Measured and Predicted Rotor-pad Transfer Functions for a Rocker-pivot Tilting-pad Journal Bearing PDF Download
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Author: Jason Christopher Wilkes
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Languages : en
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Transverse pad motion was predicted and observed. Based on phase measurements, this motion is lightly damped, and appears to be caused by pivot deflection instead of slipping. Despite observing a lightly damped phase change, an increase in magnitude at this natural frequency was not observed. Predicted direct stiffness and damping for unit loads from 0-3200 kPa (0-450 psi) fit through 1.5× running speed are within 18% of measurements at 4400 rpm, while predictions at 10200 rpm are within 10% of measurements. This is a significant improvement on the accuracy of predictions cited in literature. Comparisons between predictions from the developed bearing model neglecting pad, pivot, and pad and pivot flexibility show that predicted direct stiffness and damping coefficients for a model having a rigid pad and pivot are overestimated, respectively, by 202% and 811% at low speeds and large loads, by 176% and 513% at high speeds and high loads, and by 51% and 182% at high speeds and light loads. While the reader is likely questioning the degree to which these predictions are overestimated in regard to previous comparisons, these predictions are based on measured operating bearing clearances, which are 20-30% smaller than the cold bearing clearances that previous comparisons were based on. The effect of employing a full bearing model (retaining all of the pad degrees of freedom) versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. This overestimation of stability is due to an increase in predicted direct damping at the synchronous frequency over the subsynchronously reduced value. This increase in direct damping with excitation frequency was also seen in highly loaded test data at frequencies below approximately 2×running speed, after which direct damping decreased with increasing excitation frequency. This effect was more pronounced in predictions, occurring at all load and speed combinations. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies at 10200 rpm. It was found that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping. This outcome contrasts with the comparison between models using synchronously and subsynchronously reduced impedance predictions, which showed the subsynchronously reduced model to be the most conservative. This contrast results from a predicted increase in damping with increasing excitation frequency at all speeds and loads, while this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.
Author: Jason Christopher Wilkes
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ISBN:
Category :
Languages : en
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Book Description
Transverse pad motion was predicted and observed. Based on phase measurements, this motion is lightly damped, and appears to be caused by pivot deflection instead of slipping. Despite observing a lightly damped phase change, an increase in magnitude at this natural frequency was not observed. Predicted direct stiffness and damping for unit loads from 0-3200 kPa (0-450 psi) fit through 1.5× running speed are within 18% of measurements at 4400 rpm, while predictions at 10200 rpm are within 10% of measurements. This is a significant improvement on the accuracy of predictions cited in literature. Comparisons between predictions from the developed bearing model neglecting pad, pivot, and pad and pivot flexibility show that predicted direct stiffness and damping coefficients for a model having a rigid pad and pivot are overestimated, respectively, by 202% and 811% at low speeds and large loads, by 176% and 513% at high speeds and high loads, and by 51% and 182% at high speeds and light loads. While the reader is likely questioning the degree to which these predictions are overestimated in regard to previous comparisons, these predictions are based on measured operating bearing clearances, which are 20-30% smaller than the cold bearing clearances that previous comparisons were based on. The effect of employing a full bearing model (retaining all of the pad degrees of freedom) versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. This overestimation of stability is due to an increase in predicted direct damping at the synchronous frequency over the subsynchronously reduced value. This increase in direct damping with excitation frequency was also seen in highly loaded test data at frequencies below approximately 2×running speed, after which direct damping decreased with increasing excitation frequency. This effect was more pronounced in predictions, occurring at all load and speed combinations. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies at 10200 rpm. It was found that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping. This outcome contrasts with the comparison between models using synchronously and subsynchronously reduced impedance predictions, which showed the subsynchronously reduced model to be the most conservative. This contrast results from a predicted increase in damping with increasing excitation frequency at all speeds and loads, while this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.
