Experimental and analytical studies on air foil bearings have been performed extensively over the past decades, and significant improvement in load capacity and rotor dynamics stability have been reported. Often, advanced air foil bearings are believed to have complicated bump foil structure to provide unique underlying support mechanism, which in turn make the bearing very stable and have high load capacity. However, all the analytical studies on air foil bearings so far assume a circular profile of top foil with uniform bump stiffness distribution because detailed information on bump stiffness distribution and overall bearing shape is not known to the public. This paper investigates load capacities and rotordynamic performances of two different types of air foil bearings, e.g., circular cylindrical bearings with single continuous top foil and noncircular preloaded bearings with three top foil pads. Within the two subcategories, stiffness variations along axial and circumferential directions were given to have a total of four types of air foil bearings with different overall bearing shapes and stiffness distributions. Overall static and dynamic performance of the four different types of air foil bearings are presented and compared via calculations of load capacities and dynamic force coefficients, modal stability analyses, and time domain orbit simulations. The major difference of load capacities comes from the overall bearing shape (circular continuous foil or preloaded three pad) rather than spatial variation of bump stiffness within the bump foils. Preloaded three-pad bearings have significantly reduced load capacity compared to the circular bearings because of small pad arc length. Rotordynamic performance is also much more sensitive to the overall bearing shape than spatial variation of bump stiffness and damping within the bump foils. The linear stability analyses predict modal natural frequencies very close to those from the orbit simulations. However, onset speeds of instability from these two approaches are quite different, manifesting the limitation of the linear stability analyses. The orbit simulations show the three-pad bearings have higher onset speeds of instability than circular bearing (47,000 rpm versus 24,000 rpm).

Parametric Studies on Static and Dynamic Performance of Air Foil Bearings with Different Top Foil Geometries and Bump Stiffness Distributions

Computational methods were used to analyse the elasto-hydrodynamic lubrication of a complex rotor–bearing system. The methodology employed computational fluid dynamics (CFD), based on the Navier–Stokes equation and a fluid–structure interaction (FSI) technique. A series of models representing the system were built using the CFD–FSI methodology to investigate the interaction between the lubrication of the fluid film, and elastic dynamics of the rotor and journal bearing. All models followed an assumption of isothermal behaviour. The FSI methodology was implemented by setting nodal forces and displacements to equilibrium at the fluid–structure interface, therefore allowing the lubrication of the fluid and the elastic deformation of structures to be solved simultaneously. This is significantly different to the more common techniques—such as the Reynolds equation method—that use an iterative solution to balance the imposed load and the force resulting from the pressure of the fluid film to within a set tolerance. Predictions using the CFD–FSI method were compared with the results of an experimental study and the predictions from an ‘in-house’ lubrication code based on the Reynolds equation. The dynamic response of the system was investigated with both rigid and flexible bodies for a range of different bearing materials and dynamic unbalanced loads. Cavitation within the fluid film was represented in the CFD–FSI method using a simplified phase change boundary condition. This allowed the transition between the liquid and vapour phases to be derived from the lubricant’s properties as a function of pressure. The combination of CFD and FSI was shown to be a useful tool for the investigation of the hydrodynamic and elasto-hydrodynamic lubrications of a rotor–bearing system. The elastic deformation of the bearing and dynamic unbalanced loading of the rotor had significant effects on the position of its locus.

Application of Computational Fluid Dynamics and Fluid–Structure Interaction Method to the Lubrication Study of a Rotor–Bearing System

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

Analysis of gas foil bearings integrating FE top foil models

Forced nonlinear response of gas foil bearing supported rotors

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

Gas foil bearings (GFBs) find widespread usage in oil-free turbo expanders, APUs and micro gas turbines for distributed power due to their low drag friction and ability to tolerate high level vibrations, including transient rubs and shaft misalignment, static and dynamic. The static load capacity and dynamic forced performance of GFBs depends largely on the material properties of the support elastic structure, i.e. a smooth foil on top of bump strips. Conventional models include only the bumps as an equivalent stiffness uniformly distributed around the bearing circumference. More complex models couple directly the elastic deformations of the top foil to the bump underlying structure as well as to the hydrodynamics of the gas film. This paper details two FE models for the top foil supported on bump strips, one considers a 2D shell anisotropic structure and the other a 1D beam-like structure. The Cholesky decomposition of the stiffness matrix representing the top foil and bump strips is performed off-line prior to computations coupling it to the gas film analysis governed by Reynolds equation. The procedure greatly enhances the computational efficiency of the numerical scheme. Predictions of journal attitude angle and minimum film thickness for increasing static loads and two journal speeds are obtained for a GFB tested decades ago. 2D FE model predictions overestimate the minimum film thickness at the bearing centerline, while underestimating it at the bearing edges. Predictions from the 1D FE model compare best to the limited tests data; reproducing closely the experimental circumferential wavy-like minimum film thickness profile. The 1D top foil model is recommended due to its low computational cost. Predicted stiffness and damping coefficients versus excitation frequency show that the two FE top foil structural models result in slightly lower direct stiffness and damping coefficients than those from the simple elastic foundation model.Copyright © 2007 by ASME

