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

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Tae Ho Kim ◽  
Luis San Andrés
Keyword(s):  
Test Data ◽  
Load Capacity ◽  
Dynamic Force ◽  
Damping Force ◽  
Rotor Spinning ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Foundation Model ◽  
Accurate Performance ◽  
Force Characteristics

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 frequency-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

2005 ◽  
Author(s):  
Tae Ho Kim ◽  
Luis San Andre´s
Keyword(s):  
Test Data ◽  
Load Capacity ◽  
Stable Operation ◽  
Dynamic Force ◽  
Damping Force ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Foundation Model ◽  
Accurate Performance ◽  
Force Characteristics

Widespread usage of gas foil bearings (FBs) into micro turbomachinery to midsize gas turbine engines requires accurate performance predictions anchored to reliable test data. The 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 frequency dependent force coefficients. As the static load imposed on the foil bearing increases, predictions show 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 structural stiffness derived from contact operation at null rotor speed. 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 FB whirl frequency ratio (WFR) is examined to ensure its dynamically stable operation. 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 eccentricities.

Analysis of Gas Foil Bearings With Piecewise Linear Elastic Supports

2005 ◽  
Author(s):  
Tae Ho Kim ◽  
Luis San Andre´s
Keyword(s):  
Elastic Foundation ◽  
Load Capacity ◽  
Piecewise Linear ◽  
Thin Film Flow ◽  
Damping Force ◽  
Elastic Supports ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Linear Elastic ◽  
Simple Physical Model

Gas foil bearings (GFBs) rely on their underlying elastic foundation to support radial loads at high rotor speeds. The bump foil strip compliance determines the maximum load capacity with large rotor excursions, well in excess of the bearing nominal clearance. GFBs must be designed properly to permit their reliable (predictable) usage in aircraft engines and other heavy load applications because an elastic foundation that is too soft results in a limited load capacity. Configurations in practical use include a second bump-strip layer or stop-pins underneath the original bumps which become active above a certain load threshold. In these last configurations, the overall stiffness of the support structure has piecewise load versus deflection characteristics. Presently, a simple physical model for GFBs with piecewise linear elastic supports follows. The analysis couples the Reynolds equation for the thin film flow of an ideal gas to the elastic supports motion. An exact flow advection model is adopted to solve the partial differential equations for the zeroth- and first- order pressure fields, thus rendering the GFB load capacity and frequency dependent rotordynamic force coefficients. Predictions show that heavily loaded GFBs comprising two bump layers in series and including stop pins prevent too large bump deflections which may induce permanent plastic deformations. The structural damping or loss factor in a GFB with a two bump strip layer enhances the bearing direct damping force coefficients.

A NONHOMOGENEOUS BULK FLOW MODEL FOR GAS IN LIQUID FLOW ANNULAR SEALS: AN EFFORT TO PRODUCE ENGINEERING RESULTS

2021 ◽  
pp. 1-31
Author(s):  
Xueliang Lu ◽  
Luis San Andres ◽  
Jing Yang
Keyword(s):  
Pressure Drop ◽  
Test Data ◽  
Liquid Flow ◽  
Flow Model ◽  
Bulk Flow ◽  
Experimental Results ◽  
Pure Liquid ◽  
Dynamic Force ◽  
Force Coefficients ◽  
Direct Stiffness

