Article
1.5 GPa Grade High-Strength Steel Sheet Flattening by Roll Gap
Adjustment Considering Pattern Roll Effects
Youngjin Jeon 1,2 , Kyucheol Jeong 1,2 , Geun-ho Kim 1,2,3 and Jonghun Yoon 1,2, *
1
2
3
*
Department of Mechanical Design Engineering, Hanyang University, 55, Hanyangdaehak-ro, Sangrok-gu,
Ansan 15588, Gyeonggi, Republic of Korea; jj981226@hanyang.ac.kr (Y.J.); kcjeong0@gmail.com (K.J.);
kdh7355@secoasan.com (G.-h.K.)
2BK21 FOUR ERICA-ACE Center, Hanyang University, Ansan 15588, Gyeonggi, Republic of Korea
ASAN Co., Ltd., Pureundeulpan-ro 826-4, Paltan-Myun, Hwasung 18525, Gyeonggi, Republic of Korea
Correspondence: yooncsmd@gmail.com; Tel.: +82-31-400-5255
Abstract: This study analyzes a three-stage roll flattening process to improve the flatness of
1.5 GPa grade AHSS sheets. Unlike conventional leveler rolls, which mainly relieve residual
stress through longitudinal tension-compression, the second roll has a sloped pattern to
induce transverse deformation and redistribute local residual stresses. A twisted sheet
was processed under different roll gap settings (1.3 mm, 1.1 mm, 0.9 mm, and 0.7 mm),
and experimental measurements were compared with Abaqus Explicit simulations. At
a 1.1 mm gap, the RMSE between experiment and simulation is 0.22 mm, showing the
highest agreement. Both twist and crossbow defects are reduced by over 80%, achieving
optimal flattening. At 1.3 mm, the simulation overestimates the second roll’s effect, causing
excessive localized deformation. Reducing the gap to 0.9 mm or 0.7 mm increases discrepancies due to roll fixation differences. Experiments allow more central bending, amplifying
crossbow, while simulations assume rigid rolls, underestimating curvature. Adjusting the
second roll’s geometry to enhance transverse tension-compression and setting the gap to
1.1 mm effectively reduces defects. This method improves flatness while minimizing the
number of rolls needed in high-strength steel sheet production.
Keywords: advanced high-strength steel; flattening; finite element analysis; roll gap
optimization
Academic Editor: Zhengyi Jiang
Received: 8 March 2025
Revised: 26 March 2025
Accepted: 2 April 2025
Published: 9 April 2025
Citation: Jeon, Y.; Jeong, K.; Kim,
G.-h.; Yoon, J. 1.5 GPa Grade
High-Strength Steel Sheet Flattening
by Roll Gap Adjustment Considering
Pattern Roll Effects. Materials 2025, 18,
1702. https://doi.org/10.3390/
ma18081702
Copyright: © 2025 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/
licenses/by/4.0/).
Materials 2025, 18, 1702
1. Introduction
In modern industries, metal sheets are processed through various methods, including
roll forming, to create essential components for automotive, aerospace, and electronic
applications. In particular, the automotive and aerospace sectors have increasingly adopted
Advanced High Strength Steel (AHSS) due to its high strength and lightweight properties,
which contribute to improved fuel efficiency and enhanced safety during collisions [1]. To
clarify the application of AHSS in the automotive industry, we have explicitly described its
use in structural components such as B-pillars, door rings, front bumper beams, subframes,
and suspension arms. Furthermore, in electric vehicle (EV) manufacturing, AHSS plays
a crucial role in battery protection structures and crash-resistant designs, ensuring both
structural integrity and weight reduction. However, during the coiling and uncoiling
processes of AHSS, residual stress is generated, leading to potential defects that may
negatively affect the quality of the final products [2,3].
These defects typically appear in various forms depending on the distribution of
stress within the sheet. Figure 1 illustrates two common types of distortions observed
https://doi.org/10.3390/ma18081702
Materials 2025, 18, x FOR PEER REVIEW
Materials 2025, 18, 1702
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2 of 22
These defects typically appear in various forms depending on the distribution of
stress within the sheet. Figure 1 illustrates two common types of distortions observed in
sheet
metal.
FigureFigure
1a shows
a crossbow
defect, where
edges
of edges
the sheet
upward
in sheet
metal.
1a shows
a crossbow
defect,the
where
the
of bow
the sheet
bow
orupward
downward,
creating
an
arched
surface
across
its
width.
Figure
1b
shows
a
twist
or downward, creating an arched surface across its width. Figure 1b showsdefect,
a twist
which
combines
both longitudinal
and transverse
distortions,
resulting
in a spiraling
dedefect,
which combines
both longitudinal
and transverse
distortions,
resulting
in a spiraling
formation
that
makes
the
sheet
challenging
to
process
further.
To
minimize
such
defects,
deformation that makes the sheet challenging to process further. To minimize such defects,
flattening
flatteningprocesses
processesare
arerequired
requiredtotoimprove
improvethe
theflatness
flatnessand
andquality
qualityofofthe
thesheets.
sheets.
(a)
(b)
Figure
Sheet
metal
defects:
(a)(a)
crossbow
defect
causing
curvature
inin
the
width
direction;
(b)
twist
Figure1.1.
Sheet
metal
defects:
crossbow
defect
causing
curvature
the
width
direction;
(b)
twist
defect
resulting
in
combined
longitudinal
and
transverse
distortions.
defect resulting in combined longitudinal and transverse distortions.
Theleveler
levelerroll
rollisisaawidely
widelyused
usedand
and essential
essential technology for
The
for improving
improvingthe
theflatness
flatnessof
residual
stress
through
repetitive
bending
andand
relaxation
processes.
ofmetal
metalsheets
sheetsbybyreducing
reducing
residual
stress
through
repetitive
bending
relaxation
proThis process
allows
for the
distribution
of residual
stress
within
the the
material,
cesses.
This process
allows
foruniform
the uniform
distribution
of residual
stress
within
maenhancing
its flatness
and improving
the overall
surfacesurface
quality quality
[4,5]. During
the
terial,
enhancing
its flatness
and improving
the overall
[4,5]. flattening,
During flatmetal the
sheet
undergoes
both plastic
strain
andstrain
elasticand
recovery,
optimizes
its physical
tening,
metal
sheet undergoes
both
plastic
elastic which
recovery,
which optimizes
and contributes
to producing
high-quality
final products
itsproperties
physical properties
and contributes
to producing
high-quality
final[6].
products [6].
However,the
the
leveler
typically
requires
10for
rolls
for flattening
proHowever,
leveler
rollroll
typically
requires
moremore
than than
10 rolls
flattening
processes
cesses
[4–7].
is a necessary
design element
to improve
the of
quality
of flattening,
but
[4–7].
This
is aThis
necessary
design element
to improve
the quality
flattening,
but it also
it also
to an increase
inconsumption.
energy consumption.
As the of
number
of rolls increases,
adleads
to leads
an increase
in energy
As the number
rolls increases,
additional
ditional
energy is consumed
to the
each
and its interaction
with the
energy
is consumed
due to the due
rotation
ofrotation
each rollofand
itsroll
interaction
with the material,
material,
which subsequently
resultsoperating
in highercosts
operating
costs inprocesses
industrial[6,8].
processes
[6,8].
which
subsequently
results in higher
in industrial
FurtherFurthermore,
as theof
number
of rolls increases,
the structural
complexity
of the equipment
more,
as the number
rolls increases,
the structural
complexity
of the equipment
grows,
grows,maintenance
making maintenance
and roll replacement
more challenging.
roll replacemaking
and roll replacement
more challenging.
During rollDuring
replacement,
adment, adjustments
to the arrangement
spacing
of required,
the rolls are
required,
whichthe
can
justments
to the arrangement
and spacingand
of the
rolls are
which
can prolong
prolong
the
process
and
negatively
impact
production
efficiency
[9].
