Research Papers: Elastohydrodynamic Lubrication

Transient Dynamics of the Conformal Elastohydrodynamic Squeeze Film Problem

[+] Author and Article Information
S. Boedo

Department of Mechanical Engineering,
Rochester Institute of Technology,
Rochester, NY 14623

Convergence difficulties and long computational times encountered with the N-R method to solve counterformal EHL contact problems involving piezoviscosity have led to the development of multigrid methods [6].

A minimum set of structural restraints on the sleeve are required to prevent rigid-body motion.

In this paper, film nodes are numbered consecutively from one to N as shown in Fig. 2.

Terms x0 and xN+1 which appear in shape functions ψ1(x) and ψN(x), respectively, can be assigned arbitrary values, as the respective portions of the functions fall outside of the bearing region.

Computational details can be found in Booker and Huebner [17] and Booker and Boedo [11].

Matrices S, G, and T defined here have no special meaning and serve only as a means to simplify notation; the matrices are also unrelated to terms defined in the MIH formulation.

An alternative and equivalent form of Eq. (51) is provided in Booker [13].

The ramped load case also depends explicitly on time ratio τ.

In practical bearing design studies, the modal convergence test need be performed only once for a given structural design.

Increasing the elasticity number can be accomplished, for example, by increasing Young's modulus.

The inclusion of journal deformation has been studied previously and is found to be relatively small compared with sleeve deformation at dimensional scales and with material properties employed in this sample application [9].

Terms involving x0 and xN+1 are not evaluated; see footnote 4.

This is an exact analytical solution of Eqs. (2)(6) with δa ≡ 0.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 15, 2015; final manuscript received March 31, 2015; published online July 7, 2015. Assoc. Editor: Sinan Muftu.

J. Tribol 137(4), 041506 (Oct 01, 2015) (12 pages) Paper No: TRIB-15-1055; doi: 10.1115/1.4030691 History: Received February 15, 2015; Revised March 31, 2015; Online July 07, 2015

This paper provides the first cross-comparison of three established elastohydrodynamic computational methods to investigate the conformal long-bearing pure squeeze cylindrical bearing problem with rigid journal and elastic sleeve. The benefits of each analysis method in addressing both theoretical and practical issues in problem formulation and application are discussed. A set of nondimensional design charts for minimum film thickness and maximum film pressure under a step load are presented. With a judicious choice of load and sleeve geometry, it is found that a uniform film pressure can develop over a large film pocket in the limit of conformal journal and sleeve contact even with relatively high modulus materials such as steel.

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Booker, J. F., Boedo, S., and Bonneau, D., 2010, “Conformal EHL Analysis for Engine Bearing Design: A Brief Review,” Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci., 224(12), pp. 2648–2653. [CrossRef]
Oh, K. P., 1984, “The Numerical Solution of Dynamically Loaded Elastohydrodynamic Contact as a Nonlinear Complementarity Problem,” ASME J. Tribol., 106(1), pp. 88–95. [CrossRef]
Oh, K. P., and Goenka, P. K., 1985, “The Elastohydrodynamic Solution of Journal Bearings Under Dynamic Loading,” ASME J. Tribol., 107(3), pp. 389–394. [CrossRef]
McIvor, J. D. C., and Fenner, D. N., 1989, “Finite Element Analysis of Dynamically Loaded Flexible Journal Bearings: A Fast Newton–Raphson Method,” ASME J. Tribol., 111(4), pp. 597–604. [CrossRef]
Bonneau, D., Guines, D., Frene, J., and Toplosky, J., 1995, “EHD Analysis, Including Structural Inertia and a Mass Conserving Cavitation Model,” ASME J. Tribol., 117(3), pp. 540–547. [CrossRef]
Venner, C. H., and Lubrecht, A. A., 2000, Multilevel Methods in Lubrication, D.Dowson, ed., Elsevier, Amsterdam.
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]
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]
Boedo, S., and Booker, J. F., 2005, “Modal and Nodal EHD Analysis for Gas Journal Bearings,” ASME J. Tribol., 127(2), pp. 306–314. [CrossRef]
Booker, J. F., and Boedo, S., 2001, “Finite Element Analysis of Elastic Engine Bearing Lubrication: Theory,” Rev. Eur. Éléments Finis, 10(6), pp. 705–724.
Olson, E. G., and Booker, J. F., 2001, “EHD Analysis With Distributed Structural Inertia,” ASME J. Tribol., 123(3), pp. 462–468. [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, 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.
Dowson, D., and Higginson, G. R., 1966, Elastohydrodynamic Lubrication, Pergamon, London.
Huebner, K. H., Dewhirst, D. L., Smith, D. E., and Byrom, T. G., 2001, The Finite Element Method for Engineers, 4th ed., Wiley, 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]
Boedo, S., and Booker, J. F., 2001, “Finite Element Analysis of Elastic Engine Bearing Lubrication: Application,” Rev. Eur. Éléments Finis, 10(6–7), pp. 725–740.
Boedo, S., 1995, “A Mass-Conserving Modal-Based Elastohydrodynamic Lubrication Model: Effects of Structural Body Forces, Surface Roughness, and Mode Stiffness Variation,” Ph.D. thesis, Cornell University, Ithaca, NY.
Boedo, S., Booker, J. F., and Wilkie, M. J., 1995, “A Mass Conserving Modal Analysis for Elastohydrodynamic Lubrication,” Lubricants and Lubrication, D.Dowson, C. M.Taylor, T. H. C.Childs, and G.Dalmaz, eds., Elsevier, Amsterdam, pp. 513–523. [CrossRef]
Booker, J. F., 1965, “Dynamically Loaded Journal Bearings: Mobility Method of Solution,” ASME J. Basic Eng., 87(3), pp. 537–546. [CrossRef]


Grahic Jump Location
Fig. 2

Structural and film finite element meshes

Grahic Jump Location
Fig. 4

Film thickness and film pressure distributions at τ = 1: step load, F0T0(C0/R)2/(μLD) = 62.5, a/R = 1/2, ν = 0.3

Grahic Jump Location
Fig. 5

Film thickness and film pressure distributions at τ = 1: step load, F0T0(C0/R)2/(μLD) = 62.5, a/R = 1/2, ν = 0.3

Grahic Jump Location
Fig. 6

Effect of elasticity number on film thickness and film pressure distributions: NIH method, step load, τ = 1, F0T0(C0/R)2/(μLD) = 62.5, a/R = 1/2, ν = 0.3

Grahic Jump Location
Fig. 7

Effect of load history on film thickness ratio distributions: NIH method, τ = 1 s, a/R = 1/2, ν = 0.3

Grahic Jump Location
Fig. 8

Effect of load history on film pressure ratio distributions: NIH method, τ = 1 s, a/R = 1/2, ν = 0.3

Grahic Jump Location
Fig. 10

Maximum film pressure ratio at time τ = 1: NIH method, step load case

Grahic Jump Location
Fig. 11

Film thickness and film pressure ratio distributions at τ = 1: NIH method, step load, ELC0/F0 = 10, a/R = 1/2, ν = 0.3

Grahic Jump Location
Fig. 12

Dimensional film thickness and film pressure distributions: Sample application, NIH method, and step load

Grahic Jump Location
Fig. 9

Minimum film thickness ratio at time τ = 1: NIH method, step load case



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