Elasto-aerodynamic lubrication analysis of a self-acting air foil journal bearing

Nowadays, air foil bearings find widespread use in very high speed, lightly loaded oil-free rotating turbomachineries such as compressors and microgas turbines because they have theoretically no speed limitations and they are environmentally benign. In the design of such bearings, it is of cardinal importance to enhance their steady-state and dynamic performance characteristics for the safety operation, especially against the external dynamic excitations. Most of elasto-aerodynamic approaches under dynamic conditions proposed in the technical literature include only the static pressure induced deformation of foils. This paper presents a theoretical investigation on the effects of both static and dynamic deformations of the foils on the dynamic performance characteristics and stability of a self-acting air foil journal bearing operating under small harmonic vibrations. For the dynamic deformations of foils to be taken into account, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number and compliance factor of the bump foil. The rotor-dynamic coefficients serve as input data for the linear stability analysis of rotor-bearing system. The nonlinear stationary Reynolds' equation is solved by means of the Galerkin's finite element formulation, whereas the finite differences method are used to solve the first-order complex dynamic equations resulting from the perturbation of the transient compressible Reynolds' equation. As a first approximation, the corrugated subfoil is modelled as a simple elastic foundation, i.e. the stiffness of a bump is uniformly distributed throughout the bearing surface. It was found that the dynamic properties and stability of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition. Copyright (c) 2012 John Wiley & Sons, Ltd.