Research Article
Analysis of the punch motion curve
for the springback of U-shaped sheet
metal
Advances in Mechanical Engineering
2023, Vol. 15(3) 1–15
Ó The Author(s) 2023
DOI: 10.1177/16878132231161151
journals.sagepub.com/home/ade
Tsung-Chia Chen1, Shi-Xun Chen1, Cheng-Chi Wang2
and Tsui-Er Lee3
Abstract
Servo presses achieve high formability by using different punch motion curves, thereby increasing their applicability in
conventional processing fields. In this study, the punch motion curves of servo presses were optimized, and the effects
of punch motion curves on the springback of U-shaped sheet metal were explored. Subsequently, the optimal punch
motion curve was determined, and the springback effect after processing was investigated. Different punch motion
curves were proposed and simulated for comparison with the results of conventional methods, and the equivalent stress
values obtained using different motion curves and mold angles were analyzed. DEFORM software was used to conduct
simulations to determine the differences between processing methods. In addition, the spring-go, springback, load–
stroke characteristics, and stress and strain distributions of U-shaped sheet metal were investigated. The conventional
motion curve resulted in springback, stress, strain, and required processing force higher than those achieved by the
curves proposed in this study. The smaller the movement difference in the motion curve of the servo press was, the
lower the springback, stress, and strain were. These results indicate that the punch motion curves obtained for different
types of processing can serve as a reference for selecting appropriate parameter values for servo presses.
Keywords
Servo press, motion curve, U-shaped sheet metal, springback, spring-go
Date received: 3 August 2022; accepted: 15 February 2023
Handling Editor: Chenhui Liang
Introduction
At the end of the 17th century, the world’s first steampowered automobile was invented by French engineer
Nicolas-Joseph Cugnot. Subsequently, German inventor Gottlieb Daimler invented the world’s first fourwheel automobile in 1887. Four-wheel vehicles have
now become a vital means of transportation for
humans. At the date of writing, the automobile industry has accumulated approximately 200 years of history
and boasts mature technology. The contemporary consumer pursues lighter, faster, and streamlined automobiles, thereby making the shape of automobiles an
increasingly crucial aspect in automobile design. This
has attracted considerable research attention on the
profile of the sheet metal of automobiles. To produce
streamlined automobile designs, each automobile factory attempts to mass-produce sheet metal with the
same dimensions. With improvements in mechanical
1
Department of Mechanical Engineering, National Chin-Yi University of
Technology, Taichung
2
Department of Intelligent Automation Engineering, National Chin-Yi
University of Technology, Taichung
3
Office of Physical Education, Asia University, Taichung
Corresponding author:
Cheng-Chi Wang, Department of Intelligent Automation Engineering,
National Chin-Yi University of Technology, No. 57, Sec. 2, Zhongshan
Road, Taiping District, Taichung 41170.
Email: wcc@ncut.edu.tw
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License
(https://creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work
without further permission provided the original work is attributed as specified on the SAGE and Open Access pages
(https://us.sagepub.com/en-us/nam/open-access-at-sage).
2
technology, servo presses have been developed for the
aforementioned purpose.
Conventional presses function according to a fixed
motion curve, whereas servo presses use servo motors
to achieve functioning based on a varying motion
curve. Servo motors can achieve positioning control,
velocity control, and the precise control of the rotational speed. These motors can achieve velocity control
over a wide velocity range and can be applied in various
metal forming processes. Conventional presses can be
classified as mechanical and hydraulic presses.
