Bifurcation analysis of an automobile model negotiating a curve

Abstract

The paper deals with the bifurcation analysis of a rather simple model describing an automobile negotiating a curve. The mechanical model has two degrees of freedom and the related equations of motion contain the nonlinear tyre characteristics. Bifurcation analysis is adopted as the proper procedure for analysing steady-state cornering. Two independent parameters referring to running conditions, namely steering angle and speed, are varied. Ten different combinations of front and rear tyre characteristics (featuring understeer or oversteer automobiles) are considered for the bifurcation analysis. Many different dynamical behaviours of the model are obtained by slightly varying the parameters describing the tyre characteristics. Both simple and extremely complex bifurcations may occur. Homoclinic bifurcations, stable and unstable limit cycles (of considerable amplitude) are found, giving a sound and ultimate interpretation to some actual (rare but very dangerous) dynamic behaviours of automobiles, as reported by professional drivers. The presented results are cross-validated by exploiting handling diagram theory. The knowledge of the derived set of bifurcations is dramatically important to fully understand the actual vehicle yaw motions occurring while running on an even surface. Such a knowledge is a pre-requisite for robustly designing the chassis and for enhancing the active safety of vehicles.

Keywords:

• two-wheel model
• tyre characteristics
• handling diagram theory
• two-parameter bifurcation analysis
• active safety

Acknowledgements

The authors would like to thank Vitaliano Nobile, who participated in a preliminary stage of the research.