In
conclusion,
while
process and negatively impact production efficiency [9]. In conclusion, while the leveler
theisleveler
roll is technology
an essentialfor
technology
flattening
sheets, in
thethe
increase
in of
the
roll
an essential
flatteningfor
metal
sheets,metal
the increase
number
number
of
rolls
leads
to
a
more
complex
process
and
extended
processing
time,
which
are
rolls leads to a more complex process and extended processing time, which are significant
significant[9,10].
drawbacks [9,10].
drawbacks
This
study
proposesa anovel
novelroll
rollflattening
flatteningmethod
methodthat
thatenhances
enhancesthe
theflatness
flatnessofofmetal
metal
This study proposes
sheetswhile
whilereducing
reducingthe
thenumber
numberofofleveling
levelingrolls.
rolls.Unlike
Unlikeconventional
conventionallevelers
levelersthat
thatrely
rely
sheets
on
multiple
rolls
to
relieve
residual
stress
through
repeated
longitudinal
deformation,
the
on multiple rolls to relieve residual stress through repeated longitudinal deformation, the
proposedthree-stage
three-stagesystem
systemoptimizes
optimizesroll
rollgap
gapand
andgeometry
geometrytotoachieve
achievecomparable
comparableoror
proposed
superior
flattening
performance
with
only
three
rolls.
A
key
innovation
is
the
introduction
superior flattening performance with only three rolls. A key innovation is the introduction
slope-patternedsecond
secondroll,
roll,which
whichinduces
inducestransverse
transversedeformation
deformationand
andenables
enableslocal
local
ofofa aslope-patterned
redistribution
of
residual
stress
across
the
sheet
width—an
effect
that
conventional
methods
redistribution of residual stress across the sheet width—an effect that conventional methcannot
achieve.
ods
cannot
achieve.
This
reduction
roll
count
brings
significant
industrial
benefits,
including
simplified
This reduction ininroll
count
brings
significant
industrial
benefits,
including
simplified
equipmentdesign,
design,lower
lowermanufacturing
manufacturingcosts,
costs,and
andreduced
reducedenergy
energyconsumption
consumptiondue
duetoto
equipment
decreased
rotational
resistance.
decreased rotational resistance.
To validate the effectiveness of the method, both experimental tests and finite element
analysis (FEA) were conducted under roll gap settings of 1.3 mm, 1.1 mm, 0.9 mm, and
0.7 mm. Flattening performance was evaluated by calculating the root mean square error
Materials 2025, 18, 1702
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(RMSE) between experimental and simulation results, considering shape defects such as
crossbow and twist. Factors like contact pressure distribution, friction, and dynamic effects
were also analyzed to identify discrepancies. Based on these results, an optimal roll gap
was determined that minimizes defects and shows strong agreement between experiments
and simulations.
2. Experimental Procedure
2.1. Materials
The material used in this study is martensitic steel for cold forming with an ultimate
tensile strength of 1.5 GPa. It undergoes quenching and tempering during manufacturing,
which ensures high strength and adequate ductility. Therefore, no additional annealing
heat treatment was performed before cold working in this study.
To evaluate its mechanical properties and anisotropy, tensile tests were conducted
on specimens cut in three different directions: rolling direction (RD), diagonal direction
(DD), and transverse direction (TD). The dimensions of the test specimens are presented
in Figure 2, while the stress–strain curves obtained from these experiments are shown
in Figure 3. The results reveal minimal differences in mechanical behavior between RD,
Materials 2025, 18, x FOR PEER REVIEW
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DD, and TD, indicating that the material exhibits nearly isotropic behavior [11–13]. The
sample preparation and testing followed the ASTM E8 tensile test standard, which specifies
Materials 2025, 18, x FOR PEER REVIEW
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guidelines for specimen geometry, dimensions, and testing procedures to ensure accurate
evaluation of mechanical properties.
Figure 2. Dimension of test specimen.
Figure 2. Dimension of test specimen.
Figure 2. Dimension of test specimen.
Stress [MPa]
Stress [MPa]
2000
2000
1500
RD
DD
TD
DD
Fitting
TD
Fitting
1500
1000
RD
1000
500
500
0
0.00
0
0.00
0.01
0.01
0.02
0.02
0.03
Strain
0.03
0.04
0.04
0.05
0.05
0.06
0.06
Figure3.3.Stress–strain
Stress–straincurves
curvesfor
formartensitic
martensiticsteel
steelininRD,
RD,DD,
DD,and
andTD
TDdirections
directionswith
withfitted
fittedresults.
results.
Figure
Strain
Table3.1.Stress–strain
Mechanical properties
and Voce hardening
parameters
MPa). with fitted results.
Figure
curves for martensitic
steel in RD,
DD, and (unit:
TD directions
Parameter
Young’s modulus
Poisson’s
Parameterratio
𝝈𝒚
Young’s modulus
Value
217,000
0.33
Value
1251.73
217,000
Table 1. Mechanical properties and Voce hardening parameters (unit: MPa).
Materials 2025, 18, 1702
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Several studies have demonstrated that although some initial anisotropy may exist in
martensitic steels, the hot-forming and quenching process significantly reduces directional
differences in mechanical properties. As the microstructure transforms into fine-grained
martensite, anisotropic effects diminish, making an isotropic material model a reasonable
choice for simulations without significant loss of accuracy [11–14]. Additionally, employing
an anisotropic model significantly increases computational time, and its practical effectiveness must be carefully considered. Based on the tensile test results in this study, the
mechanical properties of martensitic steel after press hardening exhibit minimal directional
differences, confirming that assuming isotropic behavior in simulations does not significantly affect reliability. Therefore, an isotropic material model was applied in this study to
enhance computational efficiency while maintaining accuracy within acceptable limits.
The stress–strain curves were fitted using the Voce hardening model, which is widely
used to describe the plastic behavior of metals and accounts for both initial yield stress and
subsequent strain hardening [15]. The Voce model is expressed as
σ ε p = σy + n1 · p 1 − exp −n2 ε p + n3 ε p ,
(1)
where σ ε p is the reference flow stress, and σy , n1 , n2 , n3 are material parameters calibrated from the tensile test data. This model is typically applied to true stress-true strain
data, as it effectively captures strain hardening beyond yielding, making it more suitable for
describing plastic deformation compared to engineering stress–strain data. Additionally,
the Young’s modulus (E) and Poisson’s ratio (ν) were also obtained and are presented in
Table 1.
Table 1. Mechanical properties and Voce hardening parameters (unit: MPa).
Parameter
Value
Young’s modulus
Poisson’s ratio
217,000
0.33
σy
n1
n2
n3
1251.73
392.74
419.64
500
2.2. Experimental Setup
The experiment was conducted using a roll flattening machine equipped with a threestage roll configuration. Figure 4 illustrates the overall setup of the experimental equipment.
The machine consists of a first-stage roll, a second-stage roll, and a third-stage roll, each
specifically designed for its unique purpose.
Figure 5 provides a detailed representation of each roll station. Figure 5a shows the
configuration of the first roll and third roll, which are composed of flat rolls. Figure 5b
depicts the configuration of the second roll, which features a shape distinct from that of the
first and third rolls. This unique shape is shown in greater detail in Figure 5c.
Figure 5 shows the geometry of the second roll, defined by a slope angle of 9.15◦ and a
radius of R0.4, which contrasts with the flat roll design of the first and third rolls. The design
of the second roll focuses on improving flattening in the transverse direction (y in Figure 5a),
rather than the longitudinal direction typically addressed in roller flattening processes.
The slope and curvature are adjusted to leverage the alternating tension and compression
effects inherent to the flattening process, redistributing residual stress across the width of
the sheet. The metal sheet used in this experiment measured 232.2 × 1100 × 1.3 mm and
was intentionally selected with a twist defect to evaluate the flattening performance. The
roll gap was initially set to the sheet thickness of 1.3 mm and then progressively reduced
Materials 2025, 18, 1702
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to 1.1 mm, 0.9 mm, and 0.7 mm, with each configuration being tested three
times. This
5 of 25
systematic variation in roll gap allowed for the analysis of its effect on flattening efficiency.
Materials 2025, 18, x FOR PEER REVIEW
Materials 2025, 18, x FOR PEER REVIEW
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Figure 4.
setup.
Figure
4. Experimental
Experimental
setup.
Figure 5 provides a detailed representation of each roll station. Figure 5a shows the
configuration of the first roll and third roll, which are composed of flat rolls. Figure 5b
depicts the configuration of the second roll, which features a shape distinct from that of
the first and third rolls. This unique shape is shown in greater detail in Figure 5c.
