Finite Element Analysis of Spring-back Characteristics on
Asymmetrical Z-shape Parts in Wiping Z-bending Process
Wiriyakorn Phanitwong, Pakkawat Komolruji and Sutasn Thipprakmas
Dept. of Tool and Materials Engineering, King Mongkut’s University of Technology Thonburi,
PrachaUthit Rd., Bangkok, Thailand
Keywords: Z-bending Process, Wiping-bending Process, Z-shape, Spring-back, Asymmetry, Finite Element Method.
Abstract: In recent years, the Z-bending process was rarely investigated, especially for the asymmetrical Z-shape
bending process. This causes the lacks of understanding on bending mechanism and spring-back
characteristics and results in the difficulty in die design and process control for the spring-back
characteristics. In the present research, therefore, the wiping asymmetrical Z-bending process was examined
by using the finite element method (FEM) and laboratory experiments. On the basis of the stress distribution
analysis, the different of spring-back characteristics between the symmetrical and asymmetrical wiping Z-
bending processes were investigated and clearly identified. In addition, the effects of working process
parameters, including bend angle and tool radius on spring-back characteristics were investigated and
clearly identified via the changes of stress distribution analysis as well. To verify the accuracy of the FEM-
simulation results, the laboratory experiments were carried out. The experiments were carried out to validate
the FEM simulation results. The FEM simulation results showed a good agreement with the experimental
results with reference to the bend angles.
1 INTRODUCTION
A sheet-metal bending process being a common
forming process is widely employed to form curved
shapes in sheet-metal parts by using a die. The
bending die could be commonly classified on the
basis of its design shape, including L-, V-, U-, or Z-
bent shaped parts (Lange, 1985; Schuler, 1998). In
the past, most researches of bending process were
carried out to investigate for fabrication of L-, V-,
and U-bent shaped parts. Many previous researches
are aimed to assess product quality upgrades as well
as to assess precise prediction of the spring-back
characteristic (Dilip Kumar, 2014; Zong, 2014,
Phanitwong, 2014; Leu, 2015; Thipprakmas, 2015).
With the fabrication of Z-bent shape parts, in the
past, they were usually designed to perform by two
bending operations though V-bending processes.
Therefore, the theory of Z-bending process is based
on the theory of V-bending processes. For these
reasons, they resulted in a lack of research on the Z-
bending process. However, in terms of low-cost
manufacturing, the strategies against low-cost
competition have been entirely considered in recent
years. To satisfy this low-cost manufacturing, the
wiping Z-bending process, which uses the Z-shape
die and can make two bends though one stroke on a
press machine as depicted in Fig. 1, has been
proposed to reduce the number of bending
operations and production time. Although the
principle of wiping Z-bending process is similar to
wiping-bending or L-bending process, the bending
mechanisms of them are different (Komolruji,
2013). For these reasons, the previous researches on
L-bending process (Dilip Kumar, 2014;
Kuo, 2012)
could not be applied for the wiping Z-bending
process. In addition, in recent years, the complicated
Z-shape parts with the high precision such as
asymmetrical Z-shape parts are increasingly
required. Therefore, the lack of research on wiping
Z-bending process means that a basic database with
its information is insufficient to design a suitable
bending die to control the spring-back
characteristics. Therefore, understanding the
bending mechanism and spring-back characteristics
is necessary. In the present research, therefore, the
asymmetrical Z-shape parts was investigated though
the wiping Z-bending process using FEM and
laboratory experiments. On the basis of the stress
distribution analyses, the different of spring-back
Phanitwong, W., Komolruji, P. and Thipprakmas, S.
Finite Element Analysis of Spring-back Characteristics on Asymmetrical Z-shape Parts in Wiping Z-bending Process.
DOI: 10.5220/0005974502250230
In Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2016), pages 225-230
ISBN: 978-989-758-199-1
Copyright
c
 2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
225

885.153
20.0
+= εσ
Punch
Die
Initial Workpiece
Blank
holder
Bent part
Punch
Figure 1: Principle of wiping Z-bending process.
characteristics between the symmetrical and
asymmetrical wiping Z-bending processes was
investigated and clearly identified by analyzing the
changes in the stress distribution. In addition, the
effects of working process parameters, including
bend angle and tool radius on the spring-back
characteristics were investigated and clearly
identified by analyzing the changes in the stress
distribution as well. To verify the accuracy of the
FEM simulation results, laboratory experiments
were performed. The FEM simulation results
showed good agreement with the experimental
results in terms of the bend angles.