Mechanical presses boast a high, but fixed punching
speed. The punching speed of hydraulic presses can be
adjusted to a certain extent. However, hydraulic presses
have poor production efficiency. Mechanical presses
are mostly used for stamping sheet metal, whereas
hydraulic presses can be further divided into oilpressure and water-pressure presses. In particular, oilpressure presses are mainly used for industrial applications; water-pressure presses are mostly used in special
and large machines. Servo presses have the advantage
of an adjustable movement distance, which can overcome the problem of a fixed movement distance of conventional presses. Relative to conventional presses,
servo presses have a mold with a longer life span and
higher precision, a higher processing area, and a lower
energy loss. Servo presses have a programmable control
system that enables a variable punch motion curve and
a wide range of applications in plastic deformation.1
Li et al.2 developed a two-dimensional finite-element
method for analyzing the springback of V-shaped sheet
metal. They used elastic plastic and changed the hardening method of the material to increase the precision of
the springback of the sheet metal. They also considered
the changes in Young’s modulus of the material with
plastic deformation and concluded that the greater the
veracity of the hardening mode was, the greater the
springback accuracy was. Firat3 constructed a plastic
deformation model for investigating the springback of a
U-shaped sheet metal channel. By changing the material
parameters and considering the anisotropic criterion,
they investigated the forming process of the sheet metal
channel and improved the precision of sheet metal
springback. Zhang et al.4 proposed a plane-strain finite
element analysis method based on the Hill48 yielding criterion and the springback of U-shaped sheet metal. Their
results indicated that increases in the blank holder pressure and the coefficient of friction reduced the springback of sheet metal. Zang et al.5 examined the effects of
changes in the material parameter on the Young’s modulus by updating the prediction of the elasticity and correcting the plastic deformation. They found that the
simulated and experimental results were close to each
other, with the predicted springback being marginally
higher than the experimental one. Yu6 examined the elastic and inelastic springback of U-shaped sheet metal and
Advances in Mechanical Engineering
revealed that the Young’s modulus and inelastic springback must be considered in finite-element analysis to
achieve high precision in the prediction of the springback
of U-shaped sheet metal. In 2012, Abe and Takahashi7
conducted V-bending tests to reduce the springback of a
part formed by a servo press. They reported that the die
holding time at the bottom dead center of the servo press
slide affected the springback. Therefore, to clarify the
mechanisms leading to this phenomenon, they used aluminum alloy sheets as specimens to conduct V-bending
tests on the servo press. Their results indicated that the
movement of the slide in the slide motion program differed from its actual movement. Therefore, to avoid
human error, they proposed a springback angle measurement system, which is more accurate than the image processing method.
The problems of spring-go and springback occur
when U-shaped sheet metal is bent and formed. In
Leu,8 the nature of the material caused small errors in
the calculations of the springback angle. The results of
Leu8 indicated that the punch filet, diameter, and blank
thickness affected the springback angle. Thinner plates
were more likely to cause springback but less likely to
bounce. The springback increased with the angle of the
punch filet. Ultrahigh-strength steel (UHSS) springback
is a critical problem in the production of armored combat vehicles. Bending UHSS is a challenging task
because of the high springback tendency corresponding
to large minimum bending radii. Billur et al.9 conducted
simulations and experimental tests to investigate the
effects of servo presses on the bending of UHSS plates;
they conducted basic material characterization tests to
determine the material properties for the simulations.
Springback is one of the most critical problems in
the applications of high-strength steel, such as in automobiles, and servo presses can be effectively used to
address the defects, improve the processing conditions,
and increase the productivity of high-strength steel. In
2017, Song et al.10 proposed a servo press method for
solving the springback problem of high-strength steel,
but this method results in undesirable shape defects.
They conducted a U-bending test to investigate the
effect of servo press slide motion on 980-MPa highstrength steel and concluded that servo presses can be
set to function with slide motion that varies within a
single operation. In 2018, Liu11 developed a drawing
process for high-strength steel parts without blank
holder force based on numerical simulation in
Dynaform. They used simulations of high-strength steel
to draw the velocity and corresponding profile motion
of a punch and concluded that restricting the drawing
velocity and controlling the velocity profile of the
punch motion could reduce springback by approximately 31%.
In 2019, Fallahiarezoodar et al.12 performed an
experimental and numerical analysis of springback and
Chen et al.
the residual stresses induced during U-channel drawing
of Al5182-O. They reported that, during U-channel
drawing, the draw-in of the sheet material into the die
cavity was controlled by the blank holder force.
