-
g(1
rsita
construction, and low costs. These require, however, the
manu-facturing of complex bent proles from modern materials,
likehigh-strength steels, with high bending accuracy in small
batchproduction (Fig. 1). These requirements pose a challenge
forbending processes. To meet this challenge, the use of
exibleprocesses and machines is indispensable.
In the eld of tube and prole bending there are well
knownprocedures for three-dimensional bending of
semi-nishedproducts. The problem is that most of these procedures
arespecialized and optimized for tube bending, involving
proleswithcircular and simple cross-sections. These processes are
appliedby standard machines, such as the three-roll-bending,
the
with arbitrary cross-sections to arbitrary 3D bending contours.
Thetool set-up of the process (Fig. 2) consists of three pairs of
rolls,which guide and transport the prole through the bending
process(axis c), and a roll-based guiding system (bending head),
thatdenes the bending curve in a horizontal plane. This bending
axis xis realized by one horizontally located axis. The axis t
ensures thetangential orientation (angle t) to the c-axis of the
bending head.With these three axes it is possible to bend 2D
contours, even S-shapes. The 3D bending contour is controlled by a
superposedtorque having two functions. The rst one is the inuence
of thebending plane of the proles cross-section. This twisting axis
forthe denition of the 3D curve is realized by a torsion bearing
(a1),mounted around the three roll pairs, and a compensation axis
(a2),
in conventional bending processes due to the difference
betweenthe shear center and the center of gravity of the
cross-section.With
CIRP Annals - Manufacturing Technology 59 (2010) 315318
nd
ns h
the
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etry
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ces
Contents lists available at ScienceDirect
CIRP Annals - Manufa
s.ehigh shape and dimensional accuracy as well as high
reproduci-bility of stretch bending face, however, the
disadvantages of lowHexabend [4], the Nissin [5], and the TKS-MEWAG
[6] machines.For 3D prole bending, stretch bending is themost
suitable processat present. This process consists of bending the
parts over a curveddie in the presence of axial tension [7].
Stretch bending is based onthe principle of form-closed forming and
is mainly used in theautomotive industry for mass production [8,9].
The advantages of
positioned in the bending head. By this mechanism, the
bendingplane can be changed and a 3D shape is produced by rotating
theprole cross-section over the longitudinal axis (a1, a2),
butwithout the necessity to change the position of the bending head
inthe x-axis [10].
Asymmetrical proles tend to twist over their longitudinal
axisThe new TSS bending process: 3D bendin
S. Chatti, M. Hermes, A.E. Tekkaya (1)*, M. Kleiner
Institute of Forming Technology and Lightweight Construction
(IUL), Technische Unive
1. Introduction
The demand for bent steel and aluminum proles as
structuralelements in trafc systems as well as in civil engineering
hasincreased strongly. Three-dimensionally (3D) bent proles
providethe design engineer with a higher exibility and allow
theconstruction of light and stiff structures with space
savingproperties and improved aerodynamics [1]. Through a
three-dimensional exibility in shaping proles new ways for
light-weight construction can also be opened up [2,3].
The trends in designing prole structures for e.g. vehicles
arespace saving, car body safety, automated assembly,
lightweight
A R T I C L E I N F O
Keywords:
Bending
Machine
Torque Superposed Spatial (TSS)
A B S T R A C T
A new roll-based process a
asymmetrical cross-sectio
bending, the advantage of
the bending contour, leadin
To dene the spatial geom
of the analytical and nume
parameters of the new pro
journal homepage: http: / /eeexibility, expensive tools and
machines, and increasing manu-facturing costs when bending long
proles and large cross-sections. There is no appropriate procedure
available now in
* Corresponding author.
0007-8506/$ see front matter 2010
CIRP.doi:10.1016/j.cirp.2010.03.017of proles with arbitrary
cross-sections
)
t Dortmund, Germany
industry which offers a high exibility for 3D bent proles
witharbitrary cross-sections, lengths, contours, and materials at
lowcosts. These disadvantages of stretch bending and the
restrictionsof the tube bending processes justify the needs to
develop a newprocess for 3D bending of proles, allowing a freely
denablecontour, which can be manufactured and changed at any
timewithout high tool costs.
2. The Torque Superposed Spatial bending process
The new TSS bending process allows the bending of proles
machine for three-dimensional bending of proles with symmetrical
and
ave been developed. Compared to conventional processes like
stretch
Torque Superposed Spatial (TSS) bending is the kinematic
adjustment of
higher exibility and cost efciency, especially in small batch
production.
of the workpiece, a torque is superposed to the bending moment.
Results
l investigations concerning themechanics of deformation and
themachine
s are presented.
