J. HRABOVSKÝ et al.: EXPERIMENTAL AND NUMERICAL STUDY OF HOT-STEEL-PLATE FLATNESS
17–21
EXPERIMENTAL AND NUMERICAL STUDY OF
HOT-STEEL-PLATE FLATNESS
EKSPERIMENTALNI IN NUMERI^NI [TUDIJ RAVNOSTI VRO^IH
PLO[^ IZ JEKLA
Jozef Hrabovský1, Michal Pohanka1, Pil Jong Lee2, Jong Hoon Kang2
1Heat Transfer and Fluid Flow Laboratory, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, 616 69 Brno,
Czech Republic
2POSCO, Rolling Technology & Process Control Research Group, 1, Geodong-dong, Nam-gu, Pohang, Gyeongbuk 790-785, Korea
hrabovsky@fme.vutbr.cz
Prejem rokopisa – received: 2014-07-31; sprejem za objavo – accepted for publication: 2015-02-10
doi:10.17222/mit.2014.153
One aspect of the steel-product quality is the flatness of a steel plate. This is one of the reasons why it is important to describe
and understand the process of steel-plate deformation during the cooling process. The temperature distribution has the largest
impact on the deformation of a strip. The temperature distribution is affected by the cooling process. The cooling homogeneity
or inhomogeneity is the most important factor influencing the final flatness of a cooled strip or steel plate. Inhomogeneous
cooling can lead to large differences in the thermal distribution inside the material and also to high deformations. The cooling
homogeneity is mainly influenced by the water distribution in the cooling section. The goal of this paper is to experimentally
and numerically study and describe the deformation process of a hot steel plate during the cooling process. To meet these goals,
experimental measurements of a cooled steel plate were carried out and the boundary conditions and temperature field were
obtained. Based on this data, two numerical models were created. The first numerical model focused on the cooling process, the
thermal-field simulation and the input-data preparation for the next step. In the next step, the second numerical model was
generated using the finite-element method and an analysis of the structure and deformation of the steel plate was simulated. The
description of the shape deformation of cooled steel plates should lead to an improved flatness of final products.
Keywords: cooling process, deformation, flatness, numerical simulation
Eden od vidikov kvalitete izdelka iz jekla je ravnost jeklene plo{~e. To je eden od razlogov, zakaj je potrebno opisati in razumeti
postopek deformiranja plo{~e med njenim ohlajanjem. Razporeditev temperature ima glavni vpliv na deformacijo traku. Na
razporeditev temperature vpliva proces ohlajanja. Homogenost ali nehomogenost hlajenja je najpomembnej{i faktor, ki vpliva na
kon~no ravnost ohlajenega traku ali plo{~e. Nehomogeno hlajenje lahko povzro~i velike razlike v razporeditvi toplote znotraj
materiala in tudi velike deformacije. Na homogenost hlajenja najbolj vpliva razporeditev vode v podro~ju hlajenja. Namen tega
~lanka je eksperimentalni in numeri~ni {tudij ter opis procesa deformacije vro~e jeklene plo{~e med procesom hlajenja. Za
dosego namena so bile eksperimentalno izmerjene hlajene jeklene plo{~e in dobljeni so bili mejni pogoji in temperaturno polje.
Na osnovi teh podatkov sta bila postavljena dva numeri~na modela. Prvi numeri~ni model je bil osredoto~en na proces hlajenja,
simulacijo temperaturnega polja in pripravo vhodnih podatkov za naslednji korak. V naslednjem koraku je bil generiran drugi
numeri~ni model s pomo~jo metode kon~nih elementov in simulirana je bila analiza strukture ter deformacije jeklene plo{~e.
Opis deformacije oblike ohlajanih jeklenih plo{~ naj bi omogo~il bolj{o ravnost kon~nih proizvodov.
