Nonlinear Dynamics Analysis of the Body Sway of Car-trailer Combinations

Considering the nonlinear characteristics of tires and shock absorbers, a 5-DOFs theoretical dynamics model describing the lateral, yaw and roll motions of car-trailer combinations is established. Based on the theory of nonlinear dynamics, the multi-equilibrium points characteristics and the time-domain responses near the equilibrium points of car-trailer combinations are analyzed. Combining with the understeer gradient and damping ratio, the generation mechanism of the system instability is investigated. The influences of the trailer system parameters and the tire-road friction coefficient on the system critical speed are considered as well. The simulation results reveal that due to the nonlinear coupling of shock absorbers and tire, the car-trailer combination has multiple equilibrium states, and the system instability under a specific initial state is determined by the closest equilibrium point. With the understeer gradient, the jackknife phenomenon caused by the sideslip of the rear axle of the towing car is a primary system instability when the towing car is oversteered. From the perspective of stability control, the system instability can be effectively avoided via a yaw rate control strategy applied in the towing car. In addition, the stability of car-trailer combinations can be improved by increasing the wheelbase of trailer and the distance between front axle of trailer and traction point.