Identification and Prediction of Force Coefficients in a Five-Pad and Four-Pad Tilting Pad Bearing for Load-on-Pad and Load-Between-Pad Configurations

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Adolfo Delgado ◽  
Giuseppe Vannini ◽  
Bugra Ertas ◽  
Michael Drexel ◽  
Lorenzo Naldi
Keyword(s):  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Mass Term ◽  
Experimental Results ◽  
Unit Load ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Bearing Load ◽  
Frequency Independent ◽  
Modal Mass

This paper presents the identification of the rotordynamic force coefficients for direct lubrication five-pad and four-pad tilting pad bearings. The bearing is 110 mm in diameter with a L/D of 0.4 pad axial length (44 mm). The experiments include load-on-pad and load-between-pad configurations, with 0.5 and 0.6 pivot offsets, for rotor speeds ranging from 7500 rpm to 15,000 rpm. The bearing force coefficients are identified from multiple frequency excitations (20–300 Hz) exerted on the bearing housing by a pair of hydraulic shakers and are presented as a function of the excitation frequency and rotor speed for a 300 kPa unit load. The experimental results also include temperatures at the trailing edge of three pads. The direct force coefficients, identified from curve-fits of the complex dynamic stiffness, are frequency independent if considering an added mass term much smaller than the test device modal mass. The force coefficients from the four-pad bearing load-between-pad configuration show similar coefficients in the loaded and orthogonal directions. On the other hand, as expected, the five-pad bearing load-on-pad shows larger coefficients (∼25%) in the loaded direction. The maximum pad temperature recorded for the 0.5 pivot offset configurations is up to 20°C higher than those associated to the 0.6 offset configuration. Results from a predictive code are within 50% of the experimental results for the direct stiffness coefficients and within 30% for the direct damping coefficients.

Identification and Prediction of Force Coefficients in a Five-Pad and Four-Pad Tilting Pad Bearing for Load-on-Pad and Load-Between-Pad Configurations

2010 ◽  
Author(s):  
Adolfo Delgado ◽  
Giuseppe Vannini ◽  
Bugra Ertas ◽  
Michael Drexel ◽  
Lorenzo Naldi
Keyword(s):  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Mass Term ◽  
Experimental Results ◽  
Unit Load ◽  
Orthogonal Direction ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Bearing Load ◽  
Modal Mass

This paper presents the identification of the rotordynamic force coefficients for a direct lubrication five-pad and four-pad tilting pad bearing. The bearing is 110 mm in diameter with an L/D of 0.4. The experiments include load-on-pad (LOP) and load-between-pad (LBP) configurations, with a 0.5 and 0.6 pivot offset, for rotor speeds ranging from 7500 rpm to 15000 rpm. The bearing force coefficients are identified from multiple frequency excitations (20 to 300 Hz) exerted on the bearing housing by a pair of hydraulic shakers, and are presented as a function of the excitation frequency, rotor speed, for a 300 kPa unit load. The experimental results also include temperatures at the trailing edge of three pads. The direct force coefficients, identified from curve-fits of the complex dynamic stiffness, are frequency independent if considering an added mass term much smaller than the test device modal mass. The force coefficients from the four-pad bearing load-between-pad configuration show similar coefficients in the loaded and orthogonal direction. On the other hand, as expected, the five-pad bearing load-on-pad shows larger coefficients (∼25%) in the loaded direction. The maximum pad temperature recorded for the 0.5 pivot offset configurations are up to 20° C higher than those associated to the 0.6 offset configuration. Results from a predictive code are within 50% of the experimental results for the direct stiffness coefficients and within 30% for the direct damping coefficients.