(a)
(b)
(c)
Figure 5. Configuration of roll stations at (a) the first-stage and third-stage rolls and (b) the second-
Figure 5. Configuration of roll stations at (a) the first-stage and third-stage rolls and (b) the secondstage roll. (c) Shape of the second-stage roll.
stage roll. (c) Shape of the second-stage roll.
Figure 5 shows the geometry of the second roll, defined by a slope angle of 9.15° and
a radius of 𝑅0.4, which contrasts with the flat roll design of the first and third rolls. The
design of the second roll focuses on improving flattening in the transverse direction (y in
Figure 5a), rather than the longitudinal direction typically addressed in roller flattening
processes. The slope and curvature are adjusted to leverage the alternating tension and
front section dataset, the polynomial regression equation is as follows:
𝑓1 𝑥 = 4.23
10−12 𝑥5 − 3.92
10−9 𝑥4 + 5.88
10−8 𝑥3 − 5
10−5 𝑥2 −
0.0199𝑥 + 8.41,
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(2)
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The coefficient of determination (𝑹𝟐 ) is 0.940, and the standard deviation (RMSE) is
0.363.
2.3. Measurement Method
For the end section dataset, the polynomial regression equation is as follows:
The data was measured using a line scanner, as shown in Figure 6. A Keyence LJ4
𝑓1 scanner
𝑥 = 4.12
10−12
𝑥5 − was
3.85 placed
10−9 𝑥
+ 5.92
10−8 𝑥3 −and
4.85used
10a−5laser
𝑥2 − to scan
X8400
(Osaka,
Japan)
above
the specimen
(3)
0.0192𝑥 +This
8.35,
and measure the height with high accuracy.
scanner has a resolution of 3.2 µm in the
X direction
and 0.2 µm
in the Z direction,
a measurement
accuracy
of σ ≤(RMSE)
0.08 µm,
The coefficient
of determination
(𝑹𝟐 ) with
is 0.982,
and the standard
deviation
is
ensuring
very
small
errors.
The
scanner
measured
the
height
from
a
fixed
position,
covering
0.221. The fitted data for the two values is shown in Figure 3.
the entire
without needing
towas
move.
To keep
the measurements
accurate
and
Sincespecimen
the same processing
method
applied
uniformly
to all measurement
points,
consistent,
all
tests
were
done
on
a
flat
surface.
the results remain comparable across different specimens and processing conditions.
Figure 6. Scanning method and example of a measurement section.
Figure 6. Scanning method and example of a measurement section.
To check the reliability of the measured data, the standard deviations of crossbow
and twist defect reductions at different roll gaps were calculated. Table 2 shows these
results, helping to understand how much the defect reduction varies depending on the
roll gap. The standard deviation of crossbow reduction was very low at a 1.1 mm roll
gap (0.002 mm), meaning the measurements were very consistent. However, at 0.9 mm
(0.326 mm) and 0.7 mm (0.245 mm) roll gaps, the variation was larger, showing that the
measurement values changed more as the roll gap got smaller.
Table 2. Standard deviations of twist and crossbow defects at different roll gaps.
Roll Gap (Unit: mm)
Twist (Unit: Degree)
Crossbow (Unit: mm)
1.3
1.1
0.9
0.7
0.532
0.356
0.481
0.730
0.138
0.002
0.326
0.245
For twist reduction, the standard deviation also changed with different roll gaps. The
lowest variation was at 1.1 mm (0.356 mm), while the highest was at 0.7 mm (0.730 mm).
This pattern suggests that as the roll gap gets smaller, the material bends more, making
the twist reduction values less stable. The higher strain and stress at smaller roll gaps can
make small defects worse and cause more changes in the results. Even though there is
some variation, the overall trend in defect reduction remains steady, confirming that the
measured data is reliable.
As shown in Figure 6, twenty-two measurement points were selected along the width
(1100 mm) and length (232.2 mm) of the specimen. These points were positioned at regular
intervals to ensure that data from different areas of the surface could be analyzed effectively.
Materials 2025, 18, 1702
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A measurement interval of 50 mm was chosen to provide an optimal balance between
capturing detailed deformation features and maintaining computational efficiency.
This interval was determined to be sufficient for capturing critical deformation patterns
such as twist and crossbow defects while avoiding excessive computational burden. By
comparing the height values at these locations, the flattening effect could be evaluated,
and differences between processing conditions could be examined. This approach ensures
that local variations in sheet deformation are properly analyzed without introducing
unnecessary data complexity.
However, it should be noted that the rolling force was not directly measured in this
study, which may raise concerns regarding the reproducibility of the results. Since rolling
force significantly influences the deformation behavior of the sheet, the absence of direct
force measurements may present challenges in accurately validating the simulation results
and comparing them with experimental outcomes.
The direct measurement of rolling force poses considerable challenges due to limitations in equipment and experimental constraints. The roll flattening process occurs over
a very short duration under high compressive forces, making it difficult to obtain direct
stress or force measurements with high accuracy. Furthermore, the second roll has a small
curvature radius (R = 0.4 mm), resulting in a highly localized contact area. This leads to
significant concentration of local stress, which poses challenges for strain measurement
through surface patterns. Conventional optical strain measurement techniques, such as
Digital Image Correlation (DIC), may not be suitable in such conditions, as excessive local
deformation and non-uniform strain distribution can affect pattern visibility and reduce
measurement accuracy.
To reduce measurement noise, a polynomial fitting method was applied to smooth
the data. This approach ensured a consistent trend across the dataset, making it suitable
for assessing the flattening results and identifying any remaining surface irregularities.
As illustrated in Figure 7, the front and end sections are shown as examples to show the
effect of the smoothing process. The scanning method provides high-resolution height
Materials 2025, 18, x FOR PEER REVIEW
9 of 25
data, allowing for the detection of small surface variations, such as distortions caused by
residual stress.
Figure7.7.Smoothing
Smoothingofofmeasured
measureddata
datathrough
throughfitting.
fitting.
Figure
The provided data corresponds to the flattening experiment before rolling at a roll gap
3. Methods
of3.1.
1.1Analysis
mm. TheModel
X values range from −116.28 mm to 116.04 mm. A 5th-degree polynomial
The simulation roll setup shown in Figure 8 is made up of three rolls. The first roll
and third roll have a traditional flat shape, but the second roll is designed with a repeated
pattern (see Figure 5). Conventional leveler rolls mainly work by applying repeated tension and compression along the sheet’s length (X direction) to lessen residual stress and
flatten the sheet [5,16]. In this study, however, we use the shape of the second roll to
Materials 2025, 18, 1702
8 of 22
regression was applied to each dataset to approximate the measured values. For the front
section dataset, the polynomial regression equation is as follows:
f 1 ( x ) = 4.23 × 10−12 x5 − 3.92 × 10−9 x4 + 5.88 × 10−8 x3 − 5 × 10−5 x2 − 0.0199x + 8.41, (2)
The coefficient of determination (R2 ) is 0.940, and the standard deviation (RMSE) is 0.363.
For the end section dataset, the polynomial regression equation is as follows:
f 1 ( x ) = 4.12 × 10−12 x5 − 3.85 × 10−9 x4 + 5.92 × 10−8 x3 − 4.85 × 10−5 x2 − 0.0192x + 8.35, (3)
The coefficient of determination (R2 ) is 0.982, and the standard deviation (RMSE) is
0.221. The fitted data for the two values is shown in Figure 3.
Since the same processing method was applied uniformly to all measurement points,
the results remain comparable across different specimens and processing conditions.
3. Methods
Materials 2025, 18, x FOR PEER REVIEW
3.1. Analysis Model
10 of 25
The simulation roll setup shown in Figure 8 is made up of three rolls. The first roll
and third roll have a traditional flat shape, but the second roll is designed with a repeated
models(see
may
introduce
some errorsleveler
in force
and
stresswork
predictions,
they repeated
are generally
sufpattern
Figure
5). Conventional
rolls
mainly
by applying
tension
ficient
for shape along
accuracy
ultra-high-strength
steel (UHSS)
Our
numerical
and
compression
the in
sheet’s
length (X direction)
to lessenapplications.
residual stress
and
flatten
analysis
results
confirm
that
the
calibrated
spring-supported
rigid
roll
model
provides
the sheet [5,16]. In this study, however, we use the shape of the second roll to change
shape
prediction
accuracy comparable
to sheet’s
experimental
while reducing
computathe
same
tension-compression
cycle to the
width results
(Y direction),
which effectively
tional
cost.
reduces uneven local residual stress [6,9].
