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Research Papers: Hydrodynamic Lubrication

Analytical Evaluation of the Static and Dynamic Characteristics of Three-Lobe Journal Bearings With Finite Length

[+] Author and Article Information
Athanasios Chasalevris

Mem. ASME
CSBPP—Core Science Bearings
Preventive Acoustics,
BorgWarner Turbo Systems Engineering GmbH,
Marnheimer Strasse 85/87,
Kirchheimbolanden 67292, Germany
e-mail: chasalevris@sdy.tu-darmstadt.de

1Present address: ALSTOM Power/Industrial Steam Turbine Engineering, Rugby CV1 2UE, UK.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received October 7, 2014; final manuscript received March 9, 2015; published online May 6, 2015. Assoc. Editor: Bugra Ertas.

J. Tribol 137(4), 041701 (Oct 01, 2015) (16 pages) Paper No: TRIB-14-1251; doi: 10.1115/1.4030023 History: Received October 07, 2014; Revised March 09, 2015; Online May 06, 2015

The three-lobe bearings widely used in rotating machinery follow the design data evaluated using numerical methods for the solution of the Reynolds equation. This paper defines exact and approximate analytical solutions of the Reynolds equation for the case of three-lobe bearings with finite length. Dynamic characteristics are provided analytically with closed-form expressions for laminar regimes of operation, using an approximate analytical solution that proves to be reliable and of low cost of evaluation time. The results for eccentricity ratio, equilibrium locus, stiffness and damping coefficients are presented for a range of Sommerfeld number and different cases of load orientation and compared with theoretical and experimental data from the literature.

