Abstract
Handling and stability properties of automobiles are most often studied from a practical point of view by applying a reduced set of equations, where the forward velocity is kept constant. At studying the full set of equations of a basic nonlinear two-wheel vehicle model, a supercritical Hopf bifurcation is found for an oversteer vehicle. All state variables of the vehicle are involved at small amplitude limit cycles in the vicinity of the Hopf bifurcation point with the steering angle (drive torque) as bifurcation parameter. At the transition to large amplitude relaxation cycles, the cyclic motion of the vehicle may be separated into ‘slow’ longitudinal velocity-related segments, and ‘fast’ vehicle yaw and side slip-related segments, indicating a singular perturbed system. Moreover, Canard phenomenon is observed for both steering angle and drive torque bifurcation parameters.
Highlights
Nonlinear stability analysis at the limits of handling of an automobile has become an important issue to increase passive and active safety
When a human driver is controlling the lateral dynamics of the car by steering, it has been shown that the driver may destabilise the motion of the combined nonlinear vehicle–driver system depending on the available preview distance ahead of the vehicle
It is a well-known result of linear stability analysis, that the steady-state cornering motion will become monotonically unstable for an oversteer vehicle at the critical speed, resulting in a narrowing spiral motion
Summary
Nonlinear stability analysis at the limits of handling of an automobile has become an important issue to increase passive and active safety. The limit of stability can still be found from (measured) steering characteristics, when the rate of change of steering angle w.r.t. path curvature becomes zero for slowly tightening the steering wheel at constant speed [4] These findings are based on vehicle speed as given parameter, with longitudinal and lateral dynamics decoupled. In [8], the importance of the longitudinal velocity in determining the location of bifurcation points has been outlined, which was not yet addressed in [9] In the latter contribution, destabilization is shown to be caused by a saddle-node bifurcation of a limit-oversteering vehicle, which strongly depends on the saturation of the rear lateral tyre force.
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