Yaw Stability Analysis of a Tractor Semitrailer Using Yaw Plane Model

Abstract

Lateral dynamics of a road vehicle refers to its directional control and stability. Bicycle model is the classical proven model for this study. This paper presents a4 degrees of freedom mathematical model, representing a three-axle tractor semitrailer, to investigate its yaw stability in combined cornering and braking manoeuvres. The equations of motion governing the system are derived using Newtonian mechanics and then converted into a state space form for simulation. A non-linear tire model and a load transfer model are implemented to accurately incorporate the effect of braking on yaw stability. In the first step, steady state analysis is performed to determine the variation of steady state gain characteristics such as yaw velocity gain and articulation angle gain for different loading conditions of the vehicle. Yaw response characteristics such as articulation angle, articulation rate, lateral velocity and yaw rate are simulated in MATLAB. In the second step, the directional responses of the vehicle during jackknifing and trailer swing are studied by performing simulations under wheel lock-up condition on different axles and are compared with the no-wheel-lock up condition. Eigen value analysis is used to observe the variation in stability under different simulation conditions. Finally in the third step the effect of increasing forward speed on the stability is also simulated.