Measured Static and Rotordynamic Coefficient Results for a Rocker-Pivot, Tilting-Pad Bearing With 50 and 60% Offsets

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Chris D. Kulhanek ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Mass Matrix ◽  
Excitation Frequency ◽  
Quadratic Function ◽  
Added Mass ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Direct Stiffness

Static and rotordynamic coefficients are measured for a rocker-pivot, tilting-pad journal bearing (TPJB) with 50 and 60% offset pads in a load-between-pad (LBP) configuration. The bearing uses leading-edge-groove direct lubrication and has the following characteristics: 5-pads, 101.6 mm (4.0 in) nominal diameter,0.0814 -0.0837 mm (0.0032–0.0033 in) radial bearing clearance, 0.25 to 0.27 preload, and 60.325 mm (2.375 in) axial pad length. Tests were performed on a floating bearing test rig with unit loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies (20 to 320 Hz) to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the real dynamic stiffness functions were well fitted with a quadratic function with respect to frequency. This curve fit allowed for the stiffness frequency dependency to be captured by including an added mass matrix [M] to a conventional [K][C] model, yielding a frequency independent [K][C][M] model. The imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency-independent direct damping coefficients. Direct stiffness coefficients were larger for the 60% offset bearing at light unit loads. At high loads, the 50% offset configuration had a larger stiffness in the loaded direction, while the unloaded direct stiffness was approximately the same for both pivot offsets. Cross-coupled stiffness coefficients were positive and significantly smaller than direct stiffness coefficients. Negative direct added-mass coefficients were obtained for both offsets, especially in the unloaded direction. Cross-coupled added-mass coefficients are generally positive and of the same sign. Direct damping coefficients were mostly independent of load and speed, showing no appreciable difference between pivot offsets. Cross-coupled damping coefficients had the same sign and were much smaller than direct coefficients. Measured static eccentricities suggested cross coupling stiffness exists for both pivot offsets, agreeing with dynamic measurements. Static stiffness measurements showed good agreement with the loaded, direct dynamic stiffness coefficients.

Rotordynamic Characteristics of a Five Pad, Rocker-Pivot, Tilting Pad Bearing in a Load-on-Pad Configuration; Comparisons to Predictions and Load-Between-Pad Results

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Dara W. Childs ◽  
Clint R. Carter
Keyword(s):  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Bulk Flow ◽  
Quadratic Functions ◽  
Dynamic Force ◽  
Unit Load ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Computational Fluid Dynamics Analysis ◽  
Tilting Pad

Rotordynamic data are presented for a rocker-pivot tilting pad bearing in load-on-pad (LOP) configuration for (345–3101 kPa) unit loads and speeds from 4000 rpm to 13,000 rpm. The bearing was directly lubricated through a leading edge groove with five pads, 0.282 preload, 60% offset, 57.87 deg pad arc angle, 101.587 mm (3.9995 in.) rotor diameter, 0.1575 mm (0.0062 in.) diametral clearance, and 60.325 mm (2.375 in.) pad length. Measured results were reported for this bearing by Carter and Childs (2008, “Measurements Versus Predictions for the Rotordynamic Characteristics of a 5-Pad, Rocker-Pivot, Tilting-Pad Bearing in Load Between Pad Configuration,” ASME Paper No. GT2008-50069) in the load-between-pad (LBP) configuration. Results for the LOP are compared with predictions from a bulk-flow Navier–Stokes model (as utilized by San Andres (1991, “Effect of Eccentricity on the Force Response of a Hybrid Bearing,” STLE Tribol. Trans., 34, pp. 537–544)) and to the prior LBP results. Frequency effects on the dynamic-stiffness coefficients were investigated by applying dynamic-force excitation over a range of excitation frequencies. Generally, the direct real parts of the dynamic-stiffness coefficients could be modeled as quadratic functions of the excitation frequency, and accounted for by adding a mass matrix to the conventional [K][C] model to produce a frequency-independent [K][C][M] model. Measured added-mass terms in the loaded direction approached 60 kg. The static load direction in the tests was y. The direct stiffness coefficients Kyy and Kxx depend strongly on the applied unit load, more so than speed. They generally increased linearly with load, shifting to a quadratic dependence at higher unit loads. At lower unit loads, Kyy and Kxx increase monotonically with running speed. The experimental results were compared with predictions from a bulk-flow computational fluid dynamics analysis. Stiffness orthotropy was apparent in test results, significantly more than predicted, and it became more pronounced at the heavier unit loads. Measured Kyy values were consistently higher than predicted, and measured Kxx values were lower. Comparing the LOP results to prior measured LBP results for the same bearing, at higher loads, Kyy is significantly larger for the LOP configuration than LBP. Measured values for Kxx are about the same for LOP and LBP. At low unit loads, stiffness orthotropy defined as Kyy/Kxx is the same for LOP and LBP, progressively increasing with increasing unit loads. At the highest unit load, Kyy/Kxx=2.1 for LOP and 1.7 for LBP. Measured direct damping coefficients Cxx and Cyy were insensitive to changes in either load or speed, in contrast to predictions of marked Cyy sensitivity for changes in the load. Only at the highest test speed of 13,000 rpm were the direct damping coefficients adequately predicted. No frequency dependency was observed for the direct damping coefficients.

