Periodic responses of a pulley−belt system with one-way clutch under inertia excitation

The stable steady-state periodic response of a two-pulley belt drive system coupled with an accessory by a one-way clutch is presented. For the first time, the pulley−belt system is studied under double excitations. Specifically, the dual excitations consist of harmonic motion of the driving pulley and inertia excitation. The belt spans are modeled as axially moving viscoelastic beams by considering belt bending stiffness. Therefore, integro-partial-differential equations are derived for governing the transverse vibrations of the belt spans. Moreover, the transverse vibrations of the moving belt are coupled with the rotation vibrations of the pulleys by nonlinear dynamic tension. For describing the unidirectional decoupling function of the one-way device, rotation vibrations of the driven pulley and accessory are modeled as coupled piecewise ordinary differential equations. In order to eliminate the influence of the boundary of the belt spans, the non-trivial equilibriums of the pulley−belt system are numerically determined. Furthermore, A nonlinear piecewise discrete-continuous dynamical system is derived by introducing a coordinate transform. Coupled vibrations of the pulley−belt system are investigated via the Galerkin truncation. The natural frequencies of the coupled vibrations are obtained by using the fast Fourier transform. Moreover, frequency−response curves are abstracted from time histories. Therefore, resonance areas of the belt spans, the driven pulley and the accessory are presented. Furthermore, validity of the Galerkin method is examined by comparing with the differential and integral quadrature methods (DQM & IQM). By comparing the results with and without one-way device, significant damping effect of clutch on the dynamic response is discovered. Furthermore, the effects of the intensity of the driving pulley excitation and the inertia excitation are studied. Moreover, numerical results demonstrate that the two excitations interact on the steady-state response, as well as the damping effect of the one-way clutch.