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.

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.

Measurements Versus Predictions for the Rotordynamic Characteristics of a 5-Pad, Rocker-Pivot, Tilting-Pad Bearing in Load Between Pad Configuration

2008 ◽  
Author(s):  
Clint R. Carter ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Mass Matrix ◽  
Excitation Frequency ◽  
Added Mass ◽  
Quadratic Functions ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Test Conditions ◽  
Tilting Pad ◽  
Mass Terms

Rotordynamic data are presented for a rocker-pivot tilting-pad bearing in a load-between-pad (LBP) configuration for unit loads over the range [345, 3101 kPa] and speeds over the range [4k to 13k rpm]. The bearing was direct lubricated through a leading-edge groove with the following specifications: 5 pads, .282 preload, 60% offset, 57.87° pad arc angle, 101.587 mm (3.9995 in) rotor diameter, .1575 mm (.0062 in) diametral clearance, 60.325 mm (2.375 in) 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 60 kg. At low speeds, “hardening” direct dynamic stiffness coefficients that increased with increasing frequency were obtained that 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 CFD analysis. The static load direction in the tests was y. The direct stiffness coefficients Kxx and Kyy were slightly over predicted. 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 13000 rpm 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.

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.

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.

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.

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.

Rotordynamic Coefficients Measurements Versus Predictions for a High Speed Flexure-Pivot Tilting-Pad Bearing (Load-Between-Pad Configuration)

2005 ◽  
Author(s):  
Adnan Al-Ghasem ◽  
Dara Childs
Keyword(s):  
Dynamic Stiffness ◽  
Added Mass ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Radial Clearance ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Model Predictions ◽  
Frequency Independent ◽  
Stiffness And Damping

Experimental dynamic force coefficients are presented for a flexure-pivot-tilting-pad (FPTP), bearing in load-between-pad (LBP) configuration for a range of rotor speeds and bearing unit loadings. The bearing has the following design parameters: 4 pads with pad arc angle 72° and 50% pivot offset, pad axial length 0.0762 m (3 in), pad radial clearance 0.254 mm (0.010 in), bearing radial clearance 0.1905 mm (0.0075 in), preload 0.25 and shaft nominal diameter of 116.84 mm (4.600 in). Measured dynamic coefficients have been compared with theoretical predictions using an isothermal analysis for a bulk-flow Navier-Stokes model. Predictions from two models — the Reynolds equation and a bulk-flow Navier-Stokes (NS) equation model are compared with experimental, complex dynamic stiffness coefficients (direct and cross-coupled) and show the following results: (i) The real part of the direct dynamic-stiffness coefficients is strongly frequency dependent because of pad inertia, support flexibility, and the effect of fluid inertia. This frequency dependency can be accurately modeled for by adding a direct added mass term to the conventional stiffness/damping matrix model. (ii) Both models underpredict the identified added-mass coefficient (∼32 kg), but the bulk-flow NS equations predictions are modestly closer. (iii) The imaginary part of the direct dynamic-stiffness coefficient (leading to direct damping) is a largely linear function of excitation frequency, leading to a constant (frequency independent) direct damping model. (iv) The real part of the cross-coupled dynamic-stiffness coefficients shows larger destabilizing forces than predicted by either model. The direct stiffness and damping coefficients increase with load, while increasing and decreasing with rotor speed, respectively. As expected, a small whirl frequency ratio (WFR) was found of about 0.15, and it decreases with increasing load and increases with increasing speed. The two model predictions for WFR are comparable and both underpredict the measured WFR values. Rotors supported by either conventional tilting PAD bearings or FPTP bearings are customarily modeled by frequency-dependent stiffness and damping matrices, necessitating an iterative calculation for rotordynamic stability. The present results show that adding a constant mass matrix to the FPTP bearing model produces an accurate frequency-independent model that eliminates the need for iterative rotordynamic stability calculations.

The Impact of Pad Flexibility on the Rotordynamic Coefficients of Tilting-Pad Journal Bearings

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Jennifer E. Gaines ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Element Model ◽  
Bending Stiffness ◽  
Test Fluid ◽  
Unit Load ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Impact

Static and dynamic load tests were performed on a three-pad, rocker-pivot, tilting-pad journal bearing (TPJB) with three interchangeable pad configurations, each with measurably different pad flexibilities. Measured dynamic-stiffness data for the bearing were readily fitted by a frequency-independent, constant-coefficient [K][C][M] model. The test-bearing had a 101.74 mm diameter with L/D = 0.6. Tests were conducted over the speed range of 6–12 krpm, with unit loads varying from 0.172 to 1.724 MPa. An ISO VG 46 lubricant was used as the test fluid. Pad flexibility was characterized as the change in the pad's bending stiffness or the change in pad thickness. A finite-element model (FEM) was created to predict the structural bending stiffness of each pad configuration, showing a significant pad flexibility increase as pad thickness decreased. To examine the effect of pad flexibility on the rotordynamic coefficients, the measured results were compared across pad configurations and showed that the pad flexibility increase reduced the direct damping coefficients by 12–20%. As pad flexibility increased, the direct-stiffness coefficients could increase or decrease, depending on the unit load. They varied from an increase of 12% at low unit loads to a decrease of 3% at high unit loads. Results show that the pad's structural bending stiffness or flexibility is important when predicting the bearing’s dynamic performance. Damping is consistently overpredicted when neglecting pad flexibility. A nondimensional pad flexibility parameter αflex was developed. It related the average deflection across the pad surface to the pad's arc length and was to relate the pad flexibility of multiple bearings of different sizes. A bearing code was used to predict the percent change in direct damping coefficients for rigid-pad/flexible-pivot and flexible-pad/flexible-pivot models for a surface speed of 54 m/s and a unit load of 783 kPa for the three-pad configuration tested here plus five additional tested bearings from the literature. For the minimum pad thickness configuration tested here, the code predicted a 20% drop in predicted Cxx (off-load axis direct damping) when comparing a model that included pad flexibility with a model that neglected pad flexibility. In terms of αflex, the two thinnest pad configurations tested here are quite flexible compared to both TPJB's pads used in industry and previously tested TPJB pads.

