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TECHNICAL PAPERS

Thermohydrodynamic Lubrication Analysis Incorporating Bingham Rheological Model

[+] Author and Article Information
J. H. Kim, A. A. Seireg

Mechanical Engineering Department, University of Florida-Gainesville, Gainesville, FL 32611

J. Tribol 122(1), 137-146 (Dec 22, 1998) (10 pages) doi:10.1115/1.555336 History: Received August 31, 1998; Revised December 22, 1998
Copyright © 2000 by ASME
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References

Milne, A. A., 1958, “A Theory of Grease Lubrication of a Slider Bearing,” Proc. Second Intn. Cong. of Rheology, p. 427.
Szeri,  A. Z., 1987, “Some Extensions of the Lubrication Theory of Osborne Reynolds,” ASME J. Tribol., 109, p. 21.
Huang,  X. B., and Wilson,  W. R. D., 1992, “Theory of Viscoplastic Lubrication: Part I-Basic Relationships,” ASME J. Tribol., 114, p. 469.
Streator,  J. L., Gerhardstein,  J. P., and McCollum,  C. B., 1994, “The Low-Pressure Rheology of Ultra-Thin Lubricant Films and Its Influence on Sliding Contact,” ASME J. Tribol., 116, p. 119.
Sinha,  P., and Singh,  C., 1982, “Lubrication of a Cylinder on a Plane With a Non-Newtonian Fluid Considering Cavitation,” ASME J. Tribol., 104, p. 168.
Feng,  R., and Ramesh,  K. T., 1993, “The Rheology of Lubricants at High Shear Rates,” ASME J. Tribol., 115, p. 640.
Pinkus,  O., 1987, “The Reynolds Centenial: A Brief History of the Theory of Hydrodynamic Lubrication,” ASME J. Tribol., 109, p. 2.
Bair,  S., and Winer,  W. O., 1990, “The High Shear Stress Rheology of Liquid Lubricants at Pressure of 2 to 200 Mpa,” ASME J. Tribol., 112, p. 246.
Bair,  S., and Winer,  W. O., 1992, “The High Pressure, High Shear Stress Rheology of Liquid Lubricants,” ASME J. Tribol., 114, p. 1.
Houpert,  L., Flamand,  L., and Berthe,  D., 1981, “Rheological and Thermal Effects in Lubricated E.H.D. Contacts,” ASME J. Lubr. Technol., 103, p. 526.
Bai, Y., and Dodd, B., 1992, Adiabatic Shear Localization, Pergamon Press, Oxford.
Bair,  S., Qureshi,  F., and Khonsari,  M., 1994, “Adiabatic Shear Localization in Liquid Lubrication Under Pressure,” ASME J. Tribol., 116, p. 705.
Gohar, R., 1988, Elastohydrodynamics, Wiley, New York.
Hamrock, B. J., and Dowson, D., 1981, Ball Bearing Lubrication: The Elastohydrodynamics of Elliptical Contacts, Wiley, New York.
Wang,  N. Z., and Seireg,  A. A., 1994, “Thermohydrodynamic Lubrication Analysis Incorporating Thermal Expansion Across the Film,” ASME J. Tribol., 116, p. 681.
Wang,  N. Z., and Seireg,  A. A., 1995, “Empirical Prediction of the Shear Layer Thickness in Lubricating Films,” ASME J. Tribol., 117, p. 444.
Wada,  S., Hayashi,  H., and Haga,  K., 1973, “Behavior of a Bingham Solid in Hydrodynamic Lubrication: Part I, General Theory,” Bull. JSME, 16, p. 422.
Wada,  S., Hayashi,  H., and Haga,  K., 1973, “Behavior of a Bingham Solid in Hydrodynamic Lubrication: Part II, Application to Step Bearing,” Bull. JSME, 16, p. 432.
Tichy,  J. A., 1991, “Hydrodynamic Lubrication Theory for the Bingham Plastic Model,” J. Rheol., 35, p. 477.
Dorier,  C., and Tichy,  J. A., 1992, “Behavior of a Bingham-like Viscous Fluid in Lubrication Flows,” J. Non-Newtonian Fluid Mech., 45, p. 291.
Tanner, R. I., 1995, Engineering Rheology, Clarendon Press, Oxford.
Bird, R. B., Armstrong, R. C., and Hassager, O., 1987, Dynamics of Polymeric Liquids, Volume I Fluid Mechanics, Wiley, New York.
Feguson, J., and Kemblowski, 1991, Applied Fluid Rheology, Elsevier Applied Science, London and New York.
Reynolds,  O., 1886, “On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil,” Philos. Trans. R. Soc. London, Ser. A, 177, p. 157.
Anderson, D. A., Tannehill, J. C., and Pleacher, R. H., 1984, Computational Fluid Mechanics and Heat Transfer, Taylor & Francis, New York.
Seireg,  A., and Ezzat,  H., 1973, “Thermohydrodynamic Phenomena in Fluid Film Lubrication,” ASME J. Lubr. Technol., 95, p. 187.
Seireg,  A., and Dandage,  S., 1982, “Empirical Design Procedure for the Thermohydrodynamic Behavior of Journal Bearings,” ASME J. Lubr. Technol., 104, p. 135.
Zhang,  Y., and Ramesh,  K. T., 1996, “The Behavior of an Elastohydrodynamic Lubricant at Moderate Pressures and High Shear Rates,” ASME J. Tribol., 118, p. 162.

