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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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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