A Computational Model for Tilting Journal Bearings with Pad Flexibility

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Book Synopsis A Computational Model for Tilting Journal Bearings with Pad Flexibility by : Yingkun Li

Download or read book A Computational Model for Tilting Journal Bearings with Pad Flexibility written by Yingkun Li and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

A Novel Computational Model for Tilting Pad Journal Bearings with Soft Pivot Stiffnesses

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Book Synopsis A Novel Computational Model for Tilting Pad Journal Bearings with Soft Pivot Stiffnesses by : Yujiao Tao

Download or read book A Novel Computational Model for Tilting Pad Journal Bearings with Soft Pivot Stiffnesses written by Yujiao Tao and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings

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Book Synopsis A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings by : L. L. Earles

Download or read book A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings written by L. L. Earles and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general method of incorporating pad flexibility effects into tilting pad isothermal bearing analysis is developed. The pad assembly approach is extended using 2-dimensional finite elements to determine pad deformations of a single pad. The pad deformations are represented by a single degree of freedom, the change in the pad radius of curvature, thus the current method is an approximate approach. The equations to calculate frequency reduced coefficients for a single pad are presented. Synchronously reduced coefficients for a single pad are in agreement with previous curved beam approximate methods and a more rigorous iterative approach. The finite element pad model provides more versatility in modeling nonuniform pad dimensions and the skewed boundary conditions which occur at the spherical pivot-pad socket interfaces.

A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings

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Book Synopsis A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings by : L. L. Earles

Download or read book A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings written by L. L. Earles and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pad flexibility effects are studied in an actual bearing. This flexibility is shown to decrease the predicted instability onset speed of the rotor bearing system. The use of complex eigenvalue dependent bearing coefficients as compared with using synchronously reduced coefficients is seen to produce a more significant decrease in the instability onset speed. Further reductions in the instability onset speed are obtained by including pivot stiffness in the complex eigenvalue dependent bearing coefficients.

Application of Dynamic Reduction to the Modeling of Tilting-pad Journal Bearings

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ISBN 13 :
Total Pages : 278 pages
Book Rating : 4.:/5 (263 download)

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Book Synopsis Application of Dynamic Reduction to the Modeling of Tilting-pad Journal Bearings by : Theodore Scott Brockett

Download or read book Application of Dynamic Reduction to the Modeling of Tilting-pad Journal Bearings written by Theodore Scott Brockett and published by . This book was released on 1991 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Design Guide for Gas-lubricated Tilting-pad Journal and Thrust Bearings with Special Reference to High-speed Rotor

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Total Pages : 236 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Design Guide for Gas-lubricated Tilting-pad Journal and Thrust Bearings with Special Reference to High-speed Rotor by : Edgar J. Gunter

Download or read book Design Guide for Gas-lubricated Tilting-pad Journal and Thrust Bearings with Special Reference to High-speed Rotor written by Edgar J. Gunter and published by . This book was released on 1964 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Computer Model of the Tilting Pad Journal Bearing Suitable for the Micro-computer, Part 2

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Total Pages : 55 pages
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Book Synopsis A Computer Model of the Tilting Pad Journal Bearing Suitable for the Micro-computer, Part 2 by :

Download or read book A Computer Model of the Tilting Pad Journal Bearing Suitable for the Micro-computer, Part 2 written by and published by . This book was released on 1987 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Measurements Versus Predictions for the Static and Dynamic Characteristics of a Four-pad Rocker-pivot, Tilting-pad Journal Bearing

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Book Synopsis Measurements Versus Predictions for the Static and Dynamic Characteristics of a Four-pad Rocker-pivot, Tilting-pad Journal Bearing by : David Patrick Tschoepe

Download or read book Measurements Versus Predictions for the Static and Dynamic Characteristics of a Four-pad Rocker-pivot, Tilting-pad Journal Bearing written by David Patrick Tschoepe and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Modeling dynamic behavior in tilting pad gas journal bearings

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ISBN 13 : 9789517649650
Total Pages : 157 pages
Book Rating : 4.6/5 (496 download)

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Book Synopsis Modeling dynamic behavior in tilting pad gas journal bearings by : Petri Sallinen

Download or read book Modeling dynamic behavior in tilting pad gas journal bearings written by Petri Sallinen and published by . This book was released on 2004 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Measured and Predicted Rotor-pad Transfer Functions for a Rocker-pivot Tilting-pad Journal Bearing

