On the governing equation for web tension with out-of-round rolls

Abstract

In roll-to-roll (R2R) manufacturing the presence of non-ideal elements, such as out-of-round or eccentric rolls, induces periodical oscillations in the web tension signal. Model simulations based on ideal elements do not exhibit these tension oscillations but can only follow the measured tension signal in an average sense. In order for the models to predict these measured tension oscillations due to non-ideal elements, the derivation of governing equations must consider a mechanism to include the correct behavior of the non-ideal transport elements. Continuing with our previous work on this topic presented at previous IWEBs, we present additional results that provide improvements to the web span tension governing equation which can better predict measured tension signals. In particular, this work is useful for tension control in the unwind section of the web line when the unwind material roll is often out-of-round.