# Brush tyre models for large camber angles and steering speeds Journal article, 2022

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.

brush models

Tyre modelling

two-dimensional theory

transport equation

transient dynamics

nonlinear theory

## Author

### Luigi Romano

Chalmers, Mechanics and Maritime Sciences (M2), Vehicle Engineering and Autonomous Systems

### Fredrik Bruzelius

The Swedish National Road and Transport Research Institute (VTI)

Chalmers, Mechanics and Maritime Sciences (M2), Vehicle Engineering and Autonomous Systems

### Bengt J H Jacobson

Chalmers, Mechanics and Maritime Sciences (M2), Vehicle Engineering and Autonomous Systems

#### Vehicle System Dynamics

0042-3114 (ISSN) 1744-5159 (eISSN)

Vol. 60 4 1341 -13492

### COVER – Real world CO2 assessment and Vehicle enERgy efficiency

Swedish Energy Agency (2017-007895), 2018-01-01 -- 2021-12-31.

VINNOVA (2017-007895), 2018-01-01 -- 2021-12-31.

### Subject Categories

Mechanical Engineering

Applied Mechanics

Vehicle Engineering

Transport

### DOI

10.1080/00423114.2020.1854320