numerical and experimental validation for sheet metal hydroforming

NUMERICAL AND EXPERIMENTAL VALIDATION FOR SHEET METAL HYDROFORMING PROCESS RULES
Antonio Del Prete, Alfredo Anglani, Teresa Primo, Barbara Manisi
University of Salento, Department of Engineering of Innovation
ABSTRACT
A research program, whose objective is to
understand the influence and the management of the process variables in sheet
metal hydroforming, is developed [1].
The main project objective is to demonstrated how it is possible to orient the process designer choices in the n-dimensions
process space, where n is the number of
its variables.
The present work illustrates the results
obtained trying to define the best practise
rules for sheet metal hydroforming.
Keywords: sheet hydroforming, CAE,
process rules definition.
1.
INTRODUCTION
Nowadays, hydroforming techniques are
largely accepted by industries for the production of components characterized by
good surface quality, high-dimensional
accuracy together with high drawing ratio
and complex shapes [1-6]. The main distinction among the large variety of hydroforming techniques is usually based on the
used raw material: tubular or sheet material. Today the tubular material is predominantly used for the mass production; actually sheet hydroforming is used for small
batch production because both its cycle
time and clamping forces (large tooling
investments) are higher than the tube hydroforming ones [7]. However, sheet hydroforming process offers several advantages over tube Hydroforming [8].
Furthermore, conventional sheet metal
forming techniques reach their limits in
certain cases. Optimized application of
dies and presses for sheet hydroforming
leads to a reduction of product specific
costs and thus to lower costs per part. This
is extremely important for low volume
productions. As generally known, there
are great differences between conventional deep drawing and sheet hydroforming,
mainly due to the usage of a pressurized
liquid as forming tool. This leads to a frictionless force transmission to the sheet
and to a high contact pressure between
sheet and die. This results in nearly no
friction between blank and fluid and high
friction forces between rigid punch and
blank when deep drawing is realized with
counter pressure. Higher forming forces
can be transferred to the forming zone,
having as a result greater draw ratios
(parts with a higher drawing height). In
this specific case, a “shape factors” set is
defined in order to orient the designer
within the process design space for metal
components produced through the application of sheet hydroforming. These shape
factors are used to track the process performances through their variation thanks
to the usage of the numerical simulation
which is later validated with an appropriate experimental activity. Basically, it is
possible to distinguish three factors typologies which constitute the main variables
of the hydroforming process:
- geometries (tool radius, presence of
redrawing);
- materials (thickness, physical and mechanical properties);
- equipment calibration (fluid pressure,
blankholder force, friction, etc).
These three groups of factors are correlated but their relationships are not known.
For this reason the establishment of rules
which give the chance to verify their influence on the process performance can
be considered a valid support tool in the
process design definition phase. In this
paperwork the authors’ attention is con-
centrated on the influence of factors such
as: geometric parameters and material
characteristics on the process quality. The
correlation among process variables,
shape factors described below and quality
process indexes is investigated.
2.
REFERENCE
MODELS
AND
SHAPE FACTORS DEFINITION
Different geometric models, MODi (with i
= 1,…, 5), significant for the automotive
component class taken into account, are
defined. Two representative models,
MOD1 and MOD5, are taken into account
in this work [9].
Having as reference the chosen models,
the shape factors are defined to have adimensional coefficients representative for
the given geometries.
is quite common to have a redrawing height
as geometric characteristic. For this type of
components two different shape factors are
defined, Rh and Rc, by the equations (2) and
(3), respectively.
Rh = L2 / Hc
(2)
where L2 has already defined, and Hc is indicated in Figure 2.
Rc = Lc / Hc
(3)
where Lc and Hc are, respectively, the maximum dimension in top view and the maximum depth of a given redrawing area
(Figure 2).
Figure 2. MOD5 Punch numerical model:
shape factors definition.
Figure 1. Typical FE model for numerical
simulation of MOD1 with indication of L2
and the main punch dimension.
