0
Research Papers: Gas Turbines: Structures and Dynamics

The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings

[+] Author and Article Information
Luis San Andrés

Mast-Childs Professor
Fellow ASME
Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843-3123
e-mail: Lsanandres@tamu.edu

Yujiao Tao

Engineer
Analytical Engineering Group,
Samsung Techwin,
Houston, TX 77079
e-mail: y.tao@samsung.com

Uncertain is a better word, since the parameters needed for accurate predictions are not readily modeled but need be obtained from careful experiments.

In practice, the pad-pivot surface condition may cause a frictional moment that needs to be properly modeled.

The bearing stiffness and damping coefficients in Eq. (14) are not the same as those obtained from curve fits the to the impedance functions; for example, see Eq. (2) for the [K,C,M] model.

Note that the test bearing having dissimilar clearances does not show a zero eccentricity at the no load condition.

As per Ref. [27], the experimental uncertainty over the frequency range is about ±40 MN/m and ±60 MN/m for operating at rotor speeds of 6 krpm and 10 rpm, respectively.

Kpiv = 35 MN/m, 1,269 MN/m, 3,045 MN/m, and 350,000 MN/m.

1Work conducted as a Graduate Research Assistant at Texas A&M University.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 5, 2013; final manuscript received July 17, 2013; published online September 17, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(11), 112505 (Sep 17, 2013) (11 pages) Paper No: GTP-13-1235; doi: 10.1115/1.4025070 History: Received July 05, 2013; Revised July 17, 2013