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References

Pinkus, O., 1956, “Analysis of Elliptical Bearings,” Trans. ASME, 78, pp. 965–973.
Pinkus, O., 1959, “Analysis and Characteristics of Three-Lobe Bearings,” Trans. ASME, J. Basic Eng., 81, pp. 49–55.
Lund, J. W., 1965, “Rotor-Bearing Dynamics Design Technology, Part III: Design Handbook for Fluid-Film Type Bearings,” Mechanical Technology, Technical Report No. AFAPL-TR-65-45.
Lund, J. W., 1968, “Rotor-Bearing Dynamics Design Technology, Part VII: The Three-Lobe Bearing and Floating Ring Bearing,” Mechanical Technology, Technical Report No. AFAPL-TR-65-45.
Lund, J. W., and Thomsen, K. K., 1978, “A Calculation Method and Data for the Dynamic Coefficients of Oil-Lubricated Journal Bearings,” Topics in Fluid Film Bearing and Rotor Bearing System Design and Optimization, The ASME Design Engineering Conference, pp. 1–29.
Knight, J. D., and Barrett, L. E., 1983, “An Approximate Solution Technique for Multi-Lobe Journal Bearings including Thermal Effects, With Comparison to Experiment,” ASME Trans., 26(4), pp. 501–508.
Glienicke, J., Han, D. C., and Leonhard, M., 1980, “Practical Determination and Use of Bearing Dynamic Coefficients,” Trib. Int., 13(6), pp. 297–309. [CrossRef]
Eierman, R. G., 1976, “Stability Analysis and Transient Motion of Axial Groove Multi-Lobe and Tilting-Pad Bearings,” M. S., thesis, University of Virginia, Charlottesville, VA.
Shang, L., and Dien, L. K., 1989, “A Matrix Method for Computing the Stiffness and Damping Coefficients of Multi-Arc Journal Bearings,” Tribol. Trans., 32(3), pp. 396–404. [CrossRef]
Someya, T., 1989, Journal Bearing Design Data Book, Springer, Berlin.
Elrod, H. G., 1981, “A Cavitation Algorithm,” ASME J. Lubr. Technol., 103(3), pp. 350–354. [CrossRef]
Vaidyanathan, K., and Keith, T. G., 1989, “Numerical Prediction of Cavitation in Noncircular Journal Bearings,” Tribol. Trans., 32(2), pp. 215–221. [CrossRef]
Vijayaraghavan, D., and Keith., T. G., 1989, “Development and Evaluation of a Cavitation Algorithm,” Tribol. Trans., 32(2), pp. 225–233. [CrossRef]
Vijayaraghavan, D., and Keith, T. G., 1990, “An Efficient, Robust and Time Accurate Numerical Scheme Applied to Cavitation Algorithm,” ASME J. Tribol., 112(1), pp. 44–51. [CrossRef]
Swanson, E. E., and Kirk, R. G., 1997, “Survey of Experimental Data for Fixed Geometry Hydrodynamic Journal Bearings,” ASME J. Tribol., 119(4), pp. 704–710. [CrossRef]
Kostrzewsky, G. J., Flack, R. D., and Barett, L. E., 1998, “Comparison Between Measured and Predicted Performance of a Two-Axial Groove Journal Bearing,” Tribol. Trans., 39, pp. 571–578. [CrossRef]
Kostrzewsky, G. J., Taylor, D. V., Flack, R. D., and Barett, L. E., 1998, “Theoretical and Experimental Dynamic Characteristics of a Highly Preloaded Three-Lobe Journal Bearing,” Tribol. Trans., 41(3), pp. 392–398. [CrossRef]
Rao, T. V. V. L. N., and Sawicki, J. T., 2003, “Dynamic Coefficient Prediction in Multi-Lobe Journal Bearing Using a Mass Conservation Algorithm,” Tribol. Trans., 46(3), pp. 414–420. [CrossRef]
Dargaiah, K., Parthasarathy, K., and Prabhu, B. S., 1993, “Finite Element Method for Computing Dynamic Coefficients of Multilobe Bearings,” Tribol. Trans., 36(1), pp. 73–83. [CrossRef]
Malik, M., Sinhasan, R., and Chandra, M., 1981, “Design Data for Three-Lobe Bearings,” Tribol. Trans., 24(3), pp. 345–353. [CrossRef]
Ng, C. W., and Pan, C. H. T., 1965, “A Linearized Turbulent Lubrication Theory,” ASME J. Basic Eng., 87(3), pp. 675–688. [CrossRef]
Sinhasan, R., Malik, M., and Chandra, M., 1980, “Analysis of Two-Lobe Porous Hydrodynamic Journal Bearings,” Wear, 64(2), pp. 343–357. [CrossRef]
Flack, R. D., and Allaire, P. E., 1982, “An Experimental and Theoretical Examination of the Static Characteristics of Three-Lobe Bearings,” Tribol. Trans., 25(1), pp. 88–94. [CrossRef]
Khatri, R., and Childs, D., 2014, “An Experimental Investigation of the Dynamic Performance of a Vertical-Application Three-Lobe Bearing,” ASME Paper No. GT2014-25483. [CrossRef]
Khatri, R., Childs, D., and Jordan, L., 2015, “An Experimental Study of the Load Orientation Sensitivity of Three-Lobe Bearings,” ASME. J. Eng. Gas Turbines Power, 137(4), p. 042503. [CrossRef]
Khatri, R., and Childs, D., 2015, “An Experimental Investigation of the Dynamic Performance of a Vertical-Application Three-Lobe Bearing,” ASME. J. Eng. Gas Turbines Power, 137(4), p. 042504. [CrossRef]
Pettinato, B., and Flack, R. D., 2015, “Test Results for a Highly Preloaded Three-Lobe Journal Bearing-Effect of Load Orientation on Static and Dynamic Characteristics,” J. Soc. Tribol. Lubr. Eng., 57(9), pp. 23–30.
Childs, D. W., Delgado, A., and Vannini, G., 2011, “Tilting-Pad Bearings: Measured Frequency Characteristics of their Rotordynamic Coefficients,” Proceedings of the Fortieth Turbomachinery Symposium, Houston, TX, pp. 33–45.
Wilkes, J., 2011, “Measured and Predicted Transfer Functions Between Rotor Motion and Pad Motion for a Rocker-Back Tilting-Pad Bearing in LOP Configuration,” ASME Paper No. GT2011-46510. [CrossRef]
Chasalevris, A., and Sfyris, D., 2013, “Evaluation of the Finite Journal Bearing Characteristics Using the Exact Analytical Solution of the Reynolds Equation,” Tribol. Int., 57, pp. 216–234. [CrossRef]
Sfyris, D., and Chasalevris, A., 2012, “An Exact Analytical Solution of the Reynolds Equation for the Finite Journal Bearing,” Trib. Int., 55, pp. 46–58. [CrossRef]
Vogelpohl, G., 1943, “Zur Integration der Reynoldsschen Gleichung für das Zapfenlager Endlicher Breite,” Ing. Arch., 14(3), pp. 192–212. [CrossRef]
Vogelpohl, G., 1956, Über die Tragfähigkeit von Gleitlagern und ihre Berechnung, Westdeutscher Verlag/Köln und Opladen, Germany.
Vogelpohl, G., 1937, Beiträge zur Kenntnis der Gleitlagerreibung, Vol. 386, VDI-Forsch.-Heft, Düsseldorf, pp. 3–5.
Michell, A., 1929, “Progress in Fluid Film Lubrication,” Trans. ASME, 51, pp. 153–163.
Duffing, G., 1931, Die Schmiermittelreibung bei Gleitflächen von Endlicher Breite, Handbucher Phys. U. Techn., Mechanik von Auerbach-Hort, Leipzig, Germany, pp. 839–850.
Rao, T. V. V. L. N., and Sawicki, J. T., 2002, “Linear Stability Analysis for a Hydrodynamic Journal Bearing Considering Cavitation Effects,” Tribol. Trans., 45(4), pp. 450–456. [CrossRef]
Boyce, W., and DiPrima, R., 1997, Elementary Differential Equations and Boundary Value Problems , Wiley, New York.
Conte, S. D., and DeBoor, C., 1972, Elementary Numerical Analysis, McGraw-Hill, New York.
Courant, R., and Hilbert, D., 1989, Methods of Mathematical Physics, Vol. 2, Wiley-VCH, Berlin.
Polyanin, A., and Zaitsev, V., 2003, Handbook of Exact Solutions for Ordinary Differential Equations, Chapman & Hall/CRC, Boca Raton.

