3D FEM Simulations of a shape rolling process

H.H. Wisselink & J. HuetinkNetherlands Institute of Metals Research- University of Twente, P.O.box 217, 7500AE Enschede, The NetherlandsURL: www.nimr.nl; www.tm.wb.utwente.nle-mail: h.h.wisselink@wb.utwente.nl; j.huetink@wb.utwente.nl

M.H.H. van Dijk & A.J. van LeeuwenEldim b.v.- P.O.box 4341, 5944 ZG Arcen, The NetherlandsURL: www.eldim.nle-mail: m.v.dijk@eldim.nl

ABSTRACT: A finite element model has been developed for the simulation of the shape rolling of statorvanes. These simulations should support the design of rolling tools for new vane types. For the time beingonly straight vanes (vanes with a constant cross-section over the length) are studied. In that case the rollingprocess can be considered stationary and an ALE formulation is suitable to calculate the steady state. Resultsof simulations and experiments for a symmetrical straight vane are presented.

Key words: shape rolling, FEM, ALE

1 INTRODUCTION

ELDIM manufactures, among others, stator vanes foraero engines. One step in the production of these sta-tor vanes is a cold shape rolling process. The thick-ness of a strip of sheet material is reduced to ob-tain the right thickness at the right position at theright cross-section of the vane. Unfortunately some-times process redesign cycles are necessary to pro-duce vanes within the required tight tolerances. Moreknowledge of this process is needed to obtain a firsttime right design of this rolling process. Therefore afinite element model has been developed to get moreinsight in the mechanics of this process.

2 THE SHAPE ROLLING PROCESS

2.1 The tools

The shape rolling process used for the production ofstator vanes will be described in more detail here. Theroll-die and die-plate (Figure 1) contain respectivelythe convex and concave airfoil profile of the vane. Thedifference with the usual shape rolling process is thatonly one of the tools, the roll-die, rotates and that theother part, the die-plate is fixed. Therefore the lengthof the final stator vane is limited. Due to the appliedhorizontal force the roll-die rolls over the die-plate,deforming a strip, which is clamped to the die-plate,into a vane.

The vertical force controls the vertical movement ofthe roll-die. The roll-die makes contact with the die-plate in case the applied vertical force is larger thanthe force needed to roll the vane.

Roll-dieDie-plate

Fhorizontal

Fvertical

Figure 1: Tools for the rolling process.

Besides elongation, lateral spread is made possiblewith a gutter next to the vane profile (Figure 2). Su-perfluous material will be cut-off afterwards.

2.2 Investigated vane

The vane produced by the tools of Figure 2 is inves-tigated in this paper, because experimental data areavailable [1] to validate the simulations. The shapeof this symmetrical straight vane is almost similar to

R=42.5

R=52

43.5 40

gutter26

2

die-plate

roll-die

gutter

R=63.5

1

Figure 2: Dimensions [mm] of the tools used for the investigatedvane.

the shape of a real vane. The vane is 2 mm thick inthe middle and 1 mm thick at the leading and trailingedges.

3 FEM MODEL

The shape rolling process, described in Section 2, hasbeen modelled with the finite element code DiekA,developed at the University of Twente.

3.1 Stationary process

The rolling of straight vanes can be considered as astationary process, when the start and the end of theprocess are neglected. Therefore the rolling processcan be modelled as a flow problem. Only the materialin the dotted box, which moves with the same hori-zontal speed as the roll-die, is modelled.

Reality Model

Figure 3: Kinematics of the model.

3.2 ALE method

The ALE method is an appropriate method for cal-culating the steady state of a stationary process, es-pecially when dealing with free surfaces and historydependent material properties. In the ALE method it

is possible to define a grid displacement independentof the material displacements.The geometry of the initial mesh (Figure 4) is an es-timation of the expected steady state geometry. Themesh movement is kept fixed in rolling direction. Thematerial flows through the mesh in rolling direction,which results in an inflow and an outflow boundary.The mesh follows the free surfaces perpendicular tothe rolling direction. Internal nodes are repositionedin order to preserve a sufficient element quality.

Inflow

Outflow

Symmetry

Figure 4: Initial mesh.

The simulation is continued until a steady state isreached. The final mesh is shown in Figure 5.

Inflow

Symmetry

Outflow

Figure 5: Steady state mesh.

The transfer of state variables is performed with aconvection scheme which shows very little cross-wind diffusion [3].

