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Research Papers: Elastohydrodynamic Lubrication

Nodal Unsteady Inverse Elastohydrodynamic Lubrication: Axisymmetric Normal Approach

[+] Author and Article Information
J. F. Booker

Sibley School of Mechanical and
Aerospace Engineering,
Cornell University,
Ithaca, NY 14853
e-mail: booker@cornell.edu

S. Boedo

Department of Mechanical Engineering,
Rochester Institute of Technology,
Rochester, NY 14623
e-mail: sxbeme@rit.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received May 21, 2017; final manuscript received November 6, 2017; published online February 6, 2018. Assoc. Editor: Mihai Arghir.

J. Tribol 140(4), 041501 (Feb 06, 2018) (7 pages) Paper No: TRIB-17-1195; doi: 10.1115/1.4038985 History: Received May 21, 2017; Revised November 06, 2017

An “inverse” formulation is described for general problems of unsteady elastohydrodynamic lubrication (EHL). Spatial discretization gives an explicit initial-value ordinary differential equation (ODE) problem with (interior) nodal film thicknesses as state variables. Numerical results are compared with published experimental results for normal approach of a spherical surface to an elastic foundation.

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References

Booker, J. F. , Boedo, S. , and Bonneau, D. , 2010, “Conformal EHL Analysis for Engine Bearing Design: A Brief Review,” Proc. IMechE Part C J. Mech. Eng. Sci., 224(12), pp. 2648–2653. [CrossRef]
Boedo, S. , 2015, “Transient Dynamics of the Conformal Elastohydrodynamic Squeeze Film Problem,” ASME J. Tribol., 137(4), p. 041506. [CrossRef]
Booker, J. F. , 2005, “Unsteady EHL: An Inverse Hydrodynamic Formulation,” Life Cycle Tribology, D. Dowson , M. Priest , G. Dalmaz , and A. A. Lubrecht , eds., Elsevier, Amsterdam, The Netherlands, pp. 65–72. [CrossRef]
Booker, J. F. , and Shu, C. F. , 1984, “Finite Element Analysis of Transient Elasto-Hydrodynamic Lubrication,” Developments in Numerical and Experimental Methods Applied to Tribology, D. Dowson , C. M. Taylor , and M. Godet , eds., Butterworths, London, pp. 157–163.
Kumar, A. , Goenka, P. K. , and Booker, J. F. , 1990, “Modal Analysis of Elastohydrodynamic Lubrication: A Connecting Rod Application,” ASME J. Tribol., 112(3), pp. 524–534. [CrossRef]
Boedo, S. , and Booker, J. F. , 1997, “Surface Roughness and Structural Inertia in a Mode-Based Mass-Conserving Elastohydrodynamic Lubrication Model,” ASME J. Tribol., 119(3), pp. 449–455. [CrossRef]
Booker, J. F. , and Boedo, S. , 2004, “Unsteady EHL: ‘Nodal’ Versus ‘Modal’ Formulations,” IUTAM Symposium on Elastohydrodynamics and Micro-Elastohydrodynamics, Cardiff, UK, Sept. 1–3, pp. 71–80.
Kothari, M. , Booker, J. F. , and Bartel, D. L. , 1995, “Analysis of Artificial Hip Joints as Spherical Bearings,” Lubricants and Lubrication, D. Dowson , C. M. Taylor , T. H. C. Childs , and G. Dalmaz , eds., Elsevier, Amsterdam, The Netherlands, pp. 93–98; 671–672. [CrossRef]
Booker, J. F. , and Boedo, S. , 2007, “Spherical vs. cylindrical Engine Bearings,” ASME Paper No. IJTC2007-44448.
Gaman, I. D. C. , Higginson, G. R. , and Norman, R. , 1974, “Fluid Entrapment by a Soft Surface Layer,” Wear, 28(3), pp. 345–352. [CrossRef]
van Leeuwen, H. , Haagh, G. , and van Bavel, P. , 1995, “Transient EHD Lubrication Concentrated Line Contacts—Part 1: Steady-State Pure Squeeze Cases,” Lubricants and Lubrication, D. Dowson , C. M. Taylor , T. H. C. Childs , and G. Dalmaz , eds., Elsevier, Amsterdam, The Netherlands, pp. 525–543. [CrossRef]
Higginson, G. R. , and Norman, R. , 1974, “A Model Investigation of Squeeze-Film Lubrication in Animal Joints,” Phys. Med. Biol., 19(6), pp. 785–792. [CrossRef] [PubMed]
Higginson, G. R. , 1978, “Squeeze Films Between Compliant Solids,” Wear, 46(2), pp. 387–395. [CrossRef]
Johnson, K. L. , 1987, Contact Mechanics, Cambridge University Press, Cambridge, UK.
Shampine, L. F. , and Reichelt, M. W. , 1997, “The MATLAB ODE Suite,” SIAM J. Sci. Comput., 18(1), pp. 1–22. [CrossRef]
Gear, G. W. , 1971, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice Hall, Englewood Cliffs, NJ, p. 253.
Boedo, S. , and Booker, J. F. , 2000, “A Mode-Based Elastohydrodynamic Lubrication Model With Elastic Journal and Sleeve,” ASME J. Tribol., 122(1), pp. 94–102. [CrossRef]
Frêne, J. , Nicolas, D. , Degueurce, B. , Berthe, D. , and Godet, M. , 1990, Lubrification Hydrodynamique: Paliers Et Butées, Editions Eyrolles, Paris, UK.
Hamrock, B. J. , 1994, Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York.
Booker, J. F. , and Huebner, K. H. , 1972, “Application of Finite-Element Methods to Lubrication: An Engineering Approach,” ASME J. Lubr. Technol., 94(4), pp. 313–323. [CrossRef]
Booker, J. F. , and Huebner, K. H. , 1976, “Erratum: ‘Application of Finite Element Methods to Lubrication: An Engineering Approach’ (ASME J. Lubr. Technol., 1972, 94(4), pp. 313–323),” ASME J. Lubr. Technol., 98(1), p. 39.
Booker, J. F. , and Boedo, S. , 2001, “Finite Element Analysis of Elastic Engine Bearing Lubrication: Theory,” Revue Européenne Des Eléments Finis, 10(6–7), pp. 705–724. [CrossRef]
Boedo, S. , 2013, “A Corrected Displacement Solution to Linearly Varying Surface Pressure Over a Triangular Region on the Elastic Half-Space,” Tribol. Int., 60, pp. 116–118. [CrossRef]

Figures

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Fig. 1

Spatial discretization: nodal subsets

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Fig. 2

Coordinates: film (local) and system (global)

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Fig. 4

Elements and nodes: (a) 2D and (b) 1D

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Fig. 5

h(x, 0, 8) and h(r, 8): 2D and 1D meshes

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Fig. 6

h(r, t): EHL simulation and experiment

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Fig. 7

h(0, t): EHL simulation and experiment

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Fig. 8

h(r, t): EHL simulation and Hertz dry contact

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