SHM Graphing of Speed Wobble

[Rildude]

I'm trying to look into the damping of speed wobbles. A speed wobble is when at high speeds if a bike's wheel is suddenly deflected to the left for example, the bike will twist it back to the right to straighten it (because of something called trail). But the wheel has weight and momentum, so it can overshoot and go past the centre line. So now it’s turned to the right. Again the bike tries to turn the wheel back again, and it overshoots again and it keeps going back forth like that until the bike loses control). This all depends on motorbike geometry as well.

I'm trying to find an equation to graph speed wobble by using SHM which considers all of the factors which contribute to it. Looking online I can only find Root-Loci graphs which aren't what I'm looking for. Any help is appreciated!

 

[Cubist]

This is not an easy topic. Just thinking about the location of the front wheel's ground contact point in terms of the bike tilt and steering angle seems pretty difficult.

This paper came up after searching for "equations of motion for a bicycle":- http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/*FinalBicyclePaperv45wAppendix.pdf. It is also referenced from this Wikipedia page. I imagine that the analysis would be very similar for both motorbikes and bicycles although obviously the weight/ speed parameters will be quite different. The paper seems very thorough and contains many references to other works on the topic. It would take a long time (for me at least) to read and understand it. Appendix 2 seems interesting since it outlines how to run a computer simulation of a bicycle's motion in time steps, outputting forces/ speeds/ etc, and this might be useful to simulate the wobble under different conditions, and then simulate the effectiveness of your damping method.

 

[Rildude]

This is not an easy topic. Just thinking about the location of the front wheel's ground contact point in terms of the bike tilt and steering angle seems pretty difficult.

This paper came up after searching for "equations of motion for a bicycle":- http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/*FinalBicyclePaperv45wAppendix.pdf. It is also referenced from this Wikipedia page. I imagine that the analysis would be very similar for both motorbikes and bicycles although obviously the weight/ speed parameters will be quite different. The paper seems very thorough and contains many references to other works on the topic. It would take a long time (for me at least) to read and understand it. Appendix 2 seems interesting since it outlines how to run a computer simulation of a bicycle's motion in time steps, outputting forces/ speeds/ etc, and this might be useful to simulate the wobble under different conditions, and then simulate the effectiveness of your damping method.

thanks for the source! I'll have a look at it and see if I can find anything good to use.