Recent comprehensive experimental data showcasing the force coefficients of commercial size tilting pad journal bearings has brought to rest the long standing issue on the adequacy of the [K,C,M] physical model to represent frequency independent bearing force coefficients, in particular viscous damping. Most experimental works test tilting pad journal bearings (TPJBs) with large preloads, operating over a large wide range of rotor speeds, and with null to beyond normal specific loads. Predictions from apparently simple fluid film bearing models stand poor against the test data which invariably signals to theory missing pivot and pad flexibility effects, and most importantly, ignoring significant differences in bearing and pad clearances due to actual operation, poor installation and test procedures, or simply errors in manufacturing and assembly. Presently, a conventional thermo hydrodynamic bulk flow model for prediction of the pressure and temperature fields in TPJBs is detailed. The model accounts for various pivot stiffness types, all load dependent and best when known empirically, and allows for dissimilar pad and bearing clearances. The algorithm, reliable even for very soft pad-pivots, predicts frequency reduced bearing impedance coefficients and over a certain frequency range delivers the bearing stiffness, damping and virtual mass force coefficients. Good correlation of predictions against a number of experimental results available in the literature bridges the gap between a theoretical model and the applications. Predicted pad reaction loads reveal large pivot deflections, in particular for a bearing with large preloaded pads, with significant differences in pivot stiffness as a function of specific load and operating speed. The question on how pivot stiffness acts to increase (or decrease) the bearing force coefficients, in particular the dynamic stiffness versus frequency, remains since the various experimental data show contradictory results. A predictive study with one of the test bearings varies its pivot stiffness from 10% of the fluid film stiffness to an almost rigid one, 100 times larger. With certainty, bearings with nearly rigid pivot stiffness show frequency independent force coefficients. However, for a range of pad pivot stiffness, 1/10 to ten times the fluid film stiffness, TPJB impedances vary dramatically with frequency, in particular as the excitation frequency grows above synchronous speed. The bearing virtual mass coefficients become negative, thus stiffening the bearing for most excitation frequencies.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Childs, D. W., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling and Analysis, Wiley, New York, pp. 177–178.
Lund, J. W., 1987, “The Influence of Pad Flexibility on the Dynamic Coefficients of a Tilting Pad Journal Bearing,” ASME J. Tribol., 109, pp. 65–70. [CrossRef]
Rouch, K. E., 1983, “Dynamics of Pivoted-Pad Journal Bearings, Including Pad Translation and Rotation Effects,” STLE Tribol. Trans., 26, pp. 222–227. [CrossRef]
Chen, W. J., 1995, “Bearing Dynamic Coefficients of Flexible Journal Bearings,” STLE Tribol. Trans., 38, pp. 253–260. [CrossRef]
Kim, J., Palazzolo, A., and Gadangi, R., 1995, “Dynamic Characteristics of TEHD Tilt Pad Journal Bearing Simulation Including Multiple Mode Pad Flexibility Model,” ASME J. Vibr. Acoust., 117, pp. 123–135. [CrossRef]
Kirk, R. G., and Reedy, S. W., 1988, “Evaluation of Pivot Stiffness for Typical Tilting-Pad Journal Bearing Designs,” ASME J. Vib., Acoust., Stress, Reliab. Des., 110(2), pp. 165–171. [CrossRef]
Wilkes, J. C., 2011, “Measured and Predicted Rotor-Pad Transfer Functions for a Rocker-Pivot Tilting-Pad Bearing,” Ph.D. thesis, Texas A&M University, College Station, TX.
Carter, C., and Childs, D. W., 2009, “Measurements Versus Predictions for the Rotordynamic Characteristics of a Five-Pad Rocker-Pivot Tilting-Pad Bearing in Load-Between-Pad Configuration,” ASME J. Eng. Gas Turbines Power, 131, p. 012507. [CrossRef]
Childs, D. W., and Harris, H., 2009, “Static Performance Characteristics and Rotordynamic Coefficients for a Four-Pad Ball-in-Socket Tilting Pad Journal Bearing,” ASME J. Eng. Gas Turbines Power, 131, p. 062502. [CrossRef]
Kulhanek, C., and Childs, D., 2012, “Measured Static and Rotordynamic Coefficient Results for a Rocker-Pivot, Tilting-Pad Bearing With 50 and 60% Offsets,” ASME J. Eng. Gas. Turbines Power134, p. 052505. [CrossRef]
Klit, P., and Lund, J. W., 1988, “Calculation of the Dynamic Coefficients of a Journal Bearing Using a Variational Approach,” ASME J. Tribol., 108, pp. 421–425. [CrossRef]
Dimond, T. W., Sheth, P. N., Allaire, P. E., and He, M., 2009, “Identification Methods and Test Results for Tilting Pad and Fixed Geometry Journal Bearing Dynamic Coefficients—A Review,” J. Shock Vib., 16(1), pp. 13–43. [CrossRef]
Lund, J. W., 1964, “Spring and Damping Coefficients for the Tilting-Pad Journal Bearing,” ASLE Trans., 7, pp. 342–352. [CrossRef]
Kocur, J. A., Nicholas, J. C., and Lee, C. C., 2007, “Surveying Tilting Pad Journal Bearing and Gas Labyrinth Seal Coefficients and Their Effect on Rotor Stability,” Proc. 36th Turbomachinery Symposium, Houston, TX, September 10–13.
White, M. F., and Chan, S. H., 1992, “The Subsynchronous Dynamic Behavior of Tilting-Pad Journal Bearings,” ASME J. Tribol., 114(1), pp. 167–174. [CrossRef]
Childs, D. W., 2010, “Tilting-Pad Bearings: Measured Frequency Characteristics of Their Rotordynamic Coefficients,” Proc. 8th IFToMM Int. Conf. on Rotordynamics, Seoul, Korea, September 12–15.
Childs, D. W., Delgado, A., and Vannini, G., 2011, “Tilting-Pad Bearings: Measured Frequency Characteristics of Their Rotordynamic Coefficients,” Proc. 40th Turbomachinery Symposium, Houston, TX, September 12–15.
Wilkes, J. C., and Childs, D. W., 2012, “Tilting Pad Journal Bearings—A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot,” ASME J. Eng. Gas Turbines Power, 134, p. 122508. [CrossRef]
Al-Jughaiman, B., and Childs, D., 2008, “Static and Dynamic Characteristics for a Pressure-Dam Bearing,” ASME J. Eng. Gas Turbines Power, 130, p. 052501. [CrossRef]
SanAndrés, L., 2012, “Extended Finite Element Analysis of Journal Bearing Forced Performance to Include Fluid Inertia Force Coefficients,” Proc. ASME 2012 International Mechanical Engineering Congress and Exposition, Houston, TX, November 9–15, ASME Paper No. IMECE2012-87713.
San Andrés, L., 1996, “Turbulent Flow, Flexure-Pivot Hybrid Bearings for Cryogenic Applications,” ASME J. Tribol., 118(1), pp. 190–200. [CrossRef]
San Andrés, L., 2010, “Thermal Analysis of Finite Length Journal Bearings Including Fluid Effects,” Notes 07, Texas A&M University Digital Libraries, October 17, 2012, http://repository.tamu.edu/handle/1969.1/93197
Pinkus, O., 1990, Thermal Aspects of Fluid Film Tribology, ASME, New York, pp. 187–97.
Tao, Y., 2012, “A Novel Tilting Pad Journal Bearing Model With Soft Pivot Stiffnesses,” M.S. thesis, Texas A&M University, College Station, TX.
Delgado, A., Ertas, B., Drexel, M., Naldi, L., and Vannini, G., 2011, “Identification and Prediction of Force Coefficients in a Five-Pad and Four-Pad Tilting Pad Bearing for Load-on-Pad and Load-Between-Pad Configurations,” ASME J. Eng. Gas Turbines Power, 133, p. 092503. [CrossRef]
Delgado, A., Libraschi, M., and Vannini, G., 2012, “Dynamic Characterization of Tilting Pad Journal Bearings From Component and System Level Testing,” ASME Paper No. GT2012-69851.
Harris, H., 2008, “Static Characteristics and Rotordynamic Coefficients of a Four-Pad Tilting-Pad Journal Bearing With Ball-in-Socket Pivots in Load-Between-Pad Configuration,” M.S thesis, Texas A&M University, College Station, TX.