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Book Synopsis Measured and Predicted Rotor-pad Transfer Functions for a Rocker-pivot Tilting-pad Journal Bearing by : Jason Christopher Wilkes

Download or read book Measured and Predicted Rotor-pad Transfer Functions for a Rocker-pivot Tilting-pad Journal Bearing written by Jason Christopher Wilkes and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Tilting Pad Journal Bearings

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Book Synopsis Tilting Pad Journal Bearings by : Zygmunt Popowicz

Download or read book Tilting Pad Journal Bearings written by Zygmunt Popowicz and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stability of Rotors Supported by Tilting Pad Journal Bearings

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ISBN 13 : 9781109865028
Total Pages : 688 pages
Book Rating : 4.8/5 (65 download)

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Book Synopsis Stability of Rotors Supported by Tilting Pad Journal Bearings by : Charles Hunter Cloud

Download or read book Stability of Rotors Supported by Tilting Pad Journal Bearings written by Charles Hunter Cloud and published by . This book was released on 2007 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rotor supported by two tilting pad journal bearings on flexible supports serves as the test apparatus. Two magnetic actuators are also incorporated, one providing external forcing and the other applying destabilizing cross-coupled stiffness. The rotor model is reconciled using experimental modal analysis. Polynomial transfer function models for the flexible supports are developed from frequency response function measurements. Control and estimation of the actuators' forces is done using calibrated circuit models.

Performance of Gas-lubricated Cruciform-mounted Tilting-pad Journal Bearings and a Damped Flexibly Mounted Spiral-groove Thrust Bearing

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Total Pages : 28 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Performance of Gas-lubricated Cruciform-mounted Tilting-pad Journal Bearings and a Damped Flexibly Mounted Spiral-groove Thrust Bearing by : Lloyd W. Ream

Download or read book Performance of Gas-lubricated Cruciform-mounted Tilting-pad Journal Bearings and a Damped Flexibly Mounted Spiral-groove Thrust Bearing written by Lloyd W. Ream and published by . This book was released on 1974 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tilting Pad Journal Bearing

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Book Synopsis Tilting Pad Journal Bearing by : Zygmunt Popowicz

Download or read book Tilting Pad Journal Bearing written by Zygmunt Popowicz and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Paper

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ISBN 13 :
Total Pages : 466 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Paper by :

Download or read book Paper written by and published by . This book was released on 2001 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamic Behavior of Air Lubricated Pivoted Pad Journal Bearing - Rotor System

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ISBN 13 :
Total Pages : 41 pages
Book Rating : 4.:/5 (539 download)

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Book Synopsis Dynamic Behavior of Air Lubricated Pivoted Pad Journal Bearing - Rotor System by : Zolton N. Nemeth

Download or read book Dynamic Behavior of Air Lubricated Pivoted Pad Journal Bearing - Rotor System written by Zolton N. Nemeth and published by . This book was released on 1972 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rotor bearing dynamic tests were conducted with tilting-pad journal bearings having three different pad masses and two different pivot geometries. The rotor was vertically mounted and supported by two three-pad tilting-pad gas journal bearings and a simple externally pressurized thrust bearing. The bearing pads were 5.1 cm (2.02 in.) in diameter and 2.8 cm (1.5 in.) long. The length to diameter ratio was 0.75. One pad was mounted on a flexible diaphragm. The bearing supply pressure ranged from 0 to 690 kilonewtons per square meter (0 to 100 psig), and speeds ranged to 38,500 rpm. Heavy mass pad tilting-pad assemblies produced three rotor-bearing resonances above the first two rotor critical speeds. Lower supply pressure eliminated the resonances. The resonances were oriented primarily in the direction normal to the diaphragm.--P. [i].

Tilt Pad Bearing Effects on Rotordynamic Stability and Improvements in Global System Dynamic Analysis

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Total Pages : 592 pages
Book Rating : 4.:/5 (221 download)

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Book Synopsis Tilt Pad Bearing Effects on Rotordynamic Stability and Improvements in Global System Dynamic Analysis by : Larry Lee Earles

Download or read book Tilt Pad Bearing Effects on Rotordynamic Stability and Improvements in Global System Dynamic Analysis written by Larry Lee Earles and published by . This book was released on 1989 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: