A model of machine-direction tension variations in paper webs with runnability applications

Abstract

We developed a model of web dynamics to investigate tension (strain) variations, which play a major role in runnability and paper breaks.We focus on a simplified version of the model, which is valid for low-frequency tension variations (<100 Hz). The model predicts abrupt changes in the web speed and tension at contact points where external forces are applied, high strain rates at nip contacts, and tension surges during start-up, as observed in many pressrooms. We prove that the mechanical draw is an accurate estimate of the strain increment for time-independent, but not fluctuating, web speeds. We also investigate the impact of out-of-round rolls on runnability by coupling the web dynamics model to a weak-link model of web failure. We find that, for moderate roll deformations (<5 mm), the out-of-roundness contributes statistically to the increase in break frequency. The risk of web breaks is significant for extreme deformations (>6 mm), especially when a new roll begins unwinding.