Effect of elliptical profiles on the steady motions of loose rolling wheels

Kupi, Gábor and Antali, Máté (2026) Effect of elliptical profiles on the steady motions of loose rolling wheels. NONLINEAR DYNAMICS, 114 (18). No.-1160. ISSN 0924-090X

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Abstract

In this paper, the model of a rigid wheel is analysed with a pure rolling contact with a horizontal rigid plane. The profile of the wheel is assumed to be an ellipse, which shape can be used for approximating various profiles in vehicle wheels. The elliptic profile can still be a basis of analytical solution, and in the same time, includes qualitatively new types of behaviour compared to the special cases of thin wheels and toroidal wheels known in the literature. The full nonlinear differential equations are derived and compared to the related known cases of equations. The two-parametric set of steady motions are calculated. We show that because of the elliptical profile, the qualitative dynamics significantly changes compared to the classical thin wheel and even to the toroidal wheel. Through bifurcations, four scenarios are found with different dynamical behaviours and stability of the solutions.

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