Two-dimensional model to predict web-to-roller traction at small wrap angles

Abstract

We have studied the traction developed between a thin, flexible web and a rotating circumferentially grooved cylindrical roller. The traction model developed by Rice and Gans [1] is inadequate for small wrap angles, because of the two-dimensional nature of the airflow in the entrance nip. We develop a new two-dimensional analytic model that couples air film pressure, web deflection, and asperity contact to predict traction for circumferentially grooved rollers with arbitrary wrap angles. The entrance effects are incorporated into our new traction model by adapting the squeeze film concept using the distance from the entrance as a surrogate for time. We introduce 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.) over the full range of practical wrap angles. Finally, we verify this model experimentally on a series of fourteen rollers and nineteen webs. The roller surfaces range from non-grooved to circumferentially grooved.