Solution of the One Dimensional Foil Bearing Problem Using Matched Asymptotic Expansions

The foil bearing problem describes a longitudinally translating, flexible, tensioned, magnetic tape that rides on a thin film of air as it partially wraps around a stationary recording head. Equilibrium and linear, harmonic vibration analyses of the one dimensional formulation of this problem are performed using matched asymptotic expansions including the effects of tape bending stiffness, compressibility, and molecular slip as regular perturbations. Simple analytic expressions are derived for the nominal film thickness and the vibration frequencies of the free spans. These expressions give designers sharper insight into the usefulness of potential design changes that normally would be evaluated using extensive numerical computations.