Y. HUO et al.: PREDICTING THE MICROSTRUCTURE EVOLUTION FOR THE WARM SKEW ...
49–55
PREDICTING THE MICROSTRUCTURE EVOLUTION FOR THE
WARM SKEW ROLLING OF BEARING STEEL BALLS UNDER
DIFFERENT PROCESS PARAMETERS
NAPOVEDOV ANJE RAZVOJA MIKROSTRUKTURE KROGEL IZ
LE@AJNEGA JEKLA, TOPLO PO[EVNO-KOTNO V ALJANEGA PRI
RAZLI^NIH POGOJIH
Yuanming Huo
*
, Tao He, Yujia Hu, Wanbo Yang, Menglan Shen
School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Longteng Road 333,
Songjiang District, Shanghai 201620, China
Prejem rokopisa – received: 2019-05-16; sprejem za objavo – accepted for publication: 2019-08-18
doi:10.17222/mit.2019.105
The high performance of bearing steel balls (BSBs) depends on the microstructure. Carbide spheroidization is the main
mechanism in warm deformation, which leads to the metal flow dynamic softening of bearing steel. Process parameters of warm
skew rolling (SR) such as roller angle, rolling temperature and roller rotating speed have a significant influence on the carbide
spheroidization of bearing steel. A simulation system of microstructure was developed based on unified visco-plastic
constitutive equations to predict the microstructure evolution of BSB during warm SR. Next, a series of FE simulations were
conducted to investigate the effect of process parameters of warm SR on the microstructure of BSB. The predicted results show
that the degree of carbide spheroidization decreases with the increase of roller angle, rolling temperature and roller rotating
speed. The optimal process parameters of warm SR were selected as a roller angle of 2.0°, rolling temperature of 650 °C and
roller rotating speed of 70 min
–1
. More carbides participation and sufficient carbide spheroidization were achieved under the
optimal process parameters of warm SR. The application of optimal process parameters into the formation of BSB with 30 mm
diameter can reduce the special carbide spheroidization annealing time and energy consumption, and improve productivity.
Keywords: bearing steel balls, skew rolling, microstructure evolution, carbide spheroidization, process parameters optimization
Visoka kakovost krogel iz le`ajnega jekla (BSB) je odvisna od njegove mikrostrukture. Sferoidizacija (krogljenje) karbidov je
glavni mehanizem, ki poteka med toplo deformacijo, ki povzro~a dinamiko meh~anja kovinskega plasti~nega toka le`ajnega
jekla. Procesni parametri toplega po{evno-kotnega valjanja (SR), kot so: kot oz. nagib valjarni{kega kolesa, njegova hitrost in
temperatura valjanja, imajo pomemben vpliv na sferoidizacijo karbidov le`ajnega jekla. Avtorji {tudije so razvili simulacijski
model na osnovi poenotenja visoko-plasti~nih konstitutivnih ena~b za napoved razvoja mikrostrukture BSB med toplim SR.
Izvedli so serijo simulacij na osnovi metode kon~nih elementov (FE), da bi ugotovili vpliv procesnih parametrov na mikro-
strukturo toplo po{evno-kotno valjanih BSB. Rezultati so pokazali, da se stopnja sferoidizacije karbidov zmanj{uje s pove~e-
vanjem nagiba po{evnine v valju, njegovo hitrost in temperaturo valjanja. S simulacijo napovedani optimalni procesni parametri
toplega SR so bili: kot po{evnine 2°, temperatura valjanja 650 °C in vrtilna hitrost valja 70 min
–1
. Ve~ji prispevek karbidov in
zadovoljiva sferoidizacija karbidov je bila dose`ena pri optimalnih pogojih toplega SR. Zaradi uporabe optimalnih procesnih
parametrov pri izdelavi BSB premera 30 mm, so lahko skraj{ali ~as posebnega sferoidizacijskega `arjenja in s tem zmanj{ali
porabo energije in izbolj{ali produktivnost.
Klju~ne besede: krogle iz le`ajnega jekla, po{evno-kotno valjanje, razvoj mikrostrukture, sferoidizacija karbidov, optimizacija
procesnih parametrov
1 INTRODUCTION
Cold forging, hot forging, cutting and casting belong
to the traditional manufacturing method to produce
BSBs.
1,2
Compared with the traditional manufacturing
method, the SR technique has some advantages, such as
high production efficiency, saving materials and energy,
lower costs, etc.
3
The formation of BSBs using the SR
technique is increasingly becoming the preferred manu-
facturing method for researchers.
Some publications using the SR technique to form
BSB can be found. J. Tomczak et al.
4
conducted theore-
tical and experimental research on the formation of balls
with a diameter of 30 mm using the SR technique. Z. Hu
and Z. Zheng et al.
5.6
studied the metal flow law of a
steel ball using the SR technique, whose roller design
method can be adapted to manufacturing the module in
this work. Q. Cao and L. Hua et al.
7
apply the cold SR
technique to form BSB, and predict the damage distri-
bution using FE SIMUFACT software. The above
publications provide the SR forming method and
analysis of the metal flow characteristics in the process
of SR. However, the microstructure simulation of BSB
formed during warm SR was rarely studied. Particularly,
the effect of process parameters of warm SR on the
microstructure evolution has not been reported.
The high performance of BSB depends on the
microstructure formed in the manufacturing technique.
8
Process parameters have a significant effect on the
microstructure evolution in the manufacturing process.
Materiali in tehnologije / Materials and technology 54 (2020) 1, 49–55 49
UDK 620.1:669.1:669.018.26 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 54(1)49(2020)
*Corresponding author's e-mail:
yuanming.huo@sues.edu.cn (Yuanming Huo)

The variation of process parameters results in the
variation of deformation temperature, deformation rate
and stress rate in the manufacturing process. As we
expected that microstructure evolved with the variation
of these deformation parameters. As for the bearing steel
of 52100, the carbide spheroidization mechanism was
predominant during the microstructure evolution in the
process of warm deformation.
9,10
The process parameters
also have a direct effect on the evolution of dislocation,
stress state and carbide spheroidization of the bearing
steel during warm SR. Some publications reported the
carbide spheroidization mechanism during warm
deformation for bearing steel. And, unified visco-plastic
constitutive equations were developed to describe the
carbide spheroidization mechanism in
11
. However, there
is still a lack of a series of FE simulations to optimize the
process parameters of warm SR by implementing the
unified visco-plastic constitutive equations into the FE
software to develop the FE microstructure predicted
system. The optimal process parameters can be used to
guide the real manufacturing process.
The aim of this work is to study the effect of process
parameters of warm SR on the carbide spheroidization of
bearing steel. Firstly, the FE simulation system of the
microstructure was developed based on previous unified
visco-plastic constitutive equations in
11
. Secondly, a
series of FE simulations were carried out by changing
the process parameters of warm SR. And, the effects of
roller angle, rolling temperature and roller rotating speed
on carbide spheroidization were discussed. Finally, opti-
mization of the process parameters and its application in
warm SR were carried out.
2 DEVELOPMENT OF THE MICROSTRUCTURE
PREDICTED SYSTEM OF WARM SKEW
ROLLING
The calculated unified visco-plastic constitutive
equations of bearing steel 52100 during warm defor-
mation in
11
were implemented into FE software of
Deform-3D via a user routine to develop the micro-
structure-predicted system of warm SR. It is essential to
set up the FE model of warm SR. Two rollers, guide
plates and the workpiece were three-dimensional
modelled and put into Deform-3D. The detailed spiral
cavity of the rollers was designed referring to
5
so that
the process of warm SR for BSB with a diameter of 30
mm can be predicted. Two rollers and guide plates were
assumed as a rigid body. The workpiece was assumed as
the uniform and isotropic rigid-plastic body. The shear
friction coefficient between the rollers and workpiece
was defined as 0.7. Table 1 shows the material property
of steel 52100.
12,13
Table 2 shows the heat conduction
and heat capacity.
14
The heat-transfer coefficient was
defined as 40 N/s/mm/°C.
15
Figure 1 shows the FE model of the warm SR in the
software of Deform-3D. The length of the workpiece is
100 mm, and its diameter is 30 mm. The environment
temperature is 20 °C. The meshing elements of 100,000
tetrahedrons were used to mesh the workpiece. The time
increment is 0.0001 s, and it costs 1.2 s in the process of
warm SR simulation. The two rollers rotate in the same
direction.
3 SIMULATION RESULTS AND DISCUSSION
As can be seen from
16
the dual phase ( +Fe
3
C) can
be obtained for the warm deformation temperature range
from 650 °C to 750 °C for bearing steel 52100. Dislo-
cation proliferates and tangles in the matrix and many
precipitated lamellar carbides. The shear stress concen-
trates within the lamellar carbides, which expedite the
break up of the lamellar carbides. A similar globulari-
zation phenomenon exists in the deformation process of
titanium alloy, whose detailed discussion can be found
in
17–19
. When the dislocation density reaches a critical
Y. HUO et al.: PREDICTING THE MICROSTRUCTURE EVOLUTION FOR THE WARM SKEW ...
50 Materiali in tehnologije / Materials and technology 54 (2020) 1, 49–55
Table 1: Material properties of steel 52100
Elasticity modulus
(GPa)
Poisson’s ratio
Coefficient of
thermal expansion
(1/°C)
Radiation coefficient
(N/s/mm/°C
4
)
Convection
coefficient
(N/s/mm/°C)
Density (kg/m
3
)
208 0.29 1.1e-05 0.8 0.02 7810
Table 2: Heat conduction and heat capacity of steel 52100
Temperatures (°C) 100 200 300 400 500 600 700 800 900 1000
Coefficient of heat conduction (W/(m·°C)) 41 41 39.9 38.1 35.9 33.6 33.6 33.6 33.6 33.6
Heat capacity (J/kg/°C) 371 451 461 496 533 568 611 677 787 787
Figure 1: FE model of warm SR3

value, lamellar carbides were transformed into the
spheroidized microstructure in the warm forming.
Moreover, metal flow softening was induced by carbide
spheroidization in the warm forming of bearing steel.
Therefore, carbide spheroidization and dislocation
evolution are the main physical evolution mechanism for
bearing steel during the warm rolling.
The evolution of the carbide spheroidization is
dependent on the basic deformation parameters of strain,
deformation temperature, strain rates and stress state.
The main process parameters of the warm SR such as
roller angle, rolling temperature and roller rotating speed
have a direct relationship with the basic deformation
parameters. Therefore, it is important to investigate the
effect of the process parameters of warm SR on the
carbide spheroidization by comparing the simulation
results under different process parameters. Table 3
shows the simulation programs under different process
parameters of warm SR for BSB.
Table 3: Simulation programs under different process parameters of
warm SR
No. Roller angle
Rolling
temperature
Roller rotating
speed
1 2.0 750 110
2 2.5 750 110
3 3.0 750 110
4 2.5 700 110
5 2.5 650 110
6 2.5 750 90
7 2.5 750 70
3.1 Effect of roller angle on the carbide spheroidiza-
tion
The prerequisite of carbide spheroidization is carbide
precipitation during the phase transformation during
warm deformation for bearing steel. Figure 2 shows the
distribution of phase transformation fraction in the
longitudinal section of BSB at a rolling temperature of
750 °C and roller rotating speed of 110 min
–1
. It can be
seen from Figure 2 that the phase-transformation
fraction decreases with the increases of the roller angle.
Carbide phase transformation is the most at a roller angle
of 2.0°. When the roller angle is 3.0°, the carbide phase
transformation is the minimum. The amount of preci-
pitation under a roller angle of 2.5° is more than that
under a roller angle of 3.0°, but less than that under a
roller angle of 2.0°. In addition, carbide precipitation
concentrates on the equator of the BSB. The two ends of
the BSB have no phase transformation. The carbide
phase transformation depends on the temperatures and
the time. Due to this there is a short time of 1.2s during
SR, and temperature is the key factor for the carbide
precipitation. The maximum plastic deformation occurs
at the two ends of the BSB. The plastic temperature rise
leads the carbide to dissolve in two ends of the BSB.
