Bifurcation analysis of wheel shimmy with non-smooth effects and time delay in the tyre–ground contact

The nonlinear dynamics of towed wheels is analysed with the help of the brush tyre model. The time delay in the tyre–ground contact and the non-smooth nature of the system caused by contact friction are considered simultaneously. Firstly, the centre manifold reduction is performed on the infinite-di...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2019-10, Vol.98 (1), p.841-858
Main Authors: Beregi, Sandor, Takacs, Denes, Stepan, Gabor
Format: Article
Language:English
Subjects:
Automotive Engineering
Bifurcations
Canonical forms
Classical Mechanics
Control
Dynamical Systems
Engineering
Hopf bifurcation
Mechanical Engineering
Nonlinear dynamics
Original Paper
Stability
Time lag
Tires
Vibration
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The nonlinear dynamics of towed wheels is analysed with the help of the brush tyre model. The time delay in the tyre–ground contact and the non-smooth nature of the system caused by contact friction are considered simultaneously. Firstly, the centre manifold reduction is performed on the infinite-dimensional system transforming the governing equations into a normal form containing linear and piecewise-smooth second-order terms. Then, this normal form is used to establish the stability of the non-hyperbolic equilibria of the system and to give an estimation of the limit cycles emerging at the linear stability boundary. This way, it is demonstrated how subcritical Hopf bifurcations in the non-smooth delayed system generate bistable parameter ranges, which are left undetected by standard tyre models.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-019-05123-1