Abstract
In this paper, a model for transverse web vibration in a roll-to-roll system is presented. Web axial tension and web axial speed, decisive parameters in the equation of motion that describes web vibration, are rigorously obtained by considering the two rolls-web coupled system’s dynamics, coupled with the equation of motion. According to the present analysis, the idealized simply-supported boundary conditions, commonly used in studies on vibrations of axially moving structures are not needed. Instead, a mathematical model comprised of the governing equation of web transverse vibration and the roll angular velocity – web axial tension relationship is solved as a coupled system. A finite-difference based algorithm is used for solving the coupled system of differential equations. It is worth noting that the web axial speed and web-transmitted tension are not constants when a certain amount of the web material is transferred from the unwinding roll to the winding roll; they vary nonlinearly after a short transient period. The transverse vibration response at selected points on the web span shows higher (lower) frequency fluctuations corresponding to lower (higher) transport axial speed. This behavior is significantly different from that of a vibrating web under constant axial speed and tension.
Highlights
IntroductionBecause of their importance in industrial processing of thin materials (textiles, papers, polymers, metals, and composites), axially moving string models are located at the heart of web dynamics studies
Because of their importance in industrial processing of thin materials, axially moving string models are located at the heart of web dynamics studies
The transverse vibration of the axially moving web is studied in light of the coupled web vibration-R2R dynamics formulation
Summary
Because of their importance in industrial processing of thin materials (textiles, papers, polymers, metals, and composites), axially moving string models are located at the heart of web dynamics studies. (iv) Papers presenting parametrically excited nonlinear responses of axially moving strings with time-harmonic varying axial velocity and constant transmitted tension [33,34,35,36] where the effects of parameters such as mean velocity, web stiffness and damping coefficients, and a middle support on frequency response curves and bifurcation points were investigated. One does not need to assume supported boundary conditions for the vibration problem since the unwinding and rewinding rolls enter the analysis as part of the overall model This comprehensive approach couples the physics-based variations of axial web tension with angular roll velocities to the web vibration-imposed fluctuations. In order to study the coupled dynamics, the motion of the vibrating web while transferring from the unwinding roll to the rewinding roll is analyzed
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