Tyre induced vibrations of the car–trailer system

• The equations of motion of the car–trailer combination are derived.
• The time delayed tyre model is implemented.
• Governing equations are transformed into a system of delay differential equations.
• The linear stability analysis of the rectilinear motion is performed.
• Unstable parameter domains are detected.

The lateral and yaw dynamics of the car–trailer combination are analysed by means of a single track model. The equations of motion are derived rigorously by means of the Appell–Gibbs equations for constant longitudinal velocity of the vehicle. The tyres are described with the help of the so-called delayed tyre model, which is based on a brush model with pure rolling contact. The lateral forces and aligning torques of the tyre/road interaction are calculated via the instantaneous lateral deformations in the contact patches. The linear stability analysis of the rectilinear motion is performed via the analytically determined characteristic function of the system. Stability charts are constructed with respect to the vehicle longitudinal velocity and the payload position on the trailer. Self-excited lateral vibrations are detected with different vibration modes at low and at high longitudinal speeds of the vehicle. The effects of the tyre parameters are also investigated.

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