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 is developed to predict the belt response: simply supported boundary conditions are considered, neglecting the pulley curvature, and including the effect of the lower belt span. The transverse displacement field is expanded into sine series and the Galerkin method is applied to reduce the partial differential equation (PDE) into a set of ordinary differential equations. In order to forecast the belt response, the elastic characteristics only of the belt must be provided to the theoretical model. An experimental investigation is performed on a belt-pulley system with a pulley eccentricity; a laser displacement transducer is used to measure the transverse displacement. The combination of a direct and a parametric excitation is analyzed in detail. Interesting post-critical nonlinear dynamic behaviors are found: sub-harmonic responses and quasi-periodic motions seem to coexist, depending on the initial conditions. Experiments confirm the numerical results, thus validating the present theoretical model.