Brush tyre models for large camber angles and steering speeds

In this paper, we discuss three improved brush models. The first one deals with the coupling between the slip and spin parameters and is valid for relatively high steering speed and small camber angles; the second one is more complex and considers the presence of a two-dimensional velocity field inside the contact patch due to large camber angles; the third one is more general and combines both the previous formulations. For the last two models, the investigation is conducted with respect to a rectangular contact patch, for which we show that three different regions can be identified, each of them corresponding to a different steady-state solution for the deflection of the bristle. Furthermore, from the transient analysis it emerges that each region can be in turn separated into an area in which steady-state conditions reign and another one in which the transient solution takes place. An asymptotic analysis is carried out for the three models and it is shown that the solutions are equivalent to the ones predicted by the standard brush theory for small values of the spin ratio and camber angle. Finally, a comparison is performed amongst the models to highlight the differences in the predicted tyre characteristics

Unsteady-state brush theory

This paper deals with unsteady-state brush tyre models. Starting from tyre-road contact theory, we provide a full analytical solution to the partial differential equations (PDEs) describing the bristle deformation in the adhesion region of the contact patch. We show that the latter can be divided in two different regions, corresponding to two different domains for the solution of the governing PDEs of the system. In the case of constant sliding speed inputs, the steady-state solution coincides with the one provided by the classic steady-state brush theory. For a rectangular contact patch and parabolic pressure distribution, the time trend of the shear stresses is investigated. For the pure interactions (longitudinal, lateral and camber), some important conclusions are drawn about the relaxation length. Finally, an approach to derive simplified formulae for the tangential forces arising in the contact patch is introduced; the tyre formulae obtained by using the proposed approach are not based on the common slip definition, and can be employed when the rolling speed approaches zero. The outlined procedure is applied to the cases of linear tyre forces and parabolic pressure distribution

2022 Vehicle Dynamics seminar

The seminar is held annually. The full title of this year\u27s seminar was "2021 Vehicle Dynamics seminar -- Connected and Electric"

An extended LuGre-brush tyre model for large camber angles and turning speeds

This paper presents a novel tyre model which combines the LuGre formulation with the exact brush theory recently developed by the authors, and which accounts for large camber angles and turning speeds. Closed-form solutions for the frictional state at the tyre-road interface are provided for the case of constant slip inputs, considering rectangular and elliptical contact patches. The steady-state tyre characteristics resulting from the proposed approach are compared to those obtained by employing the standard formulation of the LuGre-brush tyre models and the exact brush theory for large camber angles. Then, to cope with the general situation of time-varying slips and spins, two approximated lumped models are developed that describe the aggregate dynamics of the tyre forces and moment. In particular, it is found that the transient evolution of the tangential forces may be approximated by a system of two coupled ordinary differential equations (ODEs), whilst the dynamics of the self-aligning moment may be described by combining two systems of two coupled ODEs. Given its stability properties and ease of implementation, the lumped one may be effectively employed for vehicle state estimation and control purposes

2021 Vehicle Dynamics seminar

The seminar is held annually. The full title of this year\u27s seminar was "2021 Vehicle Dynamics seminar -- for Future Mobility ...and not only Lateral"

Automated Comfortable Docking at Bus Stops

This proceedings presentation illustrates the optimization problem of autonomous bus parallel parking subjected to ride discomfort while navigating in a path with rectangular geometry constraints. During bus parking, passengers - especially standing- can experience discomfort due to acceleration and jerk components. In our project, a novel discomfort model was derived, utilizing acceleration and jerk data. This model was then implemented in an optimization problem to minimize discomfort. Simulation results and experiment results have been shown. The experiment was conducted using Volvo Autonomous Bus

Enhanced Sliding Mode Wheel Slip Controller for Heavy Goods Vehicles

This paper introduces an improved version of a sliding mode slip controller for pneumatic brake system ofheavy goods vehicles, HGVs. Using the Fast Actuating Brake Valve, FABV, allows to adopt advance control approaches forwheel-slip controllers which provide features such as fast dynamic response, stability and robustness. In this paper, the slidingmode algorithm which was developed for the speed dependent wheel slip control using the FABV hardware is analysed andimproved. The asymptotic convergence properties of the control algorithm are proven using Lyapunov stability theory and therobustness of the method is investigate

Analytical results in transient brush tyre models: theory for large camber angles and classic solutions with limited friction

This paper establishes new analytical results in the mathematical theory of brush tyre models. In the first part, the exact problem which considers large camber angles is analysed from the perspective of linear dynamical systems. Under the assumption of vanishing sliding, the most salient properties of the model are discussed with some insights on concepts as existence and uniqueness of the solution. A comparison against the classic steady-state theory suggests that the latter represents a very good approximation even in case of large camber angles. Furthermore, in respect to the classic theory, the more general situation of limited friction is explored. It is demonstrated that, in transient conditions, exact sliding solutions can be determined for all the one-dimensional problems. For the case of pure lateral slip, the investigation is conducted under the assumption of a strictly concave pressure distribution in the rolling direction