2 THE FEM SIMULATION
AND EXPERIMENTAL
PROCEDURES
In the present study, Fig. 2(a) shows the model of
the wiping Z-bending process which was
investigated. Fig. 2(b) depicted the measured bend
angles in the Z-shape parts. The details of these
models and the process parameter conditions
investigated in the present research were listed in
Table 1. Specifically, the three asymmetrical bend
angle and tool radius levels, as listed in Table 1,
were investigated. A two-dimensional plane strain
with a thickness of 3 mm was applied. The two-
dimensional, implicit, quasi-static finite element
method of a commercial analytical code, DEFORM-
2D, was used for the FEM simulation. To prevent
the excessive deformation of the elements, the
adaptive remeshing function was applied. As per
past studies (Komolruji, 2013; Phanitwong, 2014),
the punch and die were set as rigid types and the
workpiece material was set as an elasto-plastic type.
The rectangular elements approximately 4,000
elements were generated on workpiece material. To
save the calculation time, this number of element is
the least number to assess precise prediction of the
spring-back characteristic. The workpiece material
used in the present study was aluminum A1100-O
(JIS) and its properties were taken from tensile test
data. The strength coefficient and the strain
hardening exponent values were 153.5 MPa and
0.20, respectively.
Figure 2: FEM simulation model and measured bend
angles.
Table 1: FEM simulation and experimental conditions.
Simulation model Plane strain model
Object types Workpiece : Elasto-plastic
Punch/Die : Rigid
Blank holder : Rigid
Workpiece material A1100-O,
Thickness (t): 3 mm
Flow curve equation
Friction coefficient (µ) 0.1
Workpiece length (l) 60 mm
Web height ( H
d
) 20 mm
Punch radius (R
p
) 3, 5, 7 mm
Upper bend radius (R
ud
) 3 mm
Lower bend radius (R
ld
) 6, 8, 10 mm
Upper bend angle ( θ
u
) 90°
Lower bend angle ( θ
l
) 90°, 120°, 150°
Next, laboratory experiments were performed to
validate the FEM simulation results. As per
experiments from past researches (Komolruji, 2013,
Phanitwong, 2014), a 5-ton universal tensile testing
machine (Lloyd Instruments Ltd.) was used as the
press machine. Fig. 3 shows the wiping Z-die used
for the experiments. Five samples from each
bending condition were used to inspect the obtained
bend angles. After unloading a profile projector
(a) FEM simulation model
(b) Measured bend angles
Lower bend angle
(θ
l
)
Upper bend angle
(θ
u
)
Punch
Die
Work
p
iece
Blank
holder
R
p
R
ld
l
H
d
R
ud
SIMULTECH 2016 - 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications
226

(Mitutoyo model PJ-A3000) was used for the bend
angle measurement. The observed bend angle and
bending force were recorded and compared with
those analyzed by the FEM simulation.
Figure 3: The punch and die components for experiments.
3 RESULTS AND DISCUSSIONS
3.1 Asymmetrical Bend Radius
Fig. 4 shows the comparison of stress distribution
analyses before unloading phase between
symmetrical and asymmetrical bend radius cases.
Fig. 4(a) and (b) show the symmetrical and
asymmetrical bend radius cases, respectively. First,
the manners of the stress distribution analysis
corresponded well with the bending theory and the
literature (Komolruji, 2013). Specifically, the stress
distribution not only generated in bending allowance
zone as depicted in zone A and zone B, but it also
generated in the web as depicted in zone C as well as
generated in leg as depicted in zone D. Next, as the
lower bend radius increased as shown in Fig. 4(b),
the bending allowance zone increased as well as
stress distribution increased as depicted in zone B.
This manner of the stress distribution analysis again
corresponded well with the bending theory and the
literature (Lange, 1985; Schuler, 1998;
Thipprakmas, 2011). In addition, as shown in Fig.
4(b), the increase in lower bend radius resulted in
the decrease in stress distribution the web as
depicted in zone C as well as resulted in the increase
in the stress distribution in the leg as depicted in
zone D. Fig. 5 shows the comparison of predicted
bend angles after unloading. As illustrated in Fig.
5(a), in the case of symmetrical bend radius, the
predicted upper bend angle (
θ
u
) and lower bend
angle (
θ
l
) were of 90.31° and 88.83°, respectively.
Figure 4: Illustration of stress distribution analysis before
unloading with respect to the lower bend radius (θ
u
90°, θ
l
90°).
Next, in the case of asymmetrical bend radius as
shown in Fig. 5(b), the predicted upper bend angle
(
θ
u
) and lower bend angle ( θ
l
) were of 90.92° and
85.59°, respectively. In terms of predicted lower
bend angle, the results illustrated that the predicted
lower bend angle (
θ
l
) increased as the lower bend
radius increased. Specifically, the amount of spring-
back increased as the lower bend radius increased.
