Dynamics of a web accumulator
Abstract
A conventional accumulator with no driven rollers and all rollers identical is studied for avoidance of excessive tension, slackness and slippage on the rollers. The total force imposed by the web spans on the carriage is derived for the case of a constant acceleration of the web. For the usual case of several rollers on the carriage, the translational kinetic energy of the carriage (including the moving rollers) is shown to be negligible in comparison to the rotational kinetic energy of all the rollers in the accumulator. This discovery allows design and analysis of the control scheme of an accumulator with knowledge only of the parameters of the rollers. The time required for a constant acceleration of the carriage is shown to be a simple function of the acceptable difference of tension across the accumulator, the total change of velocity, the number of rollers, and J/R^2 of the rollers. Equations are derived for the ratios of tension across each roller, allowing the choice of a rate of acceleration for avoidance of slippage on a roller. The first or last roller was found to not always be the critical one for slippage. Equations are derived relating the balancing force on the carriage to the number of rollers and an acceptable magnitude of tension.
Citation
Shelton, J. J. (1999, June). Dynamics of a web accumulator. Paper presented at the Fifth International Conference on Web Handling (IWEB), Stillwater, OK.