Axle characteristics and vehicle limit cycle behaviour

Abstract

The paper discusses the limit cycle performance of the nonlinear 2DOF single track vehicle model. That means that periodic solutions arise under constant vehicle speed and steering angle, under excessive handling conditions, with axle characteristics playing a dominant role. These characteristics are modelled using the Magic Formula tyre model, with the model parameters varied to investigate the sensitivity of peak friction and slip stiffness on limit cycle occurrence. In the transition to limit cycling, different types of bifurcation are found, being mainly of homoclinic and Hopf type, and sometimes saddle-node bifurcation, or bifurcation involving unstable limit cycles. Dealing with models being strongly nonlinear, the research includes qualitative analysis tools being appropriate for such models, such as phase plane analysis and the application of the stability diagram. The paper discusses two conjectures on the necessary and sufficient conditions on axle characteristics for the existence of limit cycle behaviour, and the relationship between steering angle and vehicle speed at the transition to limit cycling. Limit cycle performance and the impact on global stability are elements of the dynamic vehicle performance under high acceleration conditions, and therefore very relevant for excessive handling situations and our understanding of active safety under critical circumstances.