Evaluation of the minimum face clearance of a high-speed gas-lubricated bearing with Navier slip boundary conditions under random excitations

Motivated by ongoing developments in aero-engine technology, a model for a coupled gas-lubricated bearing is developed in terms of an extended dynamical system. A slip boundary condition, characterised by a slip length, is incorporated on the bearing faces which can be relevant for operation in non-ideal extreme conditions, notably where external vibrations or disturbances could destabilise the bearing. A modified Reynolds equation is formulated to model the gas flow, retaining the effects of centrifugal inertia which is increasingly important for high-speed operation, and is coupled to the structural equations; spring-mass-damper systems model the axial stator and rotor displacements. A novel model is developed corresponding to a bearing experiencing an external random force to evaluate the resulting induced displacements of the bearing components. The minimum face clearance is obtained from a mapping solver for the modified Reynolds equation and structural equations simultaneously. In the case of random excitations, the solver is combined with a Monte Carlo technique. Evaluation of the average value of the minimum gap and the probability of the gap reaching a prescribed tolerance are provided. Extensive insight is given on the effect of key bearing parameters on the corresponding bearing dynamics.