Dynamics of two-wheeled trailers using different contact force models

Two-wheeled trailers are often involved in road accidents since many drivers do not select an appropriate towing speed and/or payload position. Thorough mechanical and mathematical modelling of trailers is therefore of the utmost importance to avoid these accidents. This study aims to construct such low-degree-of-freedom models that can be managed analytically but still capture all the relevant nonlinear phenomena. In vehicle handling, the modelling of tyres and the modelling of the tyre-ground contact have relevant effects on the resulting vibrations. Therefore, this research field has been investigated deeply for many decades, and several tyre models exist with different levels of complexity. This study considers single contact points for the right and the left wheels of the trailer. The widely used Magic Formula and the brush tyre models are implemented and investigated. Additionally, a family of analytical creep models is presented, which can capture the essential properties of tyre forces and are easier to construct. A linear state feedback controller with a feedback delay has been designed to reduce the unwanted vibrations and to extend the globally stable towing speed region. The results are shown on bifurcation diagrams, which highlight the effects of the applied control gain, feedback delay, and contact force models used.