Bifurcation analysis of an automobile model negotiating a curve

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.

[1]  P.A. Shavrin.  A chaotic dynamics of the vehicle on the plane , 2005, Proceedings. 2005 International Conference Physics and Control, 2005..

[2]  H B Pacejka,et al.  Simplified analysis of steady-state turning behaviour of motor vehicles , 1973 .

[3]  Ryszard Andrzejewski,et al.  Nonlinear dynamics of a wheeled vehicle , 2005 .

[4]  Zhaoheng Liu,et al.  Nonlinear oscillations and chaotic motions in a road vehicle system with driver steering control , 1996 .

[5]  Haiyan Hu,et al.  Stability and Hopf Bifurcation of Four-Wheel-Steering Vehicles Involving Driver's Delay , 2000 .

[6]  R. E. Wilson,et al.  Bifurcations and multiple traffic jams in a car-following model with reaction-time delay , 2005 .

[7]  Der-Cherng Liaw,et al.  A feedback linearization design for the control of vehicle’s lateral dynamics , 2008 .

[8]  Chien-Shu Hsieh,et al.  A Feedback Linearization Design for the Control of Vehicle's Lateral Dynamics , 2006, 2006 SICE-ICASE International Joint Conference.

[9]  H. B. Pacejka.  Non-linearities in Road Vehicle Dynamics , 1986 .

[10]  B. Catino,et al.  MCS adaptive control of vehicle dynamics: an application of bifurcation techniques to control system design , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[11]  P.J.Th. Venhovens,et al.  Investigation on Stability and Possible Chaotic Motions in the Controlled Wheel Suspension System , 1992 .

[12]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[13]  Manfred Mitschke,et al.  Dynamik der Kraftfahrzeuge , 1972 .

[14]  J. A. Kuznecov.  Elements of applied bifurcation theory , 1998 .

[15]  Shuiwen Shen,et al.  Nonlinear dynamics and stability analysis of vehicle plane motions , 2007 .

[16]  Hans B. Pacejka,et al.  Tire and Vehicle Dynamics , 1982 .

[17]  Willy Govaerts,et al.  MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs , 2003, TOMS.

[18]  Mitsuaki Ishitobi,et al.  Chaos and bifurcations in a nonlinear vehicle model , 2004 .

[19]  Shun'ichi Doi,et al.  Bifurcation in vehicle dynamics and robust front wheel steering control , 1998, IEEE Trans. Control. Syst. Technol..