Qualitative Characterization of Anti-Swirl Gas Dampers

1999 ◽  
Vol 121 (2) ◽  
pp. 342-348 ◽  
Author(s):  
N. L. Zirkelback
Keyword(s):  
Rotor Vibration ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Model Predictions ◽  
Backward Whirl ◽  
Rotor Surface ◽  
Direct Stiffness ◽  
The Cross

Anti-swirl gas dampers have applications in high-temperature turbomachinery. Nozzles comprising the circumference of the damper inject air against the direction of shaft rotation, providing a force tangential to the rotor surface that acts to damp rotor vibration. The present work involves prediction of experiments by using direct damping and cross-coupled stiffness coefficients given in Vance and Handy (1997) that characterize the rotordynamic performance of an anti-swirl damper. Direct stiffness added at the damper location is vital to representing the changes in critical speeds and the onset and cease of backward whirl given in the experiments. This direct stiffness arises due to the release of air axially across the annulus of the damper. With the addition of this significant direct stiffness, experimental results compare well with the present rotordynamic model. Predictions using the experimentally obtained damping coefficients adequately reproduce the reduction in vibration amplitudes at the critical speeds. However, applying the cross-coupled stiffness coefficients in predictions fails to show increases in the speed at which backward whirl begins and does not reproduce the wrecking instability experienced in the tests. A further study investigates the magnitude of the cross-coupled stiffness coefficient necessary to cause instability in the rotor-damper system.

scholarly journals Qualitative Characterization of Anti-Swirl Gas Dampers

1998 ◽  
Author(s):  
Nicole L. Zirkelback
Keyword(s):  
Rotor Vibration ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Model Predictions ◽  
Backward Whirl ◽  
Rotor Surface ◽  
Direct Stiffness ◽  
The Cross

Anti-swirl gas dampers have applications in high-temperature turbomachinery. Nozzles comprising the circumference of the damper inject air against the direction of shaft rotation, providing a force tangential to the rotor surface that acts to damp rotor vibration. The present work involves prediction of experiments by using direct damping and cross-coupled stiffness coefficients given in Vance and Handy (1997) that characterize the rotordynamic performance of an anti-swirl damper. Direct stiffness added at the damper location is vital to representing the changes in critical speeds and the onset and cease of backward whirl given in the experiments. This direct stiffness arises due to the release of air axially across the annulus of the damper. With the addition of this significant direct stiffness, experimental results compare well with the present rotordynamic model. Predictions using the experimentally obtained damping coefficients adequately reproduce the reduction in vibration amplitudes at the critical speeds. However, applying the cross-coupled stiffness coefficients in predictions fails to show increases in the speed at which backward whirl begins and does not reproduce the wrecking instability experienced in the tests. A further study investigates the magnitude of the cross-coupled stiffness coefficient necessary to cause instability in the rotor-damper system.

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.

scholarly journals Static and Rotordynamic Analysis of a Plain Annular (Liquid) Seal in the Laminar Regime With a Swirl Brake for Three Clearances

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Ovais Ahmed Bin Najeeb ◽  
Dara W. Childs
Keyword(s):  
Dynamic Force ◽  
Laminar Regime ◽  
Dynamic Measurements ◽  
Stiffness Coefficients ◽  
Stationary Coordinate System ◽  
Liquid Seal ◽  
Direct Stiffness ◽  
The Cross ◽  
Positive Direct ◽  
San Andres

Tests are reported for a smooth seal with radial clearances 127 μm, 254 μm, 381 μm (1×, 2×, and 3×); length 45.72 mm, diameter 101.6 mm. An insert induced upstream preswirl. Swirl brakes (SBs), comprising 36 square cuts with axial depth 5.08 mm, radial height 6.35 mm, and circumferential width 6.35 mm each. Static and rotordynamic data were produced at ω = 2, 4, 6, 8 krpm, ΔP = 2.07, 4.14, 6.21, 8.27 bar, and eccentricity ratios ε0 = e0/Cr = 0.00, 0.27, 0.53, and 0.80. ISO VG 46 oil at a range of 46–49 °C was used, netting laminar flow (total Re ≤ 650). Dynamic measurements included components of the following vectors: (a) stator–rotor relative displacements, (b) acceleration, and (c) applied dynamic force in a stationary coordinate system. SBs were effective at the 3× clearance only. With the 3× seal, the cross-coupled stiffness coefficients have the same sign (not destabilizing). However, the seal has a negative direct stiffness K that could potentially “suck” the rotor into contact with the stator wall, along with dropping the pump rotor's natural frequency, further reducing its dynamic stability. Measurements were compared to predictions from a code by Zirkelback and San Andrés. Most predictions agree well with test data. Notable exceptions are the direct and cross-coupled stiffness coefficients for the 3× clearance. Predictions showed positive direct stiffness and opposite signs for the cross-coupled stiffness coefficients.

Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor: Part 1 — Measurement

2019 ◽  
Author(s):  
Jieun Song ◽  
Suyong Kim ◽  
Tae Choon Park ◽  
Bong-Jun Cha ◽  
Dong Hun Lim ◽  
...  
Keyword(s):  
Centrifugal Compressor ◽  
System Level ◽  
Labyrinth Seals ◽  
Stiffness Coefficients ◽  
Pressure Distributions ◽  
Order Of Magnitude ◽  
Direct Stiffness ◽  
The Cross ◽  
Rotordynamic Forces ◽  
Pressure Perturbations

Abstract Centrifugal compressors can suffer from rotordynamic instability. While individual components (e.g., seals, shrouds) have been previously investigated, an integrated experimental or analytical study at the compressor system level is scarce. For the first time, non-axisymmetric pressure distributions in a statically eccentric shrouded centrifugal compressor with eye-labyrinth seals have been measured for various eccentricities. From the pressure measurements, direct and cross-coupled stiffness coefficients in the shrouded centrifugal compressor have been determined. Thus, the contributions of the pressure perturbations in the shroud cavity and labyrinth seals have been simultaneously investigated. The cross-coupled stiffness coefficients in the shroud and labyrinth seals are both positive and one order of magnitude larger than the direct stiffness coefficients. Furthermore, in the tested compressor, contrary to the common assumption, the cross-coupled stiffness in the shroud is 2.5 times larger than that in the labyrinth seals. Thus, the shroud contributes more to rotordynamic instability than the eye-labyrinth seals.

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.

Measurements Versus Predictions for Rotordynamic and Leakage Characteristics of a Convergent-Tapered, Honeycomb-Stator/Smooth-Rotor Annular Gas Seal

2008 ◽  
Author(s):  
Daniel E. van der Velde ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Excitation Frequency ◽  
Test Fluid ◽  
Low Frequencies ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Honeycomb Seals ◽  
Excitation Frequencies ◽  
The Cross

Measured results are presented for rotordynamic coefficients and leakage rates for two honeycomb-stator seal geometries, a convergent-tapered honeycomb seals (CTHC) and a constant-clearance honeycomb seals (CCHC) tested by Sprowl and Childs in 2007. The rotor diameter was 114.3 mm (4.500 in). The CTHC seals had inlet and exit clearances of 0.334 and 0.204 mm, respectively. The CCHC seal had a constant clearance of 0.204 mm. Honeycomb cells had depths of 3.175 mm (0.125 in) and widths of 0.79 mm (0.031 in). Measurements are reported with air as the test fluid, zero preswirl, ω = 20,200 rpm, a supply pressure of 69 bar (1,000 psi) and supply temperature of 18°C (64.4°F) for both seal geometries. The test pressure ratios are 0.5 for the CCHC seal, and 0.46 for the CTHC seal. The tapered seal leaks about 20% more than the constant-clearance seal. Measured and predicted dynamic coefficients are strong functions of excitation frequency. The measured direct stiffness coefficient was higher for the tapered seal at all excitation frequencies, including a projection to zero frequency, where the CCHC seal was on the order of −2MN/m versus roughly +13MN/m for the tapered seal. The CTHC seal had higher cross-coupled stiffness coefficients than the CCHC seal at all excitation frequencies. The CCHC and CTHC seals had comparable direct damping out to ∼80 Hz. For higher excitation frequencies, the CTHC seal had larger direct damping values. The effective damping Ceff combines the positive effect of direct damping and the destabilizing effect of cross-coupled-stiffness coefficients. It is negative at low frequencies and becomes positive for higher frequencies. The frequency at which it changes sign is called the cross-over frequency. The CCHC had a lower cross-over frequency (better from a stability viewpoint) and higher Ceff values out to ∼80 Hz. At higher excitation frequencies from ∼120Hz onward, the tapered seal has higher effective damping values. Kleynhans and Childs’ 1997 two-control-volume model did a generally good job of predicting the direct stiffness coefficients of both seals. It closely predicted the cross-coupled stiffness coefficients for the CCHC seal but substantially under predicted the values for the CTHC seal. It under predicted the direct damping for the CCHC seal at frequencies below ∼120Hz, but did a good job for higher frequencies. It under predicted direct damping for the CTHC seal at all frequencies. For the CCHC seal, the model did a good job of predicting Ceff at all frequencies and also accurately predicted the cross-over frequency. For the CTHC seal, the model accurately predicted the cross-over frequency but over predicted Ceff below the cross-over frequency (the seal was more destabilizing than predicted) and under predicted Ceff at higher frequencies.

