0
Research Papers

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness, and Different Pad Preloads

[+] Author and Article Information
Timothy Dimond

Principal Scientist
Mem. ASME
e-mail: dimond@virginia.edu

Amir A. Younan

Research Associate
Mem. ASME
e-mail: aay7n@virginia.edu

Paul Allaire

Mac Wade Professor
Fellow ASME
e-mail: pea@virginia.edu
ROMAC Laboratory,
Department of Mechanical and Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904-4746

John Nicholas

General Manager
Mem. ASME
Lufkin-RMT, Inc.,
Wellsville, NY 14895
e-mail: jcn@lufkin.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 2, 2010; final manuscript received January 12, 2013; published online June 6, 2013. Assoc. Editor: Alan Palazzolo.

J. Vib. Acoust 135(4), 041101 (Jun 06, 2013) (11 pages) Paper No: VIB-10-1160; doi: 10.1115/1.4024093 History: Received July 02, 2010; Revised January 12, 2013

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to nonsynchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are compared to a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced nonsynchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two-degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lund, J. W., 1964, “Spring and Damper Coefficients for the Tilting-Pad Journal Bearing,” ASLE Trans., 7(4), pp. 342–352. [CrossRef]
Shapiro, W., and Colsher, R., 1977, “Dynamic Characteristics of Fluid-Film Bearings,” Proc. 6th Turbomachinery Symposium, College Station, TX, December 6–8, M. P.Boyce, ed., Texas A&M University Press, College Station, TX, Vol. 1.
Allaire, P. E., Parsell, J. K., and Barrett, L. E., 1981, “A Pad Perturbation Method for the Dynamic Coefficients of Tilting-Pad Journal Bearings,” Wear, 72(1), pp. 29–44. [CrossRef]
Barrett, L. E., Allaire, P. E., and Wilson, B. W., 1988, “The Eigenvalue Dependence of Reduced Tilting Pad Bearing Stiffness and Damping Coefficients,” Tribol. Trans., 31(4), pp. 411–419. [CrossRef]
Dimond, T. W., Younan, A. A., and Allaire, P. E., 2009, “Comparison of Tilting-Pad Journal Bearing Dynamic Full Coefficient and Reduced Order Models Using Modal Analysis,” Proc. ASME Turbo Expo 2009, Orlando, FL, June 8–12, ASME Paper No. GT2009-60269. [CrossRef]
Rouch, K. E., 1983, “Dynamics of Pivoted-Pad Journal Bearings, Including Pad Translation and Rotation Effects,” ASLE Trans., 26(1), pp. 102–109. [CrossRef]
Kirk, R. G., and Reedy, S. W., 1988, “Evaluation of Pivot Stiffness for Typical Tilting-Pad Journal Bearing Designs,” ASME J. Vibr. Acoust., 110(2), pp. 165–171. [CrossRef]
Kirk, R. G., and Gunter, E. J., 1972, “Effect of Support Flexibility and Damping on Synchronous Response of a Single-Mass Flexible Rotor,” ASME J. Eng. Ind., 94(1), pp. 221–232. [CrossRef]
Brockwell, K., Kleinbub, D., and Dmochowski, W., 1990, “Measurement and Calculation of the Dynamic Operating Characteristics of the Five Shoe, Tilting Pad Journal Bearing,” Tribol. Trans., 33(4), pp. 481–492. [CrossRef]
Ha, H. C., and Yang, S. H., 1999, “Excitation Frequency Effects on the Stiffness and Damping Coefficients of a Five-Pad Tilting Pad Journal Bearing,” ASME J. Tribol., 121(3), pp. 517–522. [CrossRef]
Dmochowski, W., 2007, “Dynamic Properties of Tilting-Pad Journal Bearings: Experimental and Theoretical Investigation of Frequency Effects Due to Pivot Flexibility,” ASME J. Eng. Gas Turbines Power, 129(3), pp. 865–869. [CrossRef]
Childs, D., and Harris, J., 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(6), p. 062502. [CrossRef]
Carter, C. R., 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(1), p. 012507. [CrossRef]
Delgado, A., Vannini, G., Ertas, B., Drexel, M., and Naldi, L., 2010, “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,” Proc. ASME Turbo Expo 2010, Glasgow, UK, June 14–18, ASME Paper No. GT2010-23802. [CrossRef]
Qiao, G., Wang, L., and Zheng, T., 2007, “Linear Stability Analysis of a Tilting-Pad Journal Bearing System,” ASME J. Tribol., 129(2), pp. 348–353. [CrossRef]
Luneno, J.-C., Aidanpää, J.-O., and Gustavsson, R., 2011, “Model Based Analysis of Coupled Vibrations Due to the Combi-Bearing in Vertical Hydroturbogenerator Rotors,” ASME J. Vibr. Acoust., 133(6), p. 061012. [CrossRef]
Nicholas, J. C., 2003, “Tilting Pad Journal Bearings With Spray-Bar Blockers and By-Pass Cooling for High Speed, High Load Applications,” Proc. 32nd Turbomachinery Symposium, College Station, TX, September 9–11, J.Burnett, ed., Texas A&M University Press, College Station, TX, Vol. 1, pp. 27–37.
Nicholas, J. C., Elliott, G., Shoup, T. P., and Martin, E., 2008, “Tilting Pad Journal Bearing Starvation Effects,” Proc. 37th Turbomachinery Symposium, Houston, TX, September 8–11, J.Burnett, ed., Texas A&M University Press, College Station, TX, Vol. 1.
Nicholas, J. C., Gunter, E. J., and Allaire, P. E., 1979, “Stiffness and Damping Coefficients for the Five-Pad Tilting-Pad Bearing,” ASLE Trans., 22(2), pp. 113–124. [CrossRef]
He, M., and Allaire, P. E., 2002, “Thermoelastohydrodynamic Analysis of Journal Bearings With 2D Generalized Energy Equation,” Proc. 6th International Conference on Rotor Dynamics, Sydney, Australia, September 30–October 4, E. J.Hahn and R. B.Randall, eds., University of New South Wales Printing Services, Sydney, Australia, Vol. 1.
He, M., Allaire, P. E., and Barrett, L. E., 2002, “TEHD Modeling of Leading Edge Groove Tilting Pad Bearings,” Proc. 6th International Conference on Rotor Dynamics, Sydney, Australia, September 30–October 4, E. J.Hahn and R. B.Randall, eds., University of New South Wales Printing Services, Sydney, Australia, Vol. 1.
He, M., Allaire, P., and Barrett, L., 2005, “Thermoelastohydrodynamic Modeling of Leading-Edge Groove Bearings Under Starvation Condition,” Tribol. Trans., 48(3), pp. 362–369. [CrossRef]
He, M., 2003, “Thermoelastohydrodynamic Analysis of Fluid Film Journal Bearings,” Ph.D. thesis, University of Virginia, Charlottesville, VA.
Szeri, A. Z., 1998, Fluid Film Lubrication Theory & Design, Cambridge University Press, Cambridge, UK.
Elrod, H. G., and Ng, C. W., 1967, “A Theory for Turbulent Fluid Films and Its Application to Bearings,” ASME J. Lubr. Technol., 89(3), pp. 346–362. [CrossRef]
Garvey, S. D., Friswell, M. I., and Prells, U., 2002, “Co-Ordinate Transformations for Second Order Systems—Part I: General Transformations,” J. Sound Vib., 258(5), pp. 885–909. [CrossRef]
Ewins, D. J., 2000, Modal Testing: Theory, Practice, and Application, Research Studies, Baldock, UK.
Rouvas, C., and Childs, D. W., 1993, “A Parameter Identification Method for the Rotordynamic Coefficients of a High Reynolds Number Hydrostatic Bearing,” ASME J. Vibr. Acoust., 115(3), pp. 264–270. [CrossRef]
Childs, D., and Hale, K., 1994, “Test Apparatus and Facility to Identify the Rotordynamic Coefficients of High-Speed Hydrostatic Bearings,” ASME J. Tribol., 116(2), pp. 337–344. [CrossRef]
Al-Ghasem, A. M., and Childs, D. W., 2006, “Rotordynamic Coefficients Measurements Versus Predictions for a High-Speed Flexure-Pivot Tilting-Pad Bearing (Load Between Pad Configuration),” ASME J. Eng. Gas Turbines Power, 128(4), pp. 896–906. [CrossRef]
Andres, L. S., 1996, “Turbulent Flow, Flexure-Pivot Hybrid Bearings for Cryogenic Applications,” ASME J. Tribol., 118(1), pp. 190–200. [CrossRef]
Wygant, K. D., Barrett, L. E., and Flack, R. D., 1999, “Influence of Pad Pivot Friction on Tilting-Pad Journal Bearing Measurements—Part II: Dynamic Coefficients,” Tribol. Trans., 42, pp. 250–256. [CrossRef]
API, 2002, Axial and Centrifugal Compressors and Expander-Compressors for Petroleum, Chemical, and Gas Industry Service, Downstream Segment, 7th ed., American Petroleum Institute, Washington, DC, API Standard 617.
Wilkes, J. C., 2012, “Measured and Predicted Rotor-Pad Transfer Functions for a Rocker-Pivot Tilting-Pad Journal Bearing,” Ph.D. thesis, Texas A&M University, College Station, TX.

Figures

Grahic Jump Location
Fig. 1

Shaft translational degrees of freedom

Grahic Jump Location
Fig. 2

Pad rotational and translational degrees of freedom

Grahic Jump Location
Fig. 3

Maximum temperature rise, 1896 kPa static load

Grahic Jump Location
Fig. 4

Static dimensionless operating position, 6000 rpm

Grahic Jump Location
Fig. 5

Frequency response comparison, real part

Grahic Jump Location
Fig. 6

Frequency response comparison, imaginary part

Grahic Jump Location
Fig. 7

Selected eigenvalues, complex plane

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