*Corr. Author’s Address: Department of Mechanical Engineering, Eastern Mediterranean University, 
Famagusta˝, North Cyprus, Mersin 10, Turkey, mohsen.soori@emu.edu.tr
235
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244 Received for review: 2021-01-28
© 2021 Journal of Mechanical Engineering. All rights reserved.  Received revised form: 2021-04-13
DOI:10.5545/sv-jme.2021.7113 Original Scientific Paper Accepted for publication: 2021-05-04
Virtual Minimization of Residual Stress and Deflection Error  
in the Five-Axis Milling of Turbine Blades
Soori, M. – Asmael, M.
Mohsen Soori* – Mohammed Asmael
Eastern Mediterranean University, Department of Mechanical Engineering, Turkey
To simulate and analyse the real machined parts in virtual environments, virtual machining systems are applied to the production processes. 
Due to friction, chip forming, and the heat produced in the cutting zone, parts produced using machining operation have residual stress 
effects. The machining force and machining temperature can cause the deflection error in the machined turbine blades, which should be 
minimized to increase the accuracy of machined blades. To minimize the residual stress and deflection error of machined parts, optimized 
machining parameters can be obtained. In the present research work, the application of a virtual machining system is presented to predict and 
minimize the residual stress and deflection error in a five-axis milling operations of turbine blades. In order to predict the residual stress and 
deflection error in machined turbine blades, finite element analysis is implemented. Moreover, to minimize the residual stress and deflection 
error in machined turbine blades, optimized parameters of machining operations are obtained by using a genetic algorithm. To validate the 
research work, experimentally determining residual stress by using a X-ray diffraction method from the machined turbine blades is compared 
with the finite element results obtained from the virtual machining system. Also, in order to obtain the deflection error, the machined blades 
are measured by using the CMM machines. Thus, the accuracy and reliability of machined turbine blades can be increased by analysing and 
minimizing the residual stress and deflection error in virtual environments.
Keywords: virtual machining, residual stress, deflection error, parameter optimization, turbine blade
Highlights
• 	 The application of a virtual machining system is presented to predict and minimize the residual stress and deflection error in the 
five-axis milling operations of turbine blades.
• 	 In order to minimize the residual stress and deflection error in machined turbine blades, an optimization technique based on 
genetic algorithms is used.
• 	 The accuracy and reliability of machined turbine blades can be increased by analysing and minimizing the residual stress and 
deflection error in virtual environments.
0  INTRODUCTION
The residual stress in machined parts can be generated 
as a result of mechanical, thermal, and chemical 
effects in chip forming of metal cutting operations. 
The generated residual stress in the machined parts 
can impair the performance of components, such as 
fatigue life, corrosion resistance, and part distortion in 
actual working conditions. Due to the cutting forces 
and cutting temperature, the machined blades have 
deflection errors, which can cause inaccuracy in the 
machined turbine blades. As a result, the residual 
stress and deflection error should be analysed and 
decreased to increase the accuracy and reliability of 
parts produced using machining operations. 
To improve the precision of machined parts, 
the evaluation of surface error characteristics in 
thin-walled constructs during peripheral milling has 
been studied by Wimmer and Zaeh [1]. The process 
parameter optimization of thin-wall machining for 
wire arc additive manufactured parts is investigated by 
Grossi et al. [2] to decrease the deformation error in the 
thin-walled manufactured components. The method 
of error compensation during the milling operations 
of flexible thin-wall parts is presented by Ratchev 
et al. [3] to reduce the deflection error of machined 
parts. To improve the accuracy of thin-walled 
machined parts, an adaptive toolpath methodology 
for three-axis milling is presented by Grossi et al. 
[4]. The finite element method (FEM) based cutting 
velocity selection for thin-walled part machining is 
presented by Scippa et el. [5] to enhance the precision 
of machined components. Finite-Element modelling 
of workpiece vibrations is analysed by Bolsunovskiy 
et al. [6] to optimize the machining parameters and 
increase accuracy in the milling operations of thin-
walled components.
Jiang et al. [7] analysed the effects of cutting 
forces and cutting zone temperature to the residual 
stress of machined components. The application 
of response surface methodology in obtaining the 
optimized machining parameters, such as depth of cut 
and spindle speed, are investigated by Masmiati et al. 
[8] in order to minimize the residual stress, cutting 
force, and surface roughness in the end milling of 
S50C medium carbon steel. Mohammadpour et al. 
[9] investigate the effects of machining parameters 
on the residual stress of machined parts in milling 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244
236 Soori, M. – Asmael, M.
operations. To analyse the influence of the machining 
parameters, such as cutting speed as well as feed 
rate, on the surface roughness and residual stresses 
in produced parts using milling operation, the finite 
element method is used by Zhang and Wu [10]. 
To decrease the residual stress in machined parts 
using turning operations, the effects of cutting tool 
parameters, such as tool nose radius and tool wear on 
residual stresses, are investigated by Lin et al. [11]. 
Cutting tool parameters, such as tool edge radius, are 
investigated by Yang et al. [12] in order to decrease the 
residual stress in machined parts. To study the effects 
of cutting-edge radius and cutting forces on residual 
stresses of machined parts, a finite element model is 
developed by Nasr et al. [13]. 
To decrease the residual stress in machined parts 
and effects of cutting tools materials, machining 
parameters, such as cutting speeds and depth of cut 
to residual stress of machined parts, are investigated 
by Arunachalam et al. [14]. The influence of cutting 
tool parameters, such as tool nose radius on surface 
integrity and residual stresses, are investigated by 
Sharman et al. [15] to decrease the residual stress 
in machined parts. A variable depth-of-cut milling 
strategy for thin-walled workpiece is proposed by 
Yan et al. [16] in order to decrease the deflection error 
in the machined turbine blades. A five-axis adaptive 
flank milling of flexible thin-walled parts based on 
the on-machine measurement is developed by Huang 
et al. [17] to modify the cutting tool paths in terms 
of deflection error minimization. The time domain 
flutter analysis based on the blade element momentum 
(BEM) theory for bend-twist coupled large composite 
wind turbine blades is investigated by Shakya et al. 
[18] to increase the performances of wind turbines 
in actual working conditions. The blisk vibration in 
aircraft engine using similitude models is analysed by 
Luo et al. [19] to predict and decrease the vibration 
of the engine systems in the virtual environments. 
To analyse and modify the machining operations 
in virtual environments, virtual machining systems 
and applications are presented by Soori et al. [20] 
to [24]. To analyse and develop the process of part 
manufacturing using welding operations, a review in 
recent development of friction stir welding process is 
presented by Soori et al. [25]. To increase efficiency 
in process of part production using the friction stir 
spot welding, effects of machining parameters to the 
mechanical properties of aluminium sheet alloys is 
presented by Nasir et al. [26].
According to the analysis of previous published 
papers, the area of residual stress as well as deflection 
error prediction and minimization in milling 
operations by using virtual machining systems has 
been insufficiently explored. Moreover, to minimize 
the residual stress and deflection errors in machined 
parts, the applications of the virtual machining system 
is not studied. 
In this research work, the application of a virtual 
machining system is presented to predict and minimize 
the residual stress and deflection error in a five-axis 
milling operations of turbine blades. The cutting 
forces as well as cutting temperatures for each position 
of cutting tool along machining paths are calculated in 
order to obtain residual stress and deflection error of 
blades due to machining operations by using the finite 
element analysis (FEA). The optimization technique 
of a genetic algorithm is used to calculate the 
optimized machining parameters in terms of residual 
stress and deflection error minimization. To measure 
the residual stresses on the surface and in-depth of the 
machined blades, the X-ray diffraction technique is 
used in the study. The coordinate measuring machines 
(CMM) machines are sued to obtain the deflection 
error in the machined blades. Finally, the obtained 
data are compared by using diagrams.
1  CUTTING FORCE MODEL
To calculate the cutting forces in the five-axis 
machining operations, the cutting force model 
developed by Zhang et al. [27] is applied. 
The XYZ planes are defined in order to describe 
the tool motion process, workpiece geometry and tool 
path in machining operations. Also, X
r
Y
r
Z
r
 is created 
in order to describe the tool rotation coordinate system 
in machining operations. Thus, the cutting forces in 
the differential format, which is applied to the j
th
 axial 
disk element of the i
th 
tooth at rotation angle ϕ
i, j
(t), 
can be presented as:
dF tK hijtdb Kd bW t
dF tK
Tijt st pi j
Rij
,, ,
,,
() (( ,, )) (( ( )))
() (



