Driveline Stability in Racing Motorcycles: Analysis of a Three Degrees of Freedom Minimal Model

Motorcycles under heavy braking conditions can experience a self-excited oscillation known as 'chatter'. A simplified three degrees of freedom model of the rear of a motorcycle is developed to study the stability of this mode with the inclusion of lateral dynamics introduced by roll angle. Since motorcycles achieve high roll angles during operation, the study of chatter during these manoeuvres is a topic of interest. The equations of motion are linearised about a quasistatic equilibrium and simplified to accommodate symbolic inspection. Power analysis, eigensystem analysis, eigenvalue sensitivity and Routh-Hurwitz stability criterion are used to study the stability of the system in the braking region. It was found that a driveline mode can become unstable at about 19 Hz, and that its tendency towards instability is increased with added roll angle. This mode is sensitive to model parameters affecting the system inertia and stiffness, as well as the chain geometry. Finally, it is found that the lateral dynamics and roll angle play no direct role in chatter but have a significant indirect effect on it through the working point of the force characteristic function of the tyre.