Linear dynamic analysis of aero-elastic journal bearings considering both the steady-state and dynamic deformations of foils
Résumé
Air foil bearings find nowadays widespread use in very high speed, lightly loaded oil-free rotating turbo-machinery such as compressors, micro-gas 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 steady-state pressure induced deformation of foils. This work deals with a theoretical investigation on the effects of both steady-state 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. To take into account the dynamic deformations of foils, 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 rotordynamic 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 while 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 sub-foil is modeled as a simple elastic foundation, i. e. the stiffness of a bump is uniformly distributed throughout the bearing surface (first generation foil bearings). 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 steady-state one by applying the principle of superposition.
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