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Technical Brief

Warner–Sommerfeld Impedance and Mobility Maps

[+] Author and Article Information
S. Boedo

Department of Mechanical Engineering,
Rochester Institute of Technology,
Rochester, NY 14623

J. F. Booker

Sibley School of Mechanical and Aerospace Engineering,
Cornell University,
Ithaca, NY 14853

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 15, 2015; final manuscript received October 3, 2015; published online November 24, 2015. Assoc. Editor: Mihai Arghir.

J. Tribol 138(3), 034502 (Nov 24, 2015) (5 pages) Paper No: TRIB-15-1270; doi: 10.1115/1.4031753 History: Received July 15, 2015; Revised October 03, 2015

This note provides additional graphical representations and curve-fit expressions for characteristics of the Warner–Sommerfeld approximate solution of the Reynolds equation for cavitating journal finite bearings. In particular, curve-fit expressions for mobility components, end-leakage factor, and positive film pressure extent are provided in support of previously published graphical representations of the data.

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References

Booker, J. F. , 1965, “ Dynamically Loaded Journal Bearings: Mobility Method of Solution,” ASME J. Basic Eng., 87(3), pp. 537–546. [CrossRef]
Booker, J. F. , 1971, “ Dynamically Loaded Journal Bearings: Numerical Application of the Mobility Method,” ASME J. Lubr. Technol., 93(1), pp. 168–176, Errata: p. 315. [CrossRef]
Booker, J. F. , 2014, “ Mobility/Impedance Methods: A Guide for Application,” ASME J. Tribol., 136(2), p. 024501. [CrossRef]
Childs, D. , Moes, H. , and van Leeuwen, H. , 1977, “ Journal Bearing Impedance Descriptions for Rotordynamic Applications,” ASME J. Lubr. Technol., 99(2), pp. 198–214. [CrossRef]
Oberg, E., Horton, H. L., Jones, F. D., and Ryffel, H. H., 2008, Machinery’s Handbook, 28th ed., Industrial Press, New York, p. 2236.
Jakeman, R. W. , 1989, “ Influence of Sterntube Bearings on Lateral Vibration Amplitudes in Marine Propeller Shafting,” Tribol. Int., 22(2), pp. 125–136. [CrossRef]
Xing, H. , Wu, Q. , Wu, Z. , and Duan, S. , 2012, “ Elastohydrodynamic Lubrication Analysis of Marine Sterntube Bearing Based on Multi-Body Dynamics,” Energy Procedia, 16, pp. 1046–1051. [CrossRef]
Moes, H. , and Bosma, R. , 1981, “ Mobility and Impedance Definitions for Plain Journal Bearings,” ASME J. Lubr. Technol., 103(3), pp. 468–470. [CrossRef]
Booker, J. F. , 1969, “ Dynamically Loaded Journal Bearings: Maximum Film Pressure,” ASME J. Lubr. Technol., 91(3), pp. 534–543. [CrossRef]
Moes, H. , 1969, “ Discussion, IMechE 1969 Tribology Convention, Gotherburg,” Proc. Inst. Mech. Eng., 183, pp. 205–206.
Goenka, P. K. , 1984, “ Analytical Curve Fits for Solution Parameters of Dynamically Loaded Journal Bearings,” ASME J. Tribol., 106(4), pp. 421–428. [CrossRef]
Warner, P. C. , 1963, “ Static and Dynamic Properties of Partial Journal Bearings,” ASME J. Basic Eng., 85(2), pp. 247–257. [CrossRef]
Booker, J. F. , 1965, “ A Table of the Journal-Bearing Integral,” ASME J. Basic Eng., 87(2), pp. 533–535. [CrossRef]
Schmidt, M. , and Lipson, H. , 2009, “ Distilling Free-Form Natural Laws From Experimental Data,” Science, 324(5923), pp. 81–85. [CrossRef] [PubMed]
Booker, J. F. , and Huebner, K. H. , 1972, “ Application of Finite Element Methods to Lubrication: An Engineering Approach,” ASME J. Lubr. Technol., 94(4), pp. 313–323. [CrossRef]

Figures

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Fig. 1

Journal bearing geometry: pure squeeze, specified journal center velocity

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Fig. 2

Sample pressure distributions: Warner–Sommerfeld film model

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Fig. 3

Factor λ in velocity frame

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Fig. 4

Relative magnitude error for previously published long bearing impedance curve-fit [8]

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Fig. 5

Journal bearing geometry: pure squeeze, specified load

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Fig. 6

Initial angle of positive film extent

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Fig. 7

Relative magnitude error for long bearing mobility and lambda curve-fits

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Fig. 8

Absolute direction error for long bearing mobility curve-fits

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Fig. 9

Relative magnitude error for factor Π curve-fits

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