Figure8.8.Arrangement
Arrangementofofrolls
rollsand
andsheets
sheetsused
usedininthe
thesimulation.
simulation.
Figure
localConditions
deformation in the width direction from the second roll is adjusted by the
3.2. The
Analysis
nearby
lower
third
The area
stretched
in the second roll is compressed by the
3.2.1. Comparison roll.
Between
Solidthat
andisShell
Elements
flat roll of the third roll, while the area that is compressed in the second roll is stretched
A comparative analysis was conducted between shell and solid elements under idenby the third roll, restoring the overall flatness of the sheet. This method follows the same
tical mesh and boundary conditions to assess their suitability for simulating the flattening
tension-compression cycle as the traditional roll flattening method but, by switching the
process. Both models utilized the same mesh structure, with the height in the z-direction
direction of the force, it can more precisely control the residual stress across the sheet’s
treated as an integration point to ensure consistency in the evaluation. The primary objective of this comparison was to determine how accurately each element type could represent roll geometry and its interaction with the sheet. The findings showed a clear limitation of the shell element model.
As shown in Figure 9, which depicts the equivalent plastic strain (PEEQ) distribution
Materials 2025, 18, 1702
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width [6]. This approach helps solve problems with uneven residual stress that may occur
during the sheet-making process and greatly improves the uniformity of the final shape, as
confirmed by both numerical analysis and experiments [17].
The analysis model was developed using an analytic rigid body based on the roll
drawings, and the distance between rolls was set to 450 mm. The sheet was modeled
with shell elements, and the contact condition between the rolls and the sheet was set
with a friction coefficient of 0.12. In addition, an initial speed of 200 mm/s was applied to
the sheet, with the angular speeds (w = v/r) of the rolls set as follows: the upper roll at
−1.345 rad/s, lower rolls 1 and 3 at 2.5 rad/s, and the lower second roll at 2.53 rad/s to
account for a small difference in diameter. Under these conditions, the analysis shows that
the shape of the second roll plays a key role in flattening the sheet.
To account for roll elastic deformation, we modeled the bottom roll as a rigid fixed
body while the upper roll was supported by a spring to approximate its elastic behavior
under load. This approach is supported by previous studies, which have demonstrated that
a spring-supported rigid roll model effectively captures roll deformation effects while maintaining computational efficiency [18]. Adjusting the spring stiffness enables accurate shape
predictions without requiring a fully elastic roll model, which would significantly increase
computational cost. Furthermore, studies by [19,20] indicate that while rigid roll models
may introduce some errors in force and stress predictions, they are generally sufficient
for shape accuracy in ultra-high-strength steel (UHSS) applications. Our numerical analysis results confirm that the calibrated spring-supported rigid roll model provides shape
prediction accuracy comparable to experimental results while reducing computational cost.
3.2. Analysis Conditions
3.2.1. Comparison Between Solid and Shell Elements
A comparative analysis was conducted between shell and solid elements under identical mesh and boundary conditions to assess their suitability for simulating the flattening
process. Both models utilized the same mesh structure, with the height in the z-direction
treated as an integration point to ensure consistency in the evaluation. The primary objective of this comparison was to determine how accurately each element type could represent
roll geometry and its interaction with the sheet. The findings showed a clear limitation of
the shell element model.
As shown in Figure 9, which depicts the equivalent plastic strain (PEEQ) distribution
after the flattening process, the shell model failed to capture the influence of roll geometry
on the sheet [21]. Unlike the solid model, the shell model did not properly account for the
force exerted by the rolls, leading to an inaccurate representation of local stress and strain
distributions. This discrepancy arises from the structural limitations of shell elements,
which inherently assume a plane stress condition and neglect through-thickness stress
variation. As a result, shell elements are unable to represent the actual load transfer through
the thickness direction, resulting in an inaccurate PEEQ distribution.
In contrast, the solid element model effectively incorporated the detailed roll geometry
and accurately simulated the three-dimensional load transfer from the rolls to the sheet.
This enabled it to capture the actual deformation and stress distribution, including throughthickness normal and shear stresses, leading to a more realistic representation of the
flattening process. The rolling-induced deformation is characterized by large in-plane
stress variations and heavily constrained out-of-plane strain, making the deformation
state of the sheet better represented by a plane strain condition rather than a plane stress
condition. The significant through-thickness compressive stresses generated by the rolls
further support this assumption. Therefore, the solid element model, which does not
impose any restrictive stress assumptions, offers a more suitable and accurate framework
Materials 2025, 18, x FOR PEER REVIEW
11 of 25
Materials 2025, 18, 1702
10 of 22
further support this assumption. Therefore, the solid element model, which does not impose any restrictive stress assumptions, offers a more suitable and accurate framework for
for analyzing
flattening
behavior.
Given
superiorperformance
performanceininreplicating
replicatingphysical
physical
analyzing
the the
flattening
behavior.
Given
itsits
superior
behavior
and
capturing
stress
redistribution,
the
solid
model
was
ultimately
adopted
for
behavior and capturing stress redistribution, the solid model was ultimately adopted for
the analysis.
analysis.
the
Figure 9. Comparison of equivalent plastic strain (PEEQ) distribution between solid and shell models.
Figure 9. Comparison of equivalent plastic strain (PEEQ) distribution between solid and shell models.
3.2.2. Number of Elements
The total number of elements used in the simulation was approximately 153,120 (X:
220; Y: 232; Z: 3). The element size in the X direction (rolling direction) was set to 5 mm,
dividing the total length of 1100 mm into 220 elements. In the Y direction (transverse
direction), an element size of 1 mm was applied, resulting in 232 elements across a width
of 232.2 mm. The Z direction (thickness direction) was discretized with three elements to
capture the sheet’s 1.3 mm thickness accurately. Among these, the Y direction element size
had the greatest influence on simulation accuracy. While the X direction represents the
relative movement between the rolls and the sheet, variations in element size along this axis
have a relatively minor impact on contact accuracy. Similarly, in the Z direction, an adequate
number of elements is necessary to model contact pressure and strain distribution, but
explicit simulations remain stable with as few as three elements. In contrast, the Y direction
plays a crucial role in defining the roll curvature and is the key factor in determining
the accuracy of the contact simulation. Increasing the number of elements in the X or Z
direction significantly raises computational costs due to the reduction in time step size in
explicit analysis. Since the time step is governed by the smallest element size, excessive
refinement in these directions would dramatically increase computation time without a
proportional gain in accuracy. Therefore, optimizing the Y direction element size while
maintaining practical element counts in the X and Z directions provided the best balance
between accuracy and computational efficiency.
Figure 10 shows the effect of the Y direction element size on the accuracy of the roll
geometry representation in the simulation. When the Y direction element size was 10 mm,
the red line representing the second roll’s inclined pattern did not align with the sheet mesh
structure, indicating that the roll pattern was not properly reflected in the deformation. This
discrepancy led to errors in transverse deformation representation, making it impossible to
evaluate the effect of the second roll accurately.
Materials 2025, 18, x FOR PEER REVIEW
Materials 2025, 18, 1702
(a)
13 of 25
11 of 22
(b)
Figure10.
10.Effect
Effectofof
directionelement
elementsize
sizeononroll
rollgeometry
geometryrepresentation:
representation:(a)(a)element
elementsize
size1010mm
mm
Figure
YY
direction
(mismatch);
(b)
element
size
1
mm
(match).
(mismatch); (b) element size 1 mm (match).