Author: David Patrick Tschoepe
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Category :
Languages : en
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Measured and predicted static and dynamic characteristics are provided for a four-pad, rocker-pivot, tilting-pad journal bearing in the load-on-pad and load-between-pad orientations. The bearing has the following characteristics: 4 pads, .57 pad pivot offset, 0.6 L/D ratio, 60.33 mm (2.375in) pad axial length, 0.08255 mm (0.00325 in) radial clearance in the load-on-pad orientation, and 0.1189 mm (0.00468 in) radial clearance in the load-between-pad orientation. Tests were conducted on a floating test bearing design with unit loads ranging from 0 to 2903 kPa (421.1 psi) and speeds from 6.8 to 13.2 krpm. For all rotor speeds, hot-clearance measurements were taken to show the reduction in bearing clearance due to thermal expansion of the shaft and pads during testing. As the testing conditions get hotter, the rotor, pads, and bearing expand, decreasing radial bearing clearance. Hot-clearance measurements showed a 16-25% decrease in clearance compared to a clearance measurement at room temperature. For all test conditions, dynamic tests were performed over a range of excitation frequencies to obtain complex dynamic stiffness coefficients as a function of frequency. The direct real dynamic stiffness coefficients were then fitted with a quadratic function with respect to frequency. From the curve fit, the frequency dependence was captured by including a virtual-mass matrix [M] to produce a frequency independent [K][C][M] model. The direct dynamic stiffness coefficients for the load-on-pad orientation showed significant orthotropy, while the load-between-pad did not. The load-between-pad showed slight orthotropy as load increased. Experimental cross-coupled stiffness coefficients were measured in both load orientations, but were of the same sign and significantly less than direct stiffness coefficients. In both orientations the imaginary part of the measured dynamic stiffness increased linearly with increasing frequency, allowing for frequency independent direct damping coefficients. Rotordynamic coefficients presented were compared to predictions from two different Reynolds-based models. Both models showed the importance of taking into account pivot flexibility and different pad geometries (due to the reduction in bearing clearance during testing) in predicting rotordynamic coefficients. If either of these two inputs were incorrect, then predictions for the bearings impedance coefficients were very inaccurate. The main difference between prediction codes is that one of the codes incorporates pad flexibility in predicting the impedance coefficients for a tilting-pad journal bearing. To look at the effects that pad flexibility has on predicting the impedance coefficients, a series of predictions were created by changing the magnitude of the pad's bending stiffness. Increasing the bending stiffness used in predictions by a factor of 10 typically caused a 3-11% increase in predicted Kxx and Kyy, and a 10-24% increase in predicted Cxx and Cyy. In all cases, increasing the calculated bending stiffness from ten to a hundred times the calculated value caused slight if any change in Kxx, Kyy, Cxx, and Cyy. For a flexible pad an increase in bending stiffness can have a large effect on predictions; however, for a more rigid pad an increase in pad bending stiffness will have a much lesser effect. Results showed that the pad's structural bending stiffness can be an important factor in predicting impedance coefficients. Even though the pads tested in this thesis are extremely stiff, changes are still seen in predictions when the magnitude of the pad?s bending stiffness is increased, especially in Cxx, and Cyy. The code without pad flexibility predicted Kxx and Kyy much more accurately than the code with pad flexibility. The code with pad flexibility predicts Cxx more accurately, while the code without pad flexibility predicted Cyy more accurately. Regardless of prediction Code used, the Kxx and Kyy were over-predicted at low loads, but predicted more accurately as load increased. Cxx, and Cyy were modeled very well in the load-on-pad orientation, while slightly overpredicted in the load-between-pad orientation. For solid pads, like the ones tested here, both codes do a decent job at predicting impedance coefficients. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148049
Author: Clint Ryan Carter
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Languages : en
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This thesis presents the static and dynamic performance data for a 5 pad tilting pad bearing in both the load-on-pad (LOP) and the load-between-pad (LBP) configurations over a variety of different loads and speeds. The bearing tested was an Orion Advantage with direct lubrication exhibiting these specifications: 5 pads, .282 preload, 60% offset, 57.87° pad arc angle, 101.587 mm (3.9995 in) rotor diameter, .1575 mm (.0062 in) diametrical clearance, 60.325 mm (2.375 in) pad length. Dynamic tests were performed over a range of frequencies to observe any frequency effects on the dynamic stfffnesses. It was found that under most test conditions the direct real part of the dynamic stiffnesses could be approximated as quadratic functions of the excitation frequency. This frequency dependency is caused by pad inertia, pad flexibility, and fluid inertia. The observed frequency dependency can be 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. This method eliminates the often debated question over whether a stability analysis should be performed at the running speed or at the first natural frequency. Substantially large added mass terms in the loaded direction were found that approached 60 kg. Some conditions for the LBP bearing exhibited unloaded direct mass coefficients that were at or near zero, which would lead to a frequency dependent [K][C] model to be used instead. The whirl frequency ratio was found to be zero at all test conditions. Static data were also recorded which included pad temperatures, attitude angle, eccentricity, static stiffness and power loss. Some cross coupling in the form of deviation from the loaded axis was evident from the locus plots; however, the cross coupled stiffness coefficients were found to be very small relative to the direct stiffness coefficients. Both static and dynamic experimental results were compared to theoretical predictions via a bulk flow analysis. Most parameters were modeled well including the static eccentricity e0 dynamic direct stiffness coefficients Kxx and Kyy, which were slightly over predicted. However, the direct damping coefficients Cxx and Cyy were significantly over predicted.