Considering L2, the smallest dimension of
the initial blank (Figure 1), and Himb as the
drawing depth, the first shape factor R2 is
defined by the ratio:
R2 = L2 / Himb
(1)
The numerical and experimental analysis
campaigns are characterized by the same
initial blank. For this reason the variability
of R2 is due only to the different considered
drawing depths.
For industrial products, for example a metal
formed panel for fuel tanks construction, it
The L2 value, for the MOD1, is equal to
670 mm, this means that low R2 values
correspond to high drawing depths. For
MOD5, L2 is equal to 683 mm and punch
radius is equal to 10 mm. The maximum
reached drawing depth is equal to 150 mm
for all the considered models.
The commercial finite element explicit
code LS-Dyna is used for the numerical
simulations. The tooling such as: punch,
fluid chamber and upper and lower blankholders were created through the usage of
rigid materials formulation (*MAT_20 in
LS-Dyna), while anisotropic material
formulation (*MAT_37 in LS-Dyna) was
used for the blank. Considered tests are
related to numerical simulation made using a low carbon steel blank (FeP04) and
aluminium alloy Al6061 with defined
characteristics (Table 1 and and Table 2).
HyperMesh® and HyperView® are used
for pre and post processing phases.
Table 1. FeP04 Material Properties used in
the simulation.
σ y (MPa) R
E (GPa) ν
n
195.5
0.3
179
1.9 0.19
An example of the obtained relationships
by different combinations of thicknesses
and material types for the considered
model MOD1 is reported below (Figure
6). The obtained process responses refer
to a geometric model with the following
characteristics: a punch radius is equal to
50 mm and a die radius is equal to 20 mm.
Table 2. Al6061 Material Properties, used in
the simulation.
σ y (MPa) R
E (GPa) ν
n
72
0.3
255
1.9
0.09
Two initial blank thickness values are
adopted for numerical and experimental
simulation: 0.7 mm and 1 mm. For all the
considered configurations a common value is used for friction (µ=0,125).
Through the usage of the *AIRBAG
CARD, with linear fluid option of LsDyna, is defined the fluid pressure in FE
model. The blankholder force is a load
applied to a rigid body. The optimal definition of the blankholder force and fluid
pressure time-dependent characteristics is
obtained through a sequence of numerical
tests with the application of a trial and error method.
3.
PROCESS PLOT CHARTS
The numerical simulation results allow to
understand the dependency of some process performance indexes (e.i. percentage
thickness reduction, FLD map at the end
of the forming phase, etc.) on the defined
shape factors. Specific plot charts are developed to summarize these relationships.
3.1 Influence of the defined shape factors on the percentage thickness reduction
Thanks to the results obtained from the
numerical simulation of the considered
models it is possible to define the necessary plot charts. As first step, the maximum thickness reduction (in percentage)
is considered as quality process index response depending on the defined shape
factors.
Figure 3. MOD1, first plot chart typology
referred to the considered geometric configuration for different material types and initial sheet thicknesses.
The obtained plot is divided in two areas:
the lower one with thickness percentage
reduction (tpr) less than 30% can be considered the process feasibility window, the
upper one with output values higher than
30% can be considered the process unfeasibility window.
In models definition M1 or M5 stand for
Model type MOD1 or MOD5, Fe or Al
stand for considered material type, 1 or 07
stand for considered thicknesses, 50_20
stand for punch and die radius respectively.
The feasibility window is then defined by
the analytical expression: tpr < 30%.
For R2>9 it is possible to observe that the
aluminium alloy and the low carbon steel
models have the same trend. In particular,
for R2≥9 the obtained characteristics have
a trend parallel to the x-axis expressing a
low sensitivity compared with R2. For
R2<9 the obtained characteristics are
strictly dependent on the considered material. In particular, for R2<9 both materials
present an increase in tpr. This increase
has a higher gradient in the case of the aluminium alloy. Both the considered mate-
rials have an increase of the tpr gradient
when lower values of initial blank thickness are examined.
The tpr process response is investigated
for different R2 values varying punch and
die radius in the case of the most promising material (low carbon steel). The obtained results are shown in Figure 4,
where all the considered cases are included in the feasibility window (maximum
tpr < 30%).