Abstract Seals in multiple phase rotordynamic pumps must operate without compromising system efficiency and stability. Both field operation and laboratory experiments show that seals supplied with a gas in liquid mixture (bubbly flow) can produce rotordynamic instability and excessive rotor vibrations. This paper advances a nonhomogeneous bulk flow model (NHBFM) for the prediction of the leakage and dynamic force coefficients of uniform clearance annular seals lubricated with gas in liquid mixtures. Compared to a homogeneous BFM (HBFM), the current model includes diffusion coefficients in the momentum transport equations and a field equation for the transport of the gas volume fraction (GVF). Published experimental leakage and dynamic force coefficients for two seals supplied with an air in oil mixture whose GVF varies from 0 (pure liquid) to 20% serve to validate the novel model as well as to benchmark it against predictions from a HBFM. The first seal withstands a large pressure drop (~ 38 bar) and the shaft speed equals 7.5 krpm. The second seal restricts a small pressure drop (1.6 bar) as the shaft turns at 3.5 krpm. The first seal is typical as a balance piston whereas the second seal is found as a neck-ring seal in an impeller. For the high pressure seal and inlet GVF = 0.1, the flow is mostly homogeneous as the maximum diffusion velocity at the seal exit plane is just ~0.1% of the liquid flow velocity. Thus, both the NHBFM and HBFM predict similar flow fields, leakage (mass flow rate) and drag torque. The difference between the predicted leakage and measurement is less than 5%. The NHBFM direct stiffness (K) agrees with the experimental results and reduces faster with inlet GVF than the HBFM K. Both direct damping (C) and cross-coupled stiffness (k) increase with inlet GVF < 0.1.Compared to the test data, the two models generally under predict C and k by ~ 25%. Both models deliver a whirl frequency ratio (fw) ~ 0.3 for the pure liquid seal, hence closely matching the test data. fw raises to ~0.35 as the GVF approaches 0.1. For the low pressure seal the flow is laminar, the experimental results and both NHBFM and HBFM predict a null direct stiffness (K). At an inlet GVF = 0.2, the NHBFM predicted added mass (M) is ~30 % below the experimental result while the HBFM predicts a null M. C and k predicted by both models are within the uncertainty of the experimental results. For operation with either a pure liquid or a mixture (GVF = 0.2), both models deliver fw = 0.5 and equal to the experimental finding. The comparisons of predictions against experimental data demonstrate the NHBFM offers a marked improvement, in particular for the direct stiffness (K). The predictions reveal the fluid flow maintains the homogeneous character known at the inlet condition.

Experimental Identification of Dynamic Force Coefficients for a 110 mm Compliantly Damped Hybrid Gas Bearing

2014 ◽  
Author(s):  
Adolfo Delgado
Keyword(s):  
Load Capacity ◽  
Excitation Frequency ◽  
Dynamic Test ◽  
Inlet Pressure ◽  
Dynamic Force ◽  
Metal Mesh ◽  
Gas Bearings ◽  
Force Coefficients ◽  
Test Parameters ◽  
Gas Bearing

Compliant hybrid gas bearings combine key enabling features from both fixed geometry externally pressurized gas bearings and compliant foil bearings. The compliant hybrid bearing relies on both hydrostatic and hydrodynamic film pressures to generate load capacity and stiffness to the rotor system, while providing damping through integrally mounted metal mesh bearing support dampers. This paper presents experimentally identified force coefficients for a 110 mm compliantly damped gas bearing using a controlled-motion test rig. Test parameters include hydrostatic inlet pressure, excitation frequency, and rotor speed. The experiments were structured to evaluate the feasibility of implementing these bearings in large size turbomachinery. Dynamic test results indicate weak dependency of equivalent direct stiffness coefficients to most test parameters except for frequency and speed, where higher speeds and excitation frequency decreased equivalent bearing stiffness values. The bearing system equivalent direct damping was negatively impacted by increased inlet pressure and excitation frequency, while the cross-coupled force coefficients showed values an order of magnitude lower than the direct coefficients. The experiments also include orbital excitations to simulate unbalance response representative of a target machine while synchronously traversing a critical speed. The results indicate that the gas bearing can accommodate vibration levels larger than the set bore clearance while maintaining satisfactory damping levels.

