Steady Motion of a Belt in Frictional Contact with a Rotating Pulley

Abstract

The steady-state motion of belt drives is studied extensively in the literature. While traditional models rely on the theory of an extensible string, we aim to take bending effects into account. In this regard, it is well known that concentrated contact forces at the points of first and last contact with a pulley arise if shear deformations are restricted. To circumvent this issue, we utilise a shear deformable, Cosserat theory of rods. In particular, we study the contour motion of a belt that is transported over a single, rigid pulley with zones of stick, sliding friction and no contact. The Coulomb friction law governs the contact between the belt and the pulley. We present a novel finite element model that allows to obtain the steady-state solution directly. Furthermore, we deduce the corresponding closed boundary value problem and integrate it numerically. Results obtained for a particular parameter set demonstrate correspondence of the two approaches.