table is shown in 
Table 3. 
Table 2.  Factors and levels table
Level
Factors
Cycle 
[s]
Width 
[mm]
Amplitude 
[mm]
Spacing 
[mm]
1 2 0.02 0.01 0.1
2 3 0.05 0.03 0.15
3 4 0.08 0.05 0.2
Table 3.  Orthogonal experimental table for finite element 
simulation test and milling test
Experiment 
number
Cycle 
[s]
Amplitude 
[mm]
Width 
[mm]
Spacing 
[mm]
1 2 0.01 0.02 0.1
2 2 0.03 0.05 0.15
3 2 0.05 0.08 0.2
4 3 0.01 0.05 0.2
5 3 0.03 0.08 0.1
6 3 0.05 0.02  0.15
7 4 0.01 0.08  0.15
8 4 0.03 0.02 0.2
9 4 0.05 0.05 0.1
1.3  Simulation Results and Analysis
Finite element analysis was conducted on the non-
micro-textured ball end milling cutter and 9 groups of 
micro-textured ball end milling cutters. The feed and 
rotational motion of the ball end milling cutter during 
the milling process will generate milling forces,, 
including tangential force, radial force and vertical 
force. At the same time, the high-speed rotation of 
the tool generates a large amount of heat concentrated 
on the milling cutter edge. Therefore, three types of 
milling force data for each group of ball end milling 
cutters are obtained through finite element analysis. 
The combined force is calculated according to Eq. 
(6). The same node is taken at each group of milling 
cutter edges, and the milling temperature changes 
of the nodes are analyzed to obtain simulation data, 
as shown in Fig. 5. From Fig. 5 it can be seen that 
the simulation results of milling force and milling 
temperature are constantly changing due to the 
different sizes of micro-textured parameters in each 
group of experiments. 
a) 
E.0 E.1 E.2 E.3 E.4 E.5 E.6 E.7 E.8 E.9 E.10
0
50
100
150
200
250
300
350
400
450
 Sinusoidal micro-textured ball milling cutter
 Ball end milling cutter without micro-texture
Experimental group
Milling force [N]
b) 
E.0 E.1 E.2 E.3 E.4 E.5 E.6 E.7 E.8 E.9 E.10
0
50
100
150
200
250
300
 Sinusoidal micro-textured ball milling cutter
 Ball end milling cutter without micro-texture
Experimental group
Milling temperature [℃]
Fig. 5.  Finite element simulation data image  
with parameter combinations obtained from nine sets of finite 
element simulation experiments; a) milling force variation ,  
and b) variation of milling temperature
The simulation results of micro-textured ball end 
milling cutters with different parameter sizes are better 
than those of non- micro-textured ball end milling 
cutters. Analyzing the reasons, on the one hand, the 
microgroove-texture can store the chips generated 
during the milling process, effectively reducing the 
contact between the chips and the tool tip, reducing 
tool wear and thus reducing milling force. On the 
other hand, the existence of the microgroove-texture 
increases the heat dissipation space during the milling 
process, which is conducive to the release of heat 
generated during milling, thereby reducing the milling 
temperature. Combining simulation test data, it was 
found that the fifth group had the best results.
 FF FF
xyz
 
222
, (6)

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
498 Li, Q. – Wang, B. – Ma, C. – Guan, Q. – Shi, H. – Xiao, K. – Zhang, S.
among them F is milling force combined force; F
x
 
