Analysis of the tyre–road interaction with a non-smooth delayed contact model

Abstract

In this study a tyre model is developed for multibody dynamics software. Vibrations of a towed wheel excited by the lateral deformation of the tyre are analysed with the help of numerical simulations. In our calculations the time delay in the tyre-ground contact as well as the partial side slip are considered making it possible to capture the dynamic deformation of the contact patch centre-line with relatively low number of parameters and computation time. As a result the hysteresis effect in the stability of the rectilinear motion can be identified, which would be undetectable by simpler, quasi steady-state tyre models. Thus, bistable parameter regions appear in the stability charts where for the same set of system parameters a stable equilibrium and a periodic orbit coexist. The simulations are compared with measurements carried out on an experimental rig consisting of a wheel and a caster running on a conveyor belt. Keywords tyre-road contact • dynamic tyre • deformation • non-smooth delayed tyre model • lateral vibrations • wheel shimmy ACKNOWLEDGEMENT This research has been supported by theÚNKP-17-13-I. New National Excellence Program of the Ministry of Human Capacities.

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

“…Nevertheless, neither model can provide bistable parameter domains in the one degree of freedom model of towed wheels, which were otherwise experimentally presented in [5,24,39]. Additional dry friction at the king pin can be one explanation [24].…”

Theoretical and experimental study on the nonlinear dynamics of wheel-shimmy

“…As several former studies showed, these oscillations have very rich dynamics and the associated vibrations are essentially nonlinear [17,18]. In experiments, socalled bistable parameters were identified [1] where although the rectilinear motion is stable, it has a finite domain of attraction. This means that depending on the initial conditions, the system can converge either to the straight-line motion or to a large-amplitude periodic solution (shimmy) at the same towing speed.…”

“…This error could be adjusted via the stretched string tyre model [12]. As shown in [1], this model provides qualitatively similar, but quantitatively better results for the critical towing speed. However, by means of the stretched string model, sliding can be considered only with differential equations instead of pre-defined sliding limits.…”

“…Using the simplest, one-degree-of-freedom model of a towed wheel, the standard quasi-steady-state tyre models do not provide such parameter domains. In the meantime, the existence of bistable parameter regions can be shown if the so-called memory effect in the tyreground contact and the contact friction is considered simultaneously [1,4].…”

On the nonsmooth dynamics of towed wheels

“…One of the fundamental phenomena of towed wheels is the self-excited oscillations called shimmy, which has been intensively studied in the literature (see [18,21] and their references). There are many possibilities for modelling the tyre and the vehicle, and the resulting models often lead to complex mathematical models including, for example, time delay [3,4].…”