Vibration-based estimation of tension for an axially travelling web in roll-to-roll manufacturing

Precise estimation of web tension in roll-to-roll manufacturing is critical to ensure product quality. A vibration-based method to estimate web tension is proposed in this paper. By employing the Hamilton principle, the governing equations of motion are derived, which are discretized and solved by the Galerkin method. The natural frequencies are computed from the eigenvalue equation. This study attempts to derive an approximate fitting formula among the axial tension, the travelling speed and the natural frequency, from which the web tension can be calculated conveniently and quickly by employing the measured natural frequencies. A laser displacement sensor is used to measure the transverse vibration displacements of the travelling web and detect free vibration frequency. A major advantage of the proposed method is its contactless, which is more useful under conditions where load cells are not available. An experimental test is carried out to confirm the effectiveness and accuracy of the proposed approach. The web tensions estimated by the vibration method are compared with the measured tensions by load cells.