Predictive Models of Web-to-Roller Traction

We studied the traction developed between a thin, flexible web and a rotating circumferentially grooved cylindrical roller. We have developed 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 have verified this model experimentally on a series of 14 rollers and 19 webs. We tested both nongrooved and circumferentially grooved rollers. We showed experimentally that rough, ungrooved rollers that have their low areas unconnected produce significantly lower traction and do not fit the model introduced here. Such rollers should be avoided where traction is important. We introduce dimensionless groups that the roller designer can use to quantitatively assess the interactions of process variables (e.g., speed, tension, etc.) with design variables (e.g., groove depth, groove pitch, roughness, etc.) over the full range of practical wrap angles.