Abstract
In this investigation, a double brush model, which aims at predicting both the longitudinal and the lateral tyre characteristics during transient phases, is developed. The solution of the tyre-road contact equation is provided by using the method of characteristics and a time delay of the bristles deformation with respect to the time is also introduced by modelling both the tyre tread and the carcass by means of viscoelastic and elastic elements, respectively. The temporal trend of some quantities of interest such as the adherence length and the critical slip value is then obtained as explicit function of the time or, equivalently, of the travelled distance. A preliminary analysis is carried out with reference to the transition from a pure rolling condition to accelerating or braking ones. The tyre response to a constant lateral slip input is also comprehensively discussed. Finally, in the case of consecutive manoeuvre, the model shows that all the generalised forces exerted by the road on the tyre vary continuously by introducing a finite increase in the slip parameter. Several examples are presented in order to demonstrate the applicability of the proposed model to severe braking or handling dynamic scenarios.
Highlights
A significant amount of research has focused on traffic safety and in particular on investigating physical model-based control systems to be employed in emergency braking and handling dynamic scenarios [1]
Some very sophisticated FEM or Multibody models [2,3,4] are able to capture with great accuracy many phenomena related to the tyre dynamics, but they are characterised by extremely long calculation times because of their intrinsic complexity
For values of the slip parameter ey jecyritj, the values of the generalised forces are always smaller than those obtained for the steady-state cases, which correspond to the solution obtained by employing a brush model without carcass compliance
Summary
A significant amount of research has focused on traffic safety and in particular on investigating physical model-based control systems to be employed in emergency braking and handling dynamic scenarios [1]. Some specially developed functions are included in order to fit Pacejka’s curves The latter is an enhanced brush model which takes into account the deformation of the tyre carcass and it is able to provide a transient solution for both the lateral force and the self-aligning moment resulting from a first order differential equation. The need to include a flexible carcass is motivated by the possibility of obtaining a variable trend over time, since the tyre-road contact equations are based on purely kinematic considerations, and do not allow to introduce a time delay of the bristle deformation with respect to a constant slip input. The main advantage of this formulation is the possibility to obtain an analytical solution for the generalised forces resulting from the tyre-road interaction, allowing the model to be employed in real-time simulation for braking and handling applications.
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