Rotordynamic Characteristics of a 5 Pad, Rocker-Pivot, Tilting Pad Bearing in a Load-on-Pad Configuration: Comparisons to Predictions and Load-Between-Pad Results

2009 ◽  
Author(s):  
Dara W. Childs ◽  
Clint R. Carter
Keyword(s):  
Dynamic Stiffness ◽  
Mass Matrix ◽  
Excitation Frequency ◽  
Bulk Flow ◽  
Quadratic Functions ◽  
Dynamic Force ◽  
Unit Load ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad

Rotordynamic data are presented for a rocker-pivot tilting-pad bearing in load-on-pad (LOP) configuration for (345–3101 kPa) unit loads and speeds from 4k to 13k rpm. The bearing was direct lubricated through a leading-edge groove with 5 pads, .282 preload, 60% offset, 57.87° pad arc angle, 101.587 mm (3.9995 in) rotor diameter, 0.1575 mm (.0062 in) diametral clearance, and 60.325 mm (2.375 in) pad length. Measured results were reported for this bearing by Carter and Childs in 2008 in the load-between-pad (LBP) configuration. Results for the LOP are compared to predictions from a bulk-flow Navier-Stokes model (as utilized by San Andres in 1991) and to the prior LBP results. Frequency effects on the dynamic-stiffness coefficients were investigated by applying dynamic-force excitation over a range of excitation frequencies. Generally, the direct real parts of the dynamic-stiffness coefficients could be modeled as quadratic functions of the excitation frequency and accounted for by adding a mass matrix to the conventional [K][C] model to produce a frequency-independent [K][C][M] model. Measured added mass terms in the loaded direction approached 60 kg. The static load direction in the tests was y. The direct-stiffness coefficients Kyy and Kxx depend strongly on the applied unit load, more so than speed. They generally increased linearly with load, shifting to a quadratic dependence at higher unit loads. At lower unit loads, Kyy and Kxx increase monotonically with running speed. The experimental results were compared to predictions from a bulk-flow CFD analysis. Stiffness orthotropy was apparent in test results, significantly more than predicted, and it became more pronounced at the heavier unit loads. Measured Kyy values were consistently higher than predicted, and measured Kxx values were lower. Comparing the LOP results to prior measured LBP results for the same bearing, at higher loads, Kyy is significantly larger for the LOP configuration than LBP. Measured values for Kxx are about the same for LOP and LBP. At low unit loads, stiffness orthotropy defined as Kyy / Kxx is the same for LOP and LBP, progressively increasing with increasing unit loads. At the highest unit load, Kyy / Kxx = 2.1 for LOP and 1.7 for LBP. Measured direct damping coefficients Cxx and Cyy were insensitive to changes in either load or speed in contrast to predictions of marked Cyy sensitivity for changes in the load. Only at the highest test speed of 13 krpm were the direct damping coefficients adequately predicted. No frequency dependency was observed for the direct damping coefficients.