3.3 Tools

Contact elements are used to describe the contact be-tween the strip and the tools. These elements arebased on a penalty formulation [2].The tools are modelled rigid and instead of a force,the motion of the tools is prescribed. This means thatthe deformation and the mutual displacement of thetools is not taken into account. In practice this is animportant issue, as it affects the final dimensions ofthe vane. Therefore this has to be incorporated in fu-ture models.

3.4 Material model

The material, which has been used for the experi-ments, is aluminium 6061. This material is modelledwith an elasto-plastic material model with a VonMisesflow rule. The hardening is described by the stress-strain curve defined in Equation 1.

y(p) = 1+170(0:0261+ p)0:2 [MPa] (1)

4 EXPERIMENTS

In order to get some information about the elonga-tion and spread of the strip due to the rolling processan equidistant grid has been scratched onto the un-deformed strip. The deformation of this grid is mea-sured after rolling. An examination of the deformedgrids proved that the assumption of a stationary pro-cess is valid for straight vanes, except for the start andend of the process.

5 SIMULATION RESULTS

In this section some results are shown of the simu-lations of the rolling of the investigated vane. Theundeformed strip is 40mm wide and 3mm thick.

5.1 Deformations

X

Z

(a) ? rolling dir. (b) rolling dir.Figure 6: grid-lines from the simulation.

Figures 6(a) and 6(b) show lines of points having re-spectively an equal x-coordinate or z-coordinate inthe undeformed state. These calculated lines canbe compared with the measured deformations of thegrid-lines on the rolled vanes. The grid-lines from thesimulation in Figure 6(a) have the same shape as the

lines in the photograph of a deformed vane, presentedin Figure 7(a).Figure 7(b) gives the ratio of the distance between twogrid-lines in rolling direction before and after rollingtaken from the simulation and five different experi-ments. It can be seen that the width between twogrid-lines increases at the edges, but decreases in themiddle of the vane (z = 0). The results of the sim-ulations agree well with the trends found in the ex-periments. The same phenomenon can be observed inFigure 6(b); a part of the material flows towards thecenter.

(a) grid-lines ? rolling dir.

0.6

0.8

1

1.2

1.4

1.6

1.8

2

-20 -15 -10 -5 0 5 10 15 20def

orm

ed w

idth

/und

efor

med

wid

th

z-coordinate in undeformed state[mm]

simulationexp1exp2exp3exp4exp5

(b) Deformation ? to rolling dir.Figure 7: Comparison between experiments and simulation.

The equivalent plastic strain distribution is given inFigure 8. The largest values are found at the locationswith the largest thickness reduction.

5.2 Contact stresses

Figure 9 gives the stresses in the contact elementsused to describe the interaction between the sheetand the tools. The location where the shear stresseschange sign coincides with the position of the highestnormal stress. Two neutral lines can be seen, one inrolling direction and one perpendicular to the rollingdirection. The maximum hydrostatic pressure in the

(a) Normal stress (b) Shear stress ? roll. dir. (c) Shear stress in roll. dir.

Figure 9: Normal [*100 N/mm] and shear [*10 N/mm] stresses in the contact elements between the roll-die and the vane (= 0:11).

Figure 8: Equivalent plastic strain.

vane is found at the same position as the maximumnormal contact stress. The position of the maximumhydrostatic pressure determines whether the materialflows inwards or outwards to the gutter (See also Fig-ure 6(b)). The maximum hydrostatic pressure in-creases with increasing friction coefficient.

5.3 Variation of strip width and thickness

With the current model the influence of the dimen-sions of the undeformed strip on the rolling process isstudied. In this way the elongation/spread ratios canbe determined. Furthermore the minimal strip thick-ness needed for a completely filled die can be found.

6 CONCLUSIONS

A finite element model has been build to simulate therolling of straight stator vanes. The ALE method is a

suitable formulation for these kind of processes. Theresults correspond well with the trends of the exper-imental data. Therefore this model increases the un-derstanding of this process.In future work the model will be extended to therolling of straight vanes with a real airfoil shape. Alsothe deformation of the tools has to be incorporated inthe model.

ACKNOWLEDGEMENTS

The authors would like to thank A.Z. Abee for hiscontribution to this project.

References

[1] A. Z. Abee. Rolling along the river. Technical report, Uni-versity of Twente, 1999.[2] J. Huetink, P. T. Vreede, and J. van der Lugt. The simu-lation of contact problems in forming processes using a mixedEulerian-Lagrangian finite element method. In Num. Methods inInd. Form. Processes, Proc. NUMIFORM 89, pages 549554.A.A.Balkema, Rotterdam, 1989.[3] H.H. Wisselink. Analysis of Guillotining and Slitting, FiniteElement Simulations. PhD thesis, University of Twente, 2000.