Parametric instability of belts: Theory and experiments

In this paper, the dynamic stability of a power transmission belt excited by an eccentric pulley is investigated. A theoretical model has been developed in order to predict the belt response: simply supported boundary conditions are introduced, neglecting the pulley curvature, and considering the presence of the lower span of the belt. The transversal displacement field is expanded in sine series of the still belt modes; the Galerkin method is applied to reduce the partial differential equation of motion into a set of ordinary differential equations. In order performing an accurate response prediction, the following information must be supplied to the model: elastic characteristic; geometry; initial tension; damping. An experimental investigation is performed on a belt mounted on two pulleys and a tensioner, where one of the pulleys presents a variable eccentricity; measurement are performed using a Laser Displacement transducer. The combination of direct and parametric excitation is analyzed in detail. Interesting postcritical nonlinear dynamics are found: sub-harmonic responses and quasi-periodic motion seem to coexist, depending on the initial conditions. Experiments confirm the numerical findings validating the present theoretical model.