Conversely, the deformation amount of the equator is
less than that of two ends. The, temperature decreases in
the equator because of the contact heat dissipation with
two rollers. Therefore, carbide precipitation concentrates
on the equator of the BSB.
Figure 3 shows the distribution of the carbide
spheroidization fraction in the longitudinal section of the
BSB at a rolling temperature of 750 °C and a roller
rotating speed of 110 min
–1
. It can be seen from Figure 3
that the carbide spheroidization fraction is 0.6 in the
heart of the BSB. The carbide spheroidization fraction
reaches 0.99 in the part from outer surface to some
certain thickness within the BSB. Comparing with
Figure 3a to 3c, it is clear that there is no sufficient
carbide spheroidization in the heart of the BSB,
especially at the roller angle of 2.0°.
When the roller angle is 2.0°, the phase-transfor-
mation fraction is the highest shown in Figure 2, but its
carbide spheroidization fraction is the lowest, shown in
Figure 3. Because the precondition of carbide spheroidi-
zation is cementite precipitation, the multiplication term
F
c
·W between the phase-transformation fraction and the
carbides-spheroidization fraction was defined as the
Y. HUO et al.: PREDICTING THE MICROSTRUCTURE EVOLUTION FOR THE WARM SKEW ...
Materiali in tehnologije / Materials and technology 54 (2020) 1, 49–55 51
Figure 3: Distribution of carbide spheroidization fraction in the
longitudinal section of the BSB at a rolling temperature of 750 °C and
a roller rotating speed of 110 min
–1
Figure 2: Distribution of the phase transformation fraction in the
longitudinal section of the BSB at a rolling temperature of 750 °C and
a roller rotating speed of 110 min
–1

evaluation criterion in this work, to objectively evaluate
the degree of carbides spheroidization of BSB.
Figure 4 shows the distribution of the multiplication
term between the phase-transformation fraction and the
carbide-spheroidization fraction in the longitudinal
section of the BSB at a rolling temperature of 750 °C
and roller rotating speed of 110 min
–1
. It can be seen that
the degree of carbides spheroidization of BSB is the
highest when the roller angle is 2.0° by comparing
Figure 4a to 4c. The degree of carbides spheroidization
of the BSB is the lowest when the roller angle is 3.0°.
The degree of carbides spheroidization of the equator is
the most obvious. However, the degree of carbides
spheroidization is the least in the heart and two ends of
BSB. Therefore, the degree of carbides spheroidization
decreases with the increase of the roller angle.
3.2 Effect of rolling temperature on the carbide
spheroidization
Figure 5 shows the distribution of the phase-trans-
formation fraction in the longitudinal section of the BSB
at a roller angle of 2.5° and a roller rotating speed of
110 min
–1
. It can be seen from Figure 5 that the
phase-transformation fraction decreases with the in-
creases of the rolling temperature. The phase-transfor-
mation fraction is the most at the rolling temperature of
650 °C, and that it is the least at the rolling temperature
of 750 °C. The phase-transformation fraction at the
rolling temperature of 700 °C is higher than that at
rolling temperature of 750 °C, but lower than that at
rolling temperature of 650 °C. Carbide precipitation
concentrates on the equator, and there is the least at the
two ends of the BSB. The phase-transformation fraction
is related to the temperature. The plastic temperature rise
is higher at the two ends of the BSB due to the largest
deformation. Contacting heat dissipation leads to a
decrease of the temperature at the equator of the BSB.