Klju~ne besede: proces hlajenja, deformacija, ravnost, numeri~na simulacija
1 INTRODUCTION
The flatness of a hot steel plate or strip is an import-
ant issue of heat treatment in the steel industry. POSCO
Korea is also dealing with this problem. The flatness of a
final product has a significant impact on the quality and
price of the strip. The flatness of a steel plate is mainly
affected by the water distribution and cooling homo-
geneity during the quenching process. Two important
non-homogeneous types of water distribution can occur.
The first type of non-homogeneity is caused by different
intensities of the cooling from the top and bottom sides
of a steel plate. The second type of non-homogeneity
during a cooling process is created by different water
distributions in the center and corners of a steel plate.
Both of these types can occur simultaneously and pro-
duce problems with regard to the flatness of a steel
plate1,2. Non-homogeneous cooling also affects other
aspects such as material properties, phase changes,
residual stresses and so on3–5. The combination of all the
aspects has a significant impact on the final quality of a
steel plate and, therefore, the cooling process must be
studied. The description of the cooling process can be
performed using several parameters, including the cool-
ing intensity, the distribution of the heat-transfer coeffi-
cient (HTC) and so on6,7. Experimental measurements
were carried out at defined conditions to describe the
cooling process and non-homogeneity identification
during the quenching. The HTC distribution was ob-
tained from the results and a model of the steel-surface
thermal field was prepared. The inverse problem with a
sequential estimation of the time and varying boundary
conditions was used to simulate the cooling process and
time-dependent boundary conditions8. The calculated
thermal field of the steel plate was used in the next
numerical simulation. This numerical simulation was
Materiali in tehnologije / Materials and technology 50 (2016) 1, 17–21 17
UDK 519.61/.64:536.413:62-415 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 50(1)17(2016)
focused on steel-plate deformations and an analysis of
the flatness. The numerical simulation was based on the
finite-element method in Ansys, a commercial software
program.
2 EXPERIMENTAL MEASUREMENT OF
COOLING HOMOGENEITY
The cooling process under defined conditions was
experimentally measured using a laboratory apparatus
prepared in the Heat Transfer and Fluid Flow Laboratory.
The experimental apparatus is shown in Figure 1. The
experimental measurements were focused on the study of
the cooling non-homogeneity in the longitudinal and
transverse directions of the test plate and also of the
differences in the water distribution from the top and
bottom sides.
A test plate equipped with three thermocouple
sensors was used to investigate the heat transfer in the
longitudinal and transverse directions. A schematic of
the experimental measurement is depicted in Figure 2.
The thermocouples recorded the temperature history dur-
ing the cooling process and, using an inverse analysis,
the surface temperatures and heat-transfer coefficients
were computed. Both the upper and lower surfaces were
investigated.
The measurements were performed for several
conditions. The examples of the experimental conditions
are presented in Table 1. For the cooling from the top, a
pool with an adjustable height was used to set the proper
water layer.
Table 1: Examples of the measurement conditions
Tabela 1: Primeri pogojev pri meritvah
Surface Spray distance(mm)
Flow rate
(m3/min)
Water layer
(mm)
Velocity
(m/s)
Top 400 3.0 54 0.8
Top 400 4.5 65 0.8
Bottom 50 3.0 – 0.8
Bottom 50 5.3 – 0.8
The temperature history recorded during the experi-
ment was used to compute the time-dependent boundary
conditions. These boundary conditions were computed
using the sequential estimation of the time-varying
boundary conditions and the HTCs were obtained using
the inverse solution of the problem for each measure-
ment. Using the applied calculation methodology, the
HTC distribution on the steel plate was obtained. The
evaluated data for the full temperature range of the
experiments performed for the upper and lower cooling
are shown in Figure 3. These figures represent the HTC
distribution as a function of the surface temperature and
the position.