Therefore, they used a servo hydraulic cushion to
experimentally reduce the residual stresses and springback at the wall and reported significant reductions in
residual stresses and springback when poststretching
was applied. In 2020, Hetz et al.13 discovered that sheet
materials with a low elastic modulus and high yield
strength tend to have higher springback. They used
7000-series aluminum alloys (7000 series) and adopted
a novel approach to investigate the springback behavior of AA7020-T6 and AA7075-T6. They also completed cross profiles to be deeply drawn with various
parameter settings and subsequently digitized them
using a three-dimensional optical measurement system.
Li et al.14 applied warm bending on a commercial thinwalled pure titanium tube to build a coupled thermal–
mechanical finite element model of the heating/bending/unloading process to predict and verify springback
behavior during warm bending. Their results offer a
fundamental understanding of how springback behavior is affected by thermal and mechanical factors upon
local-heat-assisted bending that may be useful for
improving the forming accuracy of bent titanium tubular parts and structures. Ma et al.15 proposed a generalized analytical solution for predicting springback in the
bending of tubular materials, particularly those with
tension–compression asymmetry.
In 2020, Kuo et al.16 studied rectangular cup stamping of SUS304 and optimized the pulsating curve for a
servo press by using a finite element method. They used
the Taguchi method to obtain the optimal parameter
combination. Their optimized parameters decreased the
forming time (by 0.06 s), thinning ratio (by 0.1425%),
and forming force (by 808 N). Kriechenbauer et al.17
proposed a systematic design based on computational
science methods with free force and motion functions
for deep-drawing processes on servo presses. They
determined the optimal parameters (force and motion
functions) for the deep-drawing process with superimposed vibrations on servo screw presses. They validated
their evolutionary optimization results through experiments with a cross die. Choudhari and Khasbage18 used
numerical and experimental methods to analyze the
effects of different drawing parameters, such as blank
shape, blank thickness, load, and dry/wet lubrication,
on a square cup-drawing process for an extradeepdrawn steel sheet. They conducted experiments to validate their simulation results and reported the optimized
process parameters for the formation of a square cup
without defects, such as thinning or wrinkling.
The punch motion curve is one of the key factors
affecting springback, which is a critical deformation
behavior because it affects the accuracy, quality, and
3
Table 1. Chemical composition of the AISI-1045 steel plate.
C
Si
Mn
P
S
0.450
0.300
0.800
0.030
0.035
properties of U-shaped sheet metals. However, only a
few studies have investigated punch motion curves.
Therefore, in this study, DEFORM finite element analysis software was used to simulate the processing of Ushaped sheet metals with various punch motion curves.
Experiments were also conducted for comparison with
the numerical results. The rest of this paper is organized as follows. Section ‘‘Material properties and
experimental design’’ briefly describes the material
properties and experimental design used in this study.
Section ‘‘Processing experiment for the U-shaped sheet
metal’’ discusses the details of the processing of Ushaped sheet metals and provides a comparison of the
simulated and actual load–stroke relationships, profiles, and springback of U-shaped sheet metals after
processing. Section ‘‘Parameter analysis for the processing of the U-shaped sheet metal’’ presents and discusses
the experimental results. Finally, Section ‘‘Conclusion’’
provides brief concluding remarks.
Material properties and experimental
design
Material properties of the AISI-1045 steel plate
Material composition. In this study, tensile tests were conducted on an AISI-1045 medium carbon steel plate to
prove that the punch motion curve reduced the springback of this plate. Testing was conducted to determine
the effect of uniaxial deformation in the AISI-1045
medium carbon steel plate on the cracking of the steel
plate. The chemical composition of the aforementioned
plate is presented in Table 1.
Tensile test. U-shaped sheet metal was produced from
the AISI-1045 medium carbon steel plate at a thickness
of 1 mm. To simulate material processing, material
parameters were obtained before the finite element
analysis was performed. Data such as the load, stroke,
engineering stress, and engineering strain were obtained
during through 10 tensile tests. The average value of
the first five tensile test results was used as the first
value (indicated by the red curve in Figure 1), whereas
the average value of the remaining five results was used
as the second value (indicated by the black curve in
Figure 1). The cracks observed during the tensile tests
are depicted in Figure 2.