r rs rp ij
Ai ja s
hijtdb Kd bW t
dF tK hijtdb
(, ,) )( (( )))
() (( ,, )
,
,,



 





Kd bW t
ap ij
)( (( )))
,
,

 (1)
where h(i, j,t) is the instantaneous uncut chip thickness 
of the j
th
 axial disk element of the i
th
 tooth at t 
moment and the db is the axial height of the cutting 
disk element. Moreover, the coefficients of shearing 
specific cutting force in different directions as 
tangential, radial, and axial can be shown as:
 kabe qt ra
qs qs qs
ch t
qs
 
()
(, ,) . 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244
237 Virtual Minimization of Residual Stress and Deflection Error in the Five-Axis Milling of Turbine Blades 
Also, the coefficients of ploughing specific 
cutting force in different directions as tangential, 
radial, and axial direction can be presented as: 
 kabe qt ra
qp qp qp
ch t
qp
 
()
(, ,) . 
To determine whether the condition of disk 
element is in or out of cutting operation, the W( θ) can 
be presented as:
     wt
t
ij
st ij ij ex ij
(( ( )))
(( ))
,
,
,, ,, ,

 

 


1
0o thers
 (2)
where θ
ex,i, j
 stand for entry and exit angle of j
th
 disk 
element on i
th
 tooth respectively, as shown in Fig. 1 
[27].
Fig. 1.  Entry and exit angle model of cutting tool [27]
Thus, the overall cutting forces that are applied 
to the t moment can be calculated by summing three 
cutting forces acting on disk element within axial 
depth of cut as is shown in Eq. (3).
 
