Limitations to sensing of web tension by means of roller reaction forces

Abstract

Classical frequency response analysis of a dancer or a roller mounted on load cells reveals that such devices are severely limited in their ability to sense the dynamic tension in a web. The response of a tension control system may therefore be limited by the dynamics of the sensor instead of the drive motor and its controller.

Natural frequencies of rollers in translation and rotation are shown to limit the bandwidth of tension control systems. Dancers are shown to often increase dynamic tension variations when compared to a simple span of web, instead of performing their intended function of reducing or eliminating these variations.

Transfer functions of web dynamics reveal that a tension control system may appear to be one "type" (as defined by the number of pure integrations in the open loop), but the tension output does not benefit from the integrations, yet the control system suffers the difficulty of stabilization associated with integration(s). A dancer which controls a torque device (contrasted with control of velocity) is particularly difficult to stabilize because of the double integration (type 2) and the great variations of important parameters.

Dimensionless groups of parameters were developed for evaluation of the performance of roller-reaction sensors of tension. Performance is shown to depend upon the stiffness and velocity of the web, as well as such parameters of machine design as the number of the idlers between the driven rollers, mass and radius of each roller, stiffness of the load cells, and lengths of spans between drive stations. A subgroup of parameters (not dimensionless) is the inertia of a roller divided by the square of its radius. Because this subgroup is never separated into its two components, the inertia by itself is unimportant.