Leakage and Dynamic Force Coefficients of a Pocket Damper Seal Operating Under a Wet Gas Condition: Tests Versus Predictions

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Jing Yang ◽  
Luis San Andrés ◽  
Xueliang Lu
Keyword(s):  
Test Data ◽  
Mass Flow ◽  
Mass Fraction ◽  
Dynamic Stiffness ◽  
Dynamic Force ◽  
Rotor Speed ◽  
Force Coefficients ◽  
Supply Pressure ◽  
Liquid Mass ◽  
Wet Gas

AbstractHigh-performance centrifugal compressors presently favor pocket damper seals (PDSs) as a choice of secondary flow control element offering a large effective damping coefficient to mitigate rotor subsynchronous whirl motions. Current and upcoming multiple-phase compression systems in subsea production facilities must demonstrate long-term operation and continuous availability, free of harmful rotor instabilities. Plain annular seals and labyrinth (LABY) seals are notoriously bad choices, whereas a PDS, by stopping the circulation of trapped liquid, operates stably. This paper presents experimental and computational fluid dynamics (CFD) results for the leakage and dynamic force coefficients obtained in a dedicated test facility hosting a fully partitioned PDS (FPPDS), four ribbed and with eight pockets per cavity. The test PDS, operating at a rotor speed 5250 rpm (surface speed 35 m/s) and under a supply pressure/discharge pressure ratio up to 3.2, is supplied with a mixture of air and ISO VG 10 oil whose maximum liquid volume fraction (LVF) is 2.2%, equivalent to a liquid mass fraction of 84%. When supplied with just air (dry condition), the measured leakage increases nonlinearly with supply pressure. Under a wet gas condition, the recorded mass flow increases on account of the large difference in density between the liquid and the gas. CFD-derived mass flow rates for both dry and wet gas conditions agree with the measured ones. The test dry gas PDS produces a direct dynamic stiffness (HR) increasing with frequency, whereas the direct damping (C) and cross-coupled dynamic stiffness (hR) coefficients remain relatively constant. The CFD-predicted damping agrees best with the test C albeit overpredicting HR at low excitation frequencies and hR at all frequencies (<175 Hz ∼ twice rotor speed). Under a wet gas condition with LVF  =  0.4%, the test force coefficients show great variability over the excitation frequency range; in particular, HR < 0, though growing with frequency due to the large liquid mass fraction. The CFD predictions, on the other hand, produce a dynamic direct stiffness HR > 0 for all frequencies. Both experimental hR and C for the wet gas PDS are larger than their counterparts for the dry gas seal. The CFD-predicted C and hR, wet versus dry, show a modest growth, yet remaining lower than the test data. The CFD-derived flow field for a wet gas condition shows that the seal radial partition walls (ridges) reduce the circumferential flow velocity and liquid accumulation within a pocket. Both the test data and the CFD prediction show that the magnitude of the flexibility function for the PDS test system reduces when the two-component mixture flows through the seal, hence revealing the additional effective damping, more pronounced for the test data rather than that from the predictions. Further work, experimental and CFD based, will continue to advance the technology of wet gas seals while bridging the gap between test data and computational physics model simulations.

Leakage and Dynamic Force Coefficients of a Pocket Damper Seal Operating Under a Wet Gas Condition: Tests vs. Predictions

2019 ◽  
Author(s):  
Jing Yang ◽  
Luis San Andrés ◽  
Xueliang Lu
Keyword(s):  
Test Data ◽  
Mass Flow ◽  
Mass Fraction ◽  
Dynamic Stiffness ◽  
Dynamic Force ◽  
Rotor Speed ◽  
Force Coefficients ◽  
Supply Pressure ◽  
Liquid Mass ◽  
Wet Gas

Abstract High performance centrifugal compressors presently favor pocket damper seals (PDSs) as a choice of secondary flow control element offering a large effective damping coefficient to mitigate rotor sub synchronous whirl motions. Current and upcoming multiple-phase compression systems in subsea production facilities must demonstrate long term operation and continuous availability, free of harmful rotor instabilities. Plain annular seals and labyrinth seals are notoriously bad choices, whereas a PDS, by stopping the circulation of trapped liquid, operates stably. This paper presents experimental and computational fluid dynamics (CFD) results for the leakage and dynamic force coefficients obtained in a dedicated test facility hosting a fully partitioned PDS, four ribbed and with eight pockets per cavity. The test PDS, operating at a rotor speed 5,250 rpm (surface speed 35 m/s) and under a supply pressure/discharge pressure ratio up to 3.2, is supplied with a mixture of air and ISO VG 10 oil whose maximum liquid volume fraction (LVF) is 2.2%, equivalent to a liquid mass fraction of 84%. When supplied with just air (dry condition), the measured leakage increases nonlinearly with supply pressure. Under a wet gas condition, the recorded mass flow increases on account of the large difference in density between the liquid and the gas. CFD derived mass flow rates for both dry and wet gas conditions agree with the measured ones. The test dry gas PDS produces a direct dynamic stiffness (HR) increasing with frequency whereas the direct damping (C) and cross-coupled dynamic stiffness (hR) coefficients remain relatively constant. The CFD predicted damping agrees best with the test C albeit over predicting HR at low excitation frequencies and hR at all frequencies (< 175 Hz ∼ twice rotor speed). Under a wet gas condition with LVF = 0.4%, the test force coefficients show great variability over the excitation frequency range; in particular HR < 0, though growing with frequency due to the large liquid mass fraction. The CFD predictions, on the other hand, produce a dynamic direct stiffness HR > 0 for all frequencies. Both experimental hR and C for the wet gas PDS are larger than their counterparts for the dry gas seal. The CFD predicted C and hR, wet vs. dry, show a modest growth, yet remaining lower than the test data. The CFD derived flow field for a wet gas condition shows the seal radial partition walls (ridges) reduce the circumferential flow velocity and liquid accumulation within a pocket. Both the test data and CFD prediction show that the magnitude of the flexibility function for the PDS test system reduces when the two component mixture flows through the seal, hence revealing the additional effective damping, more pronounced for the test data rather than that from the predictions. Further work, experimental and CFD based, will continue to advance the technology of wet gas seals while bridging the gap between test data and computational physics model simulations.

Effects of Mesh Density on Static Load Performance of Metal Mesh Gas Foil Bearings

2011 ◽  
Author(s):  
Yong-Bok Lee ◽  
Chang Ho Kim ◽  
Tae Ho Kim ◽  
Tae Young Kim
Keyword(s):  
Test Data ◽  
Loss Factor ◽  
Static Load ◽  
Stiffness Coefficient ◽  
Metal Mesh ◽  
Rotor Spinning ◽  
Foil Bearings ◽  
Mesh Density ◽  
Damping Loss Factor ◽  
Mesh Structures

Metal mesh materials have been used successfully in vibration isolators and bearing dampers due to their superior friction or hysteresis damping mechanism. These materials are formed to metal mesh (or wire mesh) structures in ring-shape by compressing a weave of metal wires, in general. Recently, oil-free rotating machinery implement metal mesh structures into hydrodynamic gas foil bearings by replacing bump strip layers with them, to increase its bearing structural damping. A metal mesh foil bearing (MMFB) consists of a top foil and support elastic metal mesh pads installed between a rotating shaft and a housing. The present research presents load capacity tests of a MMFB at rotor rest (0 rpm) and 30 krpm for three metal mesh densities of 13.1%, 23.2%, and 31.6%. The metal mesh pad of test MMFB is made using a stainless steel wire with a diameter of 0.15 mm. Test rig comprises a rigid rotor with a diameter of 60 mm supported on two ball bearings at both ends and test MMFB with an axial length of 50 mm floats on the rotor. Static loads is provided with a mechanical loading device on test MMFB and a strain gauge type load cell measures the applied static loads. A series of static load versus deflection tests were conducted for selected metal mesh densities at rest (0 rpm). Test data are compared to further test results of static load versus journal eccentricity recorded at the rotor speed of 30 krpm. Test data show a strong nonlinearity of bearing deflection (journal eccentricity) with static load, independent of rotor spinning. Observed hysteresis loops imply significant structural damping of test MMFB. Measured journal deflections at 0 rpm are in similar trend to recorded journal eccentricities at the finite rotor speed, thus implying that the MMFB performance depends mainly on the metal mesh structures. The paper also estimates linearlized stiffness coefficient and damping loss factor of test MMFB using the measured static load versus deflection test data at 0 rpm and 30 krpm. The results show that the highest mesh density of 31.6% produces highest linearlized stiffness coefficient and damping loss factor. With rotor spinning at 30 krpm, the linearlized stiffness coefficient and damping loss factor decrease slightly, independent of metal mesh densities. The present test data will serve as a database for benchmarking MMFB predictive models.

A Metal Mesh Foil Bearing and a Bump-Type Foil Bearing: Comparison of Performance for Two Similar Size Gas Bearings

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Luis San Andrés ◽  
Thomas Abraham Chirathadam
Keyword(s):  
Manufacturing Cost ◽  
Dynamic Force ◽  
Metal Mesh ◽  
Gas Bearings ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Advantages And Disadvantages ◽  
Foil Bearing ◽  
Start Up ◽  
Lift Off

Gas bearings in oil-free microturbomachinery for gas process applications and power generation (<400 kW) must be reliable and inexpensive, ensuring low drag power and thermal stability. Bump-type foil bearings (BFBs) and overleaf-type foil bearings are in use in specialized applications, though their development time (design and prototyping), exotic materials, and excessive manufacturing cost still prevent their widespread usage. Metal mesh foil bearings (MMFBs), on the other hand, are an inexpensive alternative that use common materials and no restrictions on intellectual property. Laboratory testing shows that prototype MMFBs perform similarly as typical BFBs, but offer significantly larger damping to dissipate mechanical energy due to rotor vibrations. This paper details a one-to-one comparison of the static and dynamic forced performance characteristics of a MMFB against a BFB of similar size and showcases the advantages and disadvantages of MMFBs. The bearings for comparison are a generation I BFB and a MMFB, both with a slenderness ratio L/D = 1.04. Measurements of rotor lift-off speed and drag friction at start-up and airborne conditions were conducted for rotor speeds to 70 krpm and under identical specific loads (W/LD = 0.06 to 0.26 bar). Static load versus bearing elastic deflection tests evidence a typical hardening nonlinearity with mechanical hysteresis, the MMFB showing two to three times more material damping than the BFB. The MMFB exhibits larger drag torques during rotor start-up, and shut-down tests though bearing lift-off happens at lower rotor speeds (∼15 krpm). As the rotor becomes airborne, both bearings offer very low drag friction coefficients, ∼0.03 for the MMFB and ∼0.04 for the BFB in the speed range 20–40 krpm. With the bearings floating on a journal spinning at 50 krpm, the MMFB dynamic direct force coefficients show little frequency dependency, while the BFB stiffness and damping increases with frequency (200–400 Hz). The BFB has a much larger stiffness and viscous damping coefficients than the MMFB. However, the MMFB material loss factor is at least twice as large as that in the BFB. The experiments show that the MMFB, when compared to the BFB, has a lower drag power and earlier lift-off speed and with dynamic force coefficients having a lesser dependency on whirl frequency excitation.

Dynamic Force Coefficients of Hydrostatic Gas Films for Recessed Flat Plates: Experimental Identification and Numerical Predictions

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Adolfo Delgado ◽  
Bugra Ertas
Keyword(s):  
Film Thickness ◽  
Pressure Ratio ◽  
Experimental Results ◽  
Dynamic Force ◽  
Test Rig ◽  
Flat Plates ◽  
Damping Force ◽  
Force Coefficients ◽  
Numerical Predictions ◽  
Stiffness And Damping

The following paper focuses on an experimental and analytical study aimed at identifying the dynamic force coefficients of hydrostatic gas films for recessed flat plates. The motivation for the effort was brought upon by the necessity of generating more accurate models for hydrostatic gas films found in hybrid gas bearings. Pressurized air at room temperature up to 120 psi was used to test different recess geometries on a flat plate test rig, capable of characterizing the stiffness and damping force coefficients for varying supply pressures, gas film thickness values, excitation frequencies, and vibration amplitudes. The test rig design and operation is described. Experimental results include frequency-dependent stiffness and damping coefficients, and leakage. The test results show that using external pressurization can generate large stiffness values while exhibiting small leakage. However, the results also show that the majority of the test configurations portray high negative damping values. An analytical model is presented and numerical predictions are compared to experimental results. Example damping trends as a function of frequency, pressure, and film thickness are presented in addition to force coefficient plots as functions of pressure ratio.

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