Combined stresses for webs going over rollers

Abstract

In research it is typical that only one source of stresses is studied at a time. In entry-level mechanics textbooks, you may see the occasional combined stresses taught where a couple of sources are superposed. Yet, seldom do webs experience only a single significant source of stress. Indeed, most webs in the open web span see two or three sources; any or all of which could be significant. More stresses are added when going over a roller. This paper uses superposition to combine stresses commonly found in web handling including the not-so-'simple' web tensioning due to drive systems, bending due to in-plane roller misalignment and bending due to the radius of curvature of a roller. Bending over rollers has become much more important in recent years with thicker materials, such as electronics made as webs, and with more brittle chemistries, such as about half of all vacuum deposition materials. We also consider residual stresses of manufacturing such as bagginess and curl. Finally, we combine all stresses appropriately and use a safety factor to observe how far from yield the most stressed portion of the web is. This safety factor can serve as a proxy to estimate process reliability with regard to tensile failure of the web due to handling.