A novel method for calculating the dynamic force coefficients of Gas Foil Bearings and its application in the rotordynamic analysis

2021 ◽  
Vol 515 ◽  
pp. 116466
Author(s):  
Yongpeng Gu ◽  
Gexue Ren ◽  
Ming Zhou
Keyword(s):  
Dynamic Force ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Novel Method

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.

Identification of Dynamic Characteristics of Hybrid Bump-Metal Mesh Foil Bearings

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Zilong Zhao ◽  
Kai Feng ◽  
Xueyuan Zhao ◽  
Wanhui Liu
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Dynamic Stiffness ◽  
Load Test ◽  
Dynamic Force ◽  
Static Load Test ◽  
Metal Mesh ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Foil Bearing

The stability of oil-free high-speed turbo-machinery can be effectively improved by increasing the damping characteristic of the gas foil bearing (GFB). Novel hybrid bump-metal mesh foil bearings (HB-MFBs) have been previously developed. Prior experimental results show that the parallel combination of bump structure and metal mesh not only can improve the structure stiffness but also provide better damping property compared with the bump-type foil structure. To investigate the dynamic behavior of floating HB-MFBs and promote its application, this study measured the dynamic force coefficients of HB-MFBs on a rotating test rig. The vibrations of HB-MFBs with different mesh densities (40%, 32.5%, and 25%) and a generation І bump-type foil bearing (BFB) with similar size are measured under static and impact loads to estimate the bearing characteristics. Static load test results show that the linear stiffness decreases when the air film is generated (from 0 rpm to 20 krpm) but increases gradually with speed (from 20 krpm to 30 krpm, and 40 krpm). Moreover, the dynamic force coefficients of HB-MFBs indicate the significant influence of metal mesh density on bearing dynamic characteristics. The growth in block density increases the dynamic stiffness and damping coefficients of bearing. The comparison of HB-MFB (32.5% and 40%) and BFB emphasizes the good damping characteristics of HB-MFB.

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.

Performance Characteristics of Metal Mesh Foil Bearings: Predictions vs. Measurements

2013 ◽  
Author(s):  
Luis San Andrés ◽  
Thomas Abraham Chirathadam
Keyword(s):  
Low Cost ◽  
Excitation Frequency ◽  
Element Model ◽  
Rotating Machinery ◽  
Performance Characteristics ◽  
Dynamic Force ◽  
Metal Mesh ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Damping Coefficients

Proven low-cost gas bearing technologies are sought to enable more compact rotating machinery products with extended maintenance intervals. The paper presents an analysis for predicting the static and dynamic forced performance characteristics of metal mesh foil bearings (MMFBs) which comprise of a top foil supported on a layer of metal mesh of certain compactness. The analysis couples a finite element model of the top foil and underspring support with the gas film Reynolds equation. Comparison of predictions against laboratory measurements with two bearings aims to validate the analysis. The predicted drag friction factor in one bearing (L = D = 28.00 mm) during full film operation is just f ∼ 0.03 at ∼ 50 krpm, agreeing well with measurements at increasing applied loads. The predictions further elucidate the effect of the applied load and rotor speed on the bearing minimum film thickness, journal eccentricity and attitude angle. For a second bearing (L = 38.0 mm, D = 36.5 mm), predicted bearing force coefficients show magnitudes comparable with the measurements, with less than 20% difference, in the 250–350 Hz excitation frequency range. While the predicted direct stiffness coefficients are rather constant, the experimental force coefficients increase with frequency (max. 400 Hz), due mainly to the increasing amplitudes of dynamic force applied to excite the bearing with a set amplitude of motion. The analysis under predicts the direct damping coefficients at high frequencies (>300 Hz). The cross-coupled stiffness and damping coefficients are typically lower (< 40%) than the direct ones. The bearings operated stable at all speeds without any sub synchronous whirl. The reasonable agreement of the predictions with the available test data promote the better design and further development of MMFB supported rotating machinery.

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.

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

2012 ◽  
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 (B-FBs) 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 uses common materials and no restrictions on intellectual property. Laboratory testing shows that prototype MMFBs perform similarly as typical BFBs but offering 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 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.

Performance Characteristics of Metal Mesh Foil Bearings: Predictions Versus Measurements

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Luis San Andrés ◽  
Thomas Abraham Chirathadam
Keyword(s):  
Low Cost ◽  
Excitation Frequency ◽  
Element Model ◽  
Rotating Machinery ◽  
Performance Characteristics ◽  
Dynamic Force ◽  
Metal Mesh ◽  
Force Coefficients ◽  
Foil Bearings ◽  
Damping Coefficients

Proven low-cost gas bearing technologies are sought to enable more compact rotating machinery products with extended maintenance intervals. The paper presents an analysis for predicting the static and dynamic forced performance characteristics of metal mesh foil bearings (MMFBs) which comprise a top foil supported on a layer of metal mesh of a certain compactness. The analysis couples a finite element model of the top foil and underspring support with the gas film Reynolds equation. A comparison of the predictions against laboratory measurements with two bearings aims to validate the analysis. The predicted drag friction factor in one bearing (L = D = 28.00 mm) during full film operation is just f ∼ 0.03 at ∼50,000 rpm, in good agreement with measurements at increasing applied loads. The predictions further elucidate the effect of the applied load and rotor speed on the bearing minimum film thickness, journal eccentricity, and attitude angle. For a second bearing (L = 38.0 mm, D = 36.5 mm), predicted bearing force coefficients show magnitudes comparable with the measurements, with less than a 20% difference, in the 250–350 Hz excitation frequency range. While the predicted direct stiffness coefficients are rather constant, the experimental force coefficients increase with frequency (maximum 400 Hz), due mainly to the increasing amplitudes of dynamic force applied to excite the bearing with a set amplitude of motion. The analysis underpredicts the direct damping coefficients at high frequencies (>300 Hz). The cross-coupled stiffness and damping coefficients are typically lower (<40%) than the direct ones. The bearings operated stably at all speeds without any subsynchronous whirl. The reasonable agreement of the predictions with the available test data promote the better design and further development of MMFB supported rotating machinery.

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 &lt; 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.

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