Basics of Vehicle Dynamics, Vehicle Models

For the understanding and knowledge of the dynamic behaviour of passenger cars it is essential to use simple mechanical models as a first step. With such kind of models overall characteristic properties of the vehicle motion can be investigated. For cornering, a planar two-wheel model helps to explain understeer–oversteer, stability and steering response, and influences of an additional rear wheel steering. Another planar model is introduced for investigating straight ahead acceleration and braking. To study ride comfort, a third planar model is introduced. Consequently, in these basic models, lateral, vertical and longitudinal dynamics are separated. To gain insight into e.g. tyre–road contact or coupled car body heave, pitch and roll motion, a 3D-model needs to be introduced, taking into account nonlinearities. Especially the nonlinear approximation of the tyre forces allows an evaluation of the four tyre–road contact conditions separately—shown by a simulation of a braking during cornering manoeuvre. A near reality vehicle model (NRVM) comprises a detailed 3D description of the vehicle and its parts, e.g. the tyres and suspensions for analysing ride properties on an arbitrary road surface. The vehicle model itself is a composition of its components, described by detailed sub-models. For the simulation of the vehicle motion, a multi-body-system (MBS)-software is necessary. The shown fundamental structure of the equations of motion allows to connect system parts by kinematic restrictions as well, using closed loop formulations. A NRVM also offers the possibility for approving a theoretical layout of control systems, generally by using one of the simple vehicle models as observer and/or part of the system. An example demonstrates the possibility of additional steering and/or yaw moment control by differential braking.