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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

Kudish, I. I. , Volkov, S. S. , Vasiliev, A. S. , and Aizikovich, S. M. , 2015, “ Some Criteria for Coating Effectiveness in Heavily Loaded Line EHL Contacts. Part 1. Dry Contacts,” ASME J. Tribol., 138(2), p. 021505. [CrossRef]
Kudish, I. I. , Volkov, S. S. , Vasiliev, A. S. , and Aizikovich, S. M. , 2015, “ Some Criteria for Coating Effectiveness in Heavily Loaded Line EHL Contacts,” Part 2. Lubricated Contacts,” ASME J. Tribol., 138(2), p. 021505. [CrossRef]
Wang, Z. , Yu, C. , and Wang, Q. , 2015, “ Model of Elastohydrodynamic Lubrication for Multilayered Materials,” ASME J. Tribol., 137(1), p. 011501. [CrossRef]
Kudish, I. I. , 2013, Elastohydrodynamic Lubrication for Line and Point Contacts. Asymptotic and Numerical Approaches, Chapman & Hall/CRC Press, Boca Raton, FL.
Kudish, I. I. , and Covitch, M. J. , 2010, Modeling and Analytical Methods in Tribology, Chapman & Hall/CRC Press, Boca Raton, FL.
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 Eequations of the Static Contact Problems for the Foundations Inhomogeneous in Depth,” Operator Theory: Advances and Applications, Birkhauser Verlag, Basel, Switzerland, p. 317.
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]
Aizikovich, S. M. , Krenev, L. I. , and Trubchik, I. S. , 2008, “ The Deformation of a Half-Space With a Gradient Elastic Coating Under Arbitrary Axisymmetric Loading,” J. Appl. Math. Mech., 72(4), pp. 461–467. [CrossRef]
Aizikovich, S. M. , Vasiliev, A. S. , and Seleznev, N. M. , 2010, “ Inverse Analysis for Evaluation of the Shear Modulus of Inhomogeneous Media in Torsion Experiments,” Int. J. Eng. Sci., 48(10), pp. 936–942. [CrossRef]
King, R. B. , and O'Sullivan, T. C. , 1987, “ Sliding Contact Stresses in a Two-Dimensional Layered Elastic Halfspace,” Int. J. Solids Struct., 23(5), pp. 581–597. [CrossRef]
Nowell, D. , and Hills, D. A. , 1988, “ Contact Problems Incorporating Elastic Layers,” Int. J. Solids Struct., 24(1), pp. 105–115. [CrossRef]
Elsharkawy, A. A. , and Hamrock, B. J. , 1994, “ EHL of Coated Surfaces. Part I. Newtonian Results,” ASME J. Tribol., 116(1), pp. 29–36. [CrossRef]
Elsharkawy, A. A. , and Hamrock, B. J. , 1994, “ EHL of Coated Surfaces. Part II. Non-Newtonian Results,” ASME J. Tribol., 116(4), pp. 786–793. [CrossRef]
Elsharkawy, A. A. , Holmes, M. J. A. , Evans, H. P. , and Snidle, R. W. , 2006, “ Microelastohydrodynamic Lubrication of Coated Cylinders Using Coupled Differential Deflection Method,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., 220(1), pp. 29–41. [CrossRef]
Jin, Z. M. , 2000, “ Elastohydrodynamic Lubrication of a Circular Point Contact for a Compliant Layered Surface Bonded to a Rigid Substrate, Part 1: Theoretical Formulation and Numerical Method,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., 214(3), pp. 267–279. [CrossRef]
Jin, Z. M. , 2000, “ Elastohydrodynamic Lubrication of a Circular Point Contact for a Compliant Layered Surface Bonded to a Rigid Substrate, Part 2: Numerical Results,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., 214(3), pp. 281–289. [CrossRef]
Guler, M. A. , and Erdogan, F. , 2004, “ Contact Mechanics of Graded Coatings,” Int. J. Solids Struct., 41(14), pp. 3865–3889. [CrossRef]
Chidlow, S. J. , Chong, W. W. F. , and Teodorescu, M. , 2013, “ On the Two-Dimensional Solution of Both Adhesive and Non-Adhesive Contact Problems Involving Functionally Graded Materials,” Eur. J. Mech., A/Solids, 39, pp. 86–103. [CrossRef]
Giannakopoulos, A. E. , and Pallot, P. , 2000, “ Two-Dimensional Contact Analysis of Elastic Graded Materials,” J. Mech. Phys. Solids, 48(8), pp. 1597–1631. [CrossRef]
Jin, F. , Guo, X. , and Gao, H. , 2013, “ Adhesive Contact on Power-Law Graded Elastic Solids: The JKR-DMT Transition Using a Double-Hertz Model,” J. Mech. Phys. Solids, 61(12), pp. 2473–2492. [CrossRef]
Ke, L. L. , and Wang, Y. S. , 2006, “ Two-Dimensional Contact Mechanics of Functionally Graded Materials With Arbitrary Spatial Variations of Material Properties,” Int. J. Solids Struct., 43(18–19), pp. 5779–5798. [CrossRef]
Ke, L. L. , and Wang, Y. S. , 2010, “ Fretting Contact of Two Dissimilar Elastic Bodies With Functionally Graded Coatings,” Mech. Adv. Mater. Struct., 17(6), pp. 433–447. [CrossRef]
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, Russia.
Hamrock, B. J. , 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York.
Aizikovich, S. M. , and Aleksandrov, V. M. , 1982, “ Properties of Compliance Functions for Layered and Continuously Nonuniform Halfspace,” Soviet Phys. Dokl., 27(9), pp. 765–767.
Alexandrov, V. M. , and Kovalenko, E. V. , 1986, Problems of Continuous Mechanics With Mixed Boundary Conditions, Nauka Publisher, Moscow, 334 p.
Kevorkian, J. , and Cole, J. D. , 1985, Perturbation Methods in Applied Mathematics (Applied Mathematics Series), Vol. 34, Springer-Verlag, New York.

Figures

Grahic Jump Location
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. 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. 1

General view of a lubricated functionally graded material

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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. 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])

Grahic Jump Location
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. 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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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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