Sun, T. and He, Y., "Phase-Plane Analysis for Evaluating the Lateral Stability of Articulated Vehicles," SAE Technical Paper 2015-01-1574, 2015, doi:10.4271/2015-01-1574.
The phase-plane analysis technique has become a powerful tool for analyzing lateral stability of single-unit vehicles. Articulated vehicles, such as car-trailer combinations, consist of multiple vehicle units. Multi-unit vehicles exhibit unique dynamic features compared against single-unit vehicles. For example, a car-trailer may exhibit one of the three unstable motion modes, i.e., jack-knifing, trailer sway and rollover. Considering the distinguished configurations and dynamic features of articulated vehicles, it is questionable whether the phase-plane analysis method based on single-unit vehicles is applicable for analyzing the lateral stability of multi-unit vehicles. In order to address the problem, case studies are conducted to test the effectiveness of the phase-plane method for analyzing the lateral stability of a car-trailer combination, which is represented by a nonlinear vehicle model generated using the CarSim software package. The phase-plane analysis, which examines the relation between the leading unit's side-slip angle and side-slip angular velocity (β − dβ/dt), the relation between the trailing unit's side-slip angle and side-slip angular velocity (β′ − dβ′/dt), and the interrelation of the side-slip angle of the leading unit, the yaw rate of the leading unit, and the articulation angle between the leading and trailing units (β − r − ψ), is conducted to assess the lateral stability of the car-trailer combination with and without an active trailer differential braking (ATDB) system. Built upon the conventional phase-plane analysis method for single-unit vehicles, an innovative phase-plane analysis technique is developed in order to effectively assess the lateral stability of articulated vehicles. The applicability and effectiveness of the newly developed technique is examined and demonstrated.