Shear compliance and self-weight effects on traction belt mechanics

Abstract

The transverse elastic deflection of a traction belt along the free span depends mainly on the flexural stiffness, but may be significantly influenced by the distributed weight and the shear compliance, which affect together the width of the arc of contact. In particular, the shear compliance yields a virtual decrease of the flexural stiffness, flattens the free span and increases the wound regions, to the advantage of the transmissible torque. Moreover, the tensioning of a given belt may be somewhat larger, in comparison with the ideal circular-straight path with the same centre distance, because of the increased length of the deflected belt trajectory due to gravity. The present paper addresses all these effects, solving for the span deflection line by a second-order approach based on the approximation called WKB by the mathematicians, after Wentzel, Kramers, and Brillouin. A first-order analysis, very useful for practical calculations, is also presented. The results point out the different geometry of the belt wrapping on the smaller and larger pulleys.