Equilibrium Analysis of Finite Width Tension Dominated Foil Bearings

A foil bearing is formed when a flexible material passes over a stationary rigid surface and entrains a thin layer of air that lubricates the relative motion. Some applications include the transport of magnetic tape, and the manufacturing of paper and metal sheets. In each case, the transverse displacement of the moving medium couples with the air film’s pressure, requiring simultaneous solution of the governing elastic and lubrication equations. Such simulations can become computationally intensive, particularly when the model incorporates the finite width effects of side flow and cross-web deformation. Of primary focus in this paper is the development of an efficient numerical algorithm for such simulations. Two improvements in that regard are discussed: inexact Newton iteration and adaptive nodal point placement. In two case studies adapted from the literature, implementation of these techniques offered roughly five-fold improvements in computational effort when the equilibrium film thickness, air pressure, and web displacement were calculated. The key advantages of the approach are a more rapid convergence rate, and the opportunity to use fewer degrees of freedom in describing the pressure and film thickness since the nodes are assigned automatically during iteration to regions where the solution is most rapidly changing.