The free and forced vibration of a moving medium is examined in an application where distributed friction guiding is used to control lateral position passively. Subambient pressure features formed in the guides intentionally modify the naturally occurring self-pressurized air bearing and increase the contact force between the medium and the guide's surface. These features increase friction to a level beyond that achievable based on the nominal wrap pressure. The moving medium is modeled as a beam that is transported over frictional regions and subjected to prescribed boundary disturbances arising from runout of a supply or take-up roll. For axial transport at a speed that is high compared to the velocity of lateral vibration, Coulomb friction between the guides and the moving medium can be well approximated by a derived expression for equivalent viscous damping. The equation of motion is developed for the cases of a single cylindrical guide and of a multiplicity of guides having arbitrary placement. The level of equivalent damping for each mode decreases with transport speed, and critical speeds exist where each vibration mode transitions between the overdamped and underdamped regimes. Parameter studies in the contact pressure, transport speed, and guide geometry identify preferred design configurations for maximizing dissipation in particular modes and for attenuating high-frequency response.
V. Kartik, J. Wickert
Journal of Vibration and Acoustics