Improvements to the Analysis of Gas Foil Bearings: Integration of Top Foil 1D and 2D Structural Models

High performance oil-free turbomachinery implements gas foil bearings (FBs) to improve mechanical efficiency in compact units. FB design, however, is still largely empirical due to their mechanical complexity. The paper provides test results for the structural parameters in a bump-type foil bearing. The stiffness and damping (Coulomb or viscous type) coefficients characterize the bearing compliant structure. The test bearing, 38.1 mm in diameter and length, consists of a thin top foil supported on bump-foil strips. A prior investigation identified the stiffness due to static loads. Presently, the test FB is mounted on a non-rotating stiff shaft and a shaker exerts single frequency loads on the bearing. The dynamic tests are conducted at shaft surface temperatures from 25 °C to 75°C. Time and frequency domain methods are implemented to determine the FB parameters from the recorded periodic load and bearing motions. Both methods deliver identical parameters. The dry friction coefficient ranges from 0.05 to 0.20, increasing as the amplitude of load increases. The recorded motions evidence a resonance at the system natural frequency, i.e. null damping. The test derived equivalent viscous damping is inversely proportional to the motion amplitude and excitation frequency. The characteristic stick-slip of dry friction is dominant at small amplitude dynamic loads leading to a hardening effect (stiffening) of the FB structure. The operating temperature produces shaft growth generating a bearing preload. However, the temperature does not affect significantly the identified FB parameters, albeit the experimental range was too small considering the bearings intended use in industry.Copyright © 2005 by ASME

Structural Stiffness, Dry-Friction Coefficient and Equivalent Viscous Damping in a Bump-Type Foil Gas Bearing

Current trends for advanced automotive engines focusing on downsizing, better fuel efficiency and lower emissions have led to several changes in turbocharger bearing systems design and technology. Automotive turbochargers run faster and use engine oils with very low viscosity under high oil inlet temperature and low feed pressure. The development of high performing bearing systems, marrying innovation with reliability, is a persistent challenge. This paper shows progress on the nonlinear dynamic behavior modeling of rotor-radial bearing system (RBS) incorporating two oil films in series: a hydrodynamic one with a squeeze film damper commonly used in turbochargers. The developed fluid bearing code predicts bearing rotational speed (in case of fully floating design), operating inner and outer bearing film clearances, effective oil viscosity taking into account its shear effect, and hydrostatic load. A rotordynamics code uses this input to predict the nonlinear lateral dynamic response of the rotor-bearing system. The model predictions are validated with test data acquired on a high speed turbocharger RBS of 6.0 mm journal diameter running up to 250,000 rpm (maximum speed), 5W30 oil type, 150 °C oil inlet temperature, and 4 bar oil feed pressure. The tests are conducted at a rotordynamics technology laboratory using a high performance data acquisition system. Turbochargers with four combinations of inner and outer RBS clearances are tested. Prediction and measured synchronous response and total motion are in good agreement. Both demonstrate the nonlinear character of RBS behavior including several subsynchronous frequencies components across the operating speed range. The non linear predictive model aids the development of high performance and optimized turbocharger RBS with faster development cycle times and increased reliability.Copyright © 2007 by ASME

Nonlinear Dynamic Behavior of Turbocharger Rotor-Bearing Systems With Hydrodynamic Oil Film and Squeeze Film Damper in Series: Prediction and Experiment

Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e. simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10 mm. Coast down rotor responses from 25 krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5 krpm to 15 krpm with a whirl frequency at ∼ 50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5 krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings’ side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Post-test inspection reveal wear spots on the top foils and rotor surface.Copyright © 2006 by ASME

Luis San Andre´s

Papers

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

Improvements to the Analysis of Gas Foil Bearings: Integration of Top Foil 1D and 2D Structural Models

Structural Stiffness, Dry-Friction Coefficient and Equivalent Viscous Damping in a Bump-Type Foil Gas Bearing

Nonlinear Dynamic Behavior of Turbocharger Rotor-Bearing Systems With Hydrodynamic Oil Film and Squeeze Film Damper in Series: Prediction and Experiment

Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions