TPT July 2010

A rticle FEM-Modelling and Simulation is done in cooperation with the Chair of Metal Forming in the Department Product Engineering at the University of Leoben in Austria. The simulation model is based on an actual corrugation process to produce an annular corrugated tube for solar application which is performed at Rosendahl Maschinen GmbH in Austria. Verification of simulation results based to trials carried out under different process parameters was a multistep interactive procedure. The corrugation process as described above is performed at high rotation speeds and so it is a highly dynamic process. Furthermore a lot of contact openings and closures will occur during simulation. To handle these problems in a numerical analysis is a challenging task. Usually explicit finite element codes are more appropriate for this kind of simulation than implicit codes. Hence, the commercial finite element software Abaqus/Explicit [4] was chosen for modelling and computation of this process. Model Parameters The basic material is a welded smooth tube with an external diameter of 21mm, a wall thickness of 0.18mm and consists of the austenitic stainless steel AISI 316L (1.4404). Though the process speed is high, practical experience shows that the increase of temperature due to plastic deformation in the forming zone is not more than 10°C. Hence, the influence of temperature can be neglected and the computation is performed isothermal at room temperature (20°C). Flow curves for the tube’s material at room temperature are taken from the work of Feaugas [5] . To obtain sufficient results from a simulation in the field of cold forming it is necessary to use an elastic-plastic material model. So, the Young’s modulus for the steel is set to 210,000 MPa and Poisson’s ratio to 0.27, respectively. Non-linear kinematic hardening of the material is set by using the “combined hardening” option in Abaqus to consider the cyclic elasto- plastic behaviour of the steel. The tool geometry provided from the company partner is shown in Figure 6a. The forming zone of the corrugation disk consists of a hole with a helical shaped engraving. The angle α between the disk’s and the tube’s axis is in the range between 1° and 6° (see Figure 7). The eccentricity e of the tool acc. to Figure 6b lies between 2 and 6mm. The revolution speed for the investigated process is 1,400 to 1,700 rpm and the feed rate is 6.4m/min. In a further simulation the feed rate will be increased up to 7m/min to Figure 6 : Geometry of the corrugation disk (a) and forming zone with eccentricity e regarding to the tube’s axis (b) Modelling Strategy Software

investigate the influence of the feed rate on the geometry of the corrugated tube. Elastic deflection of the disk is neglected in the simulation. Hence, the corrugation disk is implemented as discrete rigid part. To obtain a stable process an infeed and an outlet bearing must be placed close to the corrugation tool (Figure 8). These two bearings were also assumed to be rigid and implemented as analytical rigid bodies. The contact zone is not lubricated in the actual process and so a friction factor of µ = 0.1 has been set for the contact between tool and tube. Implementation of the tool motion One problem in simulating this process is the complex movement of the corrugation disk as described earlier in this work. To realise this complex tool motion in the simulation model the tool is driven by two connectors [4]. Point 1 rotates on the tube’s axis and drives the connector, a so called translator, with the fixed length e between the points 1 and 2 acc. to Figure 6b. The axis between the points 2 and 3 in Figure 6b represents the tool’s axis (see Figure 7) and is implemented by a so called “cylindrical connector”. With this connector the rotational degree of freedom for the axis between the points 2 and 3 can be released to provide a free rotation about this axis.

Figure 7 : Tool position regarding to the tube’s axis

Mesh strategy for the tube Because the wall thickness of the tube is low (0.18mm) and a significant change inwall thickness is not expected the tube ismeshed with linear continuum shell elements [4] . The expected wave length for the corrugated tube is about 4mm. Hence, the element length is set to 0.4mm to be fine enough to provide about ten elements over one corrugated wave. This leads to a specific element number of 410 elements per mm tube length. To prevent rotation of the tube during corrugation a torsion lock is placed 1,160mm behind the corrugation disk. This distance must be considered in the model. So it is necessary to model an entire tube’s length of 1,200mm. With the mesh density mentioned before, this would lead to a very high element number of 492,000 resulting in very low computation speed. To reduce the number of elements on the tube only the part of the tube which contacts the workpiece during the simulation (ca. 150mm length) is meshed with shell elements. The rest of the tube is modelled with beam elements which have a tube shaped profile assignment (Figure 8). The coupling between the shells and the beam elements is done by a kinematic coupling condition [4] which is shown in Detail A in Figure 8. Detail B in Figure 8 shows the back end of the beam, where v 3 denotes the feeding velocity while all the other translational and rotational degrees of freedom are locked for this point.

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J uly 2010

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