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Formula Student is a world-wide racing series where student teams build single-seater racing cars and compete in a series of races. For their car, the TU-DART team developed a carbon-fibre composite rim, using finite element modelling to optimize rim geometry and laminate structure.
(Published on November-December 2008 – JEC Magazine #45)
DR MARTIN FLEISCHHAUER R&D MANAGER COMPOSCIENCE
JAN KOENEN RACE ENGINEER TU-DART-RACING
In the Formula Student programme, teams of student sponsored by industrial organizations and university institutes develop high-tech racing cars. The vehicles are able to hold their own in terms of engineering and performance against those competing in the "big racing series". Besides vehicle performance, aspects being rated are vehicle styling and the concept’s innovative character, economic efficiency and marketability.
Carbon-fibre monocoque chassis have become a standard feature in vehicle design, and the use of CFRP is now extending to components such as drive shafts, transverse control arms, and peripheral engine parts. For its latest racing car, called the Gamma 08, the Darmstadt Technical University’s TU-DART team has developed a 38-cm carbon-fibre composite rim and introduced it on the road (Fig. 1). The objective was to replace the current aluminium rims and to further reduce the rim weight by 3 kg.
The team’s design work was sponsored by German engineering service provider compoScience, a specialist in the design and calculation of fibre-reinforced components. The first stage consisted in defining the service loads on the rim. To this end, the loads and load frequencies were determined during measurement runs. These test runs established that most of the load on the rim − more than 1.7 g − is caused by transverse acceleration stress. Maximum load combinations were determined and the frequency of the loads over the service life of the rim was calculated based on the resulting data. Transferring the wheel loads into the rim via the tyre was a particular challenge for the designers. To avoid having to model the tyre, the loads were distributed to the two rim flanges using a distribution function that was determined experimentally in advance with the help of a strain-gauged rim. Apart from the service loads, particular attention was paid to the loads on the rim during tyre mounting and demounting. Neglecting these loads during the design phase could lead to rim damage during assembly.
Finite element modelling To optimize the rim-geometry details for the three-spoke design, an isotropic three-dimensional FE model with constant wall thickness was created at the outset, to which a combination of maximum side load and maximum vertical wheel force was introduced. To optimize the initial geometry, the main stresses were analysed, and local stress maxima were reduced by modifying the rim geometry. In particular, isotropic calculation of the geometry model served to plan the laminate structure. Optimum fibre orientation was determined based on the main stress trajectories (Fig. 2).
Following geometry optimization, another FE model was created − in this case, a model with layered shell elements. For this, the rim was divided into areas with constant component thickness and constant layer structure, and a first laminate design was created based on the isotropically determined main stress directions. The rim was built up from unidirectional HT carbonfibre prepreg layers 0.3 mm thick. Woven fabric prepreg of the same thickness was used for the visible layer.
Efforts in the rim were calculated based on the action plane criterion according to Schürmann/Puck. This criterion not only has high prediction accuracy, it also serves to distinguish failure modes in fibre failure and inter-fibre failure. Hence, laminate analysis according to Schürmann/Puck shows: the magnitude of the loads acting on the component; which laminate layer is exposed to the highest loads; and which stresses actually lead to layer failure. This way, degradation analysis – i.e. investigating the reduced load-carrying capability of the laminate following inter-fibre failure – is also possible. The multitude of data available allows a more effective optimization of the laminate structure (Fig. 3).
The non-linear behaviour of a material is rarely taken into consideration in the design of fibrereinforced composite components. The shear stress/strain behaviour of composites, however, is significantly non-linear.
Taking these effects into consideration enables optimum rating of components in terms of weight saving. On the other hand, the non-linear behaviour of materials may affect the failure behaviour of individual layers and, therefore, of the component as a whole. Consequently, the increased time and cost required to measure the shear stress/strain curve appear justified. Using only a few iteration steps, the above procedure made it possible to define a laminate structure that was already very close to a weight-optimized design. The rim lay-up is influenced both by the loads acting on the component and the drapability of the prepreg cuttings. To facilitate applying the calculated laminate structure to the tool, all required cuttings (186 in total) were first derived from the CAD files and their drapability on the tool was checked. Any necessary adjustments were then transferred back to the simulation model.
Construction and testing
Once the lay-up was determined and refined in several stages, it took only a few weeks and the support of their manufacturing partners for the members of the TU-DART Racing Team to manufacture several rims. The result is impressive: weighing under 1,700 g, the rim is nearly 45% lighter than the aluminium rims used so far, and comparably stiff. Given the positive results from physical tests on a test rig, the new rim is expected to make a major contribution towards the TU-DART team’s longhoped- for success in the racing series (Fig. 4).