The recent trend towards micro-patterning of thin film webs brought stricter manufacturing tolerances than traditionally admissible vibration levels. Therefore, one has to consider roll-to-roll (R2R) systems with their system dynamics model encompassing all systems’ components, namely, the axially moving web(s),the rotating rolls and other accessories. In this study, the dynamic characteristics of an axially moving web in a two-span R2R system are investigated. Influence of geometrical parameters on the R2R dynamics and the parametric resonances of the moving web is presented. The time variations of web axial speed and web-transmitted tension are rigorously obtained by solving the web tension–roller angular speed equation, which is obtained from the conservation of mass law. The effects of system parameters such as length of the web, inertia of idler roll and radius of the rewinding/unwinding roll on the angular speed and web-transmitted tension have been discussed. The axially moving web was modelled as a string, which was mathematically represented by a second-order hyperbolic partial differential equation. The effect of the frequency of the disturbance at the roll onthe web dynamics is also discussed. The transverse vibration response at selected points on the web shows higher frequency fluctuations corresponding to lower transport axial speed. It is noted that instability in the transverse response will occur when the first and second frequencies of the oscillation converge.
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