2010 CIRP.
cturing Technology
lsevier.com/cirp/default .aspthe TSS process, it is possible to
compensate this twisting by usingthe second function of the torque
when superposing it with thebending moment. This is carried out by
different rotationaladjustments of the torsion bearing (a1) and the
compensation axis(a2). Another advantage of the TSS process is that
the friction-based roll drive does not need a pusher system and
gives the
-
owhere l3 is the lever arm of the machine and j the value of
theadjustment of the bending axis x (Fig. 3b).
Because of the elastic prole deformation, an error arises in
thebending radius that can be compensated by adjusting the value
j.
Fig. 4. Deected prole in the tool system.
S. Chatti et al. / CIRP Annals - Manufacturing Technology 59
(2010) 315318316forming mills, is possible, producing 3D bent
proles in oneprocess chain with the manufacturing of the
semi-nishedproduct. The TSS concept and the newly developed machine
wereinvented using methods of systematic engineering design
[11].
3. Analysis of process parameters
The signicant process parameters inuencing the 2D and 3Dbending
of a prole in TSS bending are the following:
the positioning of the axes x, a1, a2, and t to generate the
loadedbending radius rL, which results in the target bending radius
afterthe
chbptapth
3
nTstthan
rLpportunity to bend very long proles. Thus, the combination
ofTSS process with continuous production processes, e.g. roll
Fig. 2. Principle of the TSS bending process.Fig. 1. Example of
3D bent prole application.unloading rU after the prole leaves the
machine,the prole cross-section in the corresponding bending plane
(a1,a2), inuencing the bending behavior due to a changingmomentof
inertia, and the cross-section deformation,thematerial properties
like ow stress,modulus of elasticity, andhardening coefcient,
andthe elastic prole and machine deections due to the
bendingforce.
The material properties of the investigated proles
werearacterized by tensile tests. The prole cross-section and
theending contour are determined from the given geometricalrole
data. The calculation of the positioning of the machine axesking
into account the prole springback as well as the elasticlastic
deformations are discussed in Section 3.2. The inuence ofe elastic
deformations is analyzed in the following.
.1. Inuences of elastic deformations
Plastic bending takes place at the transportation roll pairumber
3 (Fig. 3b), where the maximum stress appears (Fig. 3a).he other
prole areas are subjected to stresses below the owress. Neglecting
these stresses, causing elastic deformations only,e loaded bending
radius rL between the transportation roll pair 3d the bending head
is given by
l23
2j j2
(1)Fig. 3. (a) Equivalent stress distribution in the prole as
computed by nite elementmethod, (b) denition of the loaded bending
radius rL.The elastic deformation is caused by the acting bending
force Fbthat leads to the bending moment. Due to the fact that the
threecounter roll pairs cannot be regarded as a xed support,
thebendingmoment distributionmust be found between the roll
pairsand the plastic bending zone in order to determine its inuence
onthe bending line of the prole (Fig. 4).
The axis value jmust be reduced byDjProle because of the
non-tangential exit of the prole at roll pair 3 and the
subsequentdeviation. The elastic beam theory supplies for small
deviations:
DjProfile Fb3EI
l1l2 l32 l2 l33 l1l2 l3 3=2l2l3 l22
2
l1 l2
!
(2)
where EI is the prole exural modulus and l1 to l3 are
thegeometrical parameters of the machine as described in Fig.
4.
Combining Eqs. (1) and (2), the elastic inuence of the
bendingforce Fb on the loaded bending radius rL for given
processdimensions is illustrated in Fig. 5. The bending force is
normalizedby the exural rigidity of the prole and assumes values
between 0and 1 mm2 for typical proles. The correction value
DrL,Prole hasto be added to the assumed loaded bending radius rL.
The inuenceof the elastic deection of the prole rises with
increasing bendingforces and loaded bending radii of up to 100% of
the bending radiusitself. This inuence has to be taken into account
for springbackcalculation to achieve accurate bending radii of the
product.
-
3.2. Springback compensation system
The system for springback compensation is developed for
thecalculation of the loaded bending radius for a dened
bendingradius after unloading. It is based on the elementary theory
ofbending and a previous work for 2D bending [12] that is
extendedfor the spatial bending of proles and has been integrated
into theCAD-program CATIA V5. On the basis of a semi-analytic
calculationof the bending moment Mb the springback (in terms of
thedifference between loaded (rL) and unloaded bending radius (rU))
isfound as
1
rL;cor 1
rUMb
EI(5)
To handle complex 3D bending workpieces the system
subdivides
Fig. 7. Force and displacement at the bending head.
