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Research Papers: Elastohydrodynamic Lubrication

Uniform Equations in the Inlet and Exit Zones of Heavily Loaded Point and Line Elastohydrodynamically Lubricated Contacts Involved in Various Steady Motions

[+] Author and Article Information
Ilya I. Kudish

Professor
Fellow ASME
Department of Mathematics,
Kettering University,
Flint, MI 48504
e-mail: ikudish@kettering.edu

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received September 16, 2014; final manuscript received December 16, 2014; published online February 11, 2015. Assoc. Editor: Sinan Muftu.

J. Tribol 137(2), 021503 (Apr 01, 2015) (9 pages) Paper No: TRIB-14-1226; doi: 10.1115/1.4029448 History: Received September 16, 2014; Revised December 16, 2014; Online February 11, 2015

Heavily loaded point elastohydrodynamically lubricated (EHL) contacts involved in steady purely transitional, skewed transitional, and transitional with spinning motions are considered. It is shown that in the central parts of the inlet and exit zones of such heavily loaded point EHL contacts the asymptotic equations governing the EHL problem along the lubricant flow streamlines for the above types of contact motions can be reduced to two sets of asymptotic equations: one in the inlet and one in the exit zones. The latter sets of equations are identical to the asymptotic equations describing lubrication process in the inlet and exit zones of the corresponding heavily loaded line EHL contact (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For each specific motion of a point contact, a separate set of formulas for the lubrication film thickness is obtained. For different types of contact motions, these film thickness formulas differ significantly (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For heavily loaded contacts, the discovered relationship between point and line EHL problems allows to apply to point contacts most of the results obtained for line contacts (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC; Kudish, I. I., and Covitch, M. J., 2010, Modeling and Analytical Methods in Tribology, Chapman and Hall/CRC).

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References

Hamrock, B. J., 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York. [CrossRef]
Venner, C. H., and Lubrecht, A. A., 2000, Multilevel Methods in Lubrication ( Tribology Series), Vol. 37, D.Dowson, ed., Elsevier, Amsterdam, The Netherlands.
Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall, CRC Press, Boca Raton, FL.
Kudish, I. I., and Covitch, M. J., 2010, Modeling and Analytical Methods in Tribology, Chapman and Hall/CRC, Boca Raton, FL. [CrossRef]
Vorovich, I. I., Aleksandrov, V. M., and Babeshko, V. A., 1974, Non–Classical Mixed Problems of Elasticity, Nauka Publishing, Moscow, Russia.
Van-Dyke, M., 1964, Perturbation Methods in Fluid Mechanics, Academic, New York.
Kudish, I. I., 2013, “Asymptotic Analysis of Lubricated Heavily Loaded Point Contacts,” Lubr. Sci., 25(8), pp. 479–505. [CrossRef]
Kudish, I. I., 2013, “Asymptotic Analysis of Lubricated Heavily Loaded Point Contacts With Skewed Direction of Entrained Lubricant,” Lubr. Sci., 26(1), pp. 23–42. [CrossRef]
Abramowitz, M., and Stegun, I. A., eds., 1964, Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables ( Applied Mathematics Series 55), National Bureau of Standards, Washington, DC.
Kudish, I. I., 2014, “Asymptotic Analysis of a Lubricated Heavily Loaded Spinning and Rolling Ball in a Parabolic Raceway,” Lubr. Sci., 26(4), pp. 203–227. [CrossRef]
Chittenden, R. J., Dowson, D., Dunn, J. F., and Taylor, C. M., 1985, “A Theoretical Analysis of the Isothermal Elastohydrodynamic Lubrication of Concentrated Contacts. II. General Case, With Lubricant Entrainment Along Either Principal Axis of the Hertzian Contact Ellipse or at Some Intermediate Angle,” Proc. R. Soc. London, Ser. A, 397(1813), pp. 245–269. [CrossRef]
Mostofi, A., and Gohar, R., 1982, “Oil Film Thickness and Pressure Distribution in Elastohydrodynamic Contacts,” J. Mech. Eng. Sci., 24(4), pp. 173–182. [CrossRef]

Figures

Grahic Jump Location
Fig. 3

Main terms of the asymptotic distributions of pressure g(s) (solid curve), gap hg(s) (dashed curve), and the Hertzian pressure asymptote ga(s) (dotted curve) in the exit zone of a fully flooded lubricated contact for A = 0.525 and μg(g)=eQ0g,Q0=QV1/5=10. (Reprinted with permission of CRC Press from Kudish, I. I., and Covitch, M. J., 2010, Modeling and Analytical Methods in Tribology, Chapman and Hall/CRC.)

Grahic Jump Location
Fig. 2

Main terms of the asymptotic distributions of pressure q(r) (solid curve), gap hq(r) (dashed curve), and Hertzian pressure asymptote qa(r) (dotted curve) in the inlet zone of a fully flooded lubricated contact for A = 0.525 and μq(q)=eQ0q, Q0 = QV1∕5= 1. (Reprinted with permission of CRC Press from Kudish, I. I., and Covitch, M. J., 2010, Modeling and Analytical Methods in Tribology, Chapman and Hall/CRC.)

Grahic Jump Location
Fig. 1

Graphs of pressure p(x) (solid curve) and gap h(x) (dashed curve) for regularized problem obtained for V = 0.1, Q = 35, and β = 0.85. (Reprinted with permission of CRC Press from Kudish, I. I., and Covitch, M. J., 2010, Modeling and Analytical Methods in Tribology, Chapman and Hall/CRC.)

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