Simple model to predict web-to-roller traction

Abstract

We have studied the traction developed between a thin, flexible web and a rotating cylindrical roller. We present a new analytic model for high-wrap, circumferentially grooved rollers that couples air film pressure, web deflection, and asperity contact to predict traction. Our model predicts the "steady state" (far from the ends of the lubrication region) air pressure between the web and roller by judicious use of the foil-bearing concept. We verified our new model experimentally for non-grooved and high-wrap, circumferentially grooved roller surfaces. We have derived dimensionless groups that the roller designer can use to quantitatively assess the interactions of process variables (e.g., speed and tension) with design variables (e.g., groove depth, groove pitch, roughness, etc.). We also give a dimensionless group that quantifies the term high wrap.