Vehicle Planar Motion Stability Study for Tyres Working in Extremely Nonlinear Region

Abstract

Many researches on vehicle planar motion stability focus on two degrees of freedom(2DOF) vehicle model, and only the lateral velocity (or side slip angle) and yaw rate are considered as the state variables. The stability analysis methods, such as phase plane analysis, equilibriums analysis and bifurcation analysis, are all used to draw many classical conclusions. It is concluded from these researches that unbounded growth of the vehicle motion during unstable operation is untrue in reality thus one limitation of the 2DOF model. The fundamental assumption of the 2DOF model is that the longitudinal velocity is treated as a constant, but this is intrinsically incorrect. When tyres work in extremely nonlinear region, the coupling between the vehicle longitudinal and lateral motion becomes significant. For the purpose of solving the above problem, the effect of vehicle longitudinal velocity on the stability of the vehicle planar motion when tyres work in extremely nonlinear region is investigated. To this end, a 3DOF model which introducing the vehicular longitudinal dynamics is proposed and the 3D phase space portrait method is employed for visualization of vehicle dynamics. Through the comparisons of the 2DOF and 3DOF models, it is discovered that the vehicle longitudinal velocity greatly affects the vehicle planar motion, and the vehicle dynamics represented in phase space portrait are fundamentally different from that of the 2DOF model. The vehicle planar motion with different front wheel steering angles is further represented by the corresponding vehicle route, yaw rate and yaw angle. These research results enhance the understanding of the stability of the vehicle system particularly during nonlinear region, and provide the insight into analyzing the attractive region and designing the vehicle stability controller, which will be the topics of future works.

Phase Plane Analysis for Vehicle Handling and Stability

“…Simulation time is 20s. There are three equilibrium points in phase plane, one is stable equilibrium point, and the others are unstable equilibrium point [29][30][31][32][33] . There is a strip stable region in phase plane, and point in this region could return to stable equilibrium point after a certain time, but the outside can't return to the stable region 29,33 .…”

Bifurcation of lane change on highway for large bus

“…For the 4DOF model with longitudinal velocity changes, the state variable of quasi-periodic vibration shows energy conservation. This is different from the exponentially growing 3DOF model with constant longitudinal velocity, which is contradictory to vehicle motion in reality [17]. Moreover, the eigenvalues change from negative real to imaginary with negative real part in accordance with the manifolds, predicting the Hopf bifurcation phenomenon.…”

“…Moreover, as a 3DOF plane model introduced vehicular longitudinal dynamics, Liu and Wang et al investigated the vehicular longitudinal velocity effect on stability for a vehicle's planar motion when tires work in an extremely non-linear region. They revealed the chaos phenomenon based on the phase plane and the Poincare method [17,18]. Ran et al used a trailing wheel suspension to analyse shimmy stability and bifurcation.…”

Stable headway prediction of vehicle platoon based on the 5-degree-of-freedom vehicle model

“…It points out that the change of vehicle velocity plays an important role in determining the location of bifurcation points of vehicle system. To analyze the impact of vehicle longitudinal acceleration on vehicle system stability, a 3DOF (longitudinal velocity, 1ateral velocity, and yaw rate) vehicle model is introduced by Liu et al 17 The simulated results show that the dynamic characteristics of vehicle system will change fundamentally when the vehicle system is moving on the high-speed and steering condition. The strong coupling among the longitudinal motion, the lateral movement, and the yaw movement of the vehicle system will eventually aggravate the instable movement of the vehicle system.…”