Dynamic Characterization of Tilting Pad Journal Bearings From Component and System Level Testing

2012 ◽  
Author(s):  
Adolfo Delgado ◽  
Mirko Librashi ◽  
Giuseppe Vannini
Keyword(s):  
Stability Analysis ◽  
High Speed ◽  
Dynamic Stiffness ◽  
Operating Conditions ◽  
Logarithmic Decrement ◽  
Experimental Results ◽  
System Level ◽  
Component Level ◽  
Force Coefficients ◽  
Tilting Pad

The dynamic response of a direct lube, 5-pad, rocker-back pivot tilting pad bearing is characterized in a controlled motion (component level) test rig, and in a spin bunker (full system level) using a dummy rotor mounted on two identical bearings. In the component level test, the force coefficients (stiffness, damping, mass) are identified from pseudorandom excitations using a 2-DOF model. N-DOF system including the pad motions has been shown to yield frequency dependent coefficients that warrant the use of asynchronous coefficients for stability analysis in centrifugal compressors. However, experimental results showed that the real part of the dynamic stiffness is well represented as a constant stiffness and mass coefficients while the imaginary part yields a constant damping coefficient (i.e. frequency independent). In the system level test, a dedicated dummy rotor (representative of a high speed centrifugal compressor rotor) is excited by a magnetic shaker throughout a frequency range covering the rotor modes of interest while spinning at constant speed. From the rotor harmonic response the damping of each mode is extracted using a curve-fitting method based on a 1-DOF model for a given set of speeds. The dummy rotor test provides reference values for system logarithmic decrement and further validates the component level test results. The logarithmic decrement prediction using identified bearing force coefficients are in good agreement with the experimental results. In addition, using for prediction identified coefficients in a classical K-C-M or synchronous K-C form yields similar results (within 15%). This indicates that for the given bearing geometry (clearance, offset and size) and operating conditions, synchronously reduced force coefficients are adequate for stability analysis. Comparison of the identified force coefficients with results from commercially available code yielded reasonable agreement on direct coefficients while some discrepancies are highlighted on the cross-coupled coefficients.

Measured Static and Rotordynamic Coefficient Results for a Rocker-Pivot, Tilting-Pad Bearing With 50 and 60% Offsets

2011 ◽  
Author(s):  
Chris D. Kulhanek ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Mass Matrix ◽  
Excitation Frequency ◽  
Quadratic Function ◽  
Added Mass ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Direct Stiffness

Static and rotordynamic coefficients are measured for a rocker-pivot, tilting-pad journal bearing (TPJB) with 50 and 60% offset pads in a load-between-pad (LBP) configuration. The bearing uses leading-edge-groove direct lubrication and has the following characteristics: 5-pads, 101.6 mm (4.0 in) nominal diameter, .0814–.0837 mm (.0032–.0033 in) radial bearing clearance, .25 to .27 preload, and 60.325 mm (2.375 in) axial pad length. Tests were performed on a floating bearing test rig with unit loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies (20 to 320 Hz) to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the real dynamic stiffness functions were well fitted with a quadratic function with respect to frequency. This curve fit allowed for the stiffness frequency dependency to be captured by including an added mass matrix [M] to a conventional [K][C] model, yielding a frequency independent [K][C][M] model. The imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency-independent direct damping coefficients. Direct stiffness coefficients were larger for the 60% offset bearing at light unit loads. At high loads, the 50% offset configuration had a larger stiffness in the loaded direction, while the unloaded direct stiffness was approximately the same for both pivot offsets. Cross-coupled stiffness coefficients were positive and significantly smaller than direct stiffness coefficients. Negative direct added-mass coefficients were obtained for both offsets, especially in the unloaded direction. Cross-coupled added-mass coefficients are generally positive and of the same sign. Direct damping coefficients were mostly independent of load and speed, showing no appreciable difference between pivot offsets. Cross-coupled damping coefficients had the same sign and were much smaller than direct coefficients. Measured static eccentricities suggested cross-coupling stiffness exists for both pivot offsets, agreeing with dynamic measurements. Static stiffness measurements showed good agreement with the loaded, direct dynamic stiffness coefficients.

scholarly journals The Effect of the Pivot Stiffness on the Performances of Five-Pad Tilting Pad Bearings

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 61 ◽  
Author(s):  
Phuoc Vinh Dang ◽  
Steven Chatterton ◽  
Paolo Pennacchi
Keyword(s):  
Excitation Frequency ◽  
Experimental Results ◽  
Dynamic Force ◽  
Dynamic Coefficients ◽  
Pivot Bearing ◽  
Tilting Pad ◽  
In Series ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

