Research Papers: Hydrodynamic Lubrication

Application of Smoothed Particle Hydrodynamics to Full-Film Lubrication

[+] Author and Article Information
Elon J. Terrell

e-mail: eterrell@columbia.edu
Mechanical Engineering Department,
Columbia University,
500 West 120th Street,
Room 220 Mudd,
New York, NY 10027

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received November 8, 2012; final manuscript received May 22, 2013; published online July 3, 2013. Assoc. Editor: C. Fred Higgs III.

J. Tribol 135(4), 041705 (Jul 03, 2013) (9 pages) Paper No: TRIB-12-1196; doi: 10.1115/1.4024708 History: Received November 08, 2012; Revised May 22, 2013

An in-house solver was created in order to simulate hydrodynamic lubrication utilizing smoothed particle hydrodynamics (SPH). SPH is a meshfree, Lagrangian, particle-based method that can be used to solve continuum problems. In this study, transient hydrodynamic lubrication in a pad bearing geometry was modeled utilizing the SPH method. The results were validated by comparison to computational fluid dynamics (CFD) and an analytical solution provided by lubrication theory. Results for the pressure distribution between SPH and CFD were agreeable while lubrication theory failed to capture any inertial effects of the fluid. Velocity profile comparisons differed slightly between all three methods. However, since smoothed particle methods have been shown to have the advantage of being able to model large deformations, as well as allowing easy definitions of fluid-solid interfaces, they can be useful tools for complex problems in tribology.

