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International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:20 No:01 1
200301-4747-IJMME-IJENS © February 2020 IJENS I J E N S
Predictive Modeling and Response Surface
Method of Operating and Geometrical Parameters
for Bending Force and Spring Back in V-Bending
Process Hussein Zein1, 2, *
1 Mechanical Engineering Department, College of Engineering, Qassim University, Buraidah 51452, Saudi Arabia
2 Mechanical Design and Production Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt * [email protected]
Abstract-- The main objective of this work is to develop a 3D
predictive model of Finite Element Analysis (FEA) to simulate
and predict the bending force and the spring back behaviour
of yellow brass alloy sheets (ASTM B36) in the V-bending
process. To achieve this objective, the FEA program
(ABAQUS/EXPLICIT) is used to create this numerical
simulation for different values of the operating and the
geometrical parameters (friction coefficients, bend radius,
and opening die dimension). Furthermore, the effect of these
process parameters on the bending force and the spring back
behaviour is investigated by using the response surface
method (RSM) in the V-bending process. Finally, the
simulation results are shown that the investigated process
parameters had much influenced on the bending force and the
spring back angle in the V-bending process by finding the
optimum design points using the predictive model of the
response surface method.
Index Term-- Finite Element Analysis; Bending Force;
Spring Back; Response Surface Method; Bend Radius;
Friction Coefficients. 1. INTRODUCTION
Sheet metal forming is one of the oldest fabrication
processes identified to mankind, and bending can most likely be regarded as its most basic variant [1]. Bending is
a process by which metal can be deformed by plastically
deforming the material and changing its shape. The
material is stressed further than the yield strength but lower
than the ultimate tensile strength.
In a mission to enhance fuel economy, the automobile
manufacturers have been significantly looking at light
metals to light-weight their vehicles. Considerable weight
saving can be achieved by replacing parts made from mild
steel with those made from light-weight materials
(aluminum and magnesium alloys) and high specific
strength materials. Such materials are less formable than mild steel, and parts made from them absence dimensional
control because of the considerable amount of spring back
that they generate after forming [2].
The elastic recovery of material is one of the main
sources of shape and dimensional accuracy of drawpieces.
Springback cannot be removed, but there are several
techniques to minimize the elastic return of the stamped
part because of the elastic recovery of sheet metal after
forming. One of the techniques is an appropriate design of
the die which takes into consideration the amount of spring back. In addition, the change in selected bending process
variables can minimize the spring back. The concept of the
modification of the die shape contains extra overbending of
the material [3]. Between the many advanced techniques of
predicting the final profile of the drawpiece, the finite
element method (FEM) is the most often utilized [4]. FEM
is the main method utilized to simulate sheet metal forming
processes to be able to figure out the distribution of stresses
and deformations in the material, forming loads and
possible locations of the defects.
The measure of the spring back value is a spring back
coefficient or angle of spring back. The value of the spring back coefficient be determined by the value of bend angle
and bend radius, sheet metal thickness, and width of the
sheet metal, the mechanical properties of the sheet material,
the bending process temperature, and the strain rate [5].
The research of Caden et al. [6] demonstrated the influence
of the coefficient of friction on the spring back value.
These computer tools enable the design engineer to
study the process and material factors. The reliability of
predicted formability and the precision of the predicted
deformed geometry for a given part depend on the
predicted computational modeling approach [7]. In spite of the well-developed material behaviour models, metal
forming simulations often do not yield the correct results.
This is generally due to utilizing a very simplified friction
model. Coulomb friction model is a simple model
frequently utilized in simulations. In this model, the ratio
between friction force and normal force defined as the
coefficient of friction μ, that considered to be constant [8].
Nevertheless, especially in lubricated systems, friction
depends on a large number of parameters, e.g., the micro-
geometry, the macro-geometry, the lubricant and the
operational factors: velocity, temperature and normal load
[9]. Dametew and Gebresenbet [10] studied by using the mathematical method the influence of sheet metal
thickness, sheet metal type, friction, tool radius and tool
shape on spring back for different materials of sheet metal.
