Vibration and stability of axially moving webs coupled to surrounding air

Abstract

High-speed web flutter is of significant importance in a variety of paper, plastics, textiles, and sheet metal industries. The natural frequencies of vibration and the onset of flutter in thin, wide, high-speed webs are investigated by modeling a web as an axially moving, partially slack Kirchhoff plate with small bending stiffness, and coupled with surrounding air. The linear partial differential equations of the web are discretized using the Assumed Modes Method and analyzed for two different air models - incompressible and compressible flow. The solutions for the aerodynamic potentials are determined numerically and accurate reduced order models of the moving web with air coupling are generated.

In the absence of air coupling the web frequencies are grouped together in clusters and aeroelastic flutter occurs at supercritical speed. Addition of incompressible potential flow air coupling reduces significantly the web frequencies and separates the frequency clusters while modifying slightly the onset and frequency of flutter at supercritical speed. Compressible flow modeling adds radiation damping to the system and shifts the onset of flutter to the critical speed. Finally it is concluded that the prediction of web flutter at subcritical speeds requires the inclusion of base flows generated by air viscosity and web motion. These results corroborate previous results in the literature and suggest systematic analytical modeling approaches for web flutter prediction.