Parametric FE analysis of bicycle frame geometries

There is evidence of increasing participation and interest in cycling and a large body of literature exists relating to bicycle technology. Mostly these relate to the common diamond “safety” framed road or mountain bicycles, and a wide range of specialist tools are now available to support bicycle development through analysis and iterative improvement. Performing Finite Element Analysis (FEA) on bicycle frames has become a common activity for bicycle designers and engineers in the hope of improving the performance of frames.

This is typically achieved by balancing priorities for key requirements, including minimising the mass of the frame (possibly using competition rules to constrain this), maximising lateral stiffness in the load transfer from the hands and feet to the drive, maximising the strength capabilities of the frame to allow for a higher load capacity or better load distribution, and adjusting the vertical compliance of the frame to tune the softness of the ride.

FEA has been used to analyse composite, aluminium and steel bicycle frames with the aim of understanding physical behaviour and improving performance. However a comprehensive study on the influence of key geometric parameters on the stiffness of frames has not been conducted.

The aim of this study was to evaluate the influence of key geometric parameters on frame stiffness using a wide range of bicycle frame designs from historical data and to compare these to an optimised solution.

For this study a FE model was created using 317 beam elements to represent a standard road bicycle frame (including road, audax and touring options), including key tube lengths and angles and an idealised stem/handlebar and BB geometry as shown below.

Load cases that were analysed include a) a vertical load through the seat post of 2400N (sitting rider) and a simulated scenario of a rider out of the saddle pushing on the right pedal such that loads are applied to the left and right ends of the handlebar and on the right side of the BB and a BB extension.

Only two load cases were analysed and these were simplifications which didn’t include varied out of plane loading conditions, or changes to the pedaling leverage during the loading cycle. Regarding the tubes, these have been simply represented using beam elements as plain gauge tubes and don’t include tube butting, profile changes, changing curvature along the length, or joining methods (i.e. fillet brazed, TIG welded or lugged construction).

Regarding the materials, no consideration has been given to the strength requirements of the frames, and other common frame materials such as aluminium, titanium and carbon fibre have not been considered. The sampling techniques could be used to further develop stochastic approaches for other structural frame designs.

This study has however focused on carrying out a comprehensive analysis specifically on the frame geometry, in order to understand the contribution of key frame parameters to the overall stiffness and compliance behaviour of the frame. The model could now be adapted to include many of the above limitations as parametric inputs to develop a fuller understanding of the physical behaviour of bicycle frames.

The optimised values show a considerable improvement over the best of the existing frames, with a 13 per cent increase in vertical displacement and 15 per cent decrease in lateral displacement when compared to the best of the analysed frames. The model has been developed to allow for further develop to include more detailed tube geometry, further analysis of more frame geometries, alternative materials, and analysis of other structural characteristics.