Figures

Grahic Jump Location
Fig. 1

Schematic view of a tilting pad and rotating journal, coordinate system, and nomenclature

Grahic Jump Location
Fig. 2

Load configuration and pad arrangements of test bearing in Ref. [9]. Nominal CB = 95.3 μm and r¯P = 0.37 (loaded pads) and 0.58 (unloaded pads).

Grahic Jump Location
Fig. 3

Journal displacements (eX,eY) versus specific load W/(LD). Rotor speed Ω = 10,000 rpm. Current predictions and test data from Ref. [27].

Grahic Jump Location
Fig. 4

Real part of TPJB impedances, Re(ZXX) and Re(ZYY), versus frequency. Specific load W/(LD) = 1,376 kPa and two rotor speeds. Predictions and test data [27].

Grahic Jump Location
Fig. 5

Imaginary part of TPJB impedances, Im(ZXX) and Im(ZYY), versus frequency. Specific load W/(LD) = 1,376 kPa and two rotor speeds. Predictions and test data [27].

Grahic Jump Location
Fig. 6

TPJB static stiffness coefficients (KXX, KYY) versus specific load W/(LD). Predictions and test data [27] at two rotor speeds.

Grahic Jump Location
Fig. 7

TPJB damping coefficients (CXX, CYY) versus specific load W/(LD). Predictions and test data [27] at two rotor speeds.

Grahic Jump Location
Fig. 8

TPJB virtual mass coefficients (MXX, MYY) versus specific load W/(LD). Predictions and test data [27] at two rotor speeds.

Grahic Jump Location
Fig. 9

Pad pivot reaction loads (Fξ/LD) versus applied load W/(LD) on bearing. Rotor speed = 6 krpm.

Grahic Jump Location
Fig. 10

Pivot radial deflection (ξpiv/CB) versus applied load W/(LD) on bearing. Rotor speed = 6 krpm.

Grahic Jump Location
Fig. 11

Effect of pivot stiffness on journal eccentricity, εY = eY/CB. W/(LD)=1,376 kPa and rotor speed = 6 krpm. Test data from Ref. [27] is shown.

Grahic Jump Location
Fig. 12

Effect of pivot stiffness on the bearing impedances Re(Z). Operation at W/(LD) = 1,376 kPa and speed Ω = 6 krpm. (Kpiv/KYYrig) = {0.03,1,3,and300}.

Grahic Jump Location
Fig. 13

Effect of pivot stiffness on bearing impedances Im(Z)/ω. Operation at W/(LD) = 1,376 kPa and rotor speed = 6 krpm. (Kpiv/KYYrig)={0.03,1,3,and300}.

Grahic Jump Location
Fig. 14

Effect of pivot stiffness on the stiffness coefficient (KYY) of a TPJB. W/(LD) = 1,376 kPa, speed = 6 krpm

Grahic Jump Location
Fig. 15

Effect of pivot stiffness on the damping coefficient (CYY) of a TPJB. W/(LD) = 1,376 kPa, speed = 6 krpm.

Grahic Jump Location
Fig. 16

Effect of pivot stiffness on the virtual mass coefficient (MYY) of a TPJB. W/(LD) = 1,376 kPa, speed = 6 krpm.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In