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 - δSW. The lateral acceleration ay 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.