An Experimental Investigation of the Dynamic Performance of a Vertical-Application Three-Lobe Bearing

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Rasish Khatri ◽  
Dara W. Childs
Keyword(s):  
Performance Test ◽  
Dynamic Performance ◽  
Load Condition ◽  
Leading Edge ◽  
Test Results ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Numerical Predictions ◽  
Frequency Independent ◽  
Direct Stiffness

Dynamic performance test results are provided for a vertical-application three-lobe bearing, geometrically similar to a three-lobe bearing tested by Leader et al. (2010, “Evaluating and Correcting Subsynchronous Vibration in Vertical Pumps,” 26th International Pump Users Symposium, Houston, TX, March 16-18) to stabilize a vertical sulfur pump. The bearing has the following specifications: 100 deg pad arc angle, 0.64 preload, 100% offset, 101.74 mm bore diameter, 0.116 mm radial pad clearance, 76.3 mm axial length, and 100 deg static load orientation from the leading edge of the loaded pad. The bearing is tested at 2000 rpm, 4400 rpm, 6750 rpm, and 9000 rpm. This bearing is tested in the no-load condition and with low unit loads of 58 kPa and 117 kPa. The dynamic performance of this bearing is evaluated to determine (1) whether a fully (100%) offset three-lobe bearing configuration is more stable than a standard plain journal bearing (0.5 whirl-frequency ratio (WFR)) and (2) whether a fully offset three-lobe bearing provides a larger direct stiffness than a standard fixed-arc bearing. Hot and cold clearances are measured for this bearing. Dynamic measurements include frequency-independent stiffness and damping coefficients. Bearing stability characteristics are evaluated using the WFR. Test results are compared to numerical predictions obtained from a fixed-arc bearing Reynolds equation solver. Dynamic tests show that the vertical-application three-lobe bearing does not improve stability over conventional fixed-arc bearings. The measured WFRs for the vertical-application bearing are approximately 0.4–0.5 for nearly all test cases. Predicted WFRs are 0.46 at all test points. The vertical-application bearing dimensionless direct stiffness coefficients were compared to those for a 70% offset three-lobe bearing. Dimensionless direct stiffness coefficients at 0 kPa are larger for the vertical-application bearing by 45–48% in the loaded direction and larger by 15–26% in the unloaded direction. Thus, the vertical-application bearing does impart a larger centering force to the journal relative to the 70% offset bearing, in the no-load condition. Predictions using both the measured hot clearance and measured cold clearance as inputs to the code are compared to the measured dynamic data. In general, the predicted direct stiffness coefficients using both the hot and cold clearances as inputs were higher than measured direct stiffnesses. The two sets of predicted cross-coupled stiffness coefficients straddle the measured cross-coupled stiffness coefficients. Predicted direct damping coefficients using both solutions were higher than measured values in most cases, but agreement between predictions and measurements improved significantly at high speeds and when applying light loads.

An Experimental Investigation of the Dynamic Performance of a Vertical-Application Three-Lobe Bearing

2014 ◽  
Author(s):  
Rasish Khatri ◽  
Dara W. Childs
Keyword(s):  
Frequency Ratio ◽  
Performance Test ◽  
Dynamic Performance ◽  
Load Condition ◽  
Leading Edge ◽  
Test Results ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Numerical Predictions ◽  
Direct Stiffness

Dynamic performance test results are provided for a vertical-application three-lobe bearing, geometrically similar to a three-lobe bearing tested by Leader [1] to stabilize a vertical sulfur pump. The bearing has the following specifications: 100° pad arc angle, 0.64 preload, 100% offset, 101.74 mm bore diameter, 0.116 mm radial pad clearance, 76.3 mm axial length, and 100° static load orientation from the leading edge of the loaded pad. The bearing is tested at 2000 rpm, 4400 rpm, 6750 rpm, and 9000 rpm. This bearing is tested in the no-load condition and with low unit loads of 58 kPa and 117 kPa. The dynamic performance of this bearing is evaluated to determine (1) whether a fully (100%) offset three-lobe bearing configuration is more stable than a standard plain journal bearing (0.5 whirl-frequency ratio), and (2) whether a fully offset three-lobe bearing provides a larger direct stiffness than a standard fixed-arc bearing. Hot and cold clearances are measured for this bearing. Dynamic measurements include frequency-independent stiffness and damping coefficients. Bearing stability characteristics are evaluated using the whirl-frequency ratio (WFR). Test results are compared to numerical predictions obtained from a fixed-arc bearing Reynolds equation solver. Dynamic tests show that the vertical-application three-lobe bearing does not improve stability over conventional fixed-arc bearings. The measured WFRs for the vertical-application bearing are approximately 0.4–0.5 for nearly all test cases. Predicted WFRs are 0.46 at all test points. The vertical-application bearing dimensionless direct stiffness coefficients were compared to those for a 70% offset three-lobe bearing. Dimensionless direct stiffness coefficients at 0 kPa are larger for the vertical-application bearing by 45–48% in the loaded direction and larger by 15–26% in the unloaded direction. Thus, the vertical-application bearing does impart a larger centering force to the journal relative to the 70% offset bearing, in the no-load condition. Predictions using both the measured hot clearance and measured cold clearance as inputs to the code are compared to the measured dynamic data. In general, the predicted direct stiffness coefficients using both the hot and cold clearances as inputs were higher than measured direct stiffnesses. The two sets of predicted cross-coupled stiffness coefficients straddle the measured cross-coupled stiffness coefficients. Predicted direct damping coefficients using both solutions were higher than measured values in most cases, but agreement between predictions and measurements improved significantly at high speeds and when applying light loads.

