A summary and conclusion of the bicycle wheel problem

I have reached, if not an final answer to the wheel problem, a stopping point.  I have used the methods of flexural-torsional bending to solve the structural mechanics problem.  The results are pretty good finally.  The predicted and measured displacements are certainly good enough to apply the LQG control theory to the truing problem.   So the part I set out to do is done.  The structural model is a success and there are many more things that could be done with it besides just truing at this point.  What I had hoped was that someone who wanted to commercialize this idea would take it over now.  The most I can offer in the future is a journal article to document the method of solution.  If you are interested in a great structural model of a bicycle wheel or a wheel truing algorithm, I am having a sale this week.  Best prices.  Can't be beat.

Here are some final images of the comparisons of prediction versus measurement.  In this comparison, a single spoke is tightened one full turn and the change in shape is plotted.  I think I nailed it.  The input wheel parameters are dead nominal.  There was no adjustment of parameters to improve the fit.  This is the raw data.

The sample wheel is a difficult wheel to model.  This wheel has a large number of spokes and a fairly high tension.  As a result, the structure is close to the flexural torsional bucking load for the rim.  The taco shape of the rim reflects how sensitive the wheel is to the spoke perturbation.  In the figures, I am also showing the earlier, less successful models that do not account for the instability.  The good comparison from the final model and experimental data  is the turquoise line (final model) and red line (experimental data) in each figure.  I previously got acceptable results on other wheels with fewer spokes or lower tension.  The wheel shown here was the one that was hard to get right.  The final model reduces naturally to the earlier model as the parameters leading to the instability are modified to make the wheel more stable.  The first model had no elastic instability modeling.  The second had flexural instability but not torsional.  The final model had flexural and torsional instability.  This mode gives the lowest buckling load.