In the present paper, a numerical treatment is given of the problem of two elastic cylinders which are pressed together, shifted with respect to each other over a small distance without rolling, and subsequently rolled over each other. Besides this problem, other transient loading and kinematic conditions of the cylinders can be studied with the proposed method, such as the application of a periodical force, and the reversal of the rolling direction. Inertial effects are neglected throughout this work. When the cylinders are not made of the same material, the normal pressure distribution will affect the tangential traction, and vice versa. It is assumed that this second effect, the tangential force perturbing the normal pressure, is so small that it can be neglected. In this article no slip is assumed to occur. This assumption is equivalent to an infinite coefficient of friction, and it is approximately verified if the tangential force is small in comparison to the normal load. It is found that the transient phenomena become negligible after one to two contact widths have been traversed.

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