Ft
Ft
Ft
Rot
dF t
dF t
dF
cx
cy
cz
Tij
Rij
A
,
,
,
,,
,,
()
()
()
()
()











,, ,
()
,
ij
j i
t










 
 (3)
where Rot is the cutter rotation matrix. With the aid 
of transformation relationship matrix in the five-axis 
machine tool, the total cutting force components 
acting on the workpiece can be obtained by:
 
Ft
Ft
Ft
RotC RotB
Ft
Ft
F
wx
wy
wz
cx
cy
c
,
,
,
,
,
()
()
()
()
()










 
,, ()
,
z
t










 (4)
where RotC · RotB is rotation matrix for B-axis and 
C-axis. 
2  CUTTING TEMPERATURE MODEL
In the machining operations, the chip formation 
process generates heat in the cutting zone. To 
model the cutting temperature regarding the cutting 
parameters, the response surface methodology 
(which is statistical) and mathematical techniques 
can be applied. The experimental values of cutting 
temperature corresponding to the control variables 
of machining parameters are incorporated into the 
response surface methodology in terms of cutting 
temperature model modification [28]. As a result, 
The equation of the cutting temperature regarding 
the cutting parameters based on response surface 
methodology is presented by Shaw [29] as,
 

CV faa
b
z
b
e
b
p
b 12 34
, (5)
where λ is temperature [°C], C
λ
 is temperature 
coefficient determined by workpiece material, 
machine tool, and cutting tool geometry parameter. 
The b
1
, b
2
, b
3
, and b
4
 are exponents influencing the 
machining parameters V, cutting speed (m/min), f
z
, 
feed rate (mm/rotation), a
e
, radial feed [mm] and a
p
, 
axial feed [mm].
To obtain the experimental values of cutting 
temperature and calculate the cutting temperature 
during machining operation, the tool-workpiece 
thermocouple device with three brushes is used. The 
electromotive force produced in the tool-workpiece 
thermocouple circuit during machining is proportional 
to the temperature difference between the tool and 
room temperature. Extruded round bars (101 mm 
× 2000 mm) of the aluminium alloys 1350-O and 
7075-T6 were used as the workpiece. The cutting tool 
used in the experiment is carbide bar (310 × 10 × 4) 
mm K15 grade, and the tool holder is (25 × 20 × 150) 
mm made of steel. The cutting speed 600 m/minute, 
feed rate 0.3 mm/rotation and axial depth of cut 
3 mm are considered as machining parameters 
of the experiments. The average of the chip-tool 
temperatures measured by the tool workpiece 
thermocouple system (average of two replicates) are 
calculated using analysis of variance of the 2
k
 factorial 
design as input variables. The coefficients of the 
temperature model are then calculated using a statistic 
analysis based on multiple nonlinear regression of the 
chip-tool interface temperature over 32 experiments. 
As a result, the equations of the cutting tool and 
workpiece temperatures in the machining operations 
of Al alloys based on multiple nonlinear regression 
analysis are presented by Santos et al. [30] as: 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244
238 Soori, M. – Asmael, M.
 
tz ep
Vfaa 116 503
0 211 0 181 0 0464 0 00391
.,
.. ..
 (6)
 
wz ep
Vfaa  43 319
0 365 0 244 0 0423 0 019
.,
.. ..
 (7)
where λ is temperature [°C], V is cutting speed [m/
min], f
z
 is feed rate [mm/rotation], a
e
 and a
p
 are radial 
feed and axial feed [mm], respectively.
3  DEFLECTION ERROR ANALYSIS OF THIN-WALL 
WORKPIECE IN MACHINING OPERATIONS
The machining operations of thin-walled parts have 
deflection errors as a result of cutting forces as well as 
cutting temperature. The workpiece deflects to a new 
position due to cutting forces and cutting temperatures 
which creates dimensional errors and inaccuracies in 
the process of machining operations.
The corresponding surface dimensional error can 
be presented as Eq. (8) [31],
 
e
pt pf p
 
,,
,
 (8)
where, δ
t,p
 and δ
f,p
 are the normal projections of 
the cutting force and cutting temperature-induced 
deflection error for the Point P, respectively.
For the convenience of study, the distance 
between the initial surface to be machined and the 
desired machined surface is named as the nominal 
radial depth of cut notated by R
N
. In the actual milling 
process, to ensure that the surface dimensional error 
does not violate the tolerance, R
A
 is often specified 
to be different from R
N
 ≠  R
A
. In this case, Eq. (9) is 
no longer applicable to the calculation of surface 
dimensional error and must be corrected as [31]:
 eR R
pt pf pNA
 
