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TECHNICAL PAPERS

A Multiscale Method Modeling Surface Texture Effects

[+] Author and Article Information
Alex de Kraker1

Laboratory of Tribology, Department of Precision & Microsystems Engineering, Faculty of 3mE, Delft University of Technology, Delft 2628 CD, The Netherlandsa.dekraker@tudelft.nl

Ron A. van Ostayen, A. van Beek

Laboratory of Tribology, Department of Precision & Microsystems Engineering, Faculty of 3mE, Delft University of Technology, Delft 2628 CD, The Netherlands

Daniel J. Rixen

Engineering Dynamics, Department of Precision & Microsystems Engineering, Faculty of 3mE, Delft University of Technology, Delft 2628 CD, The Netherlands

1

Corresponding author.

J. Tribol 129(2), 221-230 (Dec 22, 2006) (10 pages) doi:10.1115/1.2540156 History: Received March 22, 2006; Revised December 22, 2006

In this paper a multiscale method is presented that includes surface texture in a mixed lubrication journal bearing model. Recent publications have shown that the pressure generating effect of surface texture in bearings that operate in full film conditions may be the result of micro-cavitation and/or convective inertia. To include inertia effects, the Navier–Stokes equations have to be used instead of the Reynolds equation. It has been shown in earlier work (de Kraker, 2006, Tribol. Trans., in press) that the coupled two-dimensional (2D) Reynolds and 3D structure deformation problem with partial contact resulting from the soft EHL journal bearing model is not easy to solve due to the strong nonlinear coupling, especially for soft surfaces. Therefore, replacing the 2D Reynolds equation by the 3D Navier–Stokes equations in this coupled problem will need an enormous amount of computing power that is not readily available nowadays. In this paper, the development of a micro–macro multiscale method is described. The local (micro) flow effects for a single surface pocket are analyzed using the Navier–Stokes equations and compared to the Reynolds solution for a similar smooth piece of surface. It is shown how flow factors can be derived and added to the macroscopic smooth flow problem, that is modeled by the 2D Reynolds equation. The flow factors are a function of the operating conditions such as the ratio between the film height and the pocket dimensions, the surface velocity, and the pressure gradient over a surface texture unit cell. To account for an additional pressure buildup in the texture cell due to inertia effects, a pressure gain is introduced at macroscopic level. The method also allows for microcavitation. Microcavitation occurs when the pressure variation due to surface texture is larger than the average pressure level at that particular bearing location. In contrast with the work of Patir and Cheng (1978, J. Lubrication Technol., 78, pp. 1–10), where the microlevel is solved by the Reynolds equation, and the Navier–Stokes equations are used at the microlevel. Depending on the texture geometry and film height, the Reynolds equation may become invalid. A second pocket effect occurs when the pocket is located in the moving surface. In mixed lubrication, fluid can become trapped inside a pocket and squeezed out when the pocket is running into an area with higher contact load. To include this effect, an additional source term that represents the average fluid inflow due to the deformation of the surface around the pocket is added to the Reynolds equation at macrolevel. The additional inflow is computed at microlevel by numerical solution of the surface deformation for a single pocket that is subject to a contact load. The pocket volume is a function of the contact pressure. It must be emphasized that before ready-to-use results can be presented, a large number of simulations to determine the flow factors and pressure gain as a function of the texture parameters and operating conditions have yet to be done. Before conclusions can be drawn, regarding the dominanant mechanism(s), the flow factors and pressure gain have to be added to the macrobearing model. In this paper, only a limited number of preliminary illustrative simulation results, calculating the flow factors for a single 2D texture geometry, are shown to give insight into the method.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

GUFC (a) and TUFC (b)

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Figure 2

Pressure distribution at the upper surface of the TUFC for pure shear driven flow (U1=1m∕s) for different h0∕dp ratio (from top to bottom: 10, 1, 0.1, 0.01). Note the different y axis scaling.

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Figure 3

Pressure distribution at the upper surface of the TUFC for shear driven flow (U1=1m∕s) and h0∕dp=1∕100 solved from the Reynolds equation with different cavitation boundary conditions

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Figure 4

Computational domain for the 2D GUFC (a) and for the 3D TUFC (b) with suitable boundary conditions for calculation of ϕpx. Boundaries a and b are periodical in terms of the velocity field.

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Figure 5

2D TUFC geometry. Boundary a and b are periodic in terms of the velocity field. The nominal film height h0<<Lx.

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Figure 6

Pressure distribution at the upper surface for pure pressure induced flow. The solid curve represents the solution when the Navier–Stokes equations are used; the dotted curve gives the Reynolds solution. The linear curve is the solution for the macroscopic (smooth) representation of the unit cell, the GUFC.

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Figure 7

Streamlines for pure pressure induced flow at ∂p∕∂x=−1MPa∕m (a) and ∂p∕∂x=−8.5MPa∕m (b) correspond to the solution in Fig. 6

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Figure 8

Pressure distribution at the upper surface of the TUFC for pure pressure induced flow (U1=0m∕s) at different Reynolds numbers

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Figure 9

Pressure flow factor ϕpx as a function of the pressure gradient over the TUFC

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Figure 10

Computational domain for the 2D GUFC (a) and for the 3D TUFC (b) with suitable boundary conditions for calculation of ϕs. The boundaries a and b are periodical, both for the velocity variables and the pressure.

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Figure 11

Pressure distribution at the upper surface of the TUFC for pure shear boundary conditions at different Reynolds numbers

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Figure 12

Streamlines at pure shear driven flow: (top) U1=1m∕s; (bottom) U1=4m∕s. A slightly asymmetric recirculation zone is located inside the pocket for increasing surface velocity.

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Figure 13

Shear flow factor ϕs as a function of the upper surface velocity U1

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Figure 14

Pressure flow factor ϕsp,x as a function of the pressure drop over the TUFC for different surface velocities

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Figure 15

Pressure distribution at the upper surface of the TUFC. Operating conditions: U1=1m∕s, ∂p∕∂x=−7.1MPa∕m

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Figure 16

Streamlines for a flow that is driven both by an upper surface velocity U1 and pressure gradient over the TUFC. Operating conditions: ∂p∕∂x=−7.1MPa∕m, U1=1m∕s (a), U1=4m∕s (b).

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Figure 17

Pressure gain as result of convective inertia as a function of the pressure gradient for different surface velocities

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Figure 18

Surface area of the texture unit cell

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Figure 19

TUDC: 3D domain for fem solution of structure deformation equations

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Figure 20

Numerical scheme

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Figure 21

Numerical solution for the pocket volume change as a function of the average contact pressure

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