The role of the pivot flexibility in tilting-pad journal bearings (TPJBs) has become essential, particularly for bearings working at high applied load and relatively high rotor speeds. Predictions from a simple bearing model with rigid pivots show incorrect estimation of the dynamic coefficients in comparison with the experimental results. Normally, the more flexible the pad pivot, the lower the dynamic coefficients because the stiffness of the pivot takes in series with the stiffness and damping of the oil film. This paper investigates the influence of pivot stiffness on the dynamic force coefficients of two different five-pad TPJBs as a function of the applied static load and excitation frequency: rocker-backed pivot and spherical pivot bearings. In order to highlight the effect of the pivot stiffness in the spherical pivot bearing, displacement restriction components and elastic copper made shims have been used. Firstly, a thermo-elasto-hydrodynamic model for the static and dynamic characteristics of the two bearings is described. This model takes into account the flexibility of both pad and pivot. The pivot stiffnesses calculated by means of the Hertz theory and those obtained by experiments have been introduced and compared in the model. The clearance profiles of two tested bearing and the shaft center loci obtained by measurement and prediction are also shown. The dynamic coefficients of the two bearings obtained from the numerical simulation were compared with the experimental results. By the analysis it can be concluded that the effect of the pivot flexibility on the clearance profile, the shaft locus and on the dynamic coefficients is very significant. More important, it is important to estimate the pivot stiffness of each single pad using experimental measurements.

Leakage and Force Coefficients of a Grooved Wet (Bubbly Liquid) Seal for Multiphase Pumps and Comparisons With Prior Test Results for a Three Wave Seal

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Xueliang Lu ◽  
Luis San Andrés ◽  
Tingcheng Wu
Keyword(s):  
Pressure Drop ◽  
Volume Fraction ◽  
Dynamic Stiffness ◽  
Pressure Ratio ◽  
Excitation Frequency ◽  
Gas Content ◽  
Bubbly Liquid ◽  
Dynamic Force ◽  
Force Coefficients ◽  
Ring Seal

Abstract In the subsea oil and gas industry, multiphase pumps and wet gas compressors are engineered choices saving transportation and separation facility costs. In these machines, seals handling multiple phase components must be able to operate without affecting the system efficiency and its dynamic stability. This paper, extending prior work conducted with uniform clearance and wavy surface annular seals, presents measurements of leakage and dynamic force coefficients in a grooved seal whose dimensions are scaled from an impeller wear ring seal in a boiler feed pump. The 14-grooves seal has diameter D = 127 mm, length L = 0.34 D, and clearance c = 0.211 mm; each groove has shallow depth dg ∼2.6 c and length Lg ∼ 3.4% L. At a shaft speed of 3.5 krpm (surface speed = 23.3 m/s), a mixture of air in ISO VG 10 oil with inlet gas volume fraction (GVF) ranging from 0 (just oil) to 0.7 (mostly air) lubricates the seal. The pressure ratio (inlet/exit) is 2.9. The flow is laminar since the liquid is viscous and the pressure drop is low. The measured mixture mass flow decreases continuously with an increase in inlet GVF. The seal stiffnesses (direct K and cross coupled k), added mass (M), and direct damping (C) coefficients are constant when the supplied mixture is low in gas content, GVF ≤ 0.1. As the gas content increases, 0.2 ≤  GVF ≤ 0.5, the seal direct dynamic stiffness becomes nil with an increase in excitation frequency, whereas k and C reduce steadily with GVF. In general, for GVF ≤ 0.5, the direct damping is invariant with frequency; variations appearing for GVF = 0.7. Compared against a three wave annular seal, the grooved seal offers much lower force coefficients, in particular the viscous damping. Thus, for laminar flow operation (heavy oil) with a low pressure drop as in a wear ring seal, a three wave seal is recommended as it also offers a significant centering stiffness.