,,
. (9)
Note that R
N
 and R
A
 are the nominal and specified 
radial depth of cut, respectively.
4  VIRTUAL MACHINING SYSTEM 
The Visual Basic programming language is used in 
this study to develop the presented virtual machining 
system. The developed virtual machining system can 
obtain the cutting forces regarding the cutting tool 
details and parameters of machining operations. Thus, 
cutting forces at each position of the cutting tool along 
machining paths can be calculated. 
The software calculates the cutting temperature 
regarding the cutting process parameters at each 
position of the cutting tool along machining paths. 
Then, the software is linked to the Abaqus R2016X 
FEM analysis software to analyse the residual stress 
and deflection error due to machining operations. 
The calculated cutting forces and cutting temperature 
at each position of cutting tool along the machining 
paths in turbine blade machining are input to Abaqus 
software to be used for residual stress and deflection 
error calculations. As a result, the residual stress and 
deflection error due to cutting forces and cutting 
temperatures at each position of the cutting tool can 
be calculated and presented. A flowchart and the 
strategy of the virtual machining system in cutting 
force calculation, residual stress and deflection error 
prediction are shown in Fig. 2.
Fig. 2.  Flowchart of the virtual machining system
To obtain the optimized machining parameters 
in terms of residual stress and deflection error 
minimizations, the genetic algorithm is applied. 
The genetic algorithm is an advanced optimization 
method based on natural selection by which the fittest 
individuals are selected for reproduction to produce 
offspring of the next generation. The natural process 
of evolution and set of chromosomes is introduced in 
terms of optimization process. The initial population 
for the optimization process is created using the binary 
encoding process. To provide evaluation criteria in the 
optimization process and rank the chromosomes in 
the population, the fitness function is calculated as is 
presented in Eq. (10) [32].
 Fx
fx
()
()
, 

1
1
 (10)
where fitness function and objective function are 
F(x) and f(x), respectively. The main operators of the 
algorithms are reproduction, crossover, and mutation. 
The operators are applied to the initial population of 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244
239 Virtual Minimization of Residual Stress and Deflection Error in the Five-Axis Milling of Turbine Blades 
the optimization process in order to provide a faster 
convergence to the optimized parameters. 
The mathematical equation of the surface 
roughness in end milling operations is presented in 
Eq. (11) [33].
 R
f
d
a
=318
4
2
, (11)
where f is the feed rate, and d is the diameter of 
the cutting tool. Moreover, the time of machining 
operation should be minimized in order to decrease 
the cost of machined parts. The mathematical equation 
of machining time is presented in Eq. (12) [33].
 t
k
f
m
= , (12)
where k is the distance of cutting tool to reach to the 
operational zone and f is feed rate. 
Also, the cutting tool life should be maximized in 
the optimization process in order to decrease the cost 
of machining operation. The cutting tool life can be 
shown as Eq. (13) [33].
 T
Q
C
G
VA
L W
m

