S. Chatti et al. / CIRP Annals - Manufacturing Technology 59
(2010) 315318 317The bending force Fb also causes machine
deformations. Thesehave a double inuence on the loaded bending
radius rL. On the onehand, the bending axis is displaced by the
bending force Fb, causinga falsication and lowering of the actual
adjustment j, whosemeasuring is integrated in the machine measuring
system. On theother hand, Eq. (1) for calculation of rL is no
longer valid becausethe feed unit is not only displaced but also
the exit of the prole isnot perpendicular to the bending axis x
(Fig. 6). This complexcorrelation was determined by systematic
extensive elasticbending tests with a stiff solid prole and could
be reduced to apolynomial of 2nd degree. This machine specic term
(Eq. (3))describes, for a lateral force Fb, acting on the bending
axis x, thenecessary correction value DjMachine, which has to be
subtractedfrom j
DjMachine 1:496 108mm=N2 F2b 3:974 104mm=N Fb (3)
The inuences of both machine deformation and prole deforma-tion
can be detected and veried experimentally and by means ofFEM. To
verify the made assumptions, an increasing bending forcewas applied
on the machine axis x, and the displacement of thisaxis was
measured (Fig. 7). Using a hollow section steel prole (S235 JR, 40
mm 40 mm 4 mm), a bending test and an FEsimulation were carried
out. First, the determined force increaseslinear in the elastic
area and then, when entering the plastic area,the further increase
is low at a highly rising displacement. The sumof the
characteristic lines ofDjProle,analytic/FEM andDjMachine agreeswith
the experimental line. This proves the correctness of the used
Fig. 5. Inuence of the bending force Fb on the loaded bending
radius rL.assumptions so that Eq. (1) can be modied nally to
rL;cor l23
2jDjProfile DjMachine jDjProfile DjMachine
2(4)
where rL,cor is the corrected loaded bending radius, which
takesinto account the prole and the machine stiffness.
Fig. 6. Deformation of the machine components.the bending
contour over the prole axis into different segments atdifferent
radii and bending planes. For each segment, the loadedradius is
calculated. Then, a springback-compensated bendingcontour is
constructed. The NC code for the bending process isgenerated by
means of kinematics simulation using the spring-back-compensated
contour (rL,cor). The experimental vericationof these computational
results is discussed in the next section.Fig. 8. Bending of
constant prole radii in different bending planes.
-
developed, which has a high bending exibility thanks to
thekinematic forming principle and a cost efcient tool concept
forbending very long lightweight construction proles to
freelydenable 3D bending contours. The production of 3D
bendingcontours is controlled by a superposed torque, that
inuencesthe bending plane of the proles cross-section. With the
TSSprocess, it is also possible to compensate the twisting
ofasymmetrical proles by using the second function of the
torquewhen superposing it with the bending moment.
An important inuencing factor on the bending accuracy isthe
deection of the prole in the elastically loaded portions ofthe
workpiece. This inuence was calculated analytically andvalidated by
experiments and FE simulation. Another importantfactor is the
deformation of the machine components caused bythe bending forces.
This was investigated and described by a
S. Chatti et al. / CIRP Annals - Manufacturing Technology 59
(2010) 3153183184. Experimental verication of springback
calculation
Bending tests with different assumed loaded prole bendingradii
rL in different bending planes were carried out. Thedistributions
of the radii after unloading over the longitudinalaxis were
measured and compared with the results of the radiiafter unloading
rU calculated by the analysis model. A very goodagreement between
the results can be shown in Fig. 8. Thevariations of the radii
distributions result frommaterial and cross-section variations.
These yield a macroscopic average value, whichis also compared with
the computation results.
The complete experimental verication for a 3D bent part isshown
in Fig. 9. This component has two successive bending radii,r = 750
mm and r = 1000 mm, in two different bending planes,
Fig. 9. Deviation from ideal bending contour of two 3D-bent
workpieces withconsidered and neglected elastic
deformations.inclined by the angle a = 112.58. After bending, the
prolegeometry was digitalized by means of the optical GOM
ATOSsystem and compared with the CAD model. Very small
contourdeviations (max. 3.5 mm) were detected in a component length
ofabout 2200 mm. For comparison an experiment without consider-ing
the elastic deformations was carried out and greater variations(550
mm) were found.
5. Conclusions
3D bending of proles with arbitrary cross-sections can
beachieved by the TSS bending process. A special machine
wassemi-empirical model. Both inuencing factors must be takeninto
account in the calculation of the loaded bending radiuswithin the
developed process planning system, which is basedon analytical
approaches for springback calculation. With thissystem it is
possible to generate the machine data for arbitraryprole bending
contours and prole types with high accuracy.
Acknowledgment
This research project is kindly supported by the GermanResearch
Foundation (DFG).
References
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The new TSS bending process: 3D bending of profiles with
arbitrary cross-sectionsIntroductionThe Torque Superposed Spatial
bending processAnalysis of process parametersInfluences of elastic
deformationsSpringback compensation system
Experimental verification of springback
calculationConclusionsAcknowledgmentReferences