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Spinato, F., Tavner, P. J., van Bussel, G. J. W., and Koutoulakos, E., 2009, “Reliability of Wind Turbine Subassemblies,” IET Renewable Power Gener., 3(4), pp. 387–401. [CrossRef]
Buckholz, R. H., 1986, “Effect of Lubricant Inertia Near the Leading Edge of a Plane Slider Bearing,” ASME J. Tribol., 109(1), pp. 60–65. [CrossRef]
Zhao, J., Sadeghi, F., and Hoeprich, M. H., 2001, “Analysis of EHL Circular Contact Start Up: Part I—Mixed Contact Model With Pressure and Film Thickness Results,” ASME J. Tribol., 123(1), pp. 67–74. [CrossRef]
Glovnea, R., and Spikes, H., 2001, “Elastohydrodynamic Film Formation at the Start-Up of the Motion,” J. Eng. Tribol., 215(2), pp. 125–138. [CrossRef]
Glovnea, R., and Spikes, H., 2000, “The Influence of Lubricant Upon EHD Film Behavior During Sudden Halting of Motion,” Tribol. Trans., 43(4), pp. 731–739. [CrossRef]
Ren, N., Zhu, D., and Wen, S., 1991, “Experimental Method for Quantitative Analysis of Transient EHL,” Tribol. Int., 24(4), pp. 225–230. [CrossRef]
Holmes, M. J. A., Evans, H. P., and Snidle, R. W., 2003, “Comparison of Transient EHL Calculations With Start-Up Experiments,” Proceedings of the 29th Leeds-Lyon Symposium on Tribology, Tribology Series, D.Dowson, M.Priest, G.Dalmaz, and A. A.Lubrecht, eds., Elsevier, New York, pp. 79–89.
Herrebrugh, K., 1970, “Elastohydrodynamic Squeeze Films Between Two Cylinders in Normal Approach,” ASME J. Lubr. Technol., 92, pp. 292–302. [CrossRef]
Christensen, H., 1970, “Elastohydrodynamic Theory of Spherical Bodies in Normal Approach,” ASME J. Lubr. Technol., 92, pp. 145–154. [CrossRef]
Zhao, J., Sadeghi, F., and Hoeprich, M. H., 2001, “Analysis of EHL Circular Contact Start Up: Part I-Mixed Contact Model With Pressure and Film Thickness Results,” ASME J. Tribol., 123(1), pp. 67–74. [CrossRef]
Zhao, J., and Sadeghi, F., 2004, “The Effects of a Stationary Surface Pocket on EHL Line Contact Start-Up,” ASME J. Tribol., 126(4), pp. 672–680. [CrossRef]
Popovici, G., Venner, C., and Lugt, P., 2004, “Effects of Load System Dynamics on the Film Thickness in EHL Contacts During Start Up,” ASME J. Tribol., 126(2), pp. 258–266. [CrossRef]
Higgs, C. F., Ng, S. H., Borucki, L., Yoon, I., and Danyluk, S., 2005, “A Mixed-Lubrication Approach to Predicting CMP Fluid Pressure Modeling and Experiments,” J. Electrochem. Soc., 152(3), pp. 193–198. [CrossRef]
Jin, X., Keer, L. M., and Wang, Q., 2005, “A 3D EHL Simulation of CMP: Theoretical Framework of Modeling,” J. Electrochem. Soc., 152(1), pp. 7–15. [CrossRef]
Li, S., and Kahraman, A., 2010, “Prediction of Spur Gear Mechanical Power Losses Using a Transient Elastohydrodynamic Lubrication Model,” Tribol. Trans., 53, pp. 554–563. [CrossRef]
Terrell, E. J., and Higgs, C. F., 2007, “A Modeling Approach for Predicting the Abrasive Particle Motion During Chemical Mechanical Polishing,” ASME J. Tribol., 129(4), pp. 933–941. [CrossRef]
Terrell, E. J., and Higgs, C. F., III, 2006, “Hydrodynamics of Slurry Flow in Chemical Mechanical Polishing,” J. Electrochem. Soc., 153(6), pp. 15–22. [CrossRef]
Luan, Z., and Khonsari, M. M., 2008, “A Note on the Lubricating Film in Hydrostatic Mechanical Face Seals,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol., 222(J4), pp. 559–567. [CrossRef]
Ng, S. H., Borucki, L., Higgs, C. F., III, Yoon, I., Osorno, A., and Danyluk, S., 2005, “Tilt and Interfacial Fluid Pressure Measurements of a Disk Sliding on a Polymeric Pad,” ASME J. Tribol., 127(1), pp. 198–205. [CrossRef]
Patir, N., and Cheng, H. S., 1979, “Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces,” ASME J. Lubr. Technol., 101(2), pp. 220–230. [CrossRef]
Nisson, B., and Hansbo, P., 2010, “Weak Coupling of a Reynolds Model and a Stokes Model for Hydrodynamic Lubrication,” Int. J. Numer. Methods Fluids, 66, pp. 730–741. [CrossRef]
Leal, L. G., 2007, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, Cambridge University, Cambridge, UK.
Bair, S., and Qureshi, F., 2002, “Accurate Measurements of Pressure-Viscosity Behavior in Lubricants,” Tribol. Trans., 45(3), pp. 390–390. [CrossRef]
Pinkus, O., and Sternlicht, B., 1961, Theory of Hydrodynamic Lubrication, McGraw-Hill, New York.
Szeri, A. Z., Romandi, A. A., and Giron-Duarte, A., 1983, “Linear Force Coefficients for Squeeze Film Dampers,” ASME J. Lubr. Technol., 105, pp. 326–334. [CrossRef]
San Andrés, L., and Vance, J. M., 1986, “Effects of Fluid Inertia and Turbulence on the Force Coefficients for Squeeze Film Dampers,” ASME J. Eng. Gas Turbines Power, 108, pp. 332–339. [CrossRef]
Elrod, H. G., Anwar, I., and Colsher, R., 1983, “Transient Lubricating Films With Inertia,” ASME J. Lubr. Technol., 105(3), pp. 369–374. [CrossRef]
Hashimoto, H., Wada, S., and Sumitomo, M., 1988, “The Effects of Fluid Inertia Forces on the Dynamic Behavior of Short Journal Bearings in Superlaminar Flow Regime,” ASME J. Tribol., 110(3), pp. 539–547. [CrossRef]
Tichy, J., and Bou-Saïd, B., 1991, “Hydrodynamic Lubrication and Bearing Behavior With Impulsive Loads,” Tribol. Trans., 34(4), pp. 505–512. [CrossRef]
Gingold, R. A., and Monaghan, J. J., 1977, “Smoothed Particle Hydrodynamics: Theory and Application to Non-Spherical Stars,” Mon. Not. R. Astron. Soc., 181, pp. 375–389.
Lucy, L. B., 1977, “Numerical Approach to Testing the Fission Hypothesis,” Astron. J., 82, pp. 1013–1024. [CrossRef]
Antoci, C., Gallati, M., and Sibilla, S., 2007, “Numerical Simulation of Fluid-Structure Interaction by SPH,” Comput. Struct., 85, pp. 879–890. [CrossRef]
Benz, W., and Asphaug, E., 1995, “Simulations of Brittle Solids Using Smooth Particle Hydrodynamics,” Comput. Phys. Commun., 87, pp. 253–265. [CrossRef]
Gray, J. P., Monaghan, J. J., and Swift, R. P., 2001, “SPH Elastic Dynamics,” Comput. Methods Appl. Mech. Eng., 190, pp. 6641–6662. [CrossRef]
Libersky, L. D., Petschek, A. G., Carney, T. C., Hipp, J. R., and Allahdadi, F. A., 1993, “High Strain Lagrangian Hydrodynamics,” J. Comput. Phys., 109, pp. 67–75. [CrossRef]
Monaghan, J. J., 1994, “Simulating Free Surface Flows With SPH,” J. Comput. Phys., 110, pp. 399–406. [CrossRef]
Morris, J. P., Fox, P. J., and Zhu, Y., 1997, “Modeling Low Reynolds Number Incompressible Flows Using SPH,” J. Comput. Phys., 136, pp. 214–226. [CrossRef]
Takeda, H., Miyama, S. M., and Sekiya, M., 1994, “Numerical Simulation of Viscous Flow by Smoothed Particle Hydrodynamics,” Prog. Theor. Phys., 92, pp. 939–960. [CrossRef]
Booser, E. R., and Wilcock, D. F., 1991, “Hydrodynamic Lubrication,” Lubr. Eng., 47(8), pp. 645–647.
Shadloo, M. S., Zainali, A., Sadek, H., and Yildiz, M., 2011, “Improved Incompressible Smoothed Particle Hydrodynamics Method for Simulating Flow Around Bluff Bodies,” Comput. Methods Appl. Mech. Eng., 200, pp. 1008–1020. [CrossRef]
Liu, G. R., and Liu, M. B., 2003, Smoothed Particle Hydrodynamics: A Meshfree Particle Method, World Scientific, Singapore.
Courant, R., Friedrichs, K., and Lewy, H., 1928, “Über die Partiellen Differenzengleichungen der Mathematischen Physik,” Mathematische Annalen, 100, pp. 32–74. [CrossRef]
Fulk, D. A., 1994, “A Numerical Analysis of Smoothed Particle Hydrodynamics,” Ph.D. thesis, Air Force Institute of Technology, Wright-Patterson AFB, OH.
Hernquist, L., and Katz, N., 1989, “TREESPH—A Unification of SPH With the Hierarchical Tree Method,” Astrophys. J., Suppl. Ser., 70, pp. 419–446. [CrossRef]
Monaghan, J. J., 1982, “Why Particle Methods Work (Hydrodynamics),” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput., 3, pp. 422–433. [CrossRef]
Monaghan, J. J., 1992, “Smoothed Particle Hydrodynamics,” Annu. Rev. Astron. Astrophys., 30, pp. 543–574. [CrossRef]
Monaghan, J. J., and Lattanzio, J. C., 1985, “A Refined Particle Method for Astrophysical Problems,” Astron. Astrophys., 149, pp. 135–143.
Schoenberg, I. J., 1946, “Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions,” Q. Appl. Math., 4, pp. 45–88.
Randles, P. W., and Libersky, L. D., 1996, “Smoothed Particle Hydrodynamics Some Recent Improvements and Applications,” Comput. Methods Appl. Mech. Eng., 138, pp. 375–408. [CrossRef]
Brackbill, J. U., Kothe, D. B., and Zemach, C., 1991, “A Continuum Method for Modeling Surface Tension,” J. Comput. Phys., 100(2) pp. 335–354. [CrossRef]
Sulsky, D., 1995, “The Material Point Method for Large Deformation Solid Mechanics,” Proceedings of the 3rd U.S. Congress on Computational Mechanics, USACM, Dallas, TX.
Stachowiak, G. W., and Batchelor, A. W., 2006, Engineering Tribology, Elsevier, New York.
Heckelman, D. D., and McC. Ettles, C. M., 1988, “Viscous and Inertial Pressure Effects at the Inlet to a Bearing Film,” Tribol. Trans., 31(1), pp. 1–5. [CrossRef]
Lewicki, W., 1955, “Theory of Hydrodynamic Lubrication in Parallel Sliding,” The Engineer, 200, pp. 939–941.
Rodkiewicz, Cz. M., Kim, K. W., and Kennedy, J. S., 1990, “On the Significance of the Inlet Pressure Build-Up in the Design of Tilting-Pad Bearings,” ASME J. Tribol., 112, pp. 17–22. [CrossRef]


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Fig. 1

Diagram of sliding pad bearing geometry. The pad is fixed while the opposing surface moves to the right at velocity U. The bearing width is represented by L while the film thickness is h.

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Fig. 2

Particle approximation for particle i. The support domain is circular with radius κλ. The color gradient represents the weighting of the smoothing function.

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Fig. 3

Illustration depicting particle deficiency near a boundary for particle i. Particle j has a support domain completely contained within the domain, therefore, not experiencing any deficiency.

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Fig. 4

Fluid (filled) and solid (unfilled) particles interacting near an interface

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Fig. 5

Flow chart of SPH methodology. The dashed box represents a single time step.

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Fig. 6

SPH simulation of sliding wedge geometry

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Fig. 7

SPH convergence study. Relative percentage error of the bearing load at steady state was calculated.

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Fig. 8

Evolution of hydrodynamic pressure distribution with time

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Fig. 9

Pressure distribution underneath the wedge through time

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Fig. 10

Plot of load carrying capacity of the sliding wedge as a function of time. The asymptotically approaching value indicates that the pressure distribution underneath the wedge has reached steady state.

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Fig. 11

Meshing scheme for the CFD model of the sliding pad bearing

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Fig. 12

Schematic of boundary conditions for CFD model of the sliding pad bearing

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Fig. 13

Comparison of the pressure distribution between the SPH simulation and analytical solution. The difference in the inlet pressure, as well as the overprediction of the pressure in the SPH & CFD simulations, is a result of the ramming effect of the wedge.

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Fig. 14

Comparison of velocity profile prediction between SPH, lubrication theory, and CFD across the fluid film at (a) x/L = 0 (inlet), (b) x/L = 1/3, (c) x/L = 2/3, and (d) x/L = 1 (outlet)



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