60 5
1
()
, (13)
where Q is the contact proportion of cutting edge with 
workpiece per revolution, C is 33.98 for the high-
speed steel (HSS) tools and 100.05 for the carbide 
tools, g = 0.14, V is cutting speed [mm/min], w = 0.28, 
m is 0.15 for HSS tools while it reaches a maximum 
of 0.30 for carbide tools, G and A are slenderness ratio 
and chip cross-section, which can be shown as Eqs. 
(14) and (15), respectively [33].
 G
a
f
= , (14)
 Aa f , (15)
where a is a depth of cut and f is feed rate in machining 
operations. 
According to Eqs. (6) and (7), the cutting 
temperature can be decreased by reducing the feed 
rate and spindle speed. Also, according to Eq. (11), 
the surface roughness can be decreased by reducing 
the feed rate. However, the machining time will be 
increased by reducing the feed rate according to Eq. 
(12). Moreover, increasing the spindle speed can 
decrease the cutting forces according to Eq. (4) and 
cutting tool life according to Eq. (13). It is clear that 
the presented mathematical models of the cutting 
forces, cutting temperature, time of machining 
operations, surface roughness, feed rate and cutting 
tool life are related, which should be considered as 
an optimization problem. The objective function 
of the optimization process is minimizing the 
residual stress and deflection error by calculating 
the optimized machining parameters. To obtain the 
optimized machining parameters in order to minimize 
the residual stress and deflection error using the 
minimized cutting forces and cutting temperature in 
machined turbine blade, the Matlab programming 
language is used. As a result, the optimized feed rate 
and spindle speed are obtained in order to minimize 
the residual stress as well as deflection error in the 
machined parts. The complete methodology of the 
study is shown in Fig. 3.
Fig. 3.  Methodology of the study
5  VALIDATION AND COMPARISON
In order to validate the presented virtual machining 
system in the study, real turbine blades are machined 
by using the A 5-axis computer navigated control 
(CNC) milling machine tool Kondia HM 1060. The 
turbine blade material is AL 2618, which is used in 
the compressor section of gas turbines. Then, the test 
turbine blades are machined by using the five-axis 
Kondia HM 1060 CNC machine tool. The cutting 
tool used in the experiment is a carbide flat end mill 
with 10 mm diameter, helix angle 30°, flute number 
4, overall length 60 mm and flute length 30 mm. 
The feed rate and spindle speed are 100 mm/min and 
1000 rpm, respectively. The machining process of the 
turbine blade is shown in Fig. 4.
To calculate the cutting forces in virtual 
environments, the cutting force model of five-axis 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244
240 Soori, M. – Asmael, M.
CNC machine tools presented by Zhang et al. [27] is 
used in this study. 
Fig. 4.  Machining process of the turbine blades
In order to calculate the coefficients of specific 
cutting force, the average of cutting forces for twenty 
slot milling tests with 1.5 mm axial depth of cut using 
5-axis CNC milling machine tool Kondia HM 1060 
are measured with a Kistler dynamometer. The spindle 
rotating speed is 5000 rpm and the feed per tooth and 
feed rate are 0.5 mm and 100 mm/min, respectively. 
The cutting tool overhang is 60 mm. As result, the 
specific cutting force coefficients are obtained as Fig. 
6. 
The real machined Al turbine blades are shown 
in Fig. 5.
Fig. 5.  The real machined turbine blades
The cutting forces and cutting temperatures for 
each position of the cutting tool along machining paths 
are obtained by using the virtual machining system. 
Then, the cutting forces and cutting temperatures are 
entered into Abaqus software to obtain the residual 
stress and deflection error of machined blades. Thus, 
the calculated residual stresses by Von Mises yield 
criterion due to machining operation of turbine blade 
in MPa unit are shown in Fig. 7.
a) 
b) 
Fig. 6.  Specific cutting force coefficients, a) K
ts
, K
rs
, K
as
,  
and b) K
rp
, K
tp
, K
ap
Fig. 7.  The calculated residual stresses by the Von Mises yield 
criterion due to machining operation of turbine blade in MPa unit
Fig. 8.  The calculated deflection error of machined turbine blade