Different researches were done to investigate the spring
back phenomenon numerically and experimentally for
diverse shapes, and process parameters [11]–[18]. The
majority of the analytical researches concentrated on air
bending despite the fact that minimal work was carried out
on the V-die bending process because of the characteristic
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problems as a result of the coining action related to this
process [19]. Earlier investigations [19]–[21] performed on
spring back in the V-bending process displayed that the
material’s grain size got minor impact, but surface
roughness experienced a reasonably greater impact on
spring back. The spring back was additionally discovered to be affected by the punch nose radius and the process
temperature along with the minor impact of the punch
velocity. Finite element methods were utilized to analyze
the impact of various process parameters and validate
numerical models in the V-bending process through several
researchers e.g. [22], [23]. These researchers presented that
the spring back was significantly influenced by bend
radius, punch angle and die shoulder radius. Leu [24]
studied the influences of process parameters, such as
material properties, lubrication, and process geometrical
parameters, on the position deviation and spring back of
high strength steel blanks, to be able to create process design recommendations for the asymmetric V-bending
process.
Wasif et al. [25] performed experimental and numerical
analysis for the spring back in high tensile strength steel
sheet metals at divers process parameters of the V-bending
process. Wasif and his team diagramed their experimental
results to investigate the influence of the process
parameters (sheet metal thickness and width, the bending
angle, and the tool geometry) on the spring back in the V-
bending process. The diagramed figures helped them to
obtain the optimal parameters for minimizing the spring back. In addition, they used their numerical models for the
forecasting of the spring back at various values of the
process parameters. They displayed that the spring back
decreased with increasing of the sheet metal width. Also,
they concluded that the spring back increased with
decreasing the bending angle.
Ramadass et al. [26] investigated the spring back
behavior of Ti-Grade (2) blanks in the V-bending process
by utilizing the finite element technique and the
experimental work. Ramadass and his associates used the
Taguchi and analysis of variance methods to classify the
significance of process parameters such as punch radius, sheet metal thickness and die opening dimension on the
spring back behavior. Finally, they validated the finite
element results by utilizing the Taguchi (L9) orthogonal
array. They determined the classification of the most
effective process parameters in minimizing the spring back
with the following influence ratios: 56.65% for sheet metal
thickness, 31.87% for the punch radius, and 9.73% for the
die opening.
Also, the bending force to perform the V-bending
process is an important factor in selecting the capacity of
the mechanical press and the geometries of the used tools. Mori et al. [27], Jiang et al. [28], Panthi et al. [29] and
Hakan et al. [30] came to the conclusion in their researches
on spring back that bending force rises with the rise in the
yield stress of the sheet metal. Narayanasamy and
Padmanabhan [31] studied the software of response surface
methodology for forecasting the bending force throughout
the air bending process for interstitial free steel sheets. The
researchers displayed that punch stroke is the dominating
factor identifying the bend force subsequently punch speed
and bend radius. Malikov et al. [32] studied the bending
force for air bending process by using numerical and
experimental calculations. Malikov and coworkers
demonstrate that bending position and structure location significantly affect bending force.
The experimental study of Srinivasan et al. [33] focused
on studying the effect of friction parameters on the spring
back and the bending force for electro-galvanized steel
sheets in the air-bending process. This study has shown that
the spring back increased and the bending force decreased
by reducing the friction coefficient. Srinivasan and Raja
[34] conducted an experimental analysis for the V-bending
process to comprehend the spring back, bending force and
thinning of bimetallic sheets (Al/Cu). Srinivasan and Raja
studied the influence of the process parameters like die
opening, punch radius, sheet thickness, and die angle on the spring back. They found that the spring back and the
bending force reduced with decreasing the punch radius
and rising the die angle. Also, they established that the
spring back increased and the bending force reduced with
the rising of the die opening. On the contrary, they figured
out that the spring back decreased and the bending force
increased with the rising of the sheet metal thickness.
In the present work, the V-bending process of yellow
brass alloy sheet metal (ASTM B36) is investigated
numerically and experimentally. The bending force is
studied at different values of the V-bending process parameters by using a numerical simulation of a
commercial finite element software ABAQUS/EXPLICIT.
Also, the spring back behaviour in the sheet metal is
investigated for these parameters. The effect of different
values of the operating and geometrical parameters
(friction coefficients, bend radius, and opening die
dimension) on the bending force and the spring back
behaviour are presented by using the 3D predictive model
of FEA and the response surface method.
