Technical Brief

Equivalent Clearance Model for Solving Thermohydrodynamic Lubrication of Slider Bearings With Steps

[+] Author and Article Information
Hideki Ogata

IHI Corporation,
Yokohama, 235-8501, Japan
e-mail: hideki_ogata@ihi.co.jp

Joichi Sugimura

Department of Mechanical Engineering,
Kyushu University,
Fukuoka 819-0395, Japan
e-mail: sugi@mech.kyushu-u.ac.jp

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 31, 2016; final manuscript received August 11, 2016; published online November 30, 2016. Assoc. Editor: Jordan Liu.

J. Tribol 139(3), 034503 (Nov 30, 2016) (5 pages) Paper No: TRIB-16-1103; doi: 10.1115/1.4034457 History: Received March 31, 2016; Revised August 11, 2016

This study focuses on the thermohydrodynamic lubrication (THD) analysis of fluid film bearings with steps on the bearing surface, such as Rayleigh step. In general, the Reynolds equation does not satisfy the continuity of fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants by finite differential method (FDM), because the energy equation needs the velocity components explicitly. The authors have solved this issue by introducing the equivalent clearance height and the equivalent gradient of the clearance height at steps. These parameters remove the discontinuity of velocity components, and the Reynolds equations can be solved for any bearing surfaces with step regions by FDM. Moreover, this method results in pseudocontinuous velocity components, which enables the energy equation to be solved as well. This paper describes this method with one-dimensional and equal grids model. The numerical results of pressure and temperature distributions by the proposed method for an infinite width Rayleigh step bearing agree well with the results obtained by solving full Navier–Stokes equations with semi-implicit method for pressure-linked equations revised (SIMPLER) method.

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Dowson, D. , 1962, “ A Generalized Reynolds Equation for Fluid Film Lubrication,” Int. J. Mech. Sci., 4(2), pp. 159–170. [CrossRef]
Tanaka, M. , 2000, “ Recent Thermohydrodynamic Analyses and Designs of Thick-Film Bearings,” J. Eng. Tribol., 214(1), pp. 107–122.
Dobrica, M. , and Fillon, M. , 2005, “ Reynolds' Model Suitability in Simulation Rayleigh Step Bearing Thermo-Hydrodynamic Problems,” Tribol. Trans., 48(4), pp. 522–530. [CrossRef]
Dobrica, M. B. , and Fillon, M. , 2006, “ Thermo-Hydrodynamic Behavior of a Slider Pocket Bearing,” ASME J. Tribol., 128(2), pp. 312–318. [CrossRef]
Patankar, S. V. , 1981, “ A Calculation Procedure for Two-Dimensional Elliptic Situations,” Numer. Heat Transfer, 4(4), pp. 409–425. [CrossRef]


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Fig. 1

Rayleigh step bearing

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Fig. 2

Velocity distribution of Rayleigh step bearing

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Fig. 3

Grid definition: (a) continuous geometry and (b) discontinuous geometry

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Fig. 8

Temperature distribution around step in the actual clearance space (a) and the equivalent clearance space (b)

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Fig. 7

Temperature fields in fluid and solid domain: (a) THD,  °C and (b) SIMPLER,  °C

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Fig. 6

Temperature distribution on the bearing surface

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Fig. 5

Oil film pressure distribution on the slider surface

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Fig. 4

Calculation grid: (a) present method and (b) SIMPLER method



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