Figure 6 shows the distribution of the carbide
spheroidization fraction in the longitudinal section of the
BSB at a roller angle of 2.5° and a roller rotating speed
of 110 min
–1
. It can be seen from Figure 6 that the
rolling temperature has a significant influence on the
carbide spheroidization. When the rolling temperature is
650 °C, the carbide spheroidization fraction reaches
0.999 in the outer sphere of BSB, and the carbide
spheroidization fraction reaches 0.5 in the heart of the
BSB. When the rolling temperature is 700 °C, the
thickness increases for the carbide spheroidization
fraction of 0.999, and the carbide spheroidization frac-
tion reaches about 0.6 in the heart of the BSB. When the
rolling temperature is 750 °C, the thickness of the
carbide spheroidization fraction of 0.999 is greater than
that at the rolling temperature of 700 °C. Therefore, the
carbide-spheroidization fraction increases with the
increase of the rolling temperature.
Figure 7shows the distribution of the multiplication
term between the phase-transformation fraction and the
carbide-spheroidization fraction in the longitudinal
section of the BSB at a roller angle of 2.5° and a roller
Y. HUO et al.: PREDICTING THE MICROSTRUCTURE EVOLUTION FOR THE WARM SKEW ...
52 Materiali in tehnologije / Materials and technology 54 (2020) 1, 49–55
Figure 5: Distribution of the phase transformation fraction in the
longitudinal section of the BSB at a roller angle of 2.5° and a roller
rotating speed of 110 min
–1
Figure 4: Distribution of multiplication term between phase-trans-
formation fraction and carbide-spheroidization fraction in the
longitudinal section of the BSB at a rolling temperature of 750 °C and
a roller rotating speed of 110 min
–1
Figure 6: Distribution of carbide spheroidization fraction in the
longitudinal section of the BSB at a roller angle of 2.5° and a roller
rotating speed of 110 min
–1

rotating speed of 110 min
–1
. It can be seen from Figure 7
that the multiplication term increases with the decrease
of the rolling temperature. The multiplication term is the
largest at the rolling temperature of 650 °C, which
concentrates at the equator of the BSB. When the rolling
temperature is 700 °C, the multiplication term is lower
than that at the rolling temperature of 650 °C, which is
located in the equatorial band. When the rolling tem-
perature is 750 °C, the multiplication term is the lowest,
and the value is almost zero in the heart and two ends of
the BSB. Therefore, the degree of carbide spheroidi-
zation decreases with the increase of the rolling tem-
perature.
3.3 Effect of roller rotating speed on the carbide
spheroidization
Figure 8 shows the distribution of the phase-trans-
formation fraction in the longitudinal section of the BSB
at a roller angle of 2.5° and a rolling temperature of
750 °C. It can be seen from Figure 8 that the phase-
transformation fraction decreases with the increase of the
roller rotating speed. There is almost no carbide preci-
pitation at the two ends of the BSB. The phase-trans-
formation fraction is higher at the equator and the heart
of BSB. That is because the higher temperature distri-
butes at the two ends, and there is a lower temperature in
the equator and the heart of the BSB. When the roller
rotating speed is 70 min
–1
, the phase-transformation
fraction is the most, and the value reaches 0.12 in the
equator and the heart of the BSB. When the roller
rotating speed is 90 min
–1
, the phase-transformation
fraction is lower than that at the roller rotating speed of
70 min
–1
. The phase-transformation fraction reaches 0.12
in the equator of BSB, and its value is only 0.08 at the
heart of the BSB. When the roller rotating speed is 110
min
–1
, the phase-transformation fraction is the least, the
value mainly concentrates in the belt of equator. A larger
roller rotating speed means the plastic deformation rate
is higher, which leads to an increase of the temperature
due to plastic deformation. The precipitated carbides
easily dissolve at higher temperature. Therefore, the
phase-transformation fraction is lower at the higher roller
rotating speed.
Figure 9 shows the distribution of the carbide-
spheroidization fraction in the longitudinal section of the
a BSB at roller angle of 2.5° and a rolling temperature of
750 °C. It can be seen from Figure 9 that the carbide
spheroidization fraction is higher in the range from out
of the surface to some deep distance. The carbide-
spheroidization fraction is relatively lower in the heart of
the BSB. When the roller rotating speed is 70 min
–1
, the
carbide spheroidization fraction is about 0.5 in the heart
of BSB, whose occupied volume also is relatively larger.