tangential force; F
y
 radial force; and F
z 
vertical force.
Through the finite element simulation results, 
it can be concluded that micro-texture can improve 
the milling performance of milling tools to a certain 
extent. Preparing micro-texture on the surface of 
milling cutters can effectively reduce milling force 
and lower milling temperature.
2  MILLING EXPERIMENT
Prepare sinusoidal micro-textured ball end milling 
cutters with different parameters based on the 
established three-dimensional model for orthogonal 
experiments.
2.1  Experimental Materials and Equipment
The cutting tool required for this milling test is a 
hard alloy ball-end milling cutter, whose model is 
BNM-200-S, and the cutting tool style is shown in 
Fig. 6. The two-dimensional plan is shown in Fig. 7. 
The cutter is suitable for processing titanium alloy, 
stainless steel, cast iron and other materials, and 
its main dimensions are shown in Table 3. Milling 
parameters used in the test are shown in Table 4. In 
the experiment, the semiconductor single-mode laser 
marking machine zt-y-50w was used to prepare micro-
texture. Leica ultra-depth of field microscope model 
DVM2500 was used to observe the micro-texture 
morphologies of nine groups with different parameter 
sizes. Each micro-texture was observed three times 
to obtain the best results. The image displayed by 
micro-texture parameters is shown in Fig. 8. The tool 
used in the experiment is cemented carbide ball end 
milling cutter, and Ti6A14V titanium alloy is used 
as the processing workpiece. The numerical control 
milling machine model is CMV-850A. The milling 
experimental platform is shown in Fig. 9.
Fig. 6.  The carbide ball end milling cutter blade 
Fig. 7.  The carbide ball end milling cutter blade two-dimensional 
plan
Table 3.  Main dimensions of ball end milling cutter blade
Dimension 
[mm]
Name 
d s R L H
5 5 10 15 20
Table 4.  Main dimensions of ball end milling cutter blade
v
c 
[mm/s] f
z 
[mm/z] a
p 
[mm]
120 0.08 0.5
Fig. 8.  Sinusoidal micro-textured images under a microscope
Fig. 9.  Milling experiment platform

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
499 Study on the Properties of Sinusoidal Micro-Textured Ball End Milling Cutter for Milling Titanium Alloy
2.2  Analysis of the Milling Force
Measure the radial force, axial force, and tangential 
force using a force measuring instrument, and combine 
the forces in the three directions to obtain the cutting 
force. The measured milling force of the non-micro-
textured tool and the milling force of each group of 
micro-textured tools are shown in Fig. 10. From Fig. 
10 it can be seen that the milling force generated by 
the micro-textured tool during the milling process 
is reduced at a certain rate compared to the non-
micro-textured tool. After calculation, the highest 
reduction rate of milling force generated by the sine 
type micro-textured ball end milling cutter compared 
to the non-micro-textured ball end milling cutter in 
the nine groups of experiments can be close to 30 %. 
Furthermore, it has been verified that micro-textured 
structures can improve the cutting performance of 
cutting tools, and it was found in the experiment that 
the fifth group of tests generated the smallest milling 
force, which was 318.58 N.
E.0 E.1 E.2 E.3 E.4 E.5 E.6 E.7 E.8 E.9 E.10
0
200
400
600
800
Milling force [N]
Experimental group
 Sinusoidal micro-textured ball end milling cutter
 Ball end milling cutter without micro-texture
 Reduction rate of milling force
0
5
10
15
20
25
30
35
Milling force reduction [%]
Fig. 10.  Comparison of milling force data between nine different 
parameter combinations of sinusoidal micro-textured ball end 
milling cutter milling experiments and non-micro-textured tool 
milling experiments
The transverse comparison of the percentage 
difference between the experimental results of milling 
force obtained and the data obtained on the simulation 
platform is made, and the results are shown in Fig. 
11. The error between the two is between 9 % and 
19 %, which belongs to a reasonable error range. In 
addition, it can be found that the experimental results 
of each group are slightly higher than the simulation 
results, because the simulation analysis is carried 
out under absolutely ideal conditions compared with 
the experiment. In the real process, the experimental 
results are often affected by the vibration of the 
machine tool, the change of ambient temperature 
and other factors, which leads to the increase of the 
milling force.
E.0 E.1 E.2 E.3 E.4 E.5 E.6 E.7 E.8 E.9 E.10
0
100
200
300
400
500
600
Milling force [N]
Experimental group
 Experimental milling force
 Simulation milling force
 Percentage of milling force difference
0
5
10
15
20
Percent difference [%]
Fig. 11.  Comparison of milling force experiments values  
and simulation values
Calculate the average and range of milling forces 
for four different factors at different levels, as shown 
in Table 5, for intuitive analysis. Through the analysis 
of experimental results, it is found that the influence 
of micro-textured period, amplitude, spacing, and 
width on the milling force at different levels, shown 
in Fig. 12. It can be clearly seen from Fig. 12 that as 
the micro-textured period, amplitude, and spacing 
increase, the milling force of the tool first decreases 
and then increases, and gradually decreases with the 
increase of micro-textured width. Further analysis 
shows that the reason for its change is that as the 
micro-textured cycle increases to a certain extent, 
the storage capacity of chips is improved, effectively 
reducing wear and further reducing milling force. 
As the cycle further increases, the range of micro-
textured participation in the milling process decreases, 
thereby increasing milling force. When the amplitude 
of micro-texture increases within a certain range, the 
sharpness of the micro-textured surface increases, 
making it easier for the milling edge to penetrate the 
surface of the workpiece during the milling process, 
thereby effectively reducing milling force. When the 
amplitude of micro-texture continues to increase, 
it will cause significant vibration during the milling 
process, thereby increasing the milling force. The 
reason for the variation of milling force with the size 
of micro-textured spacing is that when the micro-
textured spacing initially increases, a lubricating 
oil film is formed during the milling process, which 
can effectively reduce the friction in the milling 
area and thus reduce milling force. When the micro-