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244
241 Virtual Minimization of Residual Stress and Deflection Error in the Five-Axis Milling of Turbine Blades 
The calculated deflection error of the machined 
turbine blade by using the FEM method is presented 
in Fig. 8.
Residual stresses of the machined blade are 
measured by using an X-ray diffraction method. In 
order to obtain the residual stress in the machined 
turbine blades, two-circle Bragg Brentano-
Diffractometer of the type Philips X’PERT MPD is 
used by Cr k
α
 radiation with 35 kV and 35 mA. The 
sin2 ψ method is the most widely used methodology 
for stress assessment. Several XRD measurements are 
performed by considering the different tilts angle of ψ. 
In this experiment, the tilting angles are set at 0°, 13.8°, 
18.7°, 24.3°, 29.4°, 32.2°, 34.8°, 36.5°, and 40.4°. The 
inter-planar spacing or two-theta peak is calculated in 
order to obtain a plot or a curve for the measured data. 
As a result, the stress can be determined using the 
obtained plot by measuring the line gradient and with 
simple knowledge of the material’s elastic properties. 
In order to measure the residual stress in the machined 
turbine blades, the X-ray diffraction method is used, 
as shown in Fig. 9.
Fig. 9.  The X-ray diffraction method to measure  
the residual stress of machined turbine blade
The residual stresses in the depth of machined 
blade are measured and presented in the Fig. 10.
Experiment
Fig. 10.  Measured residual stress in depth of produced blade
A 90.4 % compatibility is obtained in the 
comparison of the results of the experimental test and 
FEM simulation. Optimized machining parameters 
are calculated using the optimization techniques 
developed in the study based on the genetic algorithm. 
To measure the cutting forces in the machining 
operation, the Kistler dynamometer is used. To 
provide input data for the optimization process, the 
measured cutting forces and cutting temperature, 
cutting condition and cutting tool geometry are entered 
in the optimization algorithm. In the optimization 
process, a population size of 28 is selected with the 
iterated for 228 generations. Also, the probability of 
crossover of 0.85 and mutation of 0.001 are selected. 
As a result, the feed rate 87 mm/min, radial feed a
e
 0.2 
mm and axial feed a
p
 12 mm and the spindle speed 
1269 rpm are obtained. Measured residual stress in the 
depth of machined blade using optimized machining 
parameters is shown in Fig. 11.
Experiment
Fig. 11.  Measured residual stress in depth of machined blade 
using optimized machining parameters
In order to measure the deflection error in the 
machined turbine blades, the CMM machine is used. 
The used probe in the error measuring is the Renishaw 
RSH  250  probe  while  its  repeated  accuracy  is  1 μm  in 
touching directions. The sweep scan method is used 
to obtain the surface condition of the machined blade.  
A NURBS surface “patch” is generated for each 
of the sweep scans in order to obtain the deflection 
error in the machined turbine blades. Then, to obtain 
the deflection error, sections are taken along the 
generated surfaces at any required height. The amount 
of error between the CAD model of turbine blade and 
fitted NURBS surfaces from the measured data of 
the CMM machine are calculated in each section of 
generated surface as the deflection error of machined 
turbine blade. 
The process of surface generation and deflection 
error calculation due to cutting forces and cutting 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244
242 Soori, M. – Asmael, M.
temperature for the machined blade are shown in Fig. 
12. 
Fig. 12.  The deflection error calculation from the CAD model of 
turbine blade and generated NURBS surfaces of machined turbine 
blades
As a result, the measured and predicted deflection 
errors in the machined turbine blade without and with 
the optimized machining parameters for the L7 line in 
Fig. 12 is presented in Fig. 13.
Fig. 13.  The measured and predicted deflection errors in the 
machined turbine blade without and with optimized machining 
parameters for the L7 line in the Fig. 12
The predicted deflection error due to the cutting 
forces and cutting temperatures without optimized 
machining parameters for the L7 line in Fig. 12 is 
presented in Fig. 14.
The optimized machining parameters can 
decrease the unnecessary cutting forces and the cutting 
temperature in the machining operation. Therefore, 
a reduction in the residual stress of produced blades 
using optimized machining parameters can be 
achieved, which can increase accuracy as well as 
reliability of machined turbine blades. Moreover, the 
deflection error due to machining forces and cutting 
temperature is minimized to increase the accuracy of 
machined turbine blades.
Fig. 14.  The predicted deflection error due to the cutting 
forces and cutting temperatures without  optimized machining 
parameters for the L7 line in the Fig. 12
6  CONCLUSIONS
To predict and minimize residual stress and deflection 
error in a five-axis turbine blade milling operations, 
a virtual machining system is developed in the study. 
The system can calculate the cutting forces and 
cutting temperature at each position of the cutting tool 
along machining paths with regard to the parameters 
of machining operations, geometries, and material 
properties of cutting tools as well as workpieces. 
Then, FEA is used to obtain residual stress and 
deflection error of the turbine blades in machining 
operations. The real turbine blades are produced and 
experimentally tested using a five-axis CNC milling 
machine tool in order to validate the developed system 
in the study. Then, the residual stress in the machined 
turbine blades are measured using X-ray diffraction 
machines. To measure the deflection error in the 
machined blades, the CMM machine is used. Finally, 
the obtained results from the virtual machining system 
and experimental tests are compared to present the rate 
of compatibility in the developed system. Therefore, 
a 90.4 % and 94.3 % compatibility are obtained in 
comparison to the experimental and virtual machining 
system results for the residual stress and deflection 
error, respectively.
To minimize the residual stress and deflection 
error in machining operation, optimized machining 
parameters using the genetic algorithm is obtained. 
