Centrifugal inertia effects in high-speed hydrostatic air thrust bearings

A modified Reynolds equation for compressible flow is used to model the dynamics of pressurised air bearings in a simplified axisymmetric geometry. The formulation incorporates the effect of centrifugal inertia for high-speed operation. A steady-state analysis is presented with a fixed rotor–stator clearance. The load-carrying capacity of the bearing is assessed for both inward and outward pressurisation and the air-flow characteristics are seen to depend on the level and direction of pressurisation. A critical shaft speed is identified that maintains no-net flow by balancing inertia and pressurisation effects. The nonlinear air–rotor–stator dynamics are investigated by modelling the axial stator position using a spring–mass–damper system coupled to the air-film dynamics. Solutions are presented to illustrate the effect of various frequencies and amplitudes of forcing for a range of rotation speeds. The time-averaged axial force and mass flow of air are used as characteristic measures of bearing performance, and further numerical results are presented as part of a parameter space analysis. Using the method of arc-length continuation key measures of the numerical solutions are tracked for changing values of the physical parameters. The minimum rotor–stator clearance is used to evaluate the limit of stable periodic operation without resonant stator dynamics and incorporating high operating speeds.