Vehicle Handling Analysis Using Linearisation Around Non-Linear Operating Conditions

A non-linear example vehicle model including four degrees of freedom (yaw, sideslip, roll and steering), non-linear kinematics and the Magic Formula tyre model has been developed. With the assumption of small perturbations around any steady-state working condition, the linearised equations are derived. A novel approach is used for the linearisation of external forces and moments from the tyres. They are linearised in terms of the state variables rather than the slip angle, camber angle and vertical load which are themselves functions of the state variables. The results of this process are expressed in terms of stability derivatives. In order to use the method, the steady-state solution of the non-linear equations is first obtained for a particular value of lateral acceleration, then after the calculation of the stability derivatives, a linear analysis can be performed for the linear equations in terms of perturbed variables. It is shown how this approach provides additional insight into the vehicle behaviour by allowing powerful linear methods to be used throughout the entire range of lateral acceleration.