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Figure 1. Stress–strain curve of the AISI-1045 medium carbon
steel plate.
Figure 3. SD1-160 servo press.
Figure 2. Cracks observed in the tensile tests.
Table 2. Material parameters of AISI-1045 medium carbon
steel in DEFORM software.
E (GPa)
sy (MPa)
n
K (MPa)
n
e0
210
430
0.3
646
0.24
0.063
E: Young’s modulus; v: Poisson’s ratio; sy: yielding stress.
The engineering stress and strain were converted into
the true stress and strain, respectively. The following
equation, which indicates the true stress–strain relationship, was then used to calculate the material parameters
K and n19:
s
= K e0 + ep Þn
ð1Þ
The material parameters of AISI-1045 medium carbon
steel are listed in Table 2. The true stress and strain
were input into the DEFORM software to simulate the
forming process.
Experimental device and mold design
The main experimental device used in this study was the
SD1-160 servo press, which is depicted in Figure 3. This
device was used to process the U-shaped sheet metal.
To determine the difference between the simulated and
actual processing of the U-shaped sheet metal and to
reduce the time required for completing finite-element
analysis, the one-half symmetrical model was used in
finite-element analysis in this study. Therefore, the Ushaped sheet metal was cut in half by using the Excetek
NP400L wire-cutting electrical discharge machining
system. The springback of the U-shaped sheet metal
was measured using the Keyence VHX-5000 optical
microscope. The coordinates of the corners of the Ushaped sheet metal were measured using the threedimensional coordinate measurement machine. This
machine was used because the corners were rounded
and their coordinates were difficult to measure. After
the U-shaped sheet metal was processed, the Delta
ultrasonic cleaner was used to clean it. Next, the TOP
TECH automatic mounting press was used to mount
the U-shaped sheet metal to increase the convenience of
the subsequent grinding process. After the U-shaped
sheet metal was mounted, the metal was grinded using
the metallographic grinding and polishing machine.
Finally, the precision diamond saw was used to cut the
U-shaped sheet metal into the required dimensions.
The servo press was used in conjunction with a mold
to process the U-shaped sheet metal. SOLIDWORKS
was used to draw the extrusion mold of the circular cup
placed in the servo press (Figure 4). The length, width,
and thickness of the adopted blank were 110, 50, and
1 mm, respectively. The punch angle (cp) was 94°, and
the punch filet was R2 mm. The angle (cd) and the filet
of the die was 94° and R3 mm, respectively. The mold
Chen et al.
5
Figure 4. Extrusion mold of the circular cup placed in a servo
press.
material was SKD11. The one-half symmetrical model
was used to reduce the time required to perform finiteelement analysis. The dimensions of the one-half Ushaped sheet metal processing mold are displayed in
Figure 5.
Processing experiment for the U-shaped
sheet metal
Selection of the simulation parameters and setup of
the experimental device for processing the U-shaped
sheet metal
The DEFORM finite-element analysis software was
used to simulate the processing of U-shaped sheet
metal. First, two types of punch motion curves were
created. The first type of simulated curve was the conventional punch motion curve (Case 0). In Case 0, the
punch moved down for a distance of 29 mm and then
moved upward. The simulated servo motor processed
the U-shaped sheet metal. An elastoplastic body was
used, and its grid number was 80,000. The Coulomb
friction was considered in the simulation, and its value
was 0.08. The parameters adopted in the simulation of
the processing of the U-shaped sheet metal are presented in Table 3. The punch motion curves for the
processing was simulated. The downward movement of
the punch is displayed in Figure 6, and the upward
movement of the punch and the release of stress by it
are illustrated in Figure 7.
The changes in different punch motion curves were
used as a basis for performing processing analysis.
Four punch motion curves, one each for Cases 1, 2, 3,
and 4, were constructed. Figure 8 and Table 4 show the
differences in punch movement distance among the
Figure 5. Dimensions of the one-half U-shaped sheet metal
processing mold.
Table 3. Parameters used in the simulation of the processing of
the U-shaped sheet metal.