Figures

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Illustration of the multi-layer lubrication film
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The normalized computational domain
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Program flow chart of THD analysis based on the Rheological behavior of the film
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Pressure distribution for various bearing running speed along the centerline of the journal bearing in the direction of sliding motion, D=80.112 mm,L=50.8 mm,C=0.3404 mm,ε=0.9, SAE 10, Tln=53.3°C, —▴— Calculated 2100 rpm τ0=15, —□— Calculated 1050 rpm τ0=20, —○— Experimental
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Journal bearing pressure speed characteristics, D=80.112 mm,L=50.8 mm,C=0.3404 mm, SAE 10, Tin=53.3°C,ε=0.9,N=1050 rpm:=20,N=2100 rpm:=15, ○ Present study, □ Isoviscous theory, ▴ Calculated with empirical shear zone (Ref. 16), ▾ Experimental
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Shear zone ratio along film flow direction, D=80.112 mm,L=50.8 mm,C=0.3404 mm,ε=0.9,Tln=53.3°C, SAE 10, Time=0.5 s,N=2100 rpm,τ̄0=15, —— Calculated shear zone, ⋯ Empirical shear zone (Ref. 16)
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Dimensionless film temperature distribution at the journal bearing mid plane in the sliding direction, D=80.112 mm,L=50.8 mm,C=0.3404 mm,ε=0.9, SAE 10 Tln=53.3°C,Time=0.5 s,τ̄0=15,N=2100 rpm
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Pressure distribution for various shear yield parameters along the centerline of the journal bearing in the direction of sliding motion, D=80.112 mm,L=50.8 mm,C=0.3404 mm,ε=0.6, SAE 30, Tln=41.7°C, —○— Calculated with τ0=7,rpm=2000, —▵— Calculated with τ0=8,rpm=1000, ▴ Experimental, rpm=2000, —▴— Calculated with empirical shear zone, rpm=2000 (Ref. 16)
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Journal bearing pressure-speed characteristics D=80.112 mm,L=50.8 mm,C=0.3404 mm, SAE 30, Tln=41.7°C,ε=0.6,N=1000 rpm:τ0=8,N=2000 rpm:τ0=7, ○ Present study, □ Isoviscous theory, ▴ Empirical shear zone (Wang and Seireg), ▿ Experimental
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Shear zone ratio along film flow direction, D=80.112 mm,L=50.8 mm,C=0.3404 mm,ε=0.6,Tln=41.7°C,N=2000 rpm, SAE 30, τ̄0=7, —— Calculated shear zone, ⋯ Empirical shear zone (Ref. 16)
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Pressure distribution along the centerline of the journal bearing in the direction of sliding, D=80.112 mm,L=50.8 mm,C=0.3404 mm,ε=0.87,N=2400 rpm, SAE 50, Tln=71.1°C,τ0=8, —•— Calculated, —□— Experimental
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Pressure distribution along the centerline of the slider bearing in the direction of sliding, SAE 10, hmin=0.1016 mm,hmax=0.2032 mm,Tln=37.8°C,U=12.192 m/sec,B=L=76.2 mm, —▿— Calculated with τ̄0=8.0, —○— Calculated with τ̄0=10, —▴— Experimental
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Slider bearing pressure speed characteristics, B=L=76.2 mm,hmin=0.1016 mm,hmax=0.2032 mm, SAE 10, Tln=37.8°C,τ̄0=8.0, • Empirical shear zone (Ref. 16), ▪ Present study, ▴ Isoviscous theory
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Shear zone ratio along the film flow direction, B=L=76.2 mm,hmin=0.1016 mm,hmax=0.2032 mm,Tln=37.8°C,Time=0.2 s,U=12.192 m/s, SAE 10, τ0=8, —— Calculated shear zone, ⋯ Empirical shear zone (Ref. 16)
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Shear zone ratio along film flow direction, B=L=76.2 mm,hmin=0.1016 mm,hmax=0.2032 mm,Tln=37.8°C,Time=0.2 s,U=6.096 m/s, SAE 10, τ0=8, —— Calculated shear zone, ⋯ Empirical shear zone (Ref. 16)
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Velocity profile in the shear zone, hs/h along the mid-plane of the slider bearing in the direction of motion B=L=76.2 mm,hmin=0.1016 mm,hmax=0.2032 mm,U=12.192 m/sec, SAE 10, τ̄0=8.0,Tln=37.8°C
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Dimensionless film temperature distribution along the central line of the slider bearing in the direction of flow, B=L=76.2 mm,hmin=0.1016 mm,hmax=0.2032 mm, SAE 10, Tln=37.8°C,τ̄0=8.0,U=12.192 m/s
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Shear yield stress versus maximum pressure for the considered cases

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