A Novel Computational Model for Tilting Pad Journal Bearings with Soft Pivot Stiffnesses PDF Download
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Author: Yujiao Tao
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Languages : en
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A novel tilting pad journal bearing model including pivot flexibility as well as temporal fluid inertia effects on the thin film fluid flow aims to accurately predict the bearing forced performance. The predictive model also accounts for the thermal energy transport effects in a TPJB. A Fortran program with an Excel GUI models TPJBs and delivers predictions of the bearing static and dynamic forced performance. The calculation algorithm uses a Newton-Raphson procedure for successful iterations on the equilibrium pad radial and transverse displacements and journal center displacements, even for bearings pads with very soft pivots. The predictive model accounts for the effect of film temperature on the operating bearing and pad clearances by calculating the thermal expansion of the journal and pad surfaces. The pad inlet thermal mixing coefficient (lambda) influences moderately the predicted fluid film temperature field. Pad pivot flexibility decreases significantly and dominates the bearing stiffness and damping coefficients when the pivot stiffness is lower than 10% of the fluid film stiffness coefficients (with rigid pivots). Pivot flexibility has a more pronounced effect on reducing the bearing damping coefficients than the stiffness coefficients. Pad pivot flexibility may still affect the bearing behavior at a light load condition for a bearing with a large pad preload. Pad pivot flexibility, as well as the fluid inertia and the pads' mass and mass moment of inertia, could influence the bearing impedance coefficients, in particular at high whirl frequencies. The stiffness and damping coefficients of a TPJB increase with a reduction in the operating bearing and pad clearances. The work delivers a predictive tool benchmarked against a number of experimental results for test bearings available in the recent literature. The static and dynamic forced performance characteristics of actual TPJBs can not be accurately predicted unless their pad flexibility and pivot flexibility, fluid film temperature, pad inlet thermal mixing coefficient, operating bearing and pad clearances, among others are well known in advance. However, the extensive archival literature showcasing test procedures and experimental results for TPJBs does not report the above parameters. Thus, reasonable assumptions on the magnitude of certain elusive parameters for use in the predictive TPJB model are necessary. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148299
Author: Yujiao Tao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
A novel tilting pad journal bearing model including pivot flexibility as well as temporal fluid inertia effects on the thin film fluid flow aims to accurately predict the bearing forced performance. The predictive model also accounts for the thermal energy transport effects in a TPJB. A Fortran program with an Excel GUI models TPJBs and delivers predictions of the bearing static and dynamic forced performance. The calculation algorithm uses a Newton-Raphson procedure for successful iterations on the equilibrium pad radial and transverse displacements and journal center displacements, even for bearings pads with very soft pivots. The predictive model accounts for the effect of film temperature on the operating bearing and pad clearances by calculating the thermal expansion of the journal and pad surfaces. The pad inlet thermal mixing coefficient (lambda) influences moderately the predicted fluid film temperature field. Pad pivot flexibility decreases significantly and dominates the bearing stiffness and damping coefficients when the pivot stiffness is lower than 10% of the fluid film stiffness coefficients (with rigid pivots). Pivot flexibility has a more pronounced effect on reducing the bearing damping coefficients than the stiffness coefficients. Pad pivot flexibility may still affect the bearing behavior at a light load condition for a bearing with a large pad preload. Pad pivot flexibility, as well as the fluid inertia and the pads' mass and mass moment of inertia, could influence the bearing impedance coefficients, in particular at high whirl frequencies. The stiffness and damping coefficients of a TPJB increase with a reduction in the operating bearing and pad clearances. The work delivers a predictive tool benchmarked against a number of experimental results for test bearings available in the recent literature. The static and dynamic forced performance characteristics of actual TPJBs can not be accurately predicted unless their pad flexibility and pivot flexibility, fluid film temperature, pad inlet thermal mixing coefficient, operating bearing and pad clearances, among others are well known in advance. However, the extensive archival literature showcasing test procedures and experimental results for TPJBs does not report the above parameters. Thus, reasonable assumptions on the magnitude of certain elusive parameters for use in the predictive TPJB model are necessary. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148299
Author: Yingkun Li
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Languages : en
