Nonlinear effects on the self-excited chatter oscillations in motorcycle dynamics, including tyre relaxation

Nonlinear effects on the stability of the motorcycle rear 'chatter' phenomenon are investigated by means of a minimal two degrees of freedom model, including tyre relaxation since this aspect has not been investigated in-depth in previous studies. Motorcycle 'chatter' manifests itself as a self-excited oscillation, which arises during braking in the frequency range between 17 and 22 Hz, affecting safety and performance. The study of the linearised system gives indications on the initiation of self-excited vibrations and thus helps to prevent them using proper design techniques. Post-bifurcation behaviour is analysed focusing on limit cycles and bifurcation diagrams, studied by means of specific applications of the harmonic balance method and Floquet theory. This allows the detection of the validity of the linear results, and to identify the meaningful parameters in limit cycle generation, their amplitude, and their stability.