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Research Papers: Elastohydrodynamic Lubrication

Effectiveness of Coatings With Constant, Linearly, and Exponentially Varying Elastic Parameters in Heavily Loaded Line Elastohydrodynamically Lubricated Contacts

[+] Author and Article Information
Ilya I. Kudish

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

Sergey S. Volkov

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

Andrey S. Vasiliev, Sergey M. Aizikovich

Research Fellows and Head of 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 September 9, 2015; final manuscript received March 20, 2016; published online August 11, 2016. Assoc. Editor: Ning Ren.

J. Tribol 139(2), 021502 (Aug 11, 2016) (15 pages) Paper No: TRIB-15-1333; doi: 10.1115/1.4033360 History: Received September 09, 2015; Revised March 20, 2016

In contacts of functionally graded elastic solids, the conditions produced are significantly different from the ones in similar contacts of homogeneous elastic materials. Especially it is true for heavily loaded lubricated contacts. The situation is even more diverse due to different dependences of the material elastic parameters on material depth. In the previous papers, the cases of lubricated contacts with coatings made of homogeneous materials are considered using asymptotic and semi-analytical methods. The goal of the paper is to determine the behavior of the coating effectiveness criteria in heavily loaded elastohydrodynamically lubricated (EHL) contacts for coatings with elastic modulus varying linearly and exponentially across the coating thickness as well as to compare the results with the case of coatings made of homogeneous materials. The above criteria include the criteria on the lubrication film thickness and friction force. 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 the authors. The analysis is based on splitting the problem into two distinct parts: the problem for dry (nonlubricated) contacts and a problem for lubricated contacts. The bridge between the two problems is the asymptotic behavior of pressure in the vicinity of the end points of the contacts. More specifically, in the central part of the contact the solution of the EHL problem for functionally graded materials is close to the one for the dry contact of these materials while in the narrow zones near the inlet and exit points of the contact the lubrication effects become comparable to the effects due to the elasticity of the solids. This approach to the EHL problem solution reveals its structure.

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References

Figures

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Fig. 1

General view of a lubricated functionally graded material

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Fig. 2

Variations of the Young's modulus and Poisson's ratio across coatings of DLC1-hom, DLC1-lin, and DLC1-exp materials, β=0.5051

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Fig. 3

Variations of the Young's modulus and Poisson's ratio across coatings of DLC2-hom, DLC2-lin, and DLC2-exp materials, β=2.8571

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Fig. 4

Graphs of the integral equation kernel transform L(u) versus u for different coatings materials

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Fig. 5

Graphs of contact semiwidth a0s versus relative coating thickness λs for different coatings materials

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Fig. 6

Graphs of parameter Na=N0ca0c versus relative coating thickness λs for different coatings materials

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Fig. 7

Graphs of pressure distribution p0s(xs) versus xs for the coatings made of DLC1-hom material

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Fig. 8

Graphs of pressure distribution p0s(xs) versus xs for the coatings made of DLC2-hom material

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Fig. 9

Graphs of pressure distribution p0s(xs) versus xs for the coatings made of DLC1-exp material

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Fig. 10

Graphs of pressure distribution p0s(xs) versus xs for the coatings with relative thickness λs=1.583 made of DLC1-hom, DLC1-lin, and DLC1-exp materials

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Fig. 12

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 of homogeneous materials for A = 0.525 and Q0=1 (Reprinted with permission from CRC Press [4])

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Fig. 13

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 of homogeneous materials for A = 0.525 and Q0=2.5 (Reprinted with permission from CRC Press [4])

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Fig. 14

Graphs of parameter Rinhom from Eq. (4.15) versus relative coating thickness λs obtained for fully flooded lubrication regimes with abundant supply of lubricant, constant lubricant viscosity (Qs = 0), and different coating materials

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Fig. 11

Graphs of pressure distributions p0s(xs) and phom(xs) versus xs for the coatings with relative thickness λs=0.28 made of DLC1-hom and DLC2-hom materials

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Fig. 15

Graphs of parameter Kinhom from Eqs. (4.15) and (4.22) versus relative coating thickness λs obtained for fully flooded lubrication regimes with abundant supply of lubricant, constant lubricant viscosity (Qs = 0), and different coating materials

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