Conversely,
when the Y direction element size was reduced to 1 mm, the red line per3.2.3. Spring
Stiffness
fectly matched the roll pattern, confirming that the roll geometry was accurately captured
To improve the accuracy of the analysis and better model the interactions between
in the simulation. Given that transverse deformation is a crucial factor, as emphasized in
the sheet and the rolls, this study introduced spring stiffness as a key variable to account
the introduction, reducing the Y direction element size is essential for accurately analyzing
for elastic deformation effects. In practical roll flattening processes, the contact between
the effect of the second roll. Furthermore, Figure 5c indicates that the roll pattern has an
the sheet and the rolls is influenced by local elastic deflection of the rolls, which affects the
R value of 0.4 mm, suggesting that a finer mesh in the Y direction is required to properly
load transfer and overall flattening performance. Previous studies [22] have shown that
reflect the actual roll geometry.
incorporating elastic compliance into roll models can significantly reduce discrepancies
The analysis systematically examined the boundary conditions, element types, mesh
between experimental and numerical results.
configuration, and contact modeling approach in the FEM simulations. The impact of
To determine the optimal spring stiffness, an experimental calibration approach was
Y direction element size on contact accuracy was analyzed in detail using Figure 10,
employed. The initial stiffness was set to 10 N/mm and progressively increased in steps
leading to the selection of the optimal element size. As shown in Figure 10, when the Y
of ten to examine the deformation behavior under two critical conditions: the widest roll
direction element size was 10 mm, the roll pattern and sheet mesh did not align, reducing
gap of 1.3 mm and the narrowest of 0.7 mm. Specifically, in the second roll, the optimal
the reliability of the contact simulation. However, with a 1 mm element size, the roll
spring stiffness was determined by noting the state just before excessive marking began
pattern was accurately reflected in the sheet deformation, improving the precision of the
at the 1.3 mm gap and by finding the critical point when marks formed at the 0.7 mm gap.
simulation results.
The experimental verification showed that a spring stiffness of 10 N/mm behaved most
Since transverse deformation is particularly important and is primarily influenced by
like the experimental data, and this value was chosen as optimal. This result not only supthe second roll, minimizing the Y direction element size is essential to ensure an accurate
ports the model’s validity but also shows its potential for use in actual processes. In addirepresentation of the roll-sheet interaction. Additionally, as shown in Figure 5c, the roll
tion, while the lower roll was kept fixed, the three upper rolls were allowed to move freely
pattern has an R value of 0.4 mm, further emphasizing the need for a finer Y direction
in the z-direction, with all degrees of freedom except rotation around the y-axis being
mesh for greater accuracy. Based on these findings, the optimal Y direction element size
restricted. With this setup, spring stiffness was applied to the upper rolls to accurately
was determined to be 1 mm, ensuring strong agreement between the simulation and
model the elastic interaction between the rolls and the sheet. This allowed for a more preexperimental results.
cise analysis of roll deflection and contact forces.
In Spring
summary,
introducing spring stiffness significantly enhanced the model’s accu3.2.3.
Stiffness
racy and
reliability,
particularly
capturing
effects
impact local
deTo improve the
accuracy ofinthe
analysisroll
anddeflection
better model
thethat
interactions
between
formation
redistribution.
By incorporating
a calibrated
stiffness
value,
the sheet and
and stress
the rolls,
this study introduced
spring stiffness
as a spring
key variable
to account
the
simulation
better
approximates
experimental
conditions,
ultimately
improving
prefor elastic deformation effects. In practical roll flattening processes, the contact between
dictive
accuracy
inrolls
roll flattening
simulations.
the sheet
and the
is influenced
by local elastic deflection of the rolls, which affects the
load transfer and overall flattening performance. Previous studies [22] have shown that
3.2.4. Contact and Dynamic Influences
incorporating elastic compliance into roll models can significantly reduce discrepancies
In thisexperimental
analysis, the and
effects
of contact
pressure and friction were considered by setting
between
numerical
results.
the friction
coefficient
to
0.12
because
the
experimental
setup involved
a approach
lightly oiled
To determine the optimal spring stiffness,
an experimental
calibration
was
metal
sheet surface,
which
typically
results
a friction
coefficient ranging
from
employed.
The initial
stiffness
was set
to 10 in
N/mm
and progressively
increased
in0.10
stepstoof
0.15
The median
value of 0.12
was chosen
represent
behaviorthe
accurately.
ten[23].
to examine
the deformation
behavior
undertotwo
critical this
conditions:
widest rollAdgap
ditionally,
combination
of general
contact
with hardincontact
conditions
was
used to
efof 1.3 mmaand
the narrowest
of 0.7 mm.
Specifically,
the second
roll, the
optimal
spring
fectively
the interaction
between
sheet
the rolls,
ensuring
that began
the contact
stiffnessmodel
was determined
by noting
thethe
state
justand
before
excessive
marking
at the
pressure
accurately
captured
the simulation.
1.3 mm is
gap
and by finding
theincritical
point when marks formed at the 0.7 mm gap. The
Materials 2025, 18, 1702
12 of 22
experimental verification showed that a spring stiffness of 105 N/mm behaved most like
the experimental data, and this value was chosen as optimal. This result not only supports
the model’s validity but also shows its potential for use in actual processes. In addition,
while the lower roll was kept fixed, the three upper rolls were allowed to move freely in the
z-direction, with all degrees of freedom except rotation around the y-axis being restricted.
With this setup, spring stiffness was applied to the upper rolls to accurately model the
elastic interaction between the rolls and the sheet. This allowed for a more precise analysis
of roll deflection and contact forces.
In summary, introducing spring stiffness significantly enhanced the model’s accuracy
and reliability, particularly in capturing roll deflection effects that impact local deformation
and stress redistribution. By incorporating a calibrated spring stiffness value, the simulation
better approximates experimental conditions, ultimately improving predictive accuracy in
roll flattening simulations.
3.2.4. Contact and Dynamic Influences
In this analysis, the effects of contact pressure and friction were considered by setting
the friction coefficient to 0.12 because the experimental setup involved a lightly oiled metal
sheet surface, which typically results in a friction coefficient ranging from 0.10 to 0.15 [23].
The median value of 0.12 was chosen to represent this behavior accurately. Additionally,
a combination of general contact with hard contact conditions was used to effectively
model the interaction between the sheet and the rolls, ensuring that the contact pressure is
accurately captured in the simulation.
The frictional stress (τ = µ) is highly sensitive to variations in the friction coefficient
(µ), especially as the reduction per pass increases. Experimental studies have shown that
the friction coefficient is not constant along the roll gap and varies with rolling speed,
reduction, and lubrication conditions [24,25]. In rolling processes, pressure fluctuations are
mitigated through elastic roll deformation or lubrication adjustments, whereas simulations
typically assume rigid rolls and a constant friction coefficient, leading to discrepancies [25].
Explicit simulations also use techniques such as mass scaling (set to 1000 in this study)
and artificially increased process speeds to save computing time. However, these methods can amplify inertial effects, causing unrealistic stress wave propagation and dynamic
oscillations when the sheet meets the rolls. These effects have been widely studied in
the context of explicit finite element simulations for sheet forming, showing that the lack
of damping effects from bearings, stand structures, and frictional interfaces can lead to
overestimated deformation predictions [26]. Since explicit methods rely on dynamic time
integration without inherent energy dissipation mechanisms, exaggerated stress fluctuations and deformation patterns can occur, causing further deviations from experimental
results [26].
As a result, while this study applies the analysis conditions, differences between
simulation and experimental rolling conditions may lead to discrepancies in the results.
4. Results and Discussion
4.1. Comparison of Sheet Geometry and RMSE for Different Gaps
This study analyzed cold roll forming under four gap conditions: 1.3 mm, 1.1 mm,
0.9 mm, and 0.7 mm through experiments and finite element simulations using Abaqus
Explicit (version 2024, Dassault Systems, Johnston, RI, USA), where Figure 11 compares the
cross-sectional profiles of the sheet (blue: experiment, red: simulation, gray (original sheet)
in three sections (front, mid, end), and Figure 12 summarizes the RMSE for each section.
To further examine the experimental deformation trends, Figure 13 provides a visual
representation of the post-flattening height changes for each roll gap condition. The metal
Materials 2025, 18, 1702
13 of 22
Materials 2025, 18, x FOR PEER REVIEWspecimens are arranged in descending roll gap order (0.7 mm → 0.9 mm → 1.1 mm → 1.3 mm)
15 of 25
to highlight the differences in crossbow deformation. This side view of the specimens
allows for a clearer comparison of the effect of roll gap reduction on sheet flattening.