Figure 4. MOD1, First plot chart typology
in the case of: different punch and die radius
for the same material and initial blank
thickness.
In detail, the tpr characteristic for
M1_Fe1_10_10 with punch and die radius
both equal to 10 mm it does not show any
dependency on the R2 factor. This means
that the most critic aspect ( the process
unfeasibility reason ) is due to the punch
radius value. In fact, the tpr of the model
with the same punch radius value (10 mm)
but die radius equal to 20 mm
(M1_Fe1_10_20) shows a low dependency on R2. The two models with punch radius equal to 50 mm, instead, have similar
trend of tpr and they both show a dependency on the R2 factor. In detail, the model
with die radius equal to 10 mm
(M1_Fe1_50_10) shows two main significant variations of the tpr gradient, when
R2 is equal to 16 and 7. On the contrary,
the model with die radius equal to 20 mm
(M1_Fe1_50_20) shows two main significant variations of the tpr gradient when
R2 is equal to 13 and 7,5. Then an increase
of 100% of die radius leads to a minimum
and a maximum tpr reduction of 1% and
of 3.8% respectively. On the contrary, an
increase of punch radius of 400% involves
a minimum tpr reduction of 11.2% and a
maximum of 12.2% greater than the one
which can be obtained with a die radius
variations.
In order to consider the presence of a geometric variation like a redrawing height,
Rc and Rh factors are investigated (Figure
9). For this plot the initial blank thickness
is equal to 1 mm and a low carbon steel is
the considered material. The punch radius
for MOD5 is equal to 25 mm and die radius is equal to 10 mm.
Figure 5. First plot chart typology for
MOD5 for different considered values of
the shape factors Rc and Rh.
The plot shows that only for Rc > 10.5 it is
possible to have feasible configurations
for MOD5 and only for Hc equal to 20
mm or 25 mm. Furthermore, the three
curves have similar trend and they overlap
each other for Rc > 9,5. The better solution is when Rh factor is equal to 34, then
the quality index decreases in correspondence of an increase of this shape factor.
When Rh factor is equal to 27, there is feasibility only for Rc > 11, while when Rh
factor is equal to 23, there is not feasibility for any of the investigated cases.
3.2 Influence of the defined shape factors on the Forming Limit Curve
Distance response
In this case the used approach is different by
the one used for the other plot charts definitions. In fact, in the previous cases a scalar
process response is considered (tpr). It is
well know that metal forming process quality can be monitored thanks to the Forming
Limit Diagram (FLD) analysis which gives
a general overview of the material deformation states. In this case, an alternative
plot chart typology can be considered reducing to a scalar value the general process response overview given by the FLD. As scalar process response, the distance between
the highest deformation state of the part on
the FLD and the correspondent limit state
given by the Forming Limit Curve, is considered for the different tested conditions.
This is a defined value: Forming Limit
Curve distance (FLCd). The FLCd variation
in relation to the R2 shape factor variation
for different material types and blank thicknesses for a given geometry (MOD1) leads
to the third plot chart typology definition
(Figure 12)
Figure 6. Third plot chart typology for
MOD1 considering different combinations
given by different material types and blank
thicknesses for the same geometry.
The above reported shows plot the same
results included in Figure 3 but referred to a
different performance index. For aluminium
alloy, the FLCd plot shows a more critical
situation than tpr, for initial thickness equal
to 0.7 mm. This is due to the different behaviour of the aluminium in comparison
with the one obtained for the steel. In fact
for low carbon steel the two plots are in accordance showing that there is feasibility for
all the investigated shape factors. In the
case of the aluminium alloy, instead, the
models with initial thickness equal to 1 mm
show feasibility, with tpr index, and fracture
for R2 equal to 8 when the FLCd index is
considered. Furthermore for the models
with initial thickness equal to 0.7 mm plot it
is evident a fracture condition for R2 equal
to 6, with tpr index, and R2 equal to 9.5 with
FLCd index.
This kind of plot chart is very difficult to
obtain because of when different blank
thicknesses are considered the specific FLD
are needed. On the obtained diagram, a
positive FLCd value stands for feasible
conditions while a negative one stands for
an unfeasible condition characterized by a
situation where some areas of the formed
parts the deformation states are higher than
the maximum ones allowable by the FLC
for the given material type and thickness.