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
500 Li, Q. – Wang, B. – Ma, C. – Guan, Q. – Shi, H. – Xiao, K. – Zhang, S.
textured spacing further increases, it will affect the 
generation of lubricating oil film, increase the friction 
in the milling area and thus increase the milling 
force. As the width of the micro-texture increases, the 
protrusion area on the tool surface decreases, leading 
to a decrease in the accumulation of heat on the tool 
surface during the milling process, thereby reducing 
tool wear and extending the tool’s service life. As the 
width of the micro-texture increases, the channel for 
chip removal also widens, reducing the accumulation 
of chips and reducing milling force.
The range method was used to analyse the range 
values of four factors. The primary and secondary 
order of the influence of micro-texture parameters 
on milling force is: micro-textured spacing > micro-
textured period > micro-textured amplitude > micro-
texture width. That is, micro-texture spacing has the 
greatest impact on milling force generated by milling 
titanium alloy, while micro-textured width has the 
smallest impact on milling force.
Table 5.  Visual analysis table for the average milling force and 
factor range of four factors at different levels
Cycle 
[N]
Amplitude 
[N]
Width 
[N]
Spacing 
[N]
Average level 1 394.3 391.2 399.8 347.1 
Average level 2 360.6   372.8 389.3 358.8 
Average level 3 414.8 405.8 380.8 436.9 
Range 54.2 33 19 78.1 
level 1 level 2 level 3
350
400
450
Surface force [N]
 Cycle [s]
 Amplitude [mm]
 Width [mm]
 Spacing [mm]
Fig. 12.  The variation of milling force with different levels  
of sinusoidal micro-textured factors
2.3  Analysis of the Milling Temperature
An infrared thermal imager DM66 was used to record 
the temperature values in the milling process of each 
group of orthogonal experiments, and the average 
temperature of the milling process was calculated as 
the reference data of the milling temperature. The 
milling temperature of the measured tool without 
micro-texture and the milling temperature of each 
group of micro-texture tools were shown in Fig. 
13. As can be seen from Fig. 13 compared with the 
tool without micro-texture, the milling temperature 
generated by the micro-texture tool during the milling 
process decreases at a certain rate. By calculation, 
the maximum reduction rate of milling temperature 
produced by the sinusoidal micro-textured ball end 
milling cutter is close to 30 % compared with the 
non-micro-textured ball end milling cutter in nine 
experiments.
E.0 E.1 E.2 E.3 E.4 E.5 E.6 E.7 E.8 E.9 E.10
0
100
200
300
400
Milling temperature [℃]
Experimental group
 Sinusoidal micro-textured ball end milling cutter
 Ball end milling cutter without micro-texture
 Reduction rate of milling temperature
0
5
10
15
20
25
30
Milling temperature reduction [%]
Fig. 13.  Comparison of milling temperature data between nine 
different parameter combinations of sinusoidal micro-textured ball 
end milling cutter milling experiments and non-micro- textured tool 
milling experiments
The transverse comparison of the percentage 
difference between the experimental result of milling 
temperature obtained and the numerical value 
obtained in the simulation process is made, as shown 
in Fig. 14. The error between the two is between 2 % 
to 20 %, which is within the reasonable error range. 
E.0 E.1 E.2 E.3 E.4 E.5 E.6 E.7 E.8 E.9 E.10
0
100
200
300
400
Milling temperature [℃]
Experimental group
 Experimental milling temperature
 Simulation milling temperature
 Percentage of milling temperature difference
0
5
10
15
20
25
Percent difference [%]
Fig. 14.  Comparison of milling temperature experiments values 
and simulation values