Figure
Comparisonof
ofexperimental
experimental (blue),
(red),
original
sheet
(gray)
cross-sectional
Figure
11.11.
Comparison
(blue),simulated
simulated
(red),
original
sheet
(gray)
cross-sectional
profiles
underdifferent
different gap
gap conditions
conditions (1.3
1.11.1
mm,
0.9 0.9
mm,
0.7 mm).
profiles
under
(1.3mm,
mm,
mm,
mm,
0.7 mm).
Materials
18, x FOR PEER REVIEW
Materials 2025, 18, x FOR
PEER 2025,
REVIEW
16 of 25
Materials 2025, 18, 1702
1
14 of 22
1.2
1.2
0.4
RMSE [mm]
RMSE [mm]
0.6
Roll gap: 1.3 mm
Roll gap: 1.1 mm
Roll gap: 0.9 mm
Roll gap: 0.7 mm
Front
Mid
Mid
End
End
Section
Section
1.0
1.0
0.8
Roll gap: 1.3 mm
Roll gap: 1.1 mm
Roll gap: 0.9 mm
Roll gap: 0.7 mm
0.8
0.6
0.4
0.2
0.2
0.0
0.0
Front
Figure
12.
Comparison
of
RMSE
by section
gap position.
setting
and section position.
Figure
Comparison
of RMSE
by gap
setting
position.
Figure
12. 12.
Comparison
of RMSE
by gap
setting
andand
section
Figure
13.
Sheets
arranged
in
descending
roll
gap
order
(0.7
mm to
→illustrate
1.3
mm) to
illustrate po
Figure
13. Sheets
arranged
in descending
roll
gap order
(0.7→
mm
→ 1.3
postFigure
13. Sheets
arranged
in descending
roll gap
order
(0.7 mm
1.3
mm)
tomm)
illustrate
post-flattening
deformation
trends.
flattening
deformation
tening
deformation
trends.trends.
a 1.3
mm
roll
gap,
themm
average
RMSE
is
mm.
thethe
other
hand,
At
a 1.3
roll gap,
the
average
RMSE0.51
is
approximately
0.51
mm. On the
At At
a 1.3
mm
roll
gap,
the
average
RMSE
is approximately
approximately
0.51
mm.OnOn
other
at
a
1.1
mm
gap,
the
RMSE
falls
between
0.12
and
0.31
mm,
indicating
better
agreement
hand,
at
a
1.1
mm
gap,
the
RMSE
falls
between
0.12
and
0.31
mm,
indicating
better
hand, at a 1.1 mm gap, the RMSE falls between 0.12 and 0.31 mm, indicating better agreebetween
experiments
and
simulations.
examining
the
marks
on
ment between
experimentsHowever,
and simulations.
However,
examining
surface ma
ment
between
experiments
and
simulations.
However,
examining
thesurface
surface
marksthe
onthe
second
roll
reveals
a
key
issue.
In
the
experiments,
no
noticeable
marks
were
observed
the
second
roll
reveals
a
key
issue.
In
the
experiments,
no
noticeable
marks
the second roll reveals a key issue. In the experiments, no noticeable marks were observed atwere obs
the1.3
1.3mm
mm gap,
gap,atwhile
while
small
but
appeared
the
surface
the
1.1
the 1.3
mmbut
gap,distinct
while marks
small
distincton
marks
appeared
onatat
the
sheet
surface at t
at the
small
distinct
marksbut
appeared
on
thesheet
sheet
surface
the
1.1mm
gap
(see
Figure
14).
mm
gap
(see
Figure
14).
mm gap (see Figure 14).
In contrast,
theInsimulations
that
the
1.3
mm
gap,1.3
a mm
thin
roll
withmark
a with a
contrast,
theshow
simulations
show
that
ata the
gap,
amark
thin
roll
In contrast,
the simulations
show
that at
theat
1.3
mm
gap,
thin
roll
mark
with
a front
front
depth
of
approximately
0.1
mm
is
present,
whereas
a
more
pronounced
roll
mark
depth
of
approximately
0.1
mm
is
present,
whereas
a
more
pronounced
roll
mark ap
depth of approximately 0.1 mm is present, whereas a more pronounced roll mark appears
appears
at gap.
the at
1.1
mm
gap.
discrepancies
may be
to stress
concentration,
the
1.1
mmThese
gap. These
may
be attributed
to stress
concentration, m
at the
1.1 mm
These
discrepancies
maydiscrepancies
be attributed
toattributed
stress
concentration,
material
material
recovery
properties,
friction
effects,
and
simulation
settings.
The
second
recovery
properties,
friction
effects,
and
simulation
settings.
The
second
roll, featur
recovery properties, friction effects, and simulation settings. The second roll, featuring anroll,
◦
featuring
an inclined
repeating
at
angle
of
9.15 of
,ainduces
small height
variation
inclined
repeating
pattern
at
aninduces
angle
9.15°,
a small
height
variat
inclined
repeating
pattern
at anpattern
angle
ofan
9.15°,
small ainduces
height
variation
of
of approximately 1.59 mm (see Figure 5c). Additionally, the tip of the second roll is very
Materials 2025, 18, 1702
15 of 22
sharp (0.4 R), leading to significant local stress concentration on the sheet surface18due
to
Materials 2025, 18, x FOR PEER REVIEW
of 25
periodic changes in contact pressure.
Figure
Figure14.
14.Surface
Surfacescratches
scratcheson
onthe
thesheet
sheetcaused
causedby
bythe
thesecond
secondroll
roll at
at aa 1.1
1.1 mm
mm roll
roll gap.
gap.
The study also finds that the simulation overestimates the second roll’s effect at a roll
gap of 1.3 mm, leading to a reversed crossbow. While this may stem from inaccuracies in
friction or force distribution, no friction sensitivity analysis was conducted. Performing
simulations with varying friction coefficients (e.g., 0.10 to 0.15) would help assess the
variability and improve the robustness of the model.
If the mesh size were very small (matching the width of the experimental scratch
marks), the phenomenon could be simulated more accurately. However, since the mesh
size is set to 1 mm, the overall roll mark effect appears exaggerated. Further reducing the
mesh size would significantly impact the explicit time step, making it difficult to implement
in the simulation. Moreover, since the simulation models the roll as a rigid body, any
potential deformation of the roll that might help distribute the pressure is not captured,
leading to more pronounced roll marks in the simulation.
At a 1.3 mm gap, the measured contact pressure at the front of the sheet is about
(a)
(b)
900 MPa (see Figure 15a), which is lower than the material’s yield strength. However, the
small 15.
stress
changes
caused
by thealong
roll shape
may trigger
slight
plastic
deformation
in the
Figure
Contact
pressure
distribution
the Y-coordinate
at (a)
1.3 mm
and (b)
1.1 mm roll gaps.
simulation, making the roll marks appear worse than they are. In contrast, at a 1.1 mm
gap, the average contact pressure is higher, around 1400 to 1800 MPa (see Figure 15b). This
higher pressure makes plastic deformation more likely, and some roll marks were observed
in the experiments.
Figure 14. Surface scratches on the sheet caused by the second roll at a 1.1 mm roll gap.
Materials 2025, 18, 1702
(a)
16 of 22
(b)
Figure 15.
pressure
distribution
along
the Y-coordinate
at (a) 1.3
andmm
(b) 1.1
mm
Figure
15. Contact
Contact
pressure
distribution
along
the Y-coordinate
at mm
(a) 1.3
and
(b)roll
1.1gaps.
mm
roll gaps.
Furthermore, to evaluate the time-dependent behavior of stress in the contact region,
19 of 16
25
Figure
compares the von Mises stress distribution at the moment of contact (black line) and after a
certain period (red line).
Materials 2025, 18, x FOR PEER REVIEW
a stress relaxation analysis was conducted using finite element simulation.
