02-07-2012, 01:16 PM
Finite Element Analysis of the Classic Bicycle Wheel
Introduction
In the traditional realm of Finite Elements, there are very few practical applications where the
finite code can be compared to direct measurements. At best, Engineers can usually only
compare their computer analysis with the results predicted by established mechanical formulae.
At worst, Engineers must rely on their experience and intuition to guide them towards a workable
“right” answer.
In this exercise, we consider the classical bicycle wheel. This is a familiar structure whose
geometrical design has remained virtually unchanged for the past several decades. However,
although the design is familiar, and the design effective, it is still not very well understood from a
“textbook analysis” standpoint. The optimal design was converged upon by trail and error – not
through thorough calculation.
Measured Results
The Journal of Engineering Mechanics paper describes in detail the geometry of the classical
bicycle wheel. Figures 1 and 2 show a portion of the spoke geometry provided by the paper. In
addition, the authors provide data on moments of inertia, cross sectional areas, and other
pertinent material properties.
ANSYS Approach
Four models were generated using ANSYS scripts (See Table 1). Two of these models used
“simple” geometry, in that all spokes were linked to a common center point (see Figure 6). The
two other models used “complex” spoke geometry that more closely resembled the classical
spoke designs described by Burgoyne and Dilmaghanian (see Figure 7). To explore Goal #2
described in section 3.1, scripts were developed for both the simple and complex models to place
rim nodes at 2.5 and 10 degrees.
Beam elements (BEAM4) for the rim and truss elements (LINK8) were used to model the spokes.
Although these elements are fully capable of modeling 3D geometry, they also work quite well in
a 2D application. The material properties and dimensions used in the published results are used
for all ANSYS modeling.
Dr. Jerry Fine provided an ANSYS script that “rotated” the bicycle wheel model to better duplicate
the figures presented in the published results. This script was integrated into the models using
2.5o of rim node separation. Samples of the ANSYS scripts can be found in Appendix A and B.
Strain
Figures 10 and 11 show the resulting strain should we rotate the wheel as done in the paper.
Plots are shown for both the Simple and Complex models. Here the results are puzzling. The
overall shape of the plot compares favorably to what was expected, though the maximum strain
of about 5.5x10-5 at angle 0 is an order of magnitude less than the published result of about
6.00x10-4. The differences between the simple and complex spoke models are rather slight –
they are shown in separate plots because the lines overlap too well to differentiate one curve
from the other.
Rim Bending
Figures 13 and 14 show the results of the ANSYS bending calculation, scaled by 1/PR1 for direct
comparison to the published results. Here the results are more favorable, as the maximum
bending for the complex model shows 0.016, compared to the published result of 0.03. While not
an exact match in magnitude, the shape of the complex curve follows the published trajectory,
and the maximum value lies within the range calculated for a partially inflated tire. The simple
spoke model shows similar (though higher) magnitude, but the results are asymmetric.
Conclusion
This analysis shows that ANSYS modeling can be a useful tool for analyzing simple structures
such as the classical bicycle wheel. Although the exact magnitudes published by Burgoyne and
Dilmaghanian were not found, the results track closely with what was expected. The author feels
that with some tinkering, the ANSYS scripts could be made more accurate than they currently are
– there seems to be some hidden nuance that is being overlooked by the current approach.