Stationary and transient analyses of a pulley-belt system based on an Eulerian approach

In some engineering industries such as the transportation domain, the belt drives are widely used to transmit the power and the motion. They have a complex dynamic behavior because of the tension forces, the dimensions and the utilization purposes. In this paper, extant models are summarized to present a better understanding of the belt mechanics and the dynamic behavior of pulley-belt systems. Then, a new approach based on the Eulerian description as well as on the normal and shear stresses is introduced in order to discuss the belt mechanics, to build an analytical model of a pulley-belt system and to investigate its dynamic behavior. It can describe the zones of contact between the belt and the pulleys in the stationary and transient regimes. Analytical solutions and formulations for the tensions and the relative displacements of the belt over the pulleys in the stationary regime are established, while differential equations for the belt tensions and the driven pulley velocity in the transient regime are derived. These differential equations are solved using the explicit Runge-Kutta time-step integration scheme. The study is also conducted to observe slip phenomena due to the contact between elastic and rigid surfaces and multiple zones of slip can be found by means of an iterative Newton-Raphson method.