Blank dimensions (mm) length 3 width
Blank thickness (mm)
Punch filet (mm)
Female mold filet (mm)
Coulomb friction
Grid number
110 3 50
1
2
2
0.08
80,000
Figure 6. Stress distribution during the downward movement
of the punch in the metal processing.
cases. The relationships among the load–stroke characteristics, stress, and strain of the U-shaped sheet metal
were analyzed. The blank thickness was 1 mm. Because
the friction coefficient (Coulomb friction) was difficult
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Advances in Mechanical Engineering
Profile and springback of the U-shaped sheet metal
after processing
Figure 7. Stress distribution during the upward movement of
the punch and the release of stress.
to measure during the forming process, the force–
displacement curve of the simulation was compared
with that of the experiment. Subsequently, the friction
coefficient for the simulation was so that the force–
displacement curve approximated the experimental
curve. The friction coefficient that yielded simulated
results close to the experimental results was obtained.
The Coulomb friction was set to 0.08.
Comparison of the simulated and actual processing
of the U-shaped sheet metal
This chapter used the punch motion curves obtained
for Cases 0 and 3 in the processing of the U-shaped
sheet metal. The products produced using the punch
motion curves for Cases 0 and 3 are displayed in
Figures 9 and 10, respectively. The values simulated
using DEFORM were compared with the corresponding experimental values. The experimental and simulated load–stroke diagram, profile, and springback of
the U-shaped sheet metal were compared.
Load–stroke diagram of the U-shaped sheet metal
after processing
The simulated and actual load–stroke diagrams of the
U-shaped sheet metal for Cases 0 and 3 were compared.
The load–stroke diagram for the conventional punch
motion curve (Case 0) is depicted in Figure 11(a), and
the load–stroke diagram for the punch motion curve
corresponding to Case 3 is depicted in Figure 11(b).
The punch movement distance exhibited higher variations before 2.5 mm than after 2.5 mm. For Cases 0 and
3, when the punch movement distances were 2.5–29 mm
and 7.5–29 mm, respectively, the trends were similar,
and the error was within the acceptable engineering
limit.
The simulated and actual profile of the U-shaped sheet
metal were compared. The simulated results were
obtained using the DEFORM software. A wire-cutting
electrical discharge machining system was used to cut
the finished U-shaped sheet metal in half to observe its
profile. The experimental results for Cases 0 and 3 are
presented in Figure 12. An optical microscope, a laser
displacement meter, and an image measurement instrument were used to obtain the profile of the U-shaped
sheet metal experimentally. The simulated and experimental profiles of the U-shaped sheet metal for Case 0
are depicted in Figure 13(a). After springback, the difference in profile was not large, and errors occurred at
the corners. Figure 13(b) displays a comparison of the
simulated and experimental profiles of the U-shaped
sheet metal for Case 3. After springback, the difference
in profiles was not large. The simulated springback at
the end of the sheet metal was larger and caused the
sheet metal to bend upward.
Parameter analysis for the processing of
the U-shaped sheet metal
Effect of punch motion on the processing of the Ushaped sheet metal
This study analyzed the effect of the punch motion on
the processing of the U-shaped sheet metal. The relationships between the load–stroke diagram, stress, and
strain associated with the processing of the U-shaped
sheet metal at a punch movement distance of 29 mm
were investigated.
Load–stroke diagram of the U-shaped sheet metal. The effect
of the punch motion on the load–stroke diagram of the
U-shaped sheet metal was investigated (Figure 14). The
results indicated that when the punch moved upward
and released stress, the blank stress was immediately
released. The smallest force was associated with the
punch motion curve for Case 1 because the punch was
released frequently in this case. In Case 4, the cyclic frequency of the punch when it moved 4 mm downwards
was considered. The movement distance for Case 4 was
long, which caused high levels of strain and hardening.
Regarding the cyclic frequency of the punch in Case 2,
the force required was larger, which caused the material
to become harder and more brittle. In Case 1, the levels
of strain and hardening were low because the punch
movement distance was short and the cyclic frequency
was high. The differences between the maximum forces
associated with different punch motion curves are presented in Table 5. The results indicated that Case 1
exhibited the maximum difference in the percentage of
Chen et al.
