Vehicle Dynamics of Modern Passenger Cars

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.

Tires are the interface between vehicle and road. The forces and moments generated by the tires determine the motion of a road vehicle. Dedicated tire tests provide insight in these forces and moments and their dependency on slip, inclination angle and vertical force. The brush tire model can explain the measured characteristics qualitatively, the Magic Formula is a semi-empirical tire model to quantitatively describe them. To account for tire dynamic behavior, relaxation effects are discussed and modeled.

Fundamental ride and handling aspects of active and semi-active suspensions are presented in a systematic way starting with simple vehicle models as basic building blocks. Optimal, mostly Linear-Quadratic (H2), principles are used to gradually reveal and explore key system characteristics where each additional model Degree-of-Freedom (DoF) brings new insight into potential system benefits and limitations. The chapter concludes with practical considerations and examples including some that go beyond the more traditional ride and handling benefits.

This chapter provides an overview of the basic lateral control of a road vehicle using actuators such as individually controlled brakes and or rear-wheel steering. The main focus is on linear control system design for cornering, especially for the improvement of stability and manoeuvrability of a passenger car. Steering control is presented in the form of a simple ‘driver model’ that shows the importance of road preview in providing a stable controller. For nonlinear control, anti-lock braking and electronic stability control are described; finally there is an introduction to vehicle motion control at the limits of friction.

This part begins with an introduction to Multibody Systems (MBS). It presents the elements of MBS and discusses different modeling aspects. Then, different methods to generate the equations of motion are presented. Solvers for ordinary differential equations (ODE) as well as differential algebraic equations (DAE) are discussed. Finally, techniques for “online” and “offline” simulations including real-time applications are presented like necessary for car development. Special examples show the connection between simulation and test results.