Damping effect of winding on the lateral vibrations of axially moving tapes

The lateral vibrations of winding rapes are investigated by using a second order linens model, where lateral indicates the direction parallel to the reel rotation axis. A boundary condition describing the winding of tapes on the reel considering a perfect reel-tape adhesion is applied This condition imposes zero lateral velocity of the string as measured by a fixed observer and has a significant damping effect on the later-al vibrations. Both natural and forced vibrations are investigated. A boundary excitation is assumed in the forced vibration analysis. Numerical results show the effect of the parameters on the system dynamics. The present model is applicable to a class of tapes travelling in manufacturing machines.