FREE LINEAR VIBRATION OF SELF-PRESSURIZED FOIL BEARINGS

A foil bearing is formed when a flexible medium travels across a stati onary rigid surface and entrains a thin layer of fluid that lubricates the relative sliding motion. Such bearings are used in magnetic tape drives to prevent excessive wear of the recording head and tape interf ace. In the one-dimensional model considered here, the tape is approxi mated as an axially-moving Euler-Bernoulli beam under tension, and the air pressure in the bearing region satisfies Reynolds equation for un steady compressible flo w. To the extent that transverse deformation o f the tape couples with the air pressure, the ''foil bearing problem'' falls within the discipline of elastohydrodynamic lubrication. The go verning equations for the tape and recording head are linearized about the equilibrium displacement and pressure fields, and the two resulti ng coupled partial differential equations with nonconstant coefficient s describe the linear response. Following global discretization throug h Galerkin's method, the natural frequencies, damping, and mode shapes of the tape and recording head system are determined through numerica l solution of the generalized matrix eigenvalue problem. The coupled d isplacement and pressure modes depend on the transport speed, and they are complex because of viscous dissipation of the air and convection of the tape. For the illustrative case of a semicircular recording hea d, the dependence of the system's eigenvalues on the transport speed, and on the location of the recording head within the tape's span, is d iscussed.