Figures

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Fig. 1

Definition of the geometric properties of a three-lobe journal bearing

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Fig. 2

Fluid film thickness function hi/cb as a function of circumferential coordinate θ

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Fig. 3

Analytically estimated pressure profile in a three-lobe bearing with finite length for various eccentricities and attitude angles

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Fig. 4

Evaluated pressure distribution of the bearing for ɛ=0.25 and ϕ=135 deg and for static condition ɛ· = 0 using analytical and numerical solution under different solution parameters: (a) through the entire circumference, (b) lobe 1, (c) lobe 2, and (d) lobe 3

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Fig. 5

Evaluated pressure distribution at each lobe of the bearing for ɛ = 0.75 and ϕ = 135 deg and for static condition ɛ· = 0 using analytical and numerical solution under different solution parameters: (a) through the entire circumference, (b) lobe 1, (c) lobe 2, and (d) lobe 3

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Fig. 6

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m=0.878 and L/D=0.667

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Fig. 7

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m=0.879 and L/D=0.500

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Fig. 8

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m=0.898 and L/D=0.333

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Fig. 9

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m=0.706 and L/D=0.667

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Fig. 10

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m = 0.725 and L/D = 0.500

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Fig. 11

(a) Eccentricity ratio ɛ as a function of Sommerfeld number S' and (b) equilibrium locus for m = 0.727 and L/D = 0.333

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Fig. 12

Stiffness coefficients Kij as a function of eccentricity ratio ɛ for: (a) L/D=0.25, (b) L/D=0.5, (c) L/D=0.75, and (d) L/D=1.0

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Fig. 13

Damping coefficients Cij as a function of eccentricity ratio ɛ for: (a) L/D=0.25, (b) L/D=0.5, (c) L/D=0.75, and (d) L/D=1.0

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