Initial stress (at contact)
Relaxed stress (after time)
Initial stress (at contact)
Relaxed stress (after time)
1800
1600
1600
1400
1400
Stress [MPa]
Stress [MPa]
1800
1200
1000
800
600
1200
1000
800
600
400
400
200
200
0
0
0
25
50
75
100 125 150 175 200 225
Y-coordinate [mm]
(a)
0
25
50
75
100 125 150 175 200 225
Y-coordinate [mm]
(b)
Figure 16. Comparison of von Mises stress distributions at initial contact and after stress relaxation
(a)
(a) 1.3
1.3 mm
mm and
and (b)
(b) 1.1
1.1 mm
mm roll
roll gaps.
gaps.
At
time
contact,
the vonincreases
Mises stress
reached0.39
up toand
1200–1600
MPa
1.1 mm
At the
a 0.9
mmofgap,
the RMSE
to between
0.77 mm,
andatatthe
a 0.7
mm
roll
gap,
clearly
exceeding
the
material’s
yield
strength
and
indicating
the
possibility
of
gap, it reaches between 0.2683 and 0.77 mm. These values show a larger difference comlocalized plastic deformation. However, as time progressed, a significant reduction in
pared to the 1.1 mm gap. This indicates that as the roll gap gets smaller, the difference
the stress magnitude was observed in the contact area. This stress relaxation suggests
between the experiments and the simulation grows, especially in the front section where
that the initially concentrated stress was redistributed due to plastic flow and material
height differences (i.e., crossbow height differences) occur. The issue with the crossbow
recovery effects.
will be discussed in the next section.
The simulation results imply that although high stress levels may initially trigger
plasticity,
theDefect
actual residual stress may be much lower after stabilization, which helps
4.2. Crossbow
explain the milder surface marks observed in experiments compared to simulations.
Figure 17a shows the method used to measure crossbow using the central arch height
At a 0.9 mm gap, the RMSE increases to between 0.39 and 0.77 mm, and at a 0.7 mm gap,
relative to the straight edges of the sheet as a key indicator. Crossbow is an important
it reaches between 0.2683 and 0.77 mm. These values show a larger difference compared
shape defect in roll forming because too much arching can create problems in later proto the 1.1 mm gap. This indicates that as the roll gap gets smaller, the difference between
cessing steps. Figure 17b presents the measured crossbow values under four different roll
gap conditions.
Materials 2025, 18, 1702
At a 0.9 mm gap, the RMSE increases to between 0.39 and 0.77 mm, and at a 0.7 mm
gap, it reaches between 0.2683 and 0.77 mm. These values show a larger difference
com17 of 22
pared to the 1.1 mm gap. This indicates that as the roll gap gets smaller, the difference
between the experiments and the simulation grows, especially in the front section where
differences
crossbow height
occur.
The issue
with
the crossbow
theheight
experiments
and (i.e.,
the simulation
grows,differences)
especially in
the front
section
where
height
will be discussed
in the height
next section.
differences
(i.e., crossbow
differences) occur. The issue with the crossbow will be
discussed in the next section.
4.2. Crossbow Defect
4.2. Crossbow
FigureDefect
17a shows the method used to measure crossbow using the central arch height
Figureto
17a
shows
the method
to measure
crossbow
using
the central
height
relative
the
straight
edges ofused
the sheet
as a key
indicator.
Crossbow
is arch
an important
relative
the straight
of the
sheet as
a key
indicator.
an important
shape
shapetodefect
in rolledges
forming
because
too
much
archingCrossbow
can createisproblems
in later
prodefect
in
roll
forming
because
too
much
arching
can
create
problems
in
later
processing
cessing steps. Figure 17b presents the measured crossbow values under four different roll
steps.
17b presents the measured crossbow values under four different roll gap
gap Figure
conditions.
conditions.
(a)
(b)
Figure
Experimentaland
andsimulation
simulationcomparison
comparisonof
of the
the crossbow
crossbow under
under different
Figure
17.17.
Experimental
different roll
roll gaps:
gaps: (a)
measurement
method
of
the
crossbow;
(b)
crossbow
variations
at
different
roll
gaps.
(a)
crossbow variations at different roll gaps.
At a 1.1 mm gap, the experimental and simulation results are quite similar. The
experiment recorded a crossbow height of 1.4306 mm, while the simulation estimated it
at 1.0359 mm. This small difference suggests that the contact pressure and other process
settings are well balanced at a 1.1 mm gap.
At a 1.3 mm gap, the crossbow shape in the simulation does not match the experiment.
In particular, the front section shows a reversed crossbow pattern in the simulation, while
this is not seen in the experiment. One possible reason is that the second roll does not
have as much effect on equipment, whereas in the simulation, its influence is too strong,
causing stress to build up in specific areas and reversing the crossbow shape. Also, the
first contact area where the sheet touches the rolls is very sensitive to small changes, which
may contribute to the difference [27]. As shown in Figure 18, the variation in friction
coefficient from 0.10 to 0.15 does not lead to significant changes in the height profile along
the Y-coordinate. This indicates that friction alone is not the dominant factor influencing
the reversed crossbow formation. Instead, further investigation into stress concentration
and boundary conditions is required to better understand the underlying causes.
At 0.9 mm and 0.7 mm gaps, the difference between the experiment and simulation
becomes even larger. For example, at a 0.9 mm gap, the experiment recorded a crossbow
height of 3.2742 mm, but the simulation predicted only 1.0492 mm. In the experiment, the
crossbow gets much bigger as the roll gap gets smaller. However, in the simulation, the
increase is much slower. This happens because the way the rolls are fixed and controlled is
different in actual machines compared to computer models. In experimental, the ends of the
rolls are firmly held in place by a shaft, which means the edges do not move much, but the
center is free to bend more. Because of this, the force is not spread evenly across the width
of the roll, making the crossbow much stronger in the experiment [28]. In the simulation,
Materials 2025, 18, 1702
not have as much effect on equipment, whereas in the simulation, its influence is too
strong, causing stress to build up in specific areas and reversing the crossbow shape. Also,
the first contact area where the sheet touches the rolls is very sensitive to small changes,
18 of 22
which may contribute to the difference [27]. As shown in Figure 18, the variation in friction coefficient from 0.10 to 0.15 does not lead to significant changes in the height profile
along the Y-coordinate. This indicates that friction alone is not the dominant factor influthe rolls are treated as rigid bodies with a fixed spring stiffness. This means the force
encing the reversed crossbow formation. Instead, further investigation into stress concenfrom the rolls is applied evenly across the sheet, so there is less pressure in certain areas.
tration and boundary conditions is required to better understand the underlying causes.
Because of this, the simulation predicts a much smaller increase in crossbow compared to
the experiment.
Height [mm]
5
Friction coefficients
0.10
0.11
0.12
0.13
0.14
0.15
4
3
2
1
0
0
30
60
90
120
150
180
210
Y-coordinate [mm]
Figure
18. Height
variation
atfront
the front
section
for gap
roll gap
1.3 mm
different
friction
coefficients.
Figure
18. Height
variation
at the
section
for roll
1.3 mm
withwith
different
friction
coefficients.
Overall,
the 0.7
experiment
shows abetween
bigger crossbow
than the
simulation.
At 0.9
mm and
mm gaps,always
the difference
the experiment
and
simulationThis
is because the way the rolls are fixed and controlled affects how force is applied, and this
Materials 2025, 18, x FOR PEERbecomes
REVIEW even larger. For example, at a 0.9 mm gap, the experiment recorded a crossbow
21 of 25
effect
not fully
in the simulation.
Asonly
the roll
gapmm.
getsIn
smaller,
the uneven
force
height
of is
3.2742
mm,included
but the simulation
predicted
1.0492
the experiment,
the
distribution
caused
by the
stronger,
leadingintothe
a bigger
gap between
crossbow
gets much
bigger
asroll
thefixation
roll gapbecomes
gets smaller.
However,
simulation,
the
the
experimental
and
simulated
crossbow
results.
increase is much slower. This happens because the way the rolls are fixed and controlled
4.3. Twist Defect
is different in actual machines compared to computer models. In experimental, the ends
4.3. Twist
Defect
Figure
19a also shows the method used to measure twist. Twist is defined as the difof the rolls are firmly held in place by a shaft, which means the edges do not move much,
ference
in angle
between
the
front
and end
of to
themeasure
sheet andtwist.
is oneTwist
of theiskey
defectsasinthe
roll
Figure
19a also
shows
the
method
used
defined
but the center is free to bend more. Because of this, the force is not spread evenly across
forming. in
It is
strongly
affected
by uneven
stress
along
sheet
length.