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Figure 8. Punch motion curves for (a) Case 0, (b) Case 1, (c) Case 2, (d) Case 3, and (e) Case 4.
load (up to 45.62%) from Case 0. Therefore, when the
downward distance of the punch motion decreased, the
maximum load acting on the product also decreased.
Overall, the proposed punch motion curves (Cases 1–4)
required less force than the conventional punch motion
curve (Case 0).
Equivalent stress and strain distribution of the U-shaped sheet
metal. The stress and strain of the U-shaped sheet
metal in different cases were investigated. The highest
stress of the U-shaped sheet metal was observed in
Case 0 (Figure 15). The equivalent stress and strain
distributions for Cases 1–4 are displayed in Figures 16
to 19, respectively. When the punch moved upward in
Cases 1–4, stress was released effectively. The simulated
results indicated that the stress and strain were smaller
in Cases 1–4 than in Case 0. The maximum stress and
strain occurred at the bend of the U-shaped sheet
(marked by a red circle). Table 6 lists the differences
between the equivalent stress and strain values associated with the various motion curves. Compared with
the values for Case 0, the stress and strain values
obtained for Case 1 exhibited the largest differences.
The stress and strain differed by 1.57% and 7.97%,
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Table 4. Punch movement distances associated with different
types of punch motion curves.
Motion
curve
Type
Model diagram
Movement distance
Case 0
Downward for a distance of 29 mm
Case 1
Downward for a distance of 1.0 mm
Upward for a distance of 0.5 mm
Case 2
Downward for a distance of 2.0 mm
Upward for a distance of 0.5 mm
Case 3
Case 4
Figure 10. Finished product produced using the punch motion
curve for Case 3.
Downward for a distance of 3.0 mm
Upward for a distance of 0.5 mm
Downward for a distance of 4.0 mm
Upward for a distance of 0.5 mm
Figure 9. Finished product produced using the punch motion
curve for Case 0.
respectively. These results indicate that decreasing the
downward distance of the punch motion may reduce
the stress and strain on U-shaped sheet metals.
Accordingly, the downward distance of 1.0 mm used in
Case 1 can induced the smallest punch load, stress and
stress than the other Cases.
Effect of the mold angle on the processing of the Ushaped sheet metal
The effect of the mold angle (cd) on the processing of
the U-shaped sheet metal was examined through simulations. In these simulations, five mold angles, namely
90°, 92°, 96°, 98°, and 100°, were considered for Cases
0–4; the Coulomb friction was 0.08; and the punch
movement distance was 29 mm.
Relationship between the mold angle and the springback of the
U-shaped sheet metal. Figure 20 shows the U-shaped
sheet metal before and after springback with mold
angles of 90°, 92°, 94°, 96°, 98°, and 100°. This figure
indicates that during the processing of the U-shaped
sheet metal, some mold angles caused spring-go after
springback. Therefore, the springback angles in Cases
0–4 were examined under the aforementioned mold
angles to determine the threshold values for spring-go
or springback to occur. Table 7 present the springback
angles in Cases 0–4 under mold angles of 90°, 92°, 94°,
96°, 98°, and 100°, respectively. Figure 21 depicts the
variations in the springback angle with the mold angle
for each case. The punch movement distances for Cases
1–4 differed by 0.5, 1.5, 2.5, and 3.5 mm, respectively,
from that for Case 0.
The smallest punch movement distance was observed
in Case 1. Therefore, considerable stress was released
and relatively low springback occurred in Case 1. In
addition, spring-go occurred when the mold angle was
90° or 92° and it means that the parameter of mold
angle is designed to limit smaller than 94° as the Case 1
is applied. Therefore, the optimal precision and formability were achieved in Case 1 (with the smallest punch
movement distance) when the mold angle was smaller
than 94°. For all of Case 1 shown in Table 7, the smallest absolute value of spingback angle is shown is 0.14
with the mold angle of 94°.