2. THE NUMERICAL SIMULATION MODEL
In this research, a Finite Element Analysis (FEA) 3D
model is created to simulate the V-Bending process
by utilizing a Finite Element Analysis (FEA) program
(ABAQUS/EXPLICIT). Figure 1 shows the geometric
arrangements were utilized in these simulations. Figure 2
displays all dimensions of the V-bending die which used in
the simulation model. The tooling components (punch and
die) were considered as 3D discrete rigid and represented by the movement of a single node, identified as
the reference node of the rigid body. The die and the punch
were meshed by using the type of R3D4 elements. The
sheet metal is modeled as a deformable and meshed by
using 3D stress, eight-node, and C3D8R elements. The
dimension for each initial blank is (80 mm x 30 mm x 1
mm). Coulomb friction coefficients of 0.01, 0.05, 0.125,
0.2 are considered for the sheet metal contact surfaces with
oily lubrication for sheet metal with die and sheet metal
with a punch, respectively [35].
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Fig. 1. The assembly of the 3D finite element model in ABAQUS.
Fig. 2. All dimensions of the die in the V-bending process.
The sheet metal is created from yellow brass alloy. The material is modeled as an elastic-plastic material with isotropic
properties. Table 1 displays the material properties of the used sheet metal in the FEA simulation. Figure 3 shows the
plastic true stress, plastic true strain curve of the material behaviour for the used yellow brass alloy sheet metal.
Table I
The material properties of the used yellow brass alloy sheet metal (ASTM B36) sheet metal
Material Density
(g.cm-3)
Elastic modulus
(GPa)
Poisson’s
ratio
Yield stress
(MPa)
Thickness
(mm)
Yellow Brass ASTM B36 8.47 97 0.31 140 1
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Fig. 3. Plastic True Stress vs. Plastic True Strain curve of yellow brass ASTM B36.
3. VALIDATION OF THE FEA MODEL
Since the sheet metal bending is about applying a force
on sheet metal to deform it, the universal testing machine
was used in the experiment work as shown in Figure 4.
Additional parts were needed to be installed on the
universal testing machine to prepare the machine, those
parts are the punch and the V-die; presented in Figure 5.
Fig. 4. Universal testing machine.
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Fig. 5. Installation for the punch and the V-die on the universal testing machine.
Figure 6 describes the using of a universal testing
machine in the V-bending process. While Figure 7, and
Figure 8 illustrate the brass sheet metal before and after the bending process. By comparing the experimental result
with the FEA result using the same dimensions, it was
found that there was a convergence in the value of the
spring back angle (Δθ).
Fig. 6. The V-bending process
Fig. 7. Brass sheet metal before and after the V-bending process
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Fig. 8. The measuring tool for measuring the final bending angle after the V-bending process
Figure 9 displays a comparison of the predictable
bending force change with punch travel distance (present
FEA work) with the experimental work data (by using a
universal testing machine). Note that the present FEA work
is even closer to the experimental work.
Fig. 9. The change of the bending force with punch travel distance.
4. RESULTS AND DISCUSSION Figure 10 shows the simulation of the spring back
action in the V bending process. Figure (10.a) displays the
V bending process during the bending process. While
Figure (10.b) shows the V bending process after the spring
back action.
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(a) (b)
Fig. 10. The FEA simulation of the V bending process (a) During the bending process, (b) After the spring back action
The measure of the spring back value is an angle of spring
back (Δθ); as shown in Figure 11. The bend radius (rb)
affects on the spring back. Also, the main purpose of
lubrication is to accomplish the smallest value of the
friction coefficient with the least possible wear. Avery
useful design optimization tool is a response surface method (RSM) tool. In the following section, it will be
studied the spring back (Δθ) as the first response in the
RSM model. Figure 12 describes RSM for the variation of
the spring back angle (Δθ) with diverse values of the bend
radius (rb) of the final bending workpiece and the different
values of the friction coefficients at sheet metal interfaces
with die and punch. It is displayed that the spring back
angle (Δθ) increases with the rising of the bend radius (rb)
which is in good agreement with published results in [22 -
23], [26], and [34]. On the other hand, the spring back angle
(Δθ) decreases with an increase in the friction coefficient value (μ) which is consistent with the published results in
[33]. Figure 12 and Figure 13 display the design points
above and below the predicted value of the RMS to get the
minimum value of the spring back angle (Δθ).
Fig. 11. Measuring of spring back angle (Δθ) and bend radius (rb)
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Fig. 12. RSM for the different values of the bend radius (rb) and the coefficients of friction (μ) with Spring back angle (Δθ, Degree)
Fig. 13. Contour for the diverse values of the bend radius (rb) and the coefficient of friction (μ) with spring back angle (Δθ, Degree)
The horizontal distance between two centers of die
shoulder radius is known as opening die dimension (W);
shown in Figure 2. Figure 14 shows RSM for the change of
the spring back angle (Δθ) with different values of the bend
radius (rb) and diverse values of the opening die dimension
(W). The results of the predictive model display that the
spring back angle (Δθ) rises with the increasing of the bend
radius (rb) and the opening die dimension (W) which is in
good matching with published results in [34]. Figure 14 and
Figure 15 presents the design points above and below the
predicted value of the RSM to obtain the minimum spring
back angle (Δθ).