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
501 Study on the Properties of Sinusoidal Micro-Textured Ball End Milling Cutter for Milling Titanium Alloy
2.4  Analysis of the Surface Roughness of Titanium Alloy 
Workpiece 
The surface roughness of the milled titanium alloy 
workpiece was measured using an optical profile 
microscope model WYKO2900. In the measurement 
of the surface roughness of titanium alloy workpiece, 
the surface roughness standard Ra is used to evaluate 
the surface roughness of the workpiece surface, which 
is defined as the absolute value of the average surface 
height difference per unit length, and is usually used 
to describe the surface roughness of mechanical parts. 
In order to make the data more accurate, three nodes 
are evenly selected on each milling mark for Ra value 
detection, and finally the average Ra value of the three 
nodes is taken as the reference basis for subsequent 
analysis, and draw the surface roughness of each 
group of experimental titanium alloy workpieces as 
shown in Fig. 16. 
E.0 E.1 E.2 E.3 E.4 E.5 E.6 E.7 E.8 E.9 E.10
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
Surface roughness of titanium alloy [nm]
Experimental group
 Sinusoidal micro-textured ball end milling cutter
 Ball end milling cutter without micro-texture
 Reduction rate of surface roughness
0
5
10
15
20
25
Surface roughness reduction [%]
Fig. 16.  Comparison chart of titanium alloy workpiece surface 
roughness data for nine sets of sinusoidal micro- textured ball end 
milling cutters in milling experiments
From Fig. 16, it can be seen that the seventh 
group of experiments has the lowest surface 
roughness of titanium alloy workpiece, which is 
615.29 nm. Compared with the tool without micro-
texture, the surface roughness of the titanium alloy 
workpiece is significantly reduced after milling by 
the micro-texture tool. Through calculation, the 
maximum reduction rate of the surface roughness of 
the titanium alloy workpiece can be close to 20 % in 
nine groups of experiments. The variation of surface 
roughness of the titanium alloy workpiece under level 
changes due to different factors is shown in Fig. 17. 
It can be seen that the same factor has a significant 
impact on the surface roughness of a titanium alloy 
workpiece at different levels. As the micro-textured 
After that, orthogonal analysis was carried out on 
the experimental data, and the orthogonal test table is 
shown in Table 6. The effects of micro-texture period, 
amplitude, spacing and width on different horizontal 
milling temperatures are shown in Fig. 15. It can be 
clearly seen from Fig. 15 that with the increase of 
micro-texture period, amplitude and spacing, the 
milling temperature of the tool first decreases and then 
increases, while with the increase of micro-texture 
width, the milling temperature first increases and then 
decreases.
As for the special change of milling temperature 
with the increase of micro-texture width, the analysis 
of the reason is that with the continuous increase of 
width, the ability to accommodate chips in the space 
is strong, and at the same time, the heat cannot be 
effectively dissipated, so the milling temperature 
rises more violently. When the micro-texture width 
increases to a certain extent, there is enough space 
to dissipate heat, so the milling temperature will be 
significantly reduced. 
The range method was used to analyse the range 
values of the four factors. The order of influence of 
micro-texture parameters on milling temperature is 
as follows: micro-texture spacing > micro-texture 
amplitude > micro-texture width > micro-texture 
period. In other words, the micro-texture spacing has 
the greatest influence on the milling temperature, 
while the micro-texture period has the least influence 
on the milling temperature.
Table 6.  Visual analysis table for the average milling temperature 
and factor range of four factors at different levels
Cycle  
[°C]
Amplitude 
[°C]
Width  
[°C]
Spacing 
[°C]
Average level 1 217.8 218.6 213.9 216.5
Average level 2 251.5 212.2 245.3 211.9
Average level 3 244.3 246.8 218.3 249.2
Range 28.8 347.5 31.4 37.3
level 1 level 2 level 3
200
225
250
275
Surface temperature [℃]
 Cycle [s]
 Amplitude [mm]
 Width [mm]
 Spacing [mm]
Fig. 15.  The variation of milling temperature with different levels 
of sinusoidal micro-textured factors