In Case 2, the optimal precision and formability
occurred when the mold angle was 92.5°. In Case 3, the
optimal precision and formability occurred when the
mold angle was 92°. The punch movement distance in
Case 4 was longer than that in Case 1. Consequently,
the U-shaped sheet metal exhibited springback at every
Chen et al.
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Figure 11. Load–stroke diagram of the U-shaped sheet metal for (a) Case 0 and (b) Case 3.
Case 0 used fixed punch movement. Therefore, large
springback was observed in this case with every mold
angle. Consequently, achieving the required precision
was difficult in Case 0.
Figure 12. Experimental profile of the U-shaped sheet metal
for (a) Case 0 and (b) Case 3.
mold angle in Case 4. Therefore, when the punch movement distance was shorter, the springback reduced considerably, and the product had the expected precision.
The relationship between mold angle and the equivalent stress
of U-shaped sheet metal. Table 8 present the equivalent
stress values obtained in different cases under mold
angles (cd) of 92°, 94°, 96°, 98°, and 100°, respectively.
Figure 22 displays the variations in the equivalent stress
with the mold angles in different cases. This figure indicates that a higher mold angle resulted in a smaller
equivalent stress. The smallest equivalent stress was
observed in Case 1 because the punch movement distance was the smallest in this case. The results is consistent with the conclusion of 4.1.2 meaning that Case 1
Figure 13. Comparison of the simulated and experimental profiles of the U-shaped sheet metal for (a) Case 0 and (b) Case 3.
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Advances in Mechanical Engineering
Figure 14. Load–stroke diagram of the U-shaped sheet metal for (a) Case 1, (b) Case 2, and (c) Case 4.
Table 5. Differences between the maximum loads associated
with different types of punch motion curves.
Motion curve
Case 0
Case 1
Case 2
Case 3
Case 4
Value
Load (tons-SI)
Difference percentage
compared with Case 0 (%)
3.66
1.99
2.43
2.77
3.27
0.00
245.62
233.61
224.32
210.66
1.5, 2.5, and 3.5 mm, respectively. The average equivalent stress was between the equivalent stress in Cases 1
and 0. The largest difference between the equivalent
stresses in different cases was achieved to 15 MPa when
the mold angle was 94°. However, the smallest difference of the equivalent stresses for the mold angle of 98°
and 100° was only 7 MPa. Therefore, a larger mold
angle reduced the differences between the equivalent
stresses in different cases.
Conclusion
can induced the smallest punch load, stress and stress
than the other Cases.
The highest equivalent stress was observed in Case 0
for each mold angle. This is because only a single fixed
punch movement occurred in this case, and stress could
not be released during processing. The punch movement
distance in Case 0 differed from those in Cases 2–4 by
Punch motion curves can be applied in metal forming
with servo press to reduce the springback for sheet metal.
By controlling the cyclic frequency of the punch, the
forming stress of the sheet material can be reduced and
the metal forming rate increased. With regard to the
springback of U-shaped sheet metal after processing, the
following conclusions were obtained in this study:
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Figure 15. Equivalent stress and strain distribution of the U-shaped sheet metal in Case 0.
Figure 16. Equivalent stress and strain distribution of the U-shaped sheet metal in Case 1.
Figure 17. Equivalent stress and strain distribution of the U-shaped sheet metal in Case 2.
1.
The methods used in this study can be applied
in the analysis of the springback of U-shaped
sheet metal after processing. The analysis results
of this study are within the engineering error.
2.
The simulated and experimental profiles of the
U-shaped sheet metal agreed well. Thus, the
simulation method adopted in this study has
high precision and accuracy.
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Figure 18. Equivalent stress and strain distribution of the U-shaped sheet metal in Case 3.
Figure 19. Equivalent stress and strain distribution of the U-shaped sheet metal in Case 4.
Table 6. Equivalent stress and strain values associated with
various motion curves and differences from those in Case 0.
Motion
curve
Stress and strain
Stress
(MPa)
Stress
difference, %
Strain
(mm/mm)
Strain
difference, %
Case 0
Case 1
Case 2
Case 3
Case 4
827
814
820
821
826
0.00
21.57
20.85
20.73
20.12
0.364
0.335
0.342
0.349
0.361
0.00
27.97
26.04
24.12
20.82
3.
