The effect of time delay on the chaotic behavior of full- seven DOF ground vehicles

In this article, the chaotic vibration of a seven-degree-of-freedom ground vehicle model is investigated. Several researches have been developed about automobile vibration with linear behavior of springs and damping elements. But it is obvious that in practice, because of suspension and tires nonlinear reactions, assuming of linearity only can helps to the theory of car vibration. However, road disturbances may induce uncomfortable shake and noise. So vibration analysis of the system with nonlinear spring and damper is necessary. The quarter car model (2-dof system), the half car model (4-dof system) , and the full vehicle (7-dof system), respectively for studying the heave motion, the heave and pitch motions and the heave, pitch and roll motions have been studied in several researches.Although many studies have been carried out on the full vehicle model, but to the best of the authors’ knowledge, no work has been reported on the effect of time delay between the left and the right side wheels (right rear and right front or the left sides one) so far on the chaotic behavior of the system due to force excitation of road profile. This study begins by introducing of the mathematical model of the seven d.o.f vehicle. The equations of motion are derived by Newtons second law and the numerical simulation is conducted, then the dynamic results are discussed. Fourth order Rung-Kutta procedure provided by Matlab is used for solving the state-space equations with the sinusoid road disturbance as the input forcing function. In this model, the car rigid body motion assumed as the sprung mass with the heave, pitch and roll motions. The Wheels and their components are assumed as the un-sprung masses that connected to the each corner of the sprung mass. Springs and damping elements of the rigid body have nonlinear behavior and springs of the un-sprung masses have small nonlinear coefficient. Dampers of the un-sprung masses are linear. The nonlinear analytical tools such as bifurcation diagram, Poincare map and phase portrait are used to study the chaotic behavior of the system. The results of this study can be useful in dynamic design of a car.

Keywords:

chaotic behaviour , nonlinear vibration , seven d.o.f model , time delay