On Body Roll Angle During Transient Response Maneuver of a 3-D Model

This paper addresses the issues of mathematical modeling of a three-dimensional vehicle with 3 Degree-Of-Freedom (DOF), yaw rate r, roll rate p and side-slip angle β and computer simulation using “Matlab”. The research investigates the case of an untripped vehicle body roll angle, induced rollover on road involving a single vehicle. The untripped Body Roll Angle (BRA) and ROLLOVER risks are associated with not only the Vehicle Design Factors (VDF) but also with the driver inputs, namely forward speed u and steering wheel angle - δ_SW. The lateral acceleration a_y is reaching its peak value during transient response due to abrupt maneuvers by the driver. The magnitude of the lateral acceleration may lead to a rollover situation. LaGrange equation for a holonomic system is used to determine the equations of motion. A unique State-Space Formulation with 4 state variables is proposed in order to obtain the Linear Time Invariant (LTI) equations. Numerical and computer simulation analysis are presented. The influence of some key VDF such as weight distribution, height of the center of gravity and driver inputs are demonstrated.