A Study on the Leakage and Rotordynamic Performance of a Long Labyrinth Seal Under Mainly Air Conditions

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs
Keyword(s):  
Silicone Oil ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Labyrinth Seal ◽  
System Stability ◽  
Test Fluid ◽  
Liquid Volume ◽  
Frequency Dependent ◽  
Frequency Independent ◽  
The Impact

Abstract This paper investigates the impact of liquid presence in air on the leakage and rotordynamic coefficients of a long (length-to-diameter ratio L/D = 0.747) teeth-on-stator labyrinth seal. The test fluid is a mixture of air and silicone oil (PSF-5cSt). Tests are carried out at inlet pressure Pi = 62.1 bars, three pressure ratios from 0.21 to 0.46, three speeds from 10 to 20 krpm, and six inlet liquid volume fractions (LVFs) from 0% to 15%. Complex dynamic-stiffness coefficients Hij are measured. The real parts of Hij are too frequency dependent to be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, this paper presents frequency-dependent direct stiffness KΩ and cross-coupled stiffness kΩ. The imaginary parts of Hij produce frequency-independent direct damping C. Test results show that, under both pure- and mainly air conditions, the leakage mass flowrate m˙ of the test seal steadily increases as inlet LVF increases. KΩ is negative under all test conditions, and the magnitude of KΩ increases as inlet LVF increases, leading to a larger negative centering force on the associated compressor rotor. Under pure-air conditions, kΩ is a small negative value. Injecting oil into the air increases kΩ slightly and make the magnitude of kΩ closer to zero. Under mainly air conditions, increasing inlet LVF from 2% to 15% has little impact on kΩ. C normally increases as inlet LVF increases. The value of the effective damping Ceff = C − kΩ/Ω near 0.5ω is of significant interest to the system stability since an unstable centrifugal compressor may precess at approximately 0.5ω. Ω denotes the excitation frequency. The oil presence in the air has little impact on the value of Ceff near 0.5ω. Also, the liquid presence does not change the insensitiveness of m˙, KΩ, kΩ, C, and Ceff to change in ω; i.e., under both pure- and mainly air conditions, changes in ω has little impact on m˙, KΩ, kΩ, C, and Ceff.

Measurements Versus Predictions for the Rotordynamic Characteristics of a Five-Pad Rocker-Pivot Tilting-Pad Bearing in Load-Between-Pad Configuration

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Clint R Carter ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Added Mass ◽  
Quadratic Functions ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Test Conditions ◽  
Computational Fluid Dynamics Analysis ◽  
Tilting Pad ◽  
Mass Terms

Rotordynamic data are presented for a rocker-pivot tilting-pad bearing in the load-between-pad configuration for unit loads over the range 345–3101kPa and speeds over the range 4000–13,000rpm. The bearing was directly lubricated through a leading-edge groove with the following specifications: Five pads, 0.282 preload, 60% offset, 57.87deg pad arc angle, 101.587mm(3.9995in.) rotor diameter, 0.1575mm(0.0062in.) diametral clearance, and 60.325mm(2.375in.) pad length. Dynamic tests were performed over a range of frequencies to investigate frequency effects on the dynamic stiffness coefficients. Under most test conditions, the direct real parts of the dynamic stiffnesses could be approximated as quadratic functions of the excitation frequency and accounted for with the addition of an added-mass matrix to the conventional [K][C] matrix model to produce a frequency-independent [K][C][M] model. Measured added-mass terms in the loaded direction approached 60kg. At low speeds, “hardening” direct dynamic stiffness coefficients that increased with increasing frequency were obtained, which produced negative added-mass terms. No frequency dependency was obtained for the direct damping coefficients. The dynamic experimental results were compared to predictions from a bulk-flow computational fluid dynamics analysis. The static load direction in the tests was y. The direct stiffness coefficients Kxx and Kyy were slightly overpredicted. Measured direct damping coefficients Cxx and Cyy were insensitive to changes in either the load or speed in contrast to predictions of marked Cyy sensitivity for changes in the load. Only at the highest test speed of 13,000rpm were the direct damping coefficients adequately predicted. Measurable cross-coupled stiffness coefficients were obtained for the bearings with Kxy and Kyx being approximately equal in magnitude but opposite in sign—clearly destabilizing. However, the whirl frequency ratio was found to be zero at all test conditions indicating infinite stability for the bearing.

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