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Tilting pad journal bearings (TPJBs) supporting rotors for high performance turbomachinery have undergone steady design improvements to satisfy more stringent operating conditions that include large specific loads due to smaller footprints, and high surface speeds that produce larger drag power losses and lubricant temperature rise. Simultaneously, predictive models continuously evolve to include minute details on bearing geometry, pads and pivots' configurations, oil delivery systems, etc. This thesis introduces a fluid film flow model including both pad and pivot flexibility to predict the static and dynamic force performance of typical TPJBs. This performance encompasses journal eccentricity, drag power loss, lubricant temperature rise, fluid film thickness, fluid film pressure, bearing complex stiffnesses, static stiffnesses, damping coefficients and virtual mass coefficients. A finite element (FE) pad structural model (with/without the Babbitt layer) is coupled to a thin film flow model to determine the mechanical deformation of the pad upper surface. Recently, Gaines and Childs conducted experiments with three TPJB sets, each having three pads, over a range of load and rotational speed conditions. To quantify the effect of pad flexibility on the bearings' dynamic performance, the pad thickness varies from thin to thick, t=8.5 mm, 10 mm and 11.5mm. The test data shows that pad flexibility reduces the journal eccentricity and the dynamic force coefficients. The current model with both pad and pivot flexibility delivers predictions correlating favorably with the test data, in particular the bearing stiffnesses, yet it overestimates the bearing damping coefficients. Predictions for bearing models available in the archival literature show that the maximum pad surface deformation occurs on the loaded pad at both its leading and trailing edges; i.e. under mechanical pressure a pad opens. The deformation at the pad mid-plane (Z=0) is slightly larger than that at the pad side edges (Z=±1/2 L). Contrary to the effect of pivot flexibility that leads to an increase in journal eccentricity, pad flexibility tends to reduce the journal eccentricity, similar as in tests reported by Gaines. A soft pad (elastic) decreases significantly the bearing stiffnesses and the damping coefficients by up to 20%. A parametric study follows to quantify the influence of pad thickness on the rotordynamic force coefficients of two sample TPJBs: one with three pads of increasing preload, ( r̄[subscript p]=0, 0.25 and 0.5), and another one with four pads of null preload ( r̄[subscript p]=0). The bearing pads are either rigid or flexible by varying their thickness. For design considerations, dimensionless static and dynamic characteristics of the bearings are presented versus the Sommerfeld number (S). An appendix introduces a one-dimensional beam equation to approximate the pad deformation accounting for the Babbitt layer. Based on this equation, a dimensionless pad flexibility parameter is defined. Pad flexibility shows a more pronounced effect on the journal eccentricity and the force coefficients of a TPJB with null pad preload than for bearings with large pad preloads (0.25 and 0.5), in particular for operation with a small load or at a high surface speed (S>0.8). With the same pad preload, pad flexibility affects more the dynamic force coefficients for a load on pad (LOP) bearing than those for a load between pad (LBP) bearing. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155408
Author: Zygmunt Popowicz
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Category :
Languages : en
Pages :
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Author: Zolton N. Nemeth
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Category : Bearings (Machinery)
Languages : en
Pages : 36
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Author: Edgar J. Gunter
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Category : Gas-lubricated journal bearings
Languages : en
Pages : 236
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 55
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Theoretical study on the steady state and dynamic behaviour of the tilting pad journal bearing. A computer model considers the entire bearing and allows for the inclusion of thermal and elastic distortions, variable viscosity, hot oil carry over and turbulence within the oil film. Part 1 of the study considered the steady state analysis and results were verified against five sets of independent data. This second report examines bearing dynamic behaviour and presents stiffness and damping coefficients for the five shoe, tilting pad journal bearing. The effects of changing bearing preload and direction of loading are illustrated. This report also describes the theoretical basis of the computer model and includes a full listing of the program.
Author: Zolton N. Nemeth
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ISBN:
Category : Bearings (Machinery)
Languages : en
Pages : 52
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Author: Jason Christopher Wilkes
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Category :
Languages : en
Pages :
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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: Theodore Scott Brockett
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ISBN:
Category : Journal bearings
Languages : en
Pages : 278
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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.
