Elasto-Aerodynamic Lubrication Analysis of a Self-Acting Foil Air Journal Bearing

Abstract

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 steadystate 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.This step is necessary to solve the first-order complex dynamic Equations (22) and (23). METHOD OF SOLUTION UNDER DYNAMIC CONDITIONSThe procedure for obtaining a numerical solution to the elasto-aerodynamic problem under dynamic conditions is outlined as follows:Set the initial value of the frequency ratio g (e.g. g = 1 corresponding to a synchronous excitation). Solve the linear partial differential Equations (22) and (23) over the finite difference grid with successive over-relaxation scheme to obtain the complex dynamic pressuresQ e andQ f (Figure 8). It should Figure 13. Example of the coded half fluid-film domain. (À) Ambient or subambient static pressure region. (+) Over-ambient static pressure region.Figure 12. 3D view of the steady-state pressure field calculated without the subambient pressures.

Simulation of Static Performance of Air Foil Bearings Using Coupled Finite Element and Computational Fluid Dynamics Techniques

“…The journal's rotational speed is set to 38,000rpm, its radius is 25 mm, the AFB's length is 50 mm, the top foil's thickness is 0.102 mm, the radial clearance is set to 50 fim, the bump foil consists of 35 bumps, and the angle of the top foil is 355 degrees. This configuration is used by Bensouilah et al [5]. Figure 5 illustrates the pressure contour plot for eccentricity ratio 0.8.…”

“…Moreover, the angle between the maximum absolute values of the two lobes is 90 degrees. According to the Bensouilah [5] model, the maximum and minimum pressures are 1.65 and 0.75, respectively, and the angle between the lobes is also 90 degrees. The minimum value presents a deviation, possibly because NavierStokes equations are solved in our model, whereas the reference model uses the Reynolds equations.…”

“…Bensouilah et al [5] performed an elastoaerodynamic analysis of a self-acting air foil bearing. This study was based on a model that was analyzed using the finite element and finite difference method.…”

Analysis of couple‐stress effects in gas foil bearings using the V. K. Stokes micro‐continuum theory

“…For a compliant cylindrical bearing, the film thickness h is defined by the following expression: where C is the bearing radial clearance, X and Y are the Cartesian coordinates of the shaft centre, and is the scalar compliance operator of the bump foil in (m Pa −1 ) according to the Heshmat's analytical model by modelling the corrugated sub‐foil as a simple Winkler elastic foundation with isotropic stiffness K r as shown in Figure .…”

Hydrodynamic analysis of multileaf gas foil bearing with backing springs

“…These characteristics have expanded the applications of gas foil bearings to a large extent in auxiliary power units, gas turbines and turbochargers in the past 30 years. [2][3][4][5][6][7][8] Gas foil bearings have a huge application potential to meet the requirements of advanced high performance rotating machinery, but the lack of reliable prediction and design guidelines has hindered their technological progress in high-speed machineries, especially for multileaf foil bearings. Although multileaf foil bearings have been practically applied since the 1970s, the design methodology and calculations still have not been fully developed so that all actual products have to evolve from empirical research.…”