Rotordynamic Coefficients Measurements Versus Predictions for a High-Speed Flexure-Pivot Tilting-Pad Bearing (Load-Between-Pad Configuration)

2005 ◽  
Vol 128 (4) ◽  
pp. 896-906 ◽  
Author(s):  
Adnan M. Al-Ghasem ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Stiffness ◽  
Added Mass ◽  
Bulk Flow ◽  
Fluid Inertia ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Mass Coefficient ◽  
Stiffness And Damping

Experimental dynamic force coefficients are presented for a four pad flexure-pivot tilting-pad bearing in load-between-pad configuration for a range of rotor speeds and bearing unit loadings. Measured dynamic coefficients have been compared to theoretical predictions using an isothermal analysis for a bulk-flow Navier-Stokes (NS) model. Predictions from two models—the Reynolds equation and a bulk-flow NS equation models are compared to experimental, complex dynamic stiffness coefficients (direct and cross-coupled) and show the following results: (i) The real part of the direct dynamic-stiffness coefficients is strongly frequency dependent because of pad inertia, support flexibility, and the effect of fluid inertia. This frequency dependency can be accurately modeled for by adding a direct added-mass term to the conventional stiffness/damping matrix model. (ii) Both models underpredict the identified added-mass coefficient (∼32kg), but the bulk-flow NS equation predictions are modestly closer. (iii) The imaginary part of the direct dynamic-stiffness coefficient (leading to direct damping) is a largely linear function of excitation frequency, leading to a constant (frequency-independent) direct damping model. (iv) The real part of the cross-coupled dynamic-stiffness coefficients shows larger destabilizing forces than predicted by either model. The frequency dependency that is accounted for by the added mass coefficient is predicted by the models and arises (in the models) primarily because of the reduction in degrees of freedom from the initial 12 degrees (four pads times three degrees of freedom) to the two-rotor degrees of freedom. For the bearing and condition tested, pad and fluid inertia are secondary considerations out to running speed. The direct stiffness and damping coefficients increase with load, while increasing and decreasing with rotor speed, respectively. As expected, a small whirl frequency ratio (WFR) was found of about 0.15, and it decreases with increasing load and increases with increasing speed. The two model predictions for WFR are comparable and both underpredict the measured WFR values. Rotors supported by either conventional tilting-pad bearings or flexure-pivot tilting-pad (FPTP) bearings are customarily modeled by frequency-dependent stiffness and damping matrices, necessitating an iterative calculation for rotordynamic stability. For the bearing tested and the load conditions examined, the present results show that adding a constant mass matrix to the FPTP bearing model produces an accurate frequency-independent model that eliminates the need for iterative rotordynamic stability calculations. Different results may be obtained for conventional tilting-pad bearings (or this bearing at higher load conditions).

Experimental Rotordynamic Coefficient Results for a Load-on-Pad Flexible-Pivot Tilting-Pad Bearing With Comparisons to Predictions From Bulk-Flow and Reynolds Equation Models

2004 ◽  
Author(s):  
L. E. Rodriguez ◽  
D. W. Childs
Keyword(s):  
Reynolds Equation ◽  
Flow Model ◽  
Dynamic Stiffness ◽  
Added Mass ◽  
Bulk Flow ◽  
Quadratic Functions ◽  
Force Model ◽  
Fluid Inertia ◽  
Frequency Dependency ◽  
Tilting Pad

Experimental dynamic-stiffness-coefficient results are presented for a high-speed, lightly loaded, load-on-pad, flexible-pivot tilting-pad bearing. Results show that the real part of the direct dynamic-stiffness coefficients are quadratic functions of the excitation frequency. This frequency dependency is modeled well by an added-mass coefficient, and the resultant [M], [K], and [C] matrix model is frequency-independent versus a conventional [K] and [C] model that is frequency dependent. The dynamics introduced by the additional pad degrees of freedom (including pad inertia and web moment stiffness) and the effects of fluid inertia in the lubricant film account for part of this frequency dependency. Experimental results are compared to numerical predictions from models based on: (i) the Reynolds equation, and (ii) a Navier-Stokes (NS) equations bulk-flow model that retains the temporal and convective fluid inertia terms. The NS bulk-flow model results correlate better with experimental dynamic stiffness results, including added-mass terms. Both models underestimate the measured added-mass coefficients for the full excitation range; however, they do an adequate job for excitation frequencies up to synchronous frequency. The frequency dependency predicted by using a [K] and [C] model can be removed by adding a mass matrix to the reaction-force model with either a Reynolds equation or a bulk-flow NS model, with a very considerable speed up in calculation of damped eigenvalues for rotor-bearing systems.

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