An Experimental Study of the Load-Orientation Sensitivity of Three-Lobe Bearings

2014 ◽  
Author(s):  
Rasish Khatri ◽  
Dara W. Childs
Keyword(s):  
Performance Test ◽  
Static Load ◽  
Dynamic Performance ◽  
Dynamic Test ◽  
Load Condition ◽  
Leading Edge ◽  
Test Results ◽  
Static Data ◽  
Load Vector ◽  
All Speeds

Static and dynamic performance test results are provided for a three-lobe bearing evaluated over the following range of radial static-load orientations (taken from the leading edge of the loaded pad): 0°, 20°, 30°, 40°, 80°, 90°, and 100°. Static and dynamic test results are evaluated to determine the sensitivity of the bearing to changes in the static load direction. The bearing has the following specifications: 100o arc angle, 0.52 preload, 70% offset, 101.74 mm minimum bore diameter, 0.116 mm radial pad clearance, and 76.3 mm axial length. The bearing is tested at 6750 rpm, 9000 rpm, 10800 rpm, and 13200 rpm, and at five different unit loads. Static measurements include hot and cold clearances, static eccentricities, and pad metal temperatures. Dynamic results include stiffness coefficients, damping coefficients, and whirl-frequency ratios (WFRs). Dynamic tests show that the three-lobe bearing is very sensitive to load orientation at low speeds and high loads. Kxx is highest for the 80°, 90°, and 100° load orientations. Kyy is highest for the 20°, 30°, and 40° load orientations. Kxy is highest for the 80°, 90°, and 100° load orientations. The magnitude of Kyx is highest for the 0° and 20° load orientations. Cxx is largest for the 80°, 90°, and 100° load orientations, and Cyy is largest for the 0°, 20°, 30°, and 40° load orientations. In terms of WFRs, it is generally dynamically advantageous to orient the static load vector for this bearing towards the leading edge of the pad. WFRs at 6750 rpm with loads of 1149 kPa, 1723 kPa, and 2298 kPa are equal to zero when the static load vector is pointed towards the leading edge of the pad and between 0.25 and 0.5 when the static load vector points towards the trailing edge of the pad. The bearing is not sensitive to load orientation at high speeds and light loads. At 13200 rpm, measured WFRs are between 0.2 and 0.6 at all loads and for all load orientations. Measured WFRs at the no-load condition are approximately 0.5 at all speeds. Static data showed that the 30° and 90° load orientations yielded slightly higher measured maximum pad-metal-temperature increases at each speed relative to the other load orientations. At the highest static-load magnitudes, the pad metal temperatures are not as dependent on load orientation. The 20°, 30°, and 40° load orientations had the smallest measured eccentricity ratio, and thus the highest static stiffness.

An Experimental Study of the Load-Orientation Sensitivity of Three-Lobe Bearings

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Rasish Khatri ◽  
Dara W. Childs
Keyword(s):  
Performance Test ◽  
Static Load ◽  
Dynamic Performance ◽  
Dynamic Test ◽  
Load Condition ◽  
Leading Edge ◽  
Test Results ◽  
Static Data ◽  
Load Vector ◽  
All Speeds