When the roller rotating speed is 90 min
–1
, the carbide-
spheroidization fraction is about 0.6 in the heart of the
BSB. When the roller rotating speed is 110 min
–1
, the
carbide spheroidization fraction is about 0.6 in the heart
of BSB. However, the thickness is greater for the value
of 0.999 than that at the roller rotating speed is 90 min
–1
.
Y. HUO et al.: PREDICTING THE MICROSTRUCTURE EVOLUTION FOR THE WARM SKEW ...
Materiali in tehnologije / Materials and technology 54 (2020) 1, 49–55 53
Figure 9: Distribution of carbide-spheroidization fraction in the
longitudinal section of the BSB at a roller angle of 2.5° and a rolling
temperature of 750 °C
Figure 7: Distribution of multiplication term between the phase-trans-
formation fraction and the carbide-spheroidization fraction in the
longitudinal section of the BSB at a roller angle of 2.5° and a roller
rotating speed of 110 min
–1
Figure 8: Distribution of the phase-transformation fraction in the
longitudinal section of the BSB at a roller angle of 2.5° and a rolling
temperature of 750 °C

Therefore, the carbide spheroidization fraction increases
with the increase of the roller rotating speed.
Figure 10 shows the distribution of the multiplication
term between the phase-transformation fraction and the
carbide-spheroidization fraction in the longitudinal
section of the BSB at a roller angle of 2.5° and a rolling
temperature of 750 °C. It can be seen from Figure 10
that the multiplication term decreases with the increase
of the roller rotating speed. When the roller rotating
speed is 70 min
–1
, the value of the multiplication term is
the largest, i.e., 0.12. The carbide spheroidization mainly
distributes in the equator and the heart of the BSB. When
the roller rotating speed is 90 min
–1
,t h ev a l u eo ft h e
multiplication term is lower than that when the roller
rotating speed is 70 min
–1
. The volume of the carbide
spheroidization decreases in the equator and the heart of
the BSB. When the roller rotating speed is 110 min
–1
, the
value of the multiplication term is the smallest. The
carbide spheroidization only distributes in the equator of
the BSB, whose value is about 0.06. There is almost no
carbide spheroidization at the two ends of the BSB.
Therefore, the degree of carbide spheroidization de-
creases with an increase of the roller rotating speed.
3.4 Optimization of the process parameters and the
application
The optimal process parameters for warm SR were
selected by investigating the effect of the roller angle, the
rolling temperature and the roller rotating speed on the
carbide spheroidization, such as the roller angle of 2.0°,
the rolling temperature of 650 °C and the roller rotating
speed of 70 min
–1
. The selected process parameters for
the warm SR were applied to predict the distribution of
the phase-transformation fraction, the carbide sphero-
idization fraction and its multiplication term within the
BSB of 30 mm diameter during the warm SR.
Figure 11 shows the distribution of the phase-trans-
formation fraction, the carbide-spheroidization fraction
and its multiplication term in the longitudinal section of
the BSB at a roller angle of 2.0° and a rolling tempera-
ture of 650 °C with a roller rotating speed of 70 min
–1
.I t
can be seen from Figure 11a that the phase-trans-
formation fraction reaches about 0.2, which uniformly
distributes in all areas except for a small part of the two
ends. The phase transformation depends on the rolling
temperature. The lower rolling temperature ensures the
carbide participation within the BSB. However, carbide
spheroidization was determined by the deformation
degree and the deformation rate. Those two deformation
parameters were larger at the two ends of BSB, but
smaller in the equator and the heart of BSB. Therefore,
the carbide spheroidization fraction is higher at the two
ends, whose value reaches 0.999. The carbide-sphero-
idization fraction is the relative lower value of 0.6 in the
equator and heart of the BSB, shown in Figure 11b.