19b comdifference
angle
between
the front
and end
of the
sheetthe
and
is one
of theFigure
key defects
in
the width of the roll, making the crossbow much stronger in the experiment [28]. In the
pares
the twist
from
experiments
and stress
simulations
under
four
different
roll19b
gap
roll
forming.
It isresults
strongly
affected
by uneven
along the
sheet
length.
Figure
simulation, the rolls are treated as rigid bodies with a fixed spring stiffness. This means
conditions.
compares
the twist results from experiments and simulations under four different roll gap
the force from the rolls is applied evenly across the sheet, so there is less pressure in certain
conditions.
areas. Because of this, the simulation predicts a much smaller increase in crossbow compared to the experiment.
Overall, the experiment always shows a bigger crossbow than the simulation. This is
because the way the rolls are fixed and controlled affects how force is applied, and this
effect is not fully included in the simulation. As the roll gap gets smaller, the uneven force
distribution caused by the roll fixation becomes stronger, leading to a bigger gap between
the experimental and simulated crossbow results.
(a)
(b)
Figure19.
19.Experimental
Experimentaland
andsimulation
simulationcomparison
comparisonofoftwist
twistdefects
defectsunder
underdifferent
differentroll
rollgap
gapcondicondiFigure
tions:(a)
(a)twist
twistmeasurement
measurementmethod;
method;(b)
(b)twist
twistvariation
variationacross
acrossroll
roll
gaps.
tions:
gaps.
At
Atroll
rollgaps,
gaps,both
boththe
theexperimental
experimentaland
andsimulation
simulationresults
resultsfor
fortwist
twistexhibit
exhibitananinitial
initial
reduction
followed
by
a
subsequent
increase,
as
shown
in
Figure
19b.
In
the
experimental
reduction followed by a subsequent increase, as shown in Figure 19b. In the experimental
results, twist decreases up to a roll gap of 1.1 mm and then starts to increase from 0.9 mm.
In the simulation results, twist continues to decrease until 0.9 mm and then increases at
0.7 mm. Twist is calculated as the angular difference between the front and end tilt of the
sheet. This variation in twist originates from the stress difference between the front and
Materials 2025, 18, 1702
19 of 22
results, twist decreases up to a roll gap of 1.1 mm and then starts to increase from 0.9 mm.
In the simulation results, twist continues to decrease until 0.9 mm and then increases at
0.7 mm. Twist is calculated as the angular difference between the front and end tilt of the
sheet. This variation in twist originates from the stress difference between the front and
end sections of the sheet.
Therefore, after each roll gap analysis, the stress difference between the front and
end sections is compared [29]. Special attention is given to the region influenced by
the second roll, as indicated in Figure 20. The stress ranges at different roll gaps are as
follows: 1.3 mm gap: 209.995–376.647 MPa; 1.1 mm gap: 248.275–270.907 MPa; 0.9 mm
gap: 142.637–225.554 MPa; 0.7 mm gap: 166.053–254.638 MPa. By using the midpoints of
these stress ranges to generate a graph, a trend like the twist variation in the simulation
is observed, as shown in Figure 21. This suggests that the twist is primarily driven by
the stress imbalance between the front and end sections of the sheet. The particularly low
twist observed at the 0.9 mm gap in the simulation can be explained by the preceding
crossbow formation. The contact between the sheet and the roll in the front region plays
a significant role, where a lower roll gap increases the contact effect, reducing the stress
Materials 2025, 18, x FOR PEER REVIEW
22 of 25
imbalance between the front and end sections. As a result, both twist and crossbow defects
improve. This also explains why the simulation results predict lower twist values than the
experimental results at this specific roll gap.
(a)
(b)
(c)
(d)
Figure20.
20.Stress
Stressdifference
differencerange
rangefor
forfront
frontand
andend
endsections
sectionsatatroll
rollgaps
gapsofof(a)
(a)1.3
1.3mm,
mm,(b)
(b)1.1
1.1mm,
mm,
Figure
(c)0.9
0.9mm,
mm,and
and(d)
(d)0.7
0.7mm.
mm.
(c)
Pa]
280
260
Stress
Twist
1.2
1.0
0.8
ree]
300
(c)
(d)
Figure 20. Stress difference range for front and end sections at roll gaps of (a) 1.3 mm, (b) 1.1 mm,
(c) 0.9 mm, and (d) 0.7 mm.
20 of 22
Stress
Twist
280
1.2
1.0
260
0.8
240
0.6
220
0.4
200
0.2
180
1.3
1.1
0.9
Twist [degree]
300
Stress [MPa]
Materials 2025, 18, 1702
0.0
0.7
Roll gap [mm]
Figure
21. Stress
differences
andand
twist
changes
withwith
roll roll
gap.gap.
Figure
21. Stress
differences
twist
changes
Overall, the relationship between twist and stress imbalance shows the importance
of front-end stress distribution in sheet forming. The results show that as the roll gap
decreases, front-end contact effects become more pronounced, leading to a more balanced
state and a reduction in twist, especially at specific gaps such as 0.9 mm.
5. Conclusions
This study investigates a three-stage roll flattening process for 1.5 GPa grade AHSS,
comparing experimental and FEM results under various roll gap conditions. It focuses on a
unique transverse deformation mechanism induced by the second roll, which differs from
conventional longitudinal flattening methods.
Key findings include the following:
•
•
•
A 1.1 mm roll gap was found to be the most effective condition, reducing twist defects
by more than 80% and minimizing crossbow deformation (RMSE ≈ 0.22 mm).
At a 1.3 mm gap, simulations overestimated the effect of the second roll, leading to a
reversed crossbow pattern in the front section, which was not observed in experiments.
When the roll gap was reduced to 0.9 mm and 0.7 mm, the experiment showed a
significant increase in crossbow deformation, while the simulation underestimated this
effect due to limitations in considering friction changes and local stress accumulation.
In experimental, the end of the roll is fixed by a shaft, limiting the edge movement,
resulting in a more bent center, resulting in a disproportionate force distribution and
stronger crossbow deformation. On the other hand, the simulation lowers the crossbow
prediction by evenly applying force throughout the sheet. Due to this difference in
roll fixation, the experiment consistently shows a larger crossbow than the simulation,
and this effect becomes more pronounced as the roll gap decreases.
These findings confirm that deformation behavior is strongly influenced by frictional
changes and local stress accumulation, factors that are only partially considered in numerical models. Furthermore, optimizing the shape of the second roll and adjusting the
roll gap can significantly reduce the need for additional leveler rolls while improving
overall flattening performance. These insights contribute to enhancing the roll flattening
process for high-strength steel sheets, thereby improving both production efficiency and
product quality.
Materials 2025, 18, 1702
21 of 22
Author Contributions: Conceptualization, Y.J., K.J., G.-h.K. and J.Y.; data curation, Y.J.; methodology,
Y.J., K.J. and J.Y.; resources, G.-h.K.; supervision, J.Y.; visualization, Y.J. and K.J.; writing—original
draft, Y.J.; writing—review and editing, J.Y. All authors have read and agreed to the published version
of the manuscript.
Funding: This research was financially supported by the Ministry of Trade, Industry, and Energy
(MOTIE), Korea, under the “170 k closed section roll forming and free curvature bending technology
development for electric vehicle body” (No. 20022814) and the “Innovative Digital Manufacturing
Platform” (No. P00223311), both supervised by the Korea Institute for Advancement of Technology
(KIAT). This work was also supported by the National Research Foundation of Korea (NRF) grant
funded by the Korea government (MSIT) (No. RS-2025-00555072).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The original contributions presented in this study are included in the
article. Further inquiries can be directed to the corresponding author.
Conflicts of Interest: Author Keun-ho Kim was employed by the ASAN Co., Ltd. The remaining
authors declare that the research was conducted in the absence of any commercial or financial
relationships that could be construed as a potential conflict of interest.
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