4.
NUMERICAL EXPERIMENTAL
CORRELATION
All the produced plot charts are based on an
extensive numerical simulation campaign.
For this reason, in order to verify what is
numerically obtained, appropriate experimental tests are needed.
Thanks to the developed experimental test
rig, hydroformed parts are obtained with the
process set up studied in the numerical simulation phase. The comparison between
numerical and experimental parts are made
thanks to the thickness values monitored on
the formed parts and compared with the
ones obtained with the numerical simulations. As reference, two of the many studied
cases are reported below. In the first case
the hydroformed part MOD1 made by low
carbon steel with an initial blank thickness
of 1.0 mm in the case of a punch radius
equal to 50 mm and a die radius equal to 10
mm is compared with its numerical simulation results. The experimental and numerical thicknesses values measured along three
directions (x, y and along a generic section
A-A, Figure 10) are compared.
As it can be appreciated, thanks to the reported data, (Figure 7 – Figure 9) there is a
uniform thickness distribution and a good
agreement between numerical and experimental values with a discordance of about
4%.
Figure 7. numerical-experimental thickness
values comparison for MOD1, along X-X
section.
Figure 8. numerical-experimental thickness
values comparison for MOD1, along Y-Y
section.
Figure 9. numerical-experimental thickness
values comparison for MOD1, along A-A
section.
Figure 10 reports the thicknesses map obtained thanks to the numerical simulation
and the areas where the experimental data
are measured, while Figure 11 shows the
real hydroformed component.
Figure 11. experimental component MOD1.
The second comparison case is related to the
MOD5 model where the examined configuration is the one made by low carbon steel,
blank thickness equal to 0.7 mm, Hc=20
mm, L=65 mm (Figure 2), punch and die
radius of 10 mm. Figure 12-Figure 14 report
the comparison between numerical and experimental thickness values for MOD 5. It is
evident a uniform thickness distribution,
and a better agreement between numerical
and experimental value with a discordance
of about 2.8 %.
Figure 12. Numerical-experimental thickness values comparison for MOD5, along
X-X section.
Figure 13. Numerical-experimental thickness values comparison for MOD5, along
Y-Y section.
Figure 10. thickness map of numerical
simulation for MOD1.
Figure 14. numerical-experimental thickness values comparison for MOD5, along
A-A section.
Figure 15 reports the thicknesses map obtained thanks to the numerical simulation
and the areas where the experimental data
are taken. Figure 16 shows the real component.
Figure 17. numerical-experimental thickness values comparison for MOD5, along
X-X section.
Figure 18. Numerical-experimental thickness values comparison for MOD5, along
Y-Y section.
Figure 15. numerical simulation thickness
map for MOD1.
Figure 16. experimental component MOD5.
Finally, to evaluate the repetitiveness of the
measured thickness values, experimental
data are measured along X and Y direction
on five different hydroformed components
in the case of the MOD5 geometry and the
obtained data have been compared as it is
reported in Figure 17 and 18.
From the reported data it can be assumed
a good correlation and a very good repetitiveness.
5.
CONCLUSION
The obtained results allow to say that a
first step ahead has been done in order to
define possible orientation instruments in
the process design space for sheet metal
hydroforming. Useful suggestions can be
obtained by such a kind of process plot
chart in a preliminary process design review. The presented activity has to be
completed by industrial test cases which
can give useful feedbacks to the presented
methodology. However, it is evident how
an extensive numerical and experimental
activity is needed to develop useful process plot charts and to define quality indexes for different material types.
Through a first analysis of shape factors is
possible to establish the rules of design
process upstream of numerical simulation
of hydroforming process.
ACKNOWLEDGEMENTS
Authors are very grateful to “MUR: Ministero dell’Università e della Ricerca” for
funding this work recognized as I.T.Idro:
innovative solutions for sheet hydroforming.
Special thanks are addressed to Stamec srl
which has the role of industrial partner of
the project.
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