As a result, 24.2 % and 23.9 % reductions in 
residual stress can be obtained in the real machined 
turbine blade and virtual machining system results. 
respectively. Moreover, 26.3 % and 24.1 % reductions 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244
243 Virtual Minimization of Residual Stress and Deflection Error in the Five-Axis Milling of Turbine Blades 
in the deflection error of real and virtual machining 
systems results are respectively measured by using 
the optimized machining parameters in machining 
operations.
The accuracy and the reliability of machined 
turbine blades can be increased by using the 
application of the virtual machining system in the 
minimization of residual stress and deflection error 
due to machining operations. Furthermore, the 
amount of the deflection errors due to cutting forces 
and cutting temperatures can be accurately predicted 
in virtual environments using the FEM analysis. The 
system developed in this study can be used in the 
machining operations of free-form surfaces in aircraft 
airfoils by using the five-axis CNC machine tools in 
order to decrease the residual stress of machined parts. 
These are the concepts of future research works for 
the authors.
7  REFERENCES
[1] Wimmer, S., Zaeh, M. (2018). The prediction of surface 
error characteristics in the peripheral milling of thin-walled 
structures. Journal of Manufacturing and Materials Processing, 
vol. 2, no. 1, art. ID 13, DOI:10.3390/jmmp2010013.
[2] Grossi, N., Scippa, A., Venturini, G., Campatelli, G. (2020). 
Process parameters optimization of thin-wall machining for 
wire arc additive manufactured parts. Applied Sciences, vol. 
10, no. 21, art ID. 7575, DOI:10.3390/app10217575.
[3] Ratchev, S., Liu, S., Becker, A.A. (2005). Error compensation 
strategy in milling flexible thin-wall parts. Journal of 
Materials Processing Technology, vol. 162-163, p. 673-681, 
DOI:10.1016/j.jmatprotec.2005.02.192.
[4] Grossi, N., Scippa, A., Croppi, L., Morelli, L., Campatelli, G. 
(2019). Adaptive toolpath for 3-axis milling of thin walled parts. 
MM Science Journal, no. 04, p. 3378-3385, DOI:10.17973/
MMSJ.2019_11_2019096.
[5] Scippa, A., Grossi, N., Campatelli, G. (2014). FEM based cutting 
velocity selection for thin walled part machining. Procedia 
CIRP, vol. 14, p. 287-292, DOI:10.1016/j.procir.2014.03.023.
[6] Bolsunovskiy, S., Vermel, V., Gubanov, G., Kacharava, I., 
Kudryashov, A. (2016). Thin-walled part machining process 
parameters optimization based on finite-element modeling 
of workpiece vibrations. Procedia CIRP, vol. 8, p. 276-280, 
DOI:10.1016/j.procir.2013.06.102.
[7] Jiang, X., Li, B., Wang, L., Wang, Z., Li, H. (2016). An approach 
to evaluate the effect of cutting force and temperature on the 
residual stress generation during milling. The International 
Journal of Advanced Manufacturing Technology, vol. 87, p. 
2305-2317, DOI:10.1007/s00170-016-8605-5.
[8] Masmiati, N., Sarhan, A.A., Hassan, M.A.N., Hamdi, M. (2016). 
Optimization of cutting conditions for minimum residual 
stress, cutting force and surface roughness in end milling of 
S50C medium carbon steel. Measurement, vol. 86, p. 253-
265, DOI:10.1016/j.measurement.2016.02.049.
[9] Mohammadpour, M., Razfar, M.R., Saffar, R.J. (2010). 
Numerical investigating the effect of machining parameters on 
residual stresses in orthogonal cutting. Simulation Modelling 
Practice and Theory, vol. 18, no. 3, p. 378-389, DOI:10.1016/j.
simpat.2009.12.004.
[10] Zhang, X., Wu, H. (2018). Effect of tool angle on cutting force 
and residual stress in the oblique cutting of TC21 alloy. The 
International Journal of Advanced Manufacturing Technology, 
vol. 98, p. 791-797, DOI:10.1007/s00170-018-2324-z.
[11] Lin, K., Wang, W., Jiang, R., Xiong, Y. (2019). Effect of tool nose 
radius and tool wear on residual stresses distribution while 
turning in situ TiB2/7050 Al metal matrix composites. The 
International Journal of Advanced Manufacturing Technology, 
vol. 100, p. 143-151, DOI:10.1007/s00170-018-2742-y.
[12] Yang, D., Xiao, X., Liang, X. (2019). Analytical modeling 
of residual stress in orthogonal cutting considering tool 
edge radius effect. The International Journal of Advanced 
Manufacturing Technology, vol. 103, p. 2965-2976, 
DOI:10.1007/s00170-019-03744-9.
[13] Nasr, M.N.A., Ng, E.-G., Elbestawi, M.A. (2007). Modelling 
the effects of tool-edge radius on residual stresses when 
orthogonal cutting AISI 316L. International Journal of 
Machine Tools and Manufacture, vol. 47, no. 2, p. 401-411, 
DOI:10.1016/j.ijmachtools.2006.03.004.
[14] Arunachalam, R.M., Mannan, M.A., Spowage, A.C. (2004). 
Residual stress and surface roughness when facing age 
hardened Inconel 718 with CBN and ceramic cutting tools. 
International Journal of Machine Tools and Manufacture, vol. 
44, no. 9, p. 879-887, DOI:10.1016/j.ijmachtools.2004.02.016.
[15] Sharman, A.R.C., Hughes, J.I., Ridgway, K. (2015). The 
effect of tool nose radius on surface integrity and residual 
stresses when turning Inconel 718™. Journal of Materials 
Processing Technology, vol. 216, p. 123-132, DOI:10.1016/j.
jmatprotec.2014.09.002.
[16] Yan, Q., Luo, M., Tang, K. (2018). Multi-axis variable depth-
of-cut machining of thin-walled workpieces based on the 
workpiece deflection constraint. Computer-Aided Design, vol. 
100, p. 14-29, DOI:10.1016/j.cad.2018.02.007.
[17] Huang, N., Bi, Q., Wang, Y., Sun, C. (2014). 5-Axis adaptive 
flank milling of flexible thin-walled parts based on the on-
machine measurement. International Journal of Machine 
Tools and Manufacture, vol. 84, p. 1-8, DOI:10.1016/j.
ijmachtools.2014.04.004.
[18] Shakya, P., Sunny, M.R., Maiti, D.K. (2020). Time domain 
flutter analysis of bend-twist coupled large composite wind 
turbine blades: a parametric study. Mechanics Based Design 
of Structures and Machines, p. 1-23, DOI:10.1080/15397734
.2020.1824796.
[19] Luo, Z., Wang, Y., Zhai, J., Zhu, Y., Wang, D. (2019). Prediction 
of vibration characteristics of blisks using similitude models. 
Mechanics Based Design of Structures and Machines, vol. 47, 
no. 2, p. 121-135, DOI:10.1080/15397734.2018.1481427.
[20] Soori, M., Arezoo, B., Habibi, M. (2017). Accuracy analysis of 
tool deflection error modelling in prediction of milled surfaces 
by a virtual machining system. International Journal of 
Computer Applications in Technology, vol. 55, no. 4, p. 308-
321, DOI:10.1504/ijcat.2017.10006843.