J. HRABOVSKÝ et al.: EXPERIMENTAL AND NUMERICAL STUDY OF HOT-STEEL-PLATE FLATNESS
18 Materiali in tehnologije / Materials and technology 50 (2016) 1, 17–21
Figure 3: HTC distribution for: a) upper and b) bottom cooling
Slika 3: HTC-razporeditev za hlajenje: a) zgoraj in b) spodaj
Figure 2: Schematic illustration of the experimental measurement
Slika 2: Shemati~en prikaz izvedbe meritev
Figure 1: Experimental apparatus
Slika 1: Eksperimentalna naprava
3 NUMERICAL SIMULATION
The numerical simulation was prepared in two steps.
In the first step, a numerical model of the thermal field
was prepared. In this step, FDM methods were consi-
dered as the solver for the heat conduction. The second
step was focused on the preparation of the numerical
model for the structural analysis of the steel plate. The
second numerical model was based on the FEM.
3.1 Temperature-field simulation
A cooling test plate was simulated to verify the HTC
values obtained with the laboratory measurements. The
selected discretization equations obtained using the FDM
have a clear physical meaning – they are not simply a
formal mathematical approximation. The derived
equations represent the conservation principles (mainly
the energy conservation) for each control volume and the
resulting numerical solution correctly satisfies the con-
servation over the whole calculation domain. As the
conductivities of the neighboring volumes may be
different due to the different temperature, there may be a
discontinuity of the slope (dT/dx) at the control volume
boundary. Whenever there is a need to get the tempera-
ture at a control volume boundary (e.g., during the inter-
polation of the temperature across the control volume), a
detailed equation should be used together with the
temperature at the node.
When the mass density or specific heat becomes
more dependent on the temperature, special care must be
paid to the time integration: if the time step is too large,
the latent heat of the phase change may be neglected. In
the case of a phase change, the properties are highly
dependent on the temperature. This problem can be
eliminated by solving it using the enthalpy instead of the
specific heat and the mass density. The approach that
was used and overcomes this problem was inspired by
the apparent-heat-capacity method.
The boundary conditions were prepared from the data
presented in the previous section (Figure 3). The data
was considered as a function of three variables: HTC
(length, Tsurface, width). An example of the applied boun-
dary conditions at a time of 32 s for the upper cooling of
the test plate is shown in Figure 4.
The computed temperature histories for the entire
cooling process are shown in Figure 5. This figure
indicates a large temperature difference between the
surface and the center of the plate in the middle of the
plate. The applied method for the temperature-field
simulation agrees with the plant measurements.
3.2 Simulation of deformation
This section contains the structural analysis of the
steel plate focusing on the deformations. The measured
thermal loading produced by the simulated cooling pro-
cess was described in the previous chapter. The purpose
of this calculation was to assess the impact of the cooling
process on the deformation of the steel plate produced
experimentally.
The calculation methodology for the structural
analysis of the FE model consists of three steps. In the
first step, the 3D finite-element model was created with
respect to the real dimensions and conditions. In the
second step, the calculated temperature field, the struc-
tural boundary conditions and the initial conditions were
applied. In the final step, the analysis of the structure and
deformation of the steel plate was calculated. Two types
of loads were considered for the prepared FE model: the
experimentally measured thermal field as the thermal
load and the mechanical loads represented by the move-
ment of the plate. The analysis of the steel-plate defor-
mation due to different conditions was carried out for
two cases. In the first case, the specimen was tested
under measured cooling conditions, and the second case
was the same as the first case (the same cooling con-
ditions) but without considering the gravity. The case
without the gravity acceleration was performed to obtain
the true deformation due to the cooling process.
J. HRABOVSKÝ et al.: EXPERIMENTAL AND NUMERICAL STUDY OF HOT-STEEL-PLATE FLATNESS
Materiali in tehnologije / Materials and technology 50 (2016) 1, 17–21 19
Figure 5: Center and surface temperature histories in the middle of
the plane
Slika 5: Temperaturna zgodovina sredine in povr{ine na sredini
povr{ine
Figure 4: Temperature profile (different scales on the axes)
Slika 4: Profil temperature (razli~na merila po oseh)
The thermal loads were FDM analyzed and applied
as the body loads of the steel plate. The temperature was
evaluated at the center of the steel plate along a defined
path (the symmetry plane) on the top and bottom sides.
