Boundary Conditions for a Traveling Web Detaching From a Rotating Cylinder
Abstract High speed traveling webs appear in a number of technical applications such as plastic foil or paper production machinery and printing machines. Almost all mechanical models for the dynamic behaviour used so far, assume simple support boundary conditions. In reality, in the case of two-dimensional webs immersed in a viscous fluid, a low pressure zone will be present under the web near the point where the web detaches from the rotating drum. Other effects such as adhesion forces may also contribute. Thus, as can often also be seen already by naked-eye examination, the web does not detach tangentially from the drum. In this paper a mechanical model for small amplitude vibrations of a traveling web with small sag is developed, which takes into account the effect of the above described upstream boundary condition. The web is modeled as a one-dimensional heavy string without bending stiffness. The assumption of quasi-static stretching is made, i.e. infinitely high wave speed is assumed for longitudinal waves.