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Research Papers: Elastohydrodynamic Lubrication

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

[+] Author and Article Information
Ilya I. Kudish

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

Sergey S. Volkov

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

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), 021505 (Oct 30, 2015) (11 pages) Paper No: TRIB-15-1027; doi: 10.1115/1.4030958 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 developed earlier by the authors such as Kudish (2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman & Hall/CRC Press, Boca Raton, FL), Kudish and Covitch (2010, Modeling and Analytical Methods in Tribology, Chapman & Hall/CRC Press, Boca Raton, FL), Aizikovich et al. (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), Aizikovich et al. (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 Verlag, Basel, p. 317), Aizikovich and Vasiliev (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), Volkov et al. (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), Vasiliev et al. (2014, “Axisymmetric Contact Problems of the Theory of Elasticity for Inhomogeneous Layers,” Z. Angew. Math. Mech., 94(9), pp. 705–712), Aizikovich et al. (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), and Aizikovich et al. (2010, “Inverse Analysis for Evaluation of the Shear Modulus of Inhomogeneous Media in Torsion Experiments,” Int. J. Eng. Sci., 48(10), pp. 936–942). 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 loaded lubricated contacts. The way the solution of the EHL problem for coated/functionally graded materials is obtained provides a very clear structure of the solution. The solution of the EHL problem in the Hertzian region is very close to the solution of the dry contact problem while in the inlet and exit zones the solutions of the EHL problem with the right asymptotes coming from the solution of the dry contact problem can be related to the solutions of the classic EHL problem for homogeneous materials.

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References

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 Equations of the Static Contact Problems for the Foundations Inhomogeneous in Depth,” Operator Theory: Advances and Applications, Birkhauser Verlag, Basel, 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,” 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]
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, Fizmatgiz, Moscow.
Kudish, I. I. , Volkov, S. S. , Vasiliev, A. S. , and Aizikovich, S. M. , 2015, “Some Criteria for Coating Effectiveness in Heavily Loaded Line Elastohydrodynamically Lubricated Contacts—Part I: Dry Contacts,” ASME J. Tribol., 138(1).
Hamrock, B. J. , 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York.
Vorovich, I. I. , Aleksandrov, V. M. , and Babeshko, V. A. , 1974, Non-Classical Mixed Problems of Elasticity, Nauka Publishing, Moscow.
Van-Dyke, M. , 1964, Perturbation Methods in Fluid Mechanics, Academic, New York.
Nayfeh, A. H. , 1981, Introduction to Perturbation Techniques, Wiley, New York.

Figures

Grahic Jump Location
Fig. 1

Graphs of the lubrication film thickness ratio Rinhom from (4.15) for fully flooded lubrication regimes, constant viscosity, and different values of β versus the coating thicknesses λs

Grahic Jump Location
Fig. 2

Graphs of the friction force ratio Kinhom from (4.22) for starved lubrication regimes, constant viscosity, and different values of β versus the coating thicknesses λs

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