Article ID Journal Published Year Pages File Type
775165 European Journal of Mechanics - A/Solids 2009 10 Pages PDF
Abstract

The dynamics of wheel shimmy is studied when the self-excited vibrations are related to the elasticity of the tyre. The tyre is described by a classical stretched string model, so the tyre-ground contact patch is approximated by a contact line. The lateral deformation of this line is given via a nonholonomic constraint, namely, the contact points stick to the ground, i.e., they have zero velocities. The mathematical form of this constraint is a partial differential equation (PDE) with boundary conditions provided by the relaxation of deformation outside the contact region. This PDE is coupled to an integro-differential equation (IDE), which governs the lateral motion of the wheel. Although the conventional stationary creep force idea is not used here, the coupled PDE-IDE system can still be handled analytically. It can be rewritten as a delay differential equation (DDE) by assuming travelling wave solutions for the deformation of the contact line. This DDE expresses the intrinsic memory effect of the elastic tyre. The linear stability charts and the corresponding numerical simulations of the nonlinear system reveal periodic and quasi-periodic self-excited oscillations that are also confirmed by simple laboratory experiments. The observed quasi-periodic vibrations cannot be explained in single degree-of-freedom wheel models subject to a creep force.

Related Topics
Physical Sciences and Engineering Engineering Mechanical Engineering
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