A very simple design method for an aerodynamic compliant foil thrust bearing is presented in this paper. It is based on 3D modeling (called: complete direct calculation) of the elastoaerodynamic problem. In this approach, the structural analysis has been simplified. This enables the calculation to be carried out faster. However this model, based on the resolution of the Reynolds equation, only gives the performance of a thrust bearing for a given geometric profile. An efficient method for solving the inverse problem for predicting the desired bearing performance parameters is presented. The complete direct calculation is only used to improve the profile geometry thus found. Finally, the proposed method has been applied for the design of a 80 mm outer diameter 40 mm inner diameter thrust bearing operating between 20,000 and 50,000 rpm. It is shown that the thrust bearing designed by this approach has a high load capacity (300 kPa) at a speed of 50,000 rpm. It is also shown that the predicted performance of the bearing agrees well with the complete direct calculation.

Analysis of an Aerodynamic Compliant Foil Thrust Bearing: Method for a Rapid Design

Analytical Model of Bump-Type Foil Bearings Using a Link-Spring Structure and a Finite-Element Shell Model

Load performance of gas lubricated, compliant surface foil thrust bearings has an interlocking relationship with the compliance of the bearing and hydrodynamics of convergent wedge surface. Compliance of the bearing consists of supporting spring elements (elastic foundation) and a smooth elastic top foil. In this paper, a class of gas lubricated foil thrust bearings has been investigated analytically utilizing a novel approach which combines Finite Difference (FD) and Finite Element (FE) methods. Solution of the governing hydrodynamic equations dealing with compressible fluid is coupled with the structural resiliency of the foil bearing surfaces. FD method is utilized for hydrodynamic analysis while FE is used to model structural resiliency. Influence coefficients were generated to address the elasticity effects of combined top foil and elastic foundation on the hydrodynamics of thrust bearing, and were used to expedite the numerical solution. Within 2 to 3 iterations the convergence criterion was reached. The overall program logic proved to be an efficient technique to deal with the complex structural compliance of various foil bearing. Case study has been conducted and sample solutions are provided. Unlike prior analytical investigations, the essential effect of the top foil on the performance of the bearing has been elucidated.

Analysis of Gas Lubricated Foil Thrust Bearings Using Coupled Finite Element and Finite Difference Methods

Analysis of gas foil bearings integrating FE top foil models

Widespread usage of gas foil bearings (FBs) into microturbomachinery to midsize gas turbine engines requires accurate performance predictions anchored to reliable test data. This paper presents a simple yet accurate model predicting the static and dynamic force characteristics of gas FBs. The analysis couples the Reynolds equation for a thin gas film to a simple elastic foundation model for the top foil and bump strip layer. An exact flow advection model is adopted to solve the partial differential equations for the zeroth- and first-order pressure fields that render the FB load capacity and freguency-dependent force coefficients. As the static load imposed on the foil bearing increases, predictions show that the journal center displaces to eccentricities exceeding the bearing nominal clearance. A nearly constant FB static stiffness, independent of journal speed, is estimated for operation with large loads, and approaching closely the bearing structural stiffness derived from contact operation without rotor spinning. Predicted minimum film thickness and journal attitude angle demonstrate good agreement with archival test data for a first-generation gas FB. The bump-foil-strip structural loss factor, exemplifying a dry-friction dissipation mechanism, aids to largely enhance the bearing direct damping force coefficients. At high loads, the bump-foil structure influences most the stiffness and damping coefficients. The predictions demonstrate that FBs have greatly different static and dynamic force characteristics when operating at journal eccentricities in excess of the bearing clearance from those obtained for operation at low loads, i.e., small journal eccentricity.

Heavily Loaded Gas Foil Bearings: A Model Anchored to Test Data

Evaluation des caracteristiques de fonctionnement d'un palier a gaz utilisant comme surface portante une feuille metallique souple supportee par un systeme elastique. Analyse donnant l'influence des differentes variables de construction et de fonctionnement sur le comportement du palier, les solutions etant presentees sous forme de graphiques ou de tableaux. Caracteristiques de conception souhaitables quant au depart de l'arc, au choix de l'angle de charge, au nombre de patins, et au degre de souplesse

J. A. Walowit

Papers

Analysis of Gas-Lubricated Foil Journal Bearings

Analysis of Gas Lubricated Compliant Thrust Bearings