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
502 Li, Q. – Wang, B. – Ma, C. – Guan, Q. – Shi, H. – Xiao, K. – Zhang, S.
cycle and spacing increase, the surface roughness 
of the workpiece first decreases and then increases. 
As the micro-textured width increases, the surface 
roughness of the workpiece first increases and then 
decreases. The surface roughness of the workpiece 
continues to increase with the increase of the micro-
texture amplitude.
Calculate the average and parameter range of 
surface roughness of titanium alloy workpieces for 
four different factors at different levels, as shown in 
Table 7 for intuitive analysis. Analyse the reasons 
for the variation of surface roughness of titanium 
alloy workpieces with the parameter size of the four 
factors, As the micro-texture cycle increases, the 
micro-texture itself can provide good lubrication, 
thus effectively reducing the surface roughness of 
the titanium alloy. However, as the micro-texture 
cycle continues to increase, the milling force and heat 
generated during the milling process are concentrated 
in smaller surface areas, resulting in an increase in 
surface roughness. When the micro-texture cycle is 
too large, it can cause interference between micro-
textures, increasing instability which leads to an 
increase in surface roughness of the workpiece. 
Increasing the spacing between micro-textures to a 
certain extent can reduce the generation of vibrations 
and burrs, thereby reducing surface roughness. When 
the spacing is too large, the role of micro-texture 
weakens, thereby increasing surface roughness. When 
the width of the micro-texture increases to a certain 
extent, the storage of chips increases, resulting in 
chips not falling off in a timely manner and causing a 
certain degree of wear on the workpiece. Moreover, as 
the width increases, the number of sinusoidal micro-
textures decreases, resulting in smaller shear forces 
and leaving larger burrs and protrusions on the surface 
of the workpiece, resulting in an increase in surface 
roughness. As the width of the micro-texture gradually 
increases, the contact area between the tool and the 
workpiece decreases, enhancing the storage capacity 
of the micro-texture. On the one hand, it reduces the 
wear caused by chips on the workpiece, while also 
reducing surface burrs and protrusions, effectively 
reducing low surface roughness. As the amplitude 
of micro-texture continues to increase, it may cause 
the sharpness of the micro-textured surface to be too 
high, causing greater vibration generated by milling, 
thereby affecting surface quality and increasing the 
roughness of titanium alloy workpiece surface.
The range method was used to analyse the range 
values of four factors, and the main and secondary 
order of the influence of micro-textured factors on 
the surface roughness of titanium alloys is: micro-
texture spacing > micro-texture amplitude > micro-
texture period > micro-texture width. That is, micro-
texture spacing has the greatest impact on the surface 
roughness of titanium alloys, while micro-texture 
width has the smallest impact on milling force.
Table 7.  Visual analysis table for the average surface roughness 
and factor range of four factors at different levels
Cycle 
[nm]
Amplitude 
[nm]
Width 
[nm]
Spacing 
[nm]
Average level 1 717 661.6 698.7 682.9 
Average level 2 669.4 713.9 721.9 665.5 
Aaverage level 3 709.3 720 675.1 747.8 
Range 47.5 58.6 46.8 82.8 
level 1 level 2 level 3
600
650
700
750
800
Surface roughness [nm]
 Cycle [s]
 Amplitude [mm]
 Width [mm]
 Spacing [mm]
Fig. 17.  The variation of titanium alloy surface roughness with 
different levels of sinusoidal micro-texture factors
The experimental results show that the influence 
of the four micro-texture parameters on milling force 
is as follows: micro-texture spacing > micro-texture 
period > micro-texture amplitude > micro-texture 
width, and the influence on the surface roughness of 
the workpiece is as follows: micro-texture spacing 
> micro-texture amplitude > micro-texture period > 
micro-texture width. Micro-textured cutting tools can 
effectively improve milling performance, and micro-
texture spacing has the greatest impact on tool milling 
performance. Therefore, when milling titanium alloys 
with sinusoidal micro-textured ball end milling 
cutters, the size of micro-texture spacing should be 
given priority consideration to improve the milling 
performance of the tool.
3  PARAMETER OPTIMIZATION
By studying the orthogonal experimental group of 
sinusoidal micro-textured ball end milling cutters for 
milling titanium alloy, the magnitude of the influence 
of four micro-texture parameters on the milling 
performance of the tool was preliminarily determined. 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
503 Study on the Properties of Sinusoidal Micro-Textured Ball End Milling Cutter for Milling Titanium Alloy
In order to further explore the micro-texture parameters 
that can achieve the optimal milling performance of 
the tool, a multiple regression model was established 
with the period, width, amplitude, and spacing of the 
sinusoidal micro-texture as variables. The optimized 
parameter solution set was calculated using a genetic 
algorithm to select the optimal parameters in the 
solution set, to prepare milling tools for comparative 
experiments, and ultimately determine the optimal 
parameters for micro-texture.
3.1  Data Preprocessing
Due to the different units of milling force, milling 
temperature, and surface roughness, it is not possible 
to compare them simultaneously. Therefore, the 
formula for dimensionless reprocessing of three types 
of data is [20]:
 Bc
A
A
ci
i
i
i
i
n
 