This manner of the spring-back characteristic
corresponded well with the bending theory and the
literature (Lange, 1985, Schuler, 1998,
Thipprakmas, 2011).
In addition, the results also illustrated that the
predicted upper bend angle was changed as the
lower bend radius increased. As these results, they
confirmed that the change in bend radius on one side
resulted in the change in spring-back characteristic
on the opposite side. The effects of lower bend
radius on spring-back characteristics were also
examined. Fig. 6 shows effects of lower bend radius
on spring-back characteristics in upper and lower
bend angles. As abovementioned, as the lower bend
Punch
Die
Workpiece
(a) Symmetrical bend radius
(R
ud
3mm, R
p
3 mm, R
ld
6 mm)
(b) Asymmetrical bend radius
(R
ud
3mm, R
p
7 mm, R
ld
10 mm)
-100
Mean stress (MPa)
100 -33 33
0
A
C
B
D
A
C
B
D
Finite Element Analysis of Spring-back Characteristics on Asymmetrical Z-shape Parts in Wiping Z-bending Process
227

(a) Symmetrical bend angle (θ
u
90°, θ
l
90°)
-100
Mean stress (MPa)
100
-33 33
0
C
B
D
A
C
B
D
A
(b) Asymmetrical bend angle (θ
u
90°, θ
l
150°)
(a)
Symmetrical case
(R
ud
3mm, R
p
3 mm)
(b) Asymmetrical case
(R
ud
3mm, R
p
7 mm)
θ
u
90.31° and θ
l
88.83° θ
u
90.92° and θ
l
89.59°
Figure 5: Comparison of predicted bend angles after
unloading between symmetrical and asymmetrical bend
radius (θ
u
90°, θ
l
90°). (Komolruji, 2013).
Figure 6: Relationship between lower bend radius and the
predicted bend angles (R
ud
3 mm, θ
u
90°, θ
l
90°).
(Komolruji, 2013).
radius increased, it caused the increases in stress
distribution in bending allowance zone (zone B) and
in leg (zone D) as well as the decrease in stress
distribution in web (zone C).After compensating
these changes in stress distributions, as per the
previous research (Komolruji, 2013), the results
elucidated that as the lower bend radius were 3 mm,
5 mm, and 7 mm, the predicted upper and lower
bend angles were 90.31° and 88.83°, 90.62° and
89.35°, 90.92° and 89.59°, respectively. As these
results, the results confirmed that as the lower bend
radius increased the amount of spring-back in the
upper bend angle increased as well as the amount of
spring-back in the lower bend angle increased.
3.2 Asymmetrical Bend Angle
Fig. 7 shows the comparison of stress distribution
analyses before unloading phase between
symmetrical and asymmetrical bend angle cases.
Fig. 7(a) and (b) show the symmetrical and
asymmetrical bend angle cases, respectively. As the
lower bend angle increased, the bending allowance
zone decreased as well as stress distribution
decreased as depicted in zone B. This manner of the
stress distribution analysis again corresponded well
with the bending theory and the literature (Lange,
resulted in the decrease in the stress distribution in
the leg as depicted in zone D. Fig. 8 shows the
comparison of predicted bend angles after
unloading. As illustrated in Fig. 8(a), in the case of
1985, Schuler, 1998, Thipprakmas, 2011). In addition,
as shown in Fig. 7(b), the increase in lower bend
angle resulted in the decrease in stress distribution
the web as depicted in zone C as well as
symmetrical bend angle, the predicted upper bend
angle (
θ
u
) and lower bend angle ( θ
l
) were of 90.31°
and 88.83°, respectively. Next, in the case of
asymmetrical bend angle as shown in Fig. 8(b), the
predicted upper bend angle (
θ
u
) and lower bend
angle (
θ
l
) were of 91.64° and 149.30°, respectively.
In terms of predicted lower bend angle, the results
illustrated that the amount of spring-back decreased
as the lower bend angle increased.
Figure 7: Illustration of stress distribution analysis before
unloading with respect to the lower bend angle. (R
ud
3mm,
R
ld
6 mm, R
p
3 mm).
