Influence of Tyre and Vehicle Constructive Characteristics on Linear Stability of a Four Wheel Vehicle Model

The study of vehicle handling behaviour is of fundamental importance in order to improve vehicle safety, especially as concerns the loss of stability in the lateral direction resulting from unexpected lateral disturbances like side wind force, tyre pressure loss, μ-split braking due to different road pavements such as icy, wet, and dry pavement, etc. The interest for vehicle stability has been actually increasing, and consequently the study of the local stability has become a fundamental discipline in the field of vehicle dynamics, being a vehicle a strongly non linear system mainly because of tyres behaviour. The study of the driving stability of a vehicle travelling on a curve in steady state conditions is the first and most important step in order to understand the effects of perturbations inevitably occurring during vehicle motion. Such a study may have a dual application: first of all it can contribute to develop and optimize control logic of the vehicle subsystems; secondly it may be useful to identify the physical quantities affecting stability and to find out their optimal set under this point of view. At this purpose it is fundamental to dispose of suitable stability maps, which typically are constituted by curves in a phase plane delimiting zones in which the system of equations describing the vehicle dynamics admits stable and strongly attractive solutions. Outside of such zones only unstable or marginally stable solutions exist. In the recent years several ways to construct these maps have been proposed. A great number of studies in literature are mainly oriented to the development of control systems strategies aimed to improve vehicle stability and so in such papers the authors proposed methods based on vehicle and tyre models extremely simplified. Typical simplifications consist in considering a bicycle model (i.e. neglecting roll dynamics and the lateral load transfer) and/or in linearising the tyre-road interaction (i.e. underestimating saturation effects in the tyre lateral forces). No studies have been found aimed to find out which vehicle physical characteristics affect significantly its stability and the influence of their variation on stability. This paper pursues precisely this purpose and hence it is necessary to use a sufficiently detailed vehicle model allowing to take into account all the physical parameters on which investigate. The stability of a complete four wheel, two axle, vehicle model will be discussed, Pacejka magic formula will be adopted to model the pure tyre-road interaction, lateral load transfer will also be considered. Two different methods will be presented: a “mathematical” method consisting in the evaluation of the state matrix eigenvalues and a ”geometrical” method inspired to the so called “handling diagram” construction. The influence exerted on the stability zone extension in the phase plane by some vehicle parameters, such as tyre cornering stiffness and front/rear roll stiffness will be evidenced with the aim to suggest solutions able to increase vehicle stability.