Page 2 - Finite Element ModelMeasurements were taken of a Raleigh R700 road racing frame (seat tube length 50cm centre-to-centre). A finite element model was then created using the MSC.Patran software package. The entire frame was modelled with shell elements (mainly 4-noded quadrilateral elements) with the exception of the rear dropout castings, which were tetrahedron solid elements. To allow loads to be applied to the frame, the rear axle was modelled with wedge solid elements and the forks and handlebar stem with beam elements. The frame tubes in the physical frame were welded together so the tubes in the model frame were mitred and joined with simple line connections. The socket joints at the rear dropouts were modelled with solid elements. The complete model had 41,000 nodes and 42,000 elements. Figure 1 shows the entire frame model, Figure 2 a detail of the mesh around the top of the seat tube, Figure 3 in the bottom bracket area and Figure 4 one of the rear dropouts. |
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| Figure 1 - Frame finite element model |
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| Figure 2 - Seat cluster mesh detail | Figure 3 - Bottom bracket mesh detail | Figure 4 - Rear dropout mesh detail |
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The physical frame was constructed from Reynolds 853 tubing, an air-hardening steel.
This tubing is available in several different thicknesses depending on application and
it was not possible to measure non-destructively which gauge was actually used. An
educated guess was made as the thinnest available since this was a road racing frame for
which light weight is a key requirement. For the main tubes and chainstays this
corresponded to 0.4mm in the centre, increasing to 0.7mm at the thicker butted sections
at the ends. The seatstays were assumed a constant 0.7mm (these small-diameter tubes
are generally not butted) and bottom bracket shell and head-tube 1.5mm. Similarly the
lengths of the butted sections were not known either, so were also estimated.
Figure 5 shows the variation of tube thickness for the whole frame. For the modelling purposes, 853 material is identical to mild steel. Its yield and proof stresses are very different, as is the effect of heat treatment but these do not have any effect in an elastic analysis. This led to a material mass of 1,525 grams but the material density was factored upwards to account for the extra mass of paint and weld material, assumed uniformly distributed over the frame and estimated at 100 grams. |
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| Figure 5 - Frame tube thickness | |
| Loads were applied to the frame at three points - the centre of the bottom bracket axle, the centre of the handlebars and the centre of the sprocket on the rear wheel. The model was constrained in the centres of the front axle (lateral and vertical translational restraint) and rear axles (fore-aft, lateral, vertical translational and roll rotational restraints). | |