Figure 11c shows the value of the multiplication term is
the highest, i.e., above 0.2. In the heart of the BSB, the
value of the multiplication term is about 0.12. However,
the value of multiplication term is the lowest in the small
part of the two ends, i.e., below 0.04.
From the above analysis it can be concluded that
more carbide participation and sufficient carbide sphero-
idization were achieved under the optimal process
parameters of warm SR. The application of the optimal
process parameters into the formation of BSB of 30 mm
diameter can reduce the special spheroidizing annealing
time and energy consumption, and improve productivity.
4 CONCLUSIONS
Carbide spheroidization predominates during the
microstructure evolution for the warm deformation of
bearing steel. In order to obtain the high performance of
Y. HUO et al.: PREDICTING THE MICROSTRUCTURE EVOLUTION FOR THE WARM SKEW ...
54 Materiali in tehnologije / Materials and technology 54 (2020) 1, 49–55
Figure 11: Distribution of:a) phase-transformation fraction, b)
carbide-spheroidization fraction and c) multiplication term between
phase-transformation fraction and carbide-spheroidization fraction in
the longitudinal section of BSB at a roller angle of 2.0° and a rolling
temperature of 650 °C with a roller rotating speed of 70 min
–1
Figure 10: Distribution of the multiplication term between the
phase-transformation fraction and the carbide-spheroidization fraction
in the longitudinal section of the BSB at a roller angle of 2.5° and a
rolling temperature of 750 °C

bearing steel balls, a warm skew rolling technique was
adopted to form bearing steel in this work. The process
parameters have a great influence on the carbide
spheroidization of bearing steel. It is vital to search for
the optimal process parameters of warm skew rolling
using a FE simulation. A series of FE simulations were
conducted using the developed constitutive model to
compare the microstructure distribution of the steel
bearing balls under the different skew rolling conditions.
Some detailed conclusions were summarized:
A set of unified visco-plastic constitutive equations
of bearing steel 52100 during warm deformation were
implemented into FE software of Deform-3D via a user
routine to develop the microstructure predicted system of
warm SR. A series of FE simulations were conducted
using the microstructure predicted system to investigate
the effect of the roller angle, rolling temperature and
roller rotating speed of warm SR on carbide sphero-
idization.
Phase-transformation fraction decreases with the
increases of the roller angle. Carbide precipitation con-
centrates on the equator of the BSB. Carbide sphero-
idization fraction increases with the increase of the roller
angle. The degree of carbide spheroidization decreases
with the increase of the roller angle.
Phase-transformation fraction decreases with the
increases of the rolling temperature. Carbide precipi-
tation concentrates on the equator, and it is the least at
the two ends of the BSB. The carbide spheroidization
fraction increases with the increase of the rolling
temperature. The degree of carbide spheroidization
decreases with the increase of the rolling temperature.
Phase-transformation fraction decreases with the
increases of the roller rotating speed. The carbide-
spheroidization fraction increases with the increase of
the roller rotating speed. The degree of carbide sphero-
idization decreases with the increase of the roller rotating
speed.
The optimal process parameters for warm SR were
selected as roller angle of 2.0°, a rolling temperature of
650 °C and a roller rotating speed of 70 min
–1
. More car-
bides participation and sufficient carbide spheroidization
were achieved under the optimal process parameters of
warm SR. The application of optimal process parameters
into the formation of BSB with 30 mm diameter can
reduce the special spheroidizing annealing time and
energy consumption, and the improve productivity.
Acknowledgments
This project is funded by the National Natural
Science Foundation of China (Grant No. 51805314),
National Key Research and Development Program of
China (Grant No. 2018YFB1307900), Shanghai Science
and Technology Commission (Grant No. 16030501200),
Shanghai University of Engineering and Science (Grant
No. E3-0903-17-01006 & No. E3-0501-18-01002). The
Robot Functional Materials Preparation Laboratory in
Shanghai University of Engineering Science is also
gratefully acknowledged.
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Y. HUO et al.: PREDICTING THE MICROSTRUCTURE EVOLUTION FOR THE WARM SKEW ...
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