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)5, 235-244
244 Soori, M. – Asmael, M.
[21] Soori, M., Arezoo, B., Habibi, M. (2014). Virtual machining 
considering dimensional, geometrical and tool deflection 
errors in three-axis CNC milling machines. Journal of 
Manufacturing Systems, vol. 33, no. 4, p. 498-507, 
DOI:10.1016/j.jmsy.2014.04.007.
[22] Soori, M., Arezoo, B., Habibi, M. (2013). Dimensional and 
geometrical errors of three-axis CNC milling machines in a 
virtual machining system. Computer-Aided Design, vol. 45, no. 
11, p. 1306-1313, DOI:10.1016/j.cad.2013.06.002.
[23] Soori, M., Arezoo, B. (2021). Virtual Machining Systems for 
CNC Milling and Turning Machine Tools: A Review. International 
Journal of Engineering and Future Technology, vol. 18, no. 1, 
p. 56-104.
[24] Soori, M., Arezoo, B., Habibi, M. (2016). Tool deflection error 
of three-axis computer numerical control milling machines, 
monitoring and minimizing by a virtual machining system. 
Journal of Manufacturing Science and Engineering, vol. 138, 
no. 8, art. ID. 081005, DOI:10.1115/1.4032393.
[25] Soori, M., Asamel, M., Solyali, D. (2020). Recent development 
in friction stir welding process: A review. SAE International 
Journal of Materials and Manufacturing, vol. 14, no. 1, p. 63-
80, DOI:10.4271/05-14-01-0006.
[26] Nasir, T., Kalaf, O., Asmael, M. (2021). Effect of rotational 
speed, and dwell time on the mechanical properties and 
microstructure of dissimilar AA5754 and AA7075-T651 
aluminum sheet alloys by friction stir spot welding. Materials 
Science. Early Access, DOI: 10.5755/j02.ms.26860.
[27] Zhang, X., Zhang, J., Pang, B., Zhao, W. (2016). An accurate 
prediction method of cutting forces in 5-axis flank milling 
of sculptured surface. International Journal of Machine 
Tools and Manufacture, vol. 104, p. 26-36, DOI:10.1016/j.
ijmachtools.2015.12.003.
[28] Mia, M., Dhar, N.R., (2016). Response surface and neural 
network based predictive models of cutting temperature in 
hard turning. Journal of Advanced Research, vol. 7, no. 6, p. 
1035-1044, DOI:10.1016/j.jare.2016.05.004.
[29] Shaw, M.C. (2005). Metal Cutting Principles. 2
nd
 ed., Oxford 
University Press, Oxford.
[30] Santos, M.C., Machado, A.R., Barrozo, M.A. (2018). 
Temperature in machining of aluminum alloys. in: temperature 
sensing. IntechOpen, DOI:10.5772/intechopen.75943.
[31] Wan, M., Zhang, W.H., Qin, G., Wang, Z.P. (2008). Strategies 
for error prediction and error control in peripheral milling of 
thin-walled workpiece. International Journal of Machine 
Tools and Manufacture, vol. 48, no. 12-13, p. 1366-1374, 
DOI:10.1016/j.ijmachtools.2008.05.005.
[32] Palanisamy, P., Rajendran, I., Shanmugasundaram, S. (2007). 
Optimization of machining parameters using genetic algorithm 
and experimental validation for end-milling operations. The 
International Journal of Advanced Manufacturing Technology, 
vol. 32, p. 644-655, DOI:10.1007/s00170-005-0384-3.
[33] Tolouei-Rad, M., Bidhendi, I. (1997). On the optimization of 
machining parameters for milling operations. International 
Journal of Machine Tools and Manufacture, vol. 37, no. 1, p. 
1-16, DOI:10.1016/S0890-6955(96)00044-2.