Static and dynamic performance test results are provided for a three-lobe bearing evaluated over the following range of radial static-load orientations (taken from the leading edge of the loaded pad): 0 deg, 20 deg, 30 deg, 40 deg, 60 deg, 80 deg, 90 deg, and 100 deg. Static and dynamic test results are evaluated to determine the sensitivity of the bearing to changes in the static load direction. The bearing has the following specifications: 100 deg arc angle, 0.52 preload, 70% offset, 101.74 mm minimum bore diameter, 0.116 mm radial pad clearance, and 76.3 mm axial length. The bearing is tested at 6750 rpm, 9000 rpm, 10,800 rpm, and 13,200 rpm, and at five different unit loads. Static measurements include hot and cold clearances, static eccentricities, and pad metal temperatures. Dynamic results include stiffness coefficients, damping coefficients, and whirl-frequency ratios (WFRs). Dynamic tests show that the three-lobe bearing is very sensitive to load orientation at low speeds and high loads. Kxx is highest for the 80 deg, 90 deg, and 100 deg load orientations. Kyy is highest for the 20 deg, 30 deg, and 40 deg load orientations. Kxy is highest for the 80 deg, 90 deg, and 100 deg load orientations. The magnitude of Kyx is highest for the 0 deg and 20 deg load orientations. Cxx is largest for the 80 deg, 90 deg, and 100 deg load orientations, and Cyy is largest for the 0 deg, 20 deg, 30 deg, and 40 deg load orientations. In terms of WFRs, it is generally dynamically advantageous to orient the static load vector for this bearing toward the leading edge of the pad. WFRs at 6750 rpm with loads of 1149 kPa, 1723 kPa, and 2298 kPa are equal to zero when the static load vector is pointed toward the leading edge of the pad and between 0.25 and 0.5 when the static load vector is pointed toward the trailing edge of the pad. The bearing is not sensitive to load orientation at high speeds and light loads. At 13,200 rpm, measured WFRs are between 0.2 and 0.6 at all loads and for all load orientations. Measured WFRs at the no-load condition are between 0.3 and 0.6 at all speeds. Static data showed that the 30 deg and 90 deg load orientations yielded slightly higher measured maximum pad-metal-temperature increases at each speed relative to the other load orientations. At the highest static-load magnitudes, the pad metal temperatures are not as dependent on load orientation. The 20 deg, 30 deg, and 40 deg load orientations had the smallest measured eccentricity ratio, and thus the highest static stiffness.

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 Flexure Pivot Pad Bearing With an Active and Locked Integral Squeeze Film Damper

2012 ◽  
Author(s):  
Jeff Agnew ◽  
Dara Childs
Keyword(s):  
Added Mass ◽  
Squeeze Film ◽  
Test Results ◽  
Squeeze Film Damper ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Active Damper ◽  
Rotordynamic Coefficient

Measured rotordynamic coefficients are presented for a flexure-pivot-pad journal bearing (FPJB) in a load-between-pad configuration with: (1) an active, and (2) locked integral squeeze film damper (ISFD). Prior rotordynamic-coefficient test results have been presented for FPJBs (alone), and rotor-response results have been presented for rotors supported by FPJBS with ISFDs; however, these are the first rotordynamic-coefficient test results for FPJBs with ISFDs. A multi-frequency dynamic testing regime is employed. For both bearing configurations, quadratic curve fits provide good representation of the real portions of the dynamic-stiffness coefficients yielding a direct stiffness and a direct added-mass coefficient. The imaginary portions are well represented by linear curve fits, implying constant, frequency-independent direct-damping coefficients. Direct stiffness coefficients are ∼50% lower for the active-damper configuration, and direct damping coefficients are only modestly lower. The combination of ∼50% reduction in direct stiffness with a modest drop in direct damping indicates a very effective squeeze-film damper application. Added-mass coefficients are normally lower for the active-damper configuration, and all coefficient trends (for changes in loading and shaft speed) are “flatter” for the active flexure pivot-pad damper bearing. The measured rotordynamic coefficients are used to calculate the whirl frequency ratio and indicate high stability for both bearing configurations.

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.

Measured Static and Rotordynamic Characteristics of a Smooth-Stator/Grooved-Rotor Liquid Annular Seal

2017 ◽  
Author(s):  
J. Alex Moreland ◽  
Dara W. Childs ◽  
Joshua T. Bullock
Keyword(s):  
Frequency Ratio ◽  
Dynamic Performance ◽  
Radial Clearance ◽  
Test Results ◽  
Axial Pressure ◽  
Pressure Drops ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Annular Seal ◽  
Direct Stiffness

Electric submersible pumps utilize grooved-rotor seals to reduce leakage and break up contaminants within the pumped fluid. Additionally, due to their decreased surface area (when compared to a smooth seal), grooved seals decrease the chance of seizure in the case of rotor-stator rubs. Despite their use in industry, the literature does not contain measurements for smooth-stator/circumferentially-grooved-rotor liquid annular seals. This paper presents test results consisting of leakage measurements and rotordynamic coefficients for a smooth-stator/circumferentially-grooved-rotor liquid annular seal. Both static and dynamic performance for the grooved seal are investigated for various imposed pre-swirl ratios, static eccentricities, axial pressure drops, and running speeds. The grooved seals′ static and dynamic performance are compared to those of a smooth seal with identical length, diameter, and radial clearance. Results show that adding grooves reduces leakage at lower speeds (less than 5 krpm) and higher axial pressure drops, but does little at higher speeds. The grooved seal’s direct stiffness is generally negative, which would be detrimental to pump rotordynamics. Furthermore, increasing pre-swirl increases the magnitude of cross-coupled stiffness and increases the whirl frequency ratio. When compared to the smooth seal, the grooved seal has smaller effective damping coefficients, indicative of worse stability characteristics.