Dynamic characteristics of compound textured journal bearing

2020 ◽  
pp. 135065012095137
Author(s):  
Fanming Meng ◽  
Yifei Zhang ◽  
Linlin Su ◽  
Haiyang Yu ◽  
Yong Zheng
Keyword(s):  
Dynamic Characteristics ◽  
Critical Speed ◽  
Journal Bearing ◽  
Rotor System ◽  
Deformation Effect ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Texture Effect

An investigation of the compound texture effect on the dynamic characteristics of the journal bearing film is conducted. In this work, eight dynamic coefficients of the compound textured journal bearing and critical speed of the rotor supported by textured bearings are obtained and compared. Meanwhile, the elastic deformation effect of the bearing and rotor is obtained using the continuous convolution fast Fourier transform (CC-FFT) method. It is found that the reasonably arranged compound texture brings out an obvious increment in the direct stiffness coefficients and damping coefficients compared with the simple one, which results in the high critical speed of the bearing-rotor system. The above changes are close to the texture distribution, second-layered texture length, and width-length ratios of the compound texture. Moreover, there exists a critical compound texture depth to improve the critical speed of the bearing-rotor system.

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.

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.

Rotordynamic Performance Predictions of Flexure Pivot Tilting Pad Bearings and Comparison to Published Test Data

2016 ◽  
Author(s):  
Tae Ho Kim ◽  
Kyung Eun Jang ◽  
Tae Gyu Choi
Keyword(s):  
Predictive Model ◽  
Test Data ◽  
Frequency Ratio ◽  
Rotor Speed ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Attitude Angle ◽  
Performance Predictions ◽  
Tilting Pad ◽  
Direct Stiffness

This paper presents performance predictions for a Flexure Pivot® tilting pad bearing (FPTPB) and comparisons to published test data. The FPTPB has pads that tilt about a web pivot. The pivot is designed to have little rotational stiffness, which improves its rotordynamic stability. The Reynolds equation for an isothermal and isoviscous fluid was used to calculate the film pressure using the finite element method. The Newton–Raphson method was used to determine the journal eccentricity, journal attitude angle, and pivot deflections (tilting angle, and radial and circumferential displacements) simultaneously. A small perturbation of the journal center around its equilibrium position was employed to calculate the stiffness and damping coefficients. The whirl frequency ratio (WFR), which is the ratio of the frequency of unstable whirl motion to the rotor threshold speed, was calculated using the predicted dynamic coefficients. The predictive model used was for a four-pad FPTPB with a journal diameter of 116.81 mm and axial length of 76.2 mm. Each pad had a preload of 0.25, pivot offset of 0.5, and web pivot thickness of 2.125 mm. The rotor speed and specific load were varied up to 16 krpm and 345 kPa, respectively. Predictions were performed for the load-on-pad (LOP) and load-between-pad (LBP) configurations. The results show that the predicted journal eccentricity and attitude angle decrease as the rotor speed increases. The direct stiffness coefficients increase as the rotor speed increases, but the cross-coupled stiffness coefficients change little. As the static load increases, the direct stiffness coefficient in the vertical direction increases, but the other stiffness coefficients change little. The damping coefficients are affected little by the rotor speeds and static loads. A comparison of the predictions with published test data shows that the predictive model slightly overestimates the journal eccentricities and underestimates the absolute values of the journal attitude angles. The predicted stiffness coefficients agree well with the test data. However, large discrepancies in the damping coefficients were observed between the predictions and published data. The effect of the pivot thickness on the rotordynamic performance of the FPTPB was also studied. Predictions were performed for changes in the pivot thickness up to ± 20 percent in increments of 10 percent from the original value of 2.125 mm. The results show that the predicted maximum pressure, journal eccentricity, and attitude angle decrease with decreasing pivot thickness, but the minimum film thickness increases. As the pivot thickness decreases, the direct stiffness coefficients, direct damping coefficients, and absolute values of the cross-coupled damping coefficients increase. The whirl frequency ratio (WFR), which was found to be in reasonable agreement with the test data, decreases significantly with decreasing pivot thickness, which suggests improvement in rotordynamic stability.

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