Abstract Summary
We investigate the steady configuration of a visco-elastic belt drive and its loss of stability under varying driving speed. The belt is considered as a linearly visco-elastic slender beam with small bending stiffness. Due to the presence of the small damping parameter and the small bending stiffness, the equations of motion are severly singularly perturbed. By variation of system parameters, like the driving speed, the damping coefficient, the tension force and the radius of the drums, we calculate the steady configuration and the stability limit of the belt. Preliminary calculations show, that the viscous damping, the distributed load and the strong bending at the drums can decrease the critical driving speed significantly and lead to flutter oscillations. Drive belts are frequently used tools for power transmission and their stable behaviour is important for the proper operation of the facility. For slowly moving belts it is usually sufficient to consider the equilibrium states, but if the belt speed approaches the wave speed in the belt, the influence of the drive motion has to be taken into account. In this talk we focus on the calculation of the steady configuration for a circular belt, which is in frictional contact with two drums, and on the calculation of its stability and the possible onset of flutter. Assuming that the driving pulley rotates with constant angular velocity and a constant angular momentum acts on the driven pulley, we obtain two sets of nonlinear partial differential equations for both free spans, which are connected by the boundary conditions at the contact points. Since we assume, that due to large friction coefficients between the belt and the drums the sliding zone on the pulleys is negligible small and the tension in the belt is transferred between the run-up and run-off points, also small state-dependent time delays have to be taken into account.