(θ
l
)
(θ
u
)
87.00
87.50
88.00
88.50
89.00
89.50
90.00
90.50
91.00
θu θl
R
p
5 mm
R
ld
8 mm
R
p
3 mm
R
ld
6 mm
R
p
7 mm
R
ld
10 mm
Predicted bend angle / °
(θ
l
)
(θ
u
)
SIMULTECH 2016 - 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications
228

0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
160.00
θu θl θu θl
θu 90°, θl 90° θu 90°, θl 150°
FEM Exp
θ
u
90°
θ
l
120°
θ
u
90°
θ
l
90°
θ
u
90°
θ
l
150°
Predicted bend angle / °
80.00
90.00
100.00
110.00
120.00
130.00
140.00
150.00
θu θl
Predicted bend angle / °
(a) Symmetrical case
( θ
u
90°, θ
l
90°)
(b) Asymmetrical case
( θ
u
90°, θ
l
150°)
θ
u
90.31° and θ
l
88.83° θ
u
91.64° and θ
l
149.30°
Figure 8: Comparison of predicted bend angles after
unloading between symmetrical and asymmetrical bend
angle. (R
ud
3mm, R
ld
6 mm, R
p
3 mm).
This manner of the spring-back characteristic
corresponded well with the bending theory and the
literature (Lange, 1985, Schuler, 1998,
Thipprakmas, 2011). In addition, the results also
illustrated that the predicted upper bend angle was
changed as the lower bend angle increased. As these
results, they confirmed that the change in bend angle
on one side resulted in the change in spring-back
characteristic on the opposite side. The effects of
lower bend angle on spring-back characteristics
were also examined. Fig. 9 shows effects of lower
bend angle on spring-back characteristics in
predicted upper and lower bend angles. As
abovementioned, as the lower bend angle increased,
it caused the decreases in stress distribution in
bending allowance zone (zone B) and in leg (zone
D) as well as the decreases in stress distribution in
web (zone C). After compensating these changes in
stress distributions, the results elucidated that as the
lower bend angle were 90°, 120°, and 150°, the
Figure 9: Relationship between lower bend angle and the
predicted bend angles. (R
ud
3mm, R
ld
6 mm, R
p
3 mm).
predicted upper and lower bend angles were 90.31°
and 88.83°, 90.92° and 119.35°, 91.64° and 149.30°,
respectively. As these results, the results confirmed
that as the lower bend angle increased the amount of
spring-back in the upper bend angle increased as
well as the amount of spring-back in the lower bend
angle increased.
3.3 Validation of FEM Simulation
Results
In this research, to validate the accuracy of the FEM
simulation results, the laboratory experiments were
carried out. Fig. 10 shows the comparison of the
bend angle between the FEM simulation and
experimental results. As per the past research
(Komolruji, 2013), the FEM simulation result
showed good agreement with the experimental
result, in which the error in the bend angle as
compared to the experimental result was
approximately 1 %.
Figure 10: Comparison of the predicted bend angle
between the FEM simulation and experimental results.
(R
ud
3mm, R
ld
6 mm, R
p
3 mm).
4 CONCLUSIONS
In the present research, to study the spring-back
characteristic on asymmetrical Z-shape parts in
wiping Z-bending process, the FEM simulation was
used to identify the effects of working process
parameters, including bend radius and bend angle,
on the spring-back characteristic. Based on the stress
distribution analysis, the bending mechanism of
asymmetrical Z-shape and the spring-back
characteristic were clearly identified comparing with
those in the symmetrical Z-shape case. The results
illustrated that the change in bend radius or bend
angle on one side resulted in the change in spring-
back characteristic on its side and on the opposite
side as well. The effects of bend radius and bend
(θ
l
)
(θ
u
)
(θ
l
)
(θ
u
)
Finite Element Analysis of Spring-back Characteristics on Asymmetrical Z-shape Parts in Wiping Z-bending Process
229

angle on spring-back characteristics were also
examined by analyzing the changes in the stress
distribution. In terms of bend radius, the amount of
spring-back in the lower bend angle increased as the
lower bend radius increased. In addition, it also
caused in the change in upper bend angle, in which
the amount of spring-back in the upper bend angle
increased as the lower bend radius increased. Next,
In terms of bend angle, the amount of spring-back in
the lower bend angle increased. Again, this also
caused in the change in upper bend angle, in which
the amount of spring-back in the upper bend angle
increased as the lower bend angle increased. The
FEM simulation results, as validated by laboratory
experiments, showed that the errors in the bend
angle compared with the laboratory experimental
results were approximately 1 %.
ACKNOWLEDGEMENTS
The authors would like to express their gratitude to
the National Research University Project of
Thailand, Office of the Higher Education
Commission, under Grant No. 57000618 for their
financial assistance to this study. The authors also
thank Mr. Arkarapon Sontamino, graduate students,
for their help in this study.
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