Computations of air films and pressures between webs and rollers for steady and unsteady operating conditions

Abstract

Numerical computations have been performed to predict the lubricating air film thickness and pressure for the entire region of smooth rotating support rollers wrapped by moving impermeable and permeable webs. Results have been obtained for both steady and unsteady web tensions for a range of operating parameters and web properties. The numerical predictions required the simultaneous solution of coupled partial differential equations. One equation is the dynamic motion equation for the finite length web and the other is the transient Reynolds lubrication equation for the air film. In these two-dimensional computations, the web is assumed perfectly flexible and infinitely wide, with negligible air escape at the edges. A finite difference formulation was developed for the two governing partial differential equations. Spacing and pressure between the moving web and the support roller were obtained as a function of both time and distance along the roller for cases of constant tension, step changes in tension, and sinusoidal fluctuations in tension. For constant tension, the transient solution converges to the steady state solution from approximate initial conditions. For the unsteady tension cases, computations are started from a steady state solution. The effects of the web velocity, tension, permeability, mass per unit area, roller velocity, radius, and slip flow on the air film thickness and pressure distribution were predicted.