The evaluation of the temperature distribution along the
defined path is shown in Figure 6. The temperature
distributions (Figure 6) show that at the beginning (14 s)
and at the end of the cooling (100.5 s), the top and
bottom temperatures are almost equal. At a time of
19.5 s it is clear that the cooling is less intense on the top
and that the bottom temperatures are lower.
Different values of the temperature on both sides of
the steel plate lead to different stresses and deformations.
The presented thermal field was used for the structural
analysis and the deformation of the steel plate was cal-
culated. The final vertical deformation at the end of the
cooling reached 2.8 mm. The maximum vertical defor-
mation is located at the corner of the steel plate.
The deformation of the steel plate along the path at
the corner and along the path at the center was evaluated
(Figure 7). The comparison of these two locations
confirmed two reasons for the maximum deformation in
the corner. The first reason is the non-homogeneous ther-
mal field at the corner. The second reason is that the
corner is free and a deformation is possible. In the
center, the steel plate is constrained by the symmetry (in
reality the steel plate would continue). The gravitational
acceleration contributes to a decrease in the total
deformation.
For the second case, the same type of cooling as for
the first case was used and the gravitational acceleration
was not considered. The final vertical deformation at the
end of the cooling reached 596 mm. The maximum ver-
tical deformation is located symmetrically at the
beginning of the steel plate. The deformations of the
steel plate in this case are mainly affected by the thermal
distribution and the thermal gradients.
The presented deformation results confirm that the
more intense cooling from the bottom side of the steel
plate leads to the final deformation on the lower-cooling
side of the steel plate (the top side). This effect can be
explained with the following mechanism. On the bottom
side, which is cooled more intensely, the temperature
drops quickly and the stiffness (K) represented by the
modulus of elasticity (E) of the bottom layer is changed
to a higher value. In the middle part of the steel plate, the
temperature is still high and the stiffness is low (the
modulus of elasticity at a higher temperature). On the top
side of the steel plate, the temperature also decreases but
not as intensely as on the bottom side. The stiffness of
the top layer is lower than the stiffness of the bottom
layer.
The combination of the temperature and the stiffness
distribution of defined layers leads to different directions
of the deflection (U) in each layer. The highest deflection
in the axial direction of the steel plate is in the middle
layer due to the higher temperature and thermal expan-
J. HRABOVSKÝ et al.: EXPERIMENTAL AND NUMERICAL STUDY OF HOT-STEEL-PLATE FLATNESS
20 Materiali in tehnologije / Materials and technology 50 (2016) 1, 17–21
Figure 6: Evaluated temperatures through the path at defined time
points
Slika 6: Ocenjene temperature skozi sredino, v dolo~enih ~asovnih
trenutkih
Figure 8: Schematic illustration of the steel-plate deformation mecha-
nism
Slika 8: Shemati~en prikaz mehanizma deformacije plo{~e iz jekla
Figure 7: Evaluation of the total vertical deformation at a time of
100.5 s
Slika 7: Ocena skupne vertikalne deformacije pri ~asu 100,5 s
sion. On the bottom side of the steel plate, deflection
occurs in the opposite direction than in the middle layer
due to intense cooling. At the top layer, the lower cool-
ing intensity leads to a deflection in the same direction as
at the bottom layer, but the deflection is lower than on
the bottom side. These deflection distributions through
the thickness of the steel plate generate a deformation in
the intensely cooled side direction.
Non-homogeneous cooling on the bottom and top
sides of the steel plate cause a time shift in the tempe-
rature distribution on both sides. The time shift in the
temperatures on both sides causes a deflection inverted
from the bottom and top layers, changing the final defor-
mation of the steel plate in the direction of the actual
cooled side (the top side). A schematic illustration of the
deformation of the steel mechanism due to non-homo-
geneous cooling is depicted in Figure 8. The elastic-
plastic material properties of steel are considered in the
numerical model and, therefore, a permanent deforma-
tion occurs.