During the processing of U-shaped sheet metal,
this study discovered that products processed using
the proposed punch motion curves (Cases 1–4)
required smaller forces than those processed using
the conventional punch motion curve (Case 0).
4.
5.
In Case 1, considerable stress was released
because the punch movement distance was
short. Moreover, the highest springback reduction was achieved in this case. The aforementioned results proved that the cyclic frequency
of the punch motion curve affected the forming
precision and formability of metals. In addition,
the number of molding processes can be reduced
to increase production efficiency.
The shortest punch movement distance was that
in Case 1. Therefore, in this case, considerable
stress was released, and low springback
occurred. In addition, when the mold angle was
smaller than 94°, spring-go occurred. Moreover,
when the punch movement distance decreased,
springback considerably decreased, and the
product was formed with the expected precision.
Chen et al.
Figure 20. Comparison of the U-shaped sheet metal in Cases 0–4 before and after springback under a mold angle of (a) 90° (b)
92° (c) 94° (d) 96° (e) 98°, and (f) 100°.
13
14
Advances in Mechanical Engineering
Table 7. Springback angles for the five cases and various mold
angles.
Table 8. Equivalent stress values in the five cases with various
mold angles.
Motion curve
Motion curve
Springback
Springback angle (°)
Case 0
Case 1
Case 2
Case 3
Case 4
Case 0
Case 1
Case 2
Case 3
Case 4
Case 0
Case 1
Case 2
Case 3
Case 4
Case 0
Case 1
Case 2
Case 3
Case 4
Case 0
Case 1
Case 2
Case 3
Case 4
Case 0
Case 1
Case 2
Case 3
Case 4
Mold angle of 90°
4.08
22.76
20.9
20.56
0.11
Mold angle of 92°
2.15
21.57
20.37
0.1
0.94
Mold angle of 94°
4.02
0.14
1.39
2.09
2.31
Mold angle of 96°
5.06
0.54
2.58
2.87
3.01
Mold angle of 98°
5.38
0.77
3.19
3.73
4.11
Mold angle of 100°
5.73
2.58
3.95
4.31
5.21
Judgment
Stress (MPa)
Spring back
Spring go
Spring go
Spring go
Spring back
Case 0
Case 1
Case 2
Case 3
Case 4
Spring back
Spring go
Spring go
Spring back
Spring back
Case 0
Case 1
Case 2
Case 3
Case 4
Spring back
Spring back
Spring back
Spring back
Spring back
Case 0
Case 1
Case 2
Case 3
Case 4
Spring back
Spring back
Spring back
Spring back
Spring back
Case 0
Case 1
Case 2
Case 3
Case 4
Spring back
Spring back
Spring back
Spring back
Spring back
Case 0
Case 1
Case 2
Case 3
Case 4
Spring back
Spring back
Spring back
Spring back
Spring back
Case 0
Case 1
Case 2
Case 3
Case 4
Figure 21. Variations in the mold angle with the springback
angle in different cases.
Stress
Mold angle of 90°
849
836
843
845
846
Mold angle of 92°
841
830
832
835
837
Mold angle of 94°
827
812
817
820
824
Mold angle of 96°
820
809
813
816
817
Mold angle of 98°
810
803
805
806
807
Mold angle of 100°
809
802
804
805
806
Stress difference (%)
—
21.53
20.71
20.47
20.35
—
21.31
21.07
20.71
20.47
—
21.81
21.21
20.85
20.36
—
21.34
20.85
20.49
20.37
—
20.86
20.62
20.49
20.37
—
20.86
20.62
20.50
20.37
Figure 22. Variations in the equivalent stress with the mold
angle in different cases.
Chen et al.
15
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
article.
9.
Funding
The author(s) disclosed receipt of the following financial
support for the research, authorship, and/or publication of
this article: This research was funded by Ministry of Science
and Technology in Taiwan, grant number MOST 110-2221E-167-021.
10.
11.
ORCID iD
Cheng-Chi Wang
https://orcid.org/0000-0002-3009-6571
12.
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