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Fig. 14. RSM for the different values of the bend radius (rb) and the opening die dimension (W) with spring back angle (Δθ, Degree)
Fig. 15. Contour for the diverse values of the bend radius (rb) and the opening die dimension (W) with spring back angle (Δθ, Degree)
Figure 16 demonstrates RSM for the variation of the
spring back angle (Δθ) with dissimilar values of the friction
coefficients at sheet metal interfaces and various values of
the opening die dimension (W). From the FEA and RSM
results, it is shown that the spring back angle (Δθ)
decreases with increase in the friction coefficient value (μ).
On the other hand, the spring back angle (Δθ) increases
with the rising of the opening die dimension (W). Figure
16 and Figure 17 show the design points above and below
the predicted value of the RSM model.
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Fig. 16. RSM for the diverse values of the opening die dimension (W) and the coefficients of friction (μ) with spring back angle (Δθ, Degree)
Fig. 17. Contour for the various values of the opening die dimension (W) and the coefficients of friction (μ) with spring back angle (Δθ, Degree)
In the same way, In the remaining part of this paper, it
will be investigated the bending force (Fb)as the second
response in the RSM model. Figure 18 and Figure 19
explain RSM and Contour for the variation of the bending
force (Fb) with punch travel distance at different values of
the bend radius (rb) and the dissimilar values of the friction
coefficients at sheet metal interfaces. It clear that the
bending force (Fb) decreases with increasing the bend
radius (rb). Nevertheless, the bending force (Fb) has a lower
value when the value of the friction coefficient (μ) is used
between 0.14 to 0.3. On the other hand, the bending force
(Fb) rises at lower and higher values of the friction
coefficient (μ=0.05 or μ=0.5).
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Fig. 18. RSM for the various values of the bend radius (rb) and the coefficients of friction (μ) with bending force (Fb, ton)
Fig. 19. Contour for the several values of the bend radius (rb) and the coefficients of friction (μ) with bending force (Fb, ton)
Figure 20 and Figure 21 display RSM and Contour for
the variant of the bending force (Fb) with punch travel
distance at diverse values of the bend radius (rb) and the
different values of the opening die dimensions (W). The
predictive model of the RSM shows that the bending force
(Fb) decreases with increasing the bend radius (rb). On the
other hand, the bending force (Fb) reduces with the rising
of the opening die dimension (W) which is in good
agreement with published results in [34].
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Fig. 20. RSM for the various values of the bend radius (rb) and the opening die dimension (W) with bending force (Fb, ton)
Fig. 21. Contour for the several values of the bend radius (rb) and the opening die dimension (W) with bending force (Fb, ton)
Figure 22 and Figure 23 show RSM and Contour for the
variation of the bending force (Fb) with punch travel
distance at varied values of the opening die dimensions (W)
and the diverse values of the friction coefficients at sheet
metal interfaces. The results of FEA and RSM demonstrate
that the bending force (Fb) increases with decreasing the
opening die dimension (W). While the bending force (Fb)
reduces with rising of the friction coefficients at sheet metal
interfaces.
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Fig. 22. RSM for the various values of the opening die dimension (W) and the coefficients of friction (μ) with bending force (Fb, ton)
Fig. 23. Contour for the several values of opening die dimension (W) and the coefficients of friction (μ) with bending force (Fb, ton)
5. CONCLUSION
Simulation outcomes can essentially reduce the
manufacture expenses of high quality bending workpiece
by decreasing the lead time to manufacture and gives the
designers the ability to react quicker to market
modifications. Moreover, with the present FEA model and
RSM model, the smaller the bend radius is less spring back will be there with greater bending force. The fluid lubricant
with a higher value of the friction coefficient is more
suitable to apply between die/punch and sheet metal to
reduce the spring back action, on the other hand, the
bending force is to be high. Finally, the small die opening
dimensions are preferred to decrease the amount of the
spring back angle conversely the bending force will be
increased. As a final point, FE simulation and RSM results
in the present paper provide useful information to address the feasibility of the actual production process. Product
quality can also be improved. The risks of tool redesign and
modifications are minimized.
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