2
1
1000 12 9 ,, ,..., . (7)
The milling force, milling temperature, and 
surface roughness data were sequentially brought in to 
obtain non-quantitative data as shown in Table 8.
Table 8.  The three milling performance parameters have no 
dimensional data
Experiment Milling force Temperature Roughness
1 331.01 276.88 316.13
2 293.43 306.74 343.61
3 380.64 372.44 363.75
4 346.77 367.47 335.52
5 270.63 270.59 307.21
6 301.79 308.05 312.92
7 319.29 315.52 292.77
8 386.12 354.30 368.25
9 351.91 402.88 351.42
3.2  Mathematical Model Establishment
The accuracy of parameter optimization depends 
on the reasonable construction of the mathematical 
model. Therefore, before optimizing the parameters, a 
reasonable mathematical model should be constructed  
[21] to [23].  After conducting orthogonal experimental 
research on the milling of titanium alloy with a 
sinusoidal micro-textured ball end milling cutter, a 
multivariate linear regression equation is established 
with the period, width, amplitude, and spacing of the 
texture as independent variables regarding milling 
force, milling temperature, and workpiece surface 
roughness. The mathematical model is as follows:
 
Sa La La La La L
aL aL aL C

 
11 22 33 44 5
2
1
6
2
27
2
38
2
4
, (8)
where S is the optimization objective; S
1 
is the micro-
texture cycle; S
2
 is the micro-texture width; S
3
 is 
the micro-texture amplitude; S
4
 is the micro-texture 
spacing; a
1
; a
2
; a
3
; a
4
; a
5
; a
6
; a
7
; a
8
 are the corrections 
for each variable to be determined; The coefficient 
C is a constant, and its magnitude is related to the 
surface properties of the tool and workpiece materials. 
Substitute the data in Table 5 into Eq. (7) for multiple 
linear regression analysis, and obtain the prediction 
models S
1
, S
2
, and S
3
 for milling force, milling 
temperature, and workpiece surface roughness values, 
as follows:
 
S LLL
LL
11 23
4
2
1
215 3133 2 9657 0 3661
4 2279 37 3367 0 054
    
   
...
.. .6 6
0 0010 0 0159 907 5048
2
2
2
3
2
4
L
LL     .. ., (9)
 
SL LL
LL L
21 23
4
2
1
2
2
117 13 4703 4 8555
3 1993 22 7567 0 075
    
   
.. .
.. .
      0 0475 0 0123 566 4405
2
3
2
4
.. ., LL (10)
 