Author: Chris David Kulhanek
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Languages : en
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Static performance and rotordynamic coefficients are provided for a rocker-pivot, tilting-pad journal bearing with 50 and 60% offset pads in a load-between-pad configuration. The bearing uses leading-edge-groove 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, 60.325 mm (2.375 in) axial pad length. Operating conditions included loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the direct real dynamic stiffnesses 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, producing a frequency independent [K][C][M] model. The direct imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency independent direct damping coefficients. Compared to the 50% offset, the 60% offset configuration's direct stiffness coefficients were larger at light unit loads. At high loads, the 50% offset configuration had a larger direct stiffness in the loaded direction. Negative direct added-mass coefficients were regularly obtained for both offsets, especially in the unloaded direction. Added-mass magnitudes were below 32 kg for all test cases. No appreciable difference was measured in direct damping coefficients for both pivot offset. A bulk-flow Navier-Stokes CFD code provided rotordynamic coefficient predictions. The following stiffness and damping prediction trends were observed for both 50 and 60% offsets. The direct stiffness coefficients were modeled well at light loads and became increasingly over-predicted with increasing unit load. Stiffness orthotropy was measured at zero and light load conditions that was not predicted. Direct damping predictions in the loaded direction increased significantly with unit load while the experimental direct damping coefficients remained constant with load. The direct damping coefficients were reasonably modeled only at the highest test speed of 16 krpm. Experimental cross-coupled stiffness coefficients were larger than predicted for both offsets, but were of the same sign and considerably smaller than the direct coefficients.
Author: Edgar J. Gunter
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ISBN:
Category : Gas-lubricated journal bearings
Languages : en
Pages : 236
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Author: Zolton N. Nemeth
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ISBN:
Category : Bearings (Machinery)
Languages : en
Pages : 52
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Author: Joel Mark Harris
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Category :
Languages : en
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Static characteristics and rotordynamic coefficients were experimentally determined for a four-pad tilting-pad journal bearing with ball-in-socket pivots in loadbetween- pad configuration. A frequency-independent [M]-[C]-[K] model fit the measurements reasonably well, except for the cross-coupled damping coefficients. Test conditions included speeds from 4,000 to 12,000 rpm and unit loads from 0 to 1896 kPa (0 to 275 psi). The test bearing was manufactured by Rotating Machinery Technology (RMT), Inc. Though it has a nominal diameter of 101.78 mm (4.0070 in.), measurements indicated significant bearing crush with radial bearing clearances of 99.6 [micron] (3.92 mils) and 54.6 [micron] (2.15 mils) in the axes 45[degrees] counterclockwise and 45[degrees] clockwise from the loaded axis, respectively. The pad length is 101.6 mm (4.00 in.), giving L/D = 1.00. The pad arc angle is 73[degrees], and the pivot offset ratio is 65%. The preloads of the loaded and unloaded pads are 0.37 and 0.58, respectively. A bulk-flow Navier-Stokes model was used for predictions, using adiabatic conditions for the bearing fluid. Because the model assumes constant nominal clearances at all pads, the average of the measured clearances was used as an estimate. Eccentricities and attitude angles were markedly under predicted while power loss was under predicted at low speeds and very well predicted at high speeds. The maximum detected pad temperature was 71[degrees] C (160[degrees]F) and the rise from inlet to maximum bearing temperature was over predicted by 10-40%. Multiple-frequency force inputs were used to excite the bearing. Direct stiffness and damping coefficients were significantly over predicted, but addition of a simple stiffness-in-series model substantially improved the agreement between theory and experiment. Direct added masses were zero or negative at low speeds and increased with speed up to a maximum of about 50 kg; they were normally greater in the unloaded direction. Although significant cross-coupled stiffness terms were present, they always had the same sign. The bearing had zero whirl frequency ratio netting unconditional stability over all test conditions. Static stiffness in the y direction (obtained from steadystate loading) matched the rotordynamic stiffness Kyy (obtained from multiple-frequency excitation) reasonably at low loads but poorly at the maximum test load.
Author: Zolton N. Nemeth
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ISBN:
Category : Bearings (Machinery)
Languages : en
Pages : 36
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Author: Jinsang Kim
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Category : Bearings (Machinery)
Languages : en
Pages : 348
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Author: Adnan Mahmoud Al-Ghasem
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Languages : en
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This thesis presents the dynamic and static forced performance of a flexure-pivot tilting-pad bearing load between pad (LBP) configuration for different 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 0.11684 m (4.600 in). The dynamic coefficients and the static performance parameters of the FPB have been compared with the theoretical predictions using the isothermal analysis from the rotordynamic software suite XLTRC2-XLTFPBrg. The bearing shows a small attitude angle, about 10°, which indicates small crosscoupling stiffnesses. The pad temperatures increase in the circumferential direction of rotation with speed and load. The pads maximum temperature was measured near the trailing edge. The dependency of the stiffness and damping coefficients on the excitation frequency has been studied. The frequency dependency in the dynamic coefficients was removed by introducing an added mass coefficient to the bearing model. The direct added mass coefficients were around 32 kg. The direct stiffness and damping coefficients increase with load, while increasing and decreasing with rotor speed, respectively. A small whirl frequency ratio (WFR) was found of about 0.15, and it decreases with load and increases with speed. A comparison between the dynamic stiffnesses using a Reynolds equation and the bulk-flow Navier-Stokes models with the experimental dynamic stiffnesses shows that the Reynolds model (even for laminar flows) is not adequate, and that the bulk-flow model should be used for rotordynamic coefficients prediction. The bulk-flow model in general predicts well the static performance parameters and the direct dynamic coefficients, and underpredicts the cross-coupled coefficients (overpredicts the stability).
