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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

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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

[1] Chatti S (2005) Production of Proles for Lightweight Structures, HabilitationThesis, Books on Demand GmbH, Norderstedt, Germany.

[2] Kleiner M, Geiger M, Klaus A (2003) Manufacturing of Lightweight Compo-nents by Metal Forming, Keynote Paper. Annals of the CIRP 52(2):521542.

[3] Jeswiet J, Geiger M, Engel U, Kleiner M, Schikorra M, Duou J, Neugebauer R,Bariani P, Bruschi S (2000) Metal Forming Progress Since 2000. CIRP Journal ofManufacturing Science and Technology 1:217.

[4] Neugebauer R, Drossel W-G, Lorenz U, Luetz N (2002) HexabendA NewConcept for 3D-free-form Bending of Tubes and Proles to Preform Hydro-forming Parts and Endform Space-frame-components. Advanced Technology ofPlasticity 2:14651470.

[5] Murata M, Kuboti T, Takahashi K (2007) Characteristics of Tube Bending byMOS Bending Machine. Proc. of the 2nd Int. Conf. on New Forming Technology,Bremen, Germany, 135144.

[6] Flehmig T, Kibben M, Kuhni U, Ziswiler J (2006) Device for the Free Forming andBending of Longitudinal Proles, Particularly Pipes, and a Combined Device for FreeForming and Bending as well as Draw Bending Longitudinal Proles, ParticularlyPipes, Int. patent with application no. PCT/EP2006/00252, published on28.09.2006.

[7] Corona E (2004) A Simple Analysis for Bend-stretch Forming of AluminiumExtrusions. International Journal of Mechanical Sciences 46:433448.

[8] Geiger M, Sprenger A (1998) Controlled Bending of Aluminum Extrusions.Annals of the CIRP 47(1):197202.

[9] Vollertsen F, Sprenger A, Krause J, Arnet H (1999) Extrusion, Channel, andProle Bending: A Review. Journal of Materials Processing Technology 87:127.

[10] Hermes M, Kleiner M (2008) Vorrichtung zum Prolbiegen (device for prolebending), German Patent Application, DE102007013902A1, registr. date20.03.2007.

[11] Pahl G, BeitzW, Feldhusen J, Grote K-H (2007) Engineering Design: A SystematicApproach. Springer, Germany.

[12] Chatti S (1998) Optimierung der Fertigungsgenauigkeit beim Prolbiegen, PhDThesis, University of Dortmund, Verlag Shaker, Aachen, Germany.

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