scholarly journals Annular Honeycomb Seals: Test Results for Leakage and Rotordynamic Coefficients; Comparisons to Labyrinth and Smooth Configurations

1989 ◽  
Vol 111 (2) ◽  
pp. 293-300 ◽  
Author(s):  
D. Childs ◽  
D. Elrod ◽  
K. Hale
Keyword(s):  
Labyrinth Seal ◽  
Test Results ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Shaft Rotation ◽  
Honeycomb Seal ◽  
Cell Dimensions ◽  
Honeycomb Seals ◽  
Rotordynamic Coefficient

Test results are presented for leakage and rotordynamic coefficients for seven honeycomb seals. All seals have the same radius, length, and clearance; however, the cell depths and diameters are varied. Rotordynamic data, which are presented, consist of the direct and cross-coupled stiffness coefficients and the direct damping coefficients. The rotordynamic-coefficient data show a considerable sensitivity to changes in cell dimensions; however, no clear trends are identifiable. Comparisons of test data for the honeycomb seals with labyrinth and smooth annular seals shows the honeycomb seal had the best sealing (minimum leakage) performance, followed in order by the labyrinth and smooth seals. For prerotated fluids entering the seal, in the direction of shaft rotation, the honeycomb seal has the best rotordynamic stability followed in order by the labyrinth and smooth. For no prerotation, or fluid prerotation against shaft rotation, the labyrinth seal has the best rotordynamic stability followed in order by the smooth and honeycomb seals.

Hydraulic Fluidics

1973 ◽  
Vol 95 (2) ◽  
pp. 161-166
Author(s):  
L. R. Kelley ◽  
W. A. Boothe
Keyword(s):  
Reynolds Number ◽  
Performance Test ◽  
Dynamic Performance ◽  
Effective Means ◽  
Parameter Analysis ◽  
Test Results ◽  
High Dependency ◽  
Lumped Parameter ◽  
Fluidic Devices ◽  
Hydraulic Operation

Fluidic technology is equally applicable to liquid and gaseous operation, yet the bulk of the literature to date is concerned with the latter. This paper describes some of the unique effects encountered in fluidic devices for hydraulic operation, and compares air operation to hydraulic oil operation in several critical respects including potential response, power consumption, and Reynolds number. Test data on oil operated hydraulic elements show a high dependency on Reynolds number in the lower pressure and temperature regions. Gain as a function of Reynolds number and aspect ratio is presented. An effective means for correlating data to a modified Reynolds number is shown. Dynamic performance test results are also shown, and agree quite well with predictions based on lumped parameter analysis. The use of operational oil elements in specific open and closed-loop circuits is also described.

Test Results for Liquid “Damper” Seals Using a Round-Hole Roughness Pattern for the Stators

1999 ◽  
Vol 121 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Dara W. Childs ◽  
Patrice Fayolle
Keyword(s):  
Friction Factor ◽  
Round Hole ◽  
Test Results ◽  
Partial Explanation ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Friction Factors ◽  
Direct Stiffness ◽  
Factor Data ◽  
Pressure Driven Flow

Test results are reviewed for two annular liquid seals (L = 34.9 mm; D = 76.5 mm) at two clearances (.1 and .12 mm). The seal stators use hole-pattern-roughened stators that are identical except for hole depths of .28 and 2.0 mm. Tests are conducted at three speeds out to 24,600 rpm and three pressures out to 68 bars. Test data consist of leakage rates and rotordynamic coefficients at centered and eccentric positions with static eccentricity ratios out to 0.5. Test results are consistent with expectations in regard to the reduction of cross-coupled stiffness coefficients due to stator roughness. However, the measured direct stiffness coefficients were unexpectedly low. A partial explanation for these results is provided by measured friction factor data which show an increase in the friction factors for pressure-driven flow with an increase in clearance. A prediction model for rotordynamic coefficients, incorporating the friction-factor data, predicted a substantial loss in direct stiffness but could not explain the very low (or negative) values that were measured. The model did explain the measured drop in cross coupled stiffness (k) and provides an alternative explanation to observed reductions in k values; specifically, an increase in the friction factor with increasing clearance causes a reduction in k irrespective of any parallel reduction in the average circumferential velocity.

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