SL LL
LL
31 23
4
2
1
126 4717 2 338 1 6666
2 5644 20 7717 0 0273
   
   
  .. .
.. . L L
LL
2
2
2
3
2
4
0 0185 0 0096 600 0742     .. .. (11)
3.3  Genetic Algorithm Optimization Parameters
Four micro-texture parameter ranges are taken as the 
initial values of the variables (micro-texture period: 
2 to 4, micro-texture amplitude: 10 to 50, micro-
texture width: 20 to 80, micro-texture spacing: 100 
to 200). Set the weight ratio of milling force, milling 
temperature, and surface roughness to 0.3:0.2:0.5. 
The initial population size is set to 200, with 2000 
iterations. After undergoing iterative evolution, the 
corresponding data is obtained by substituting it into 
the mathematical model. The results are multiplied 
by the weight ratio and summed, as shown in Fig. 18. 
It can be seen that the weight ratio sum values of the 
solutions in groups 12, 15, and 17 are the smallest.
Prepare milling tools based on the numerical 
values of three sets of solutions and conduct 
experiments. Comparing the experimental data shown 
in Fig. 19, it can be seen that the 15
th
 group of data has 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
504 Li, Q. – Wang, B. – Ma, C. – Guan, Q. – Shi, H. – Xiao, K. – Zhang, S.
the best result, with a milling force of 289.52 N and 
a surface roughness of 591.22 nm on the workpiece. 
The milling force of the tool and the surface roughness 
of the workpiece are lower than the minimum results 
obtained from the previous nine sets of experiments, 
so the fifteenth set of data is used as the optimal 
parameter combination for sinusoidal micro-texture.
Group 12 Group 15 Group 17
0
100
200
300
400
500
600
700
800
Milling force [N]
 Milling force 
 Surface roughness of titanium alloy
0
100
200
300
400
500
600
700
800
Surface roughness of titanium alloy [nm]
Fig. 19.  Comparison chart of milling performance for three sets  
of optimal parameters
By constructing a mathematical model and using 
genetic algorithm to obtain three sets of optimal 
parameters, a control experiment was conducted to 
determine the cycle = 2.87 s and amplitude = 25.13 
μm, width = 79.89 μm, spacing = 134.5 μm is the 
optimal combination of sinusoidal micro-textured 
parameters.
4  CONCLUSION
This article explores the influence of micro-texture 
on the milling performance of milling tools through 
finite element simulation, using milling force and 
milling temperature as measurement standards. The 
milling experiment is used to determine the micro-
texture parameters that have the greatest impact on the 
milling performance of the tool. Furthermore, genetic 
algorithm is used to optimize the parameter size, and 
the conclusion is as follows:
1)  During the milling process, micro-texture can 
reduce milling force by storing chips, and can 
increase heat dissipation space to promote heat 
release, effectively reducing milling temperature. 
Compared with the non-textured tool, the 
reduction rate of the milling force of the micro-
textured tool in the milling process can reach 
close to 30 %, the reduction rate of the milling 
temperature can reach close to 30 %, and the 
reduction rate of the roughness of the surface of 
the titanium alloy workpiece can reach close to 
20 %. It can be seen that the micro-textured tool 
can effectively improve the milling performance 
of the tool.
2)  Under the same milling conditions, through the 
range analysis of four micro-texture parameters, 
in the analysis of milling force, the degree of 
influence of micro-texture parameters on milling 
force is as follows: micro-textured spacing 
> micro-textured period > micro-textured 
amplitude > micro-texture width. The range of 
micro-texture spacing caused by the influence 
of different factors on milling force is 78.1 N. In 
the analysis of milling temperature, the degree 
of influence of micro-texture parameters on 
milling temperature is as follows: micro-texture 
spacing > micro-texture amplitude > micro-
texture width > micro-texture period. The range 
250
260
270
280
290
300
310
320
330
340
350
Solution set result
Solution sequence number
 Sum result
0  1    2    3   4   5    6    7   8    9  10  11 12  13  14  15 16  17 18  19 20  21 22  23 24  25 26  27 28  29 30  31 32  33 34  35  36 37 38  39  40  41 42  43 44  45  46 47  48 49  50  51  52 53  54 
Fig. 18.  Comparison chart of results of dimensionless resolution

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)9-10, 494-506
505 Study on the Properties of Sinusoidal Micro-Textured Ball End Milling Cutter for Milling Titanium Alloy
of micro-texture spacing caused by the influence 
of different factors on temperature is 37.3 °C. In 
the analysis of the surface roughness of titanium 
alloy, the degree of influence of micro-texture 
parameters on the surface roughness of titanium 
alloy is in the following order: micro-texture 
spacing > micro-texture amplitude > micro-
texture period > micro-texture width. The range 
of micro-texture spacing caused by the influence 
of different factors on surface roughness is 82.8 
μm. Therefore, the improvement effect of micro-
texture spacing on cutter milling performance is 
the best among the four parameters.
3)  After optimizing the parameters using genetic 
algorithm and conducting comparative 
experiments, it was found that when the micro-
texture cycle is 2.87, the amplitude is 25.13 μm, 
the width is 79.89 μm, and the spacing is 134.54 
μm, the milling performance of the sinusoidal 
micro-textured milling cutter is optimal.
5  ACKNOWLEDGEMENTS
The authors would like to thank the members of the 
project team for their dedication and efforts, and 
the teachers and schools for their help. The authors 
declare no conflicts of interest. Here we need to 
thank the following organizations for their strong 
support “Natural Science Foundation of Jilin Province 
- General Project, Study on the Machinability of 
Milling Titanium Alloy with Micro-textured Milling 
Cutter: 20220101227JC” and “Research on Key 
Technologies and Equipment Development for 
Riveting and Inspection of Automotive Brake piston 
Components: 20220201043GX”.
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