Dynamic Analysis of Three-Foil Rotor Support System in Zero Gravity Environment

The dynamic and static behavior of a gas lubricated bearing, consisting of stretched foil sectors, is analyzed. General equations describing the fluid film and valid for shaft excursions of the order of the clearance, are derived on the basis of planar motion and negligible fluid inertia. The analysis is then specialized to the case of a bearing consisting of three equally spaced foil sectors. For the static equilibrium condition, tensions and gaps are calculated and graphs are presented. For the dynamic case, the basic equations are linearized, and equations for the in and out-of-phase steady-state response to sinusoidal excitation are derived. This serves as an illustration of foil-bearing dynamic behavior as well as for stability investigation. For the case of zero radial load, the effects of speed, rotor radius, foil thickness, wrap angle, and initial tension on the coefficients of damping and stiffness are graphically presented. Within the range of parameters investigated, the following distinct characteristics of the foil bearing have been found: (a) The bearing is stable. (b) The stiffness coefficient is not sensitive to half frequency excitation nor to excitation of any other frequency. (c) The damping coefficient assumes nearly zero values whenever the ratio of frequency of excitation to frequency of rotation is an integral multiple of π/Θ, where Θ is the wrap angle. (d) In contrast with other fluid-film bearings, the increase in mass has no unstabilizing effect.