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Research Papers: Elastohydrodynamic Lubrication

Some Criteria for Coating Effectiveness in Heavily Loaded Line Elastohydrodynamically Lubricated Contacts—Part I: Dry Contacts

[+] Author and Article Information
Ilya I. Kudish

Professor
Fellow ASME
Department of Mathematics,
Kettering University,
Flint, MI 48504

Sergey S. Volkov, Andrey S. Vasiliev, Sergey M. Aizikovich

Laboratory of Functionally Graded and
Composite Materials,
Research and Education Center “Materials,”
Don State Technical University,
Rostov-on-Don 344000, Russia

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 26, 2015; final manuscript received June 18, 2015; published online October 30, 2015. Assoc. Editor: Dong Zhu.

J. Tribol 138(2), 021504 (Oct 30, 2015) (10 pages) Paper No: TRIB-15-1026; doi: 10.1115/1.4030956 History: Received January 26, 2015

Contacts of indentors with functionally graded elastic solids may produce pressures significantly different from the results obtained for homogeneous elastic materials (Hertzian results). It is even more so for heavily loaded line elastohydrodynamically lubricated (EHL) contacts. The goal of the paper is to indicate two distinct ways the functionally graded elastic materials may alter the classic results for the heavily loaded line EHL contacts. Namely, besides pressure the other two main characteristics which are influenced by the nonuniformity of the elastic properties of the contact materials are lubrication film thickness and frictional stress/friction force produced by lubricant flow. The approach used for analyzing the influence of functionally graded elastic materials on parameters of heavily loaded line EHL contacts is based on the asymptotic methods earlier developed by authors (Kudish, 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman & Hall/CRC Press, New York; Kudish and Covitch, 2010, Modeling and Analytical Methods in Tribology, Chapman & Hall/CRC Press, New York; and Aizikovich et al., 2006, Contact Problems of Elasticity for Functionally Graded Materials, Fizmatlit, Moscow, Russia). More specifically, it is based on the analysis of contact problems for dry contacts of functionally graded elastic solids and the lubrication mechanisms in the inlet and exit zones as well as in the central region of heavily lubricated contacts.

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References

Kudish, I. I. , 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman & Hall/CRC Press, New York.
Kudish, I. I. , and Covitch, M. J. , 2010, Modeling and Analytical Methods in Tribology, Chapman & Hall/CRC Press, New York.
Aizikovich, S. M. , Alexandrov, V. M. , Belokon’, A. V. , Krenev, L. I. , and Trubchik, I. S. , 2006, Contact Problems of Elasticity for Functionally Graded Materials, Fizmatlit, Moscow.
Vorovich, I. I. , Aleksandrov, V. M. , and Babeshko, V. A. , 1974, Non–Classical Mixed Problems of Elasticity, Nauka Publishing, Moscow.
Aizikovich, S. M. , and Alexandrov, V. M. , 1982, “Properties of Compliance Functions for Layered and Continuously Nonuniform Half-Space,” Soviet Phys.-Dokl., 27(9), pp. 765–767.
Aizikovich, S. M. , 1982, “Asymptotic Solutions of Contact Problems of Elasticity Theory for Media Inhomogeneous With Depth,” ASME J. Appl. Mech., 46(1), pp. 116–124.
Aizikovich, S. M. , Alexandrov, V. M. , Kalker, J. J. , Krenev, L. I. , and Trubchik, I. S. , 2002, “Analytical Solution of the Spherical Indentation Problem for a Half-Space With Gradients With the Depth Elastic Properties,” Int. J. Solids Struct., 39(10), pp. 2745–2772. [CrossRef]
Aizikovich, S. M. , Alexandrov, V. M. , and Trubchik, I. S. , 2009, “Bilateral Asymptotic Solution of One Class of Dual Integral Equations of the Static Contact Problems for the Foundations Inhomogeneous in Depth,” Operator Theory: Advances and Applications, Birkhauser, Basel, pp. 3–17.
Aizikovich, S. M. , and Vasiliev, A. S. , 2013, “A Bilateral Asymptotic Method of Solving the Integral Equation of the Contact Problem for the Torsion of an Elastic Halfspace Inhomogeneous in Depth,” J. Appl. Math. Mech., 77(1), pp. 91–97. [CrossRef]
Volkov, S. S. , Aizikovich, S. M. , Wang, Y.-S. , and Fedotov, I. A. , 2013, “Analytical Solution of Axisymmetric Contact Problem About Indentation of a Circular Indenter Into a Soft Functionally Graded Elastic Layer,” Acta Mech. Sin., 29(2), pp. 196–201. [CrossRef]
Vasiliev, A. S. , Volkov, S. S. , Aizikovich, S. M. , and Jeng, Y.-R. , 2014, “Axisymmetric Contact Problems of the Theory of Elasticity for Inhomogeneous Layers,” ZAMM Z. Angew. Math. Mech., 94(9), pp. 705–712. [CrossRef]
Szegö, G. , 1959, Orthogonal Polynomials, American Mathematical Society, New York.
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Wang, Z. , Yu, C. , and Wang, Q. , 2015, “Model of Elastohydrodynamic Lubrication for Multilayered Materials,” ASME J. Tribol., 137(1), p. 011501. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Graphs of contact half-width a0s versus relative coating thickness λs for contacts characterized by different ratios of the elastic modules of the coating and substrate β = E'(0)/E'(H)

Grahic Jump Location
Fig. 2

Graphs of parameter N0s versus relative coating thickness λs for contacts characterized by different ratios of the elastic modules of the coating and substrate β

Grahic Jump Location
Fig. 3

Graphs of parameter N0ca0c = β1/4N0sa0s versus relative coating thickness λs for contacts characterized by different ratios of the elastic modules of the coating and substrate β

Grahic Jump Location
Fig. 4

Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some large and intermediate coating thicknesses λs.

Grahic Jump Location
Fig. 5

Graphs of pressure distributions p0s(xs) and phom(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some intermediate coating thicknesses λs.

Grahic Jump Location
Fig. 6

Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some intermediate coating thicknesses λs.

Grahic Jump Location
Fig. 7

Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some intermediate and small coating thicknesses λs.

Grahic Jump Location
Fig. 8

Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.1 and some intermediate and small coating thicknesses λs.

Grahic Jump Location
Fig. 9

Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for hard coatings with β = 0.01 and some small coating thicknesses λs.

Grahic Jump Location
Fig. 10

Graphs of pressure p0s(0) in the center of the contact. The graphs are presented for hard and soft coatings (for different values of β) versus coating thickness λs.

Grahic Jump Location
Fig. 11

Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for soft coatings with β = 100 and some intermediate and small coating thicknesses λs.

Grahic Jump Location
Fig. 12

Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for soft coatings with β = 10 and some intermediate and small coating thicknesses λs.

Grahic Jump Location
Fig. 13

Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for soft coatings with β = 100 and some small coating thicknesses λs.

Grahic Jump Location
Fig. 14

Graphs of pressure distribution p0s(xs) versus xs. The graphs are presented for soft coatings with β = 10 and some small coating thicknesses λs.

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