Mathematical Model for the Simulation of Contact-Induced Standing Waves in Tyres by a Rotating Ring Based on Experiment

Abstract

A physics-based mathematical model for the simulation of contact-induced standing waves in rotating tyres is presented. A toroidal balloon mounted on a hub, in contact with a rigid flywheel, is considered. The distance between the hub and the flywheel shafts is kept constant during rotation. The balloon is modelled as a membrane structure, i.e. as a ring on elastic support without flexural stiffness. The differential equations of motion for the ring radial and circumferential displacements are formulated according to the cylindrical shell theory. It is found that the critical rotation speed is a transition parameter from a stable to unstable state, whereas the standing waves denote ring post-buckling behaviour. Boundary conditions at the ring and flywheel contact edges are specified so as to ensure the continuity of ring deformation. The internal load due to the penetration of the flywheel into the expanded ring, as well as the reaction forces in shaft bearings, are determined. The influence of the circumferential displacement on ring response is also analysed. The analytical procedure is verified by comparing the numerical and the available experimental results. In spite of a rather simple balloon model, a good qualitative agreement between the two sets of results is obtained.

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“…The generation of standing waves has been investigated by measurements on a test bed and analysed via a simplified ring model, [7]. A sophisticated ring mathematical model based on the same experiment is presented in [25]. Roots of the characteristic equation of the governing differential equation of motion are shown in Figure 10.…”

On the Theory of Contact-induced Standing Waves in Rotating Tyres

“…The generation of standing waves has been investigated by measurements on a test bed and analysed via a simplified ring model, [7]. A sophisticated ring mathematical model based on the same experiment is presented in [25]. Roots of the characteristic equation of the governing differential equation of motion are shown in Figure 10.…”