Dynamics of a small gap gas lubricated bearing with Navier slip boundary conditions

A gas lubricated bearing model is derived which is appropriate for a very small bearing face separation by including velocity slip boundary conditions and centrifugal inertia effects. The bearing dynamics is examined when an external harmonic force is imposed on the bearing due to the bearing being situated within a larger complex dynamical system. A compressible Reynolds equation is formulated for the gas film which is coupled to the bearing structure through an axial force balance where the rotor and stator correspond to spring-mass-damper systems. Surface slip boundary conditions are derived on the bearing faces, characterised by the slip length parameter. The coupled bearing system is analysed using a stroboscopic map solver with the modified Reynolds equation and structural equations solved simultaneously. For a sufficiently large forcing amplitude a flapping motion of the bearing faces is induced when the rotor and stator are in close proximity. The minimum bearing gap over the time period of the external forcing is examined for a range of bearing parameters.