Stability analysis of the car-trailer system with a time-delayed tyre model

In this paper we investigate the dynamics of towed vehicles by means of two examples, the car-trailer combination and a towed trailer, both represented by the so-called single track model. The effect of tyre deformation is considered with the help of the brush tyre model. In our analysis we take into account the so-called 'memory effect' in the tyre-ground contact patch too, which leads to delay differential equations with distributed time-delay as governing equations. The stability of the rectilinear motion is analysed by means of stability charts with respect to the vehicle parameters. For the towed trailer we also performed nonlinear analysis which enabled us to capture the Hopf bifurcations emerging at the stability boundaries. These were compared with numerical simulation, where we studied the effect of lateral tyre-slip, too.