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Technical Briefs

Comparison Between a Meshless Method and the Finite Difference Method for Solving the Reynolds Equation in Finite Bearings

[+] Author and Article Information
Rodrigo Nicoletti

University of São Paulo,
School of Engineering of São Carlos,
Department of Mechanical Engineering,
Trabalhador São-Carlense 400,
São Carlos, 13566-590 Brazil
e-mail: rnicolet@sc.usp.br

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 7, 2013; final manuscript received May 20, 2013; published online June 24, 2013. Assoc. Editor: George K. Nikas.

J. Tribol 135(4), 044501 (Jun 24, 2013) (9 pages) Paper No: TRIB-13-1038; doi: 10.1115/1.4024752 History: Received February 07, 2013; Revised May 20, 2013

Meshless methods are an alternative procedure for solving partial differential equations in opposition to the numerical methods that require structured meshes. In this work, the meshless method with radial basis functions (MMRB) is compared to the finite difference method (FDM) for solving the Reynolds equation applied to lubricated finite bearing applications. The performance of these two methods is compared based on the precision of estimating the normal force applied to the sliding surface of the bearing. Different mesh families are tested for different bearing configurations. Results show that the MMRB is better than the FDM for nonrectangular geometries with coarser meshes. For rectangular domains without discontinuities, the FDM is still the best choice for solving the problem.

Copyright © 2013 by ASME
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References

Figures

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Fig. 1

Coordinate system attached to the sliding surface of the bearing

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Fig. 2

Mesh of points in the discretized domain

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Fig. 3

Points in the discretized domain (meshless method)

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Fig. 5

Squared and triangular meshes in the sliding surface (a) square grid, (b) uniform triangular grid

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Fig. 6

Pressure distribution on the rectangular pad (a) distribution, (b) contour plot

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Fig. 7

Percentage error to the analytical solution in the calculation of the normal force on the pad for the slider bearing: square and triangular uniform grids (a) B/L = 0.6, (b) B/L = 2.5

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Fig. 8

Modified meshes in the sliding surface (a) rectangular grid, (b) irregular triangular grid

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Fig. 9

Percentage error to the analytical solution in the calculation of the normal force on the pad for the slider bearing: rectangular and triangular nonuniform grids (a) B/L = 0.6, (b) B/L = 2.5

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Fig. 10

Percentage error to the analytical solution in the calculation of the normal force on the pad for the slider bearing: sensitivity of the MMRB to parameter c with irregular triangular grid (a) B/L = 0.6, (b) B/L = 2.5

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Fig. 11

Coordinate system and dimensions of the rectangular pad with inlet borehole in the center (mm)

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Fig. 12

Pressure distribution on the rectangular pad with oil injection (a) distribution, (b) contour plot

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Fig. 13

Percentage error in the calculation of the normal force on the pad for the rectangular pad with oil injection: squared and triangular uniform grids

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Fig. 14

Modified mesh with more nodes in the borehole area of the pad (a) rectangular grid, (b) mapped triangular grid

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Fig. 15

Percentage error in the calculation of the normal force on the pad for the rectangular pad with oil injection: nonuniform grids

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Fig. 16

Coordinate system and dimensions of the trapezoidal pad (mm)

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Fig. 17

Rectangular and irregular triangular meshes in the pad sliding surface (a) rectangular grid, (b) irregular triangular grid

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Fig. 18

Percentage error in the calculation of the normal force on the trapezoidal pad: rectangular and irregular triangular meshes

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Fig. 19

Computational time to solve the system of equations in the FDM and MMRB

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