4 CONCLUSION
The analyses presented in this paper focused on the
study of non-homogeneous cooling and its impact on the
deformation of a steel plate. Several numerical models of
steel plates were prepared. The first model computed
time-dependent temperature fields. Plant measurements
were simulated using this model. The results obtained
from the simulation agree with data obtained during the
plant measurements. The second numerical model
focused on the cooling process of the steel plate and the
impact of thermal fields on the final deformations of the
steel plate. The FE simulation of the cooling process
showed the impact of the non-homogeneity in the
thermal field on the final deformations. The simulations
confirmed that the plate is bent towards the side with the
higher cooling intensity in the initial cooling stage;
however, in the later stages, the plate is bent towards the
opposite side, with the lower cooling intensity.
Acknowledgement
The paper presented was supported through project
CZ.1.07/2.3.00/30.0005 of the Brno University of
Technology.
This work is an output of the research and scientific
activities of the NETME Centre, regional R&D center
built with the financial support from the Operational
Programme Research and Development for Innovations
within the project NETME Centre (New Technologies
for Mechanical Engineering), Reg. No. CZ.1.05/2.1.00/
01.0002 and, in the follow-up sustainability stage,
supported through NETME CENTRE PLUS (LO1202)
by the financial means from the Ministry of Education,
Youth and Sports under the National Sustainability
Programme I.
5 REFERENCES
1 X. Wang, Q. Yang, A. He, Calculation of thermal stress affecting
strip flatness change during run-out table cooling in hot steel strip
rolling, Journal of Materials Processing Technology, 207 (2008),
130–146, doi:10.1016/j.jmatprotec.2007.12.076
2 Y. J. Jung, G. T. Lee, C. G. Kang, Coupled thermal deformation
analysis considering strip tension and with/without strip crown in
coiling process of cold rolled strip, Journal of Materials Processing
Technology, 130–131 (2002), 195–201, doi:10.1016/S0924-0136
(02)00705-7
3 H. N. Han, J. K. Lee, H. J. Kim, Y. S. Jin, A model for deformation,
temperature and phase transformation behavior of steel on run-out
table in hot strip mill, Journal of Materials Processing Technology,
128 (2002), 216–225, doi:10.1016/S0924-0136(02)00454-5
4 X. Wang, F. Li, Q. Yang, A. He, FEM analysis for residual stress
prediction in hot rolled steel strip during the run-out table cooling,
Applied Mathematical Modelling, 37 (2013), 586–609, doi:10.1016/
j.apm.2012.02.042
5 S. Serajzadeh, Prediction of temperature distribution and phase
transformation on the run-out table in the process of hot strip rolling,
Applied Mathematical Modelling, 27 (2003), 861–875, doi:10.1016/
S0307-904X(03)00085-4
6 M. Chabicovsky, M. Raudensky, Experimental Investigation of a
Heat Transfer Coefficient, Mater. Tehnol., 47 (2013) 3, 395–398
7 M. Raudensky, Heat Transfer Coefficient Estimation by Inverse Con-
duction Algorithm, International Journal of Numerical Methods for
Heat and Fluid Flow, 3 (1993) 3, 257–266, doi:10.1108/eb017530
8 M. Pohanka, P. Kotrbacek, Design of cooling units for heat
treatment, In: F. Czerwinski (Ed.), Heat Treatment – Conventional
and Novel Applications, InTech, 2012, 1–20, doi:10.5772/50492
J. HRABOVSKÝ et al.: EXPERIMENTAL AND NUMERICAL STUDY OF HOT-STEEL-PLATE FLATNESS
Materiali in tehnologije / Materials and technology 50 (2016) 1, 17–21 21