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Research Papers: Elastohydrodynamic Lubrication

Elastohydrodynamic Lubrication Analysis of Finite Line Contact Problem With Consideration of Two Free End Surfaces

[+] Author and Article Information
Haibo Zhang, Shengguang Zhang, Ziqiang Zhao

School of Mechanical Engineering,
Beijing Institute of Technology,
Beijing 100081, China

Wenzhong Wang

School of Mechanical Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: wangwzhong@bit.edu.cn

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 11, 2016; final manuscript received July 4, 2016; published online November 9, 2016. Assoc. Editor: Xiaolan Ai.

J. Tribol 139(3), 031501 (Nov 09, 2016) (11 pages) Paper No: TRIB-16-1013; doi: 10.1115/1.4034248 History: Received January 11, 2016; Revised July 04, 2016

Elastohydrodynamic lubrication (EHL) analysis in finite line contacts is usually modeled by a finite-length roller contacting with a half-space, which ignores effect of the two free boundaries existing in many applications such as gears or roller bearings. This paper presents a semi-analytical method, involving the overlapping method and matrix formation, for EHL analysis in the finite line contact problem to consider the effect of two free end surfaces. Three half-spaces with mirrored loads to be solved are overlapped to cancel out the stresses at expected surfaces, and three matrices can be obtained and reused for the same finite-length space. The isothermal Reynolds equation is solved to obtain the pressure distribution and the fast Fourier transform (FFT) is used to speed up the elastic deformation and stress related calculation. Different line contact situations, including straight rollers, tapered rollers, and Lundberg profile rollers, are discussed to explore the effect of free end surfaces.

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References

Wymer, D. G. , and Cameron, A. , 1974, “ Elastohydrodynamic Lubrication of a Line Contact,” Proc. Inst. Mech. Eng., 188(1974), pp. 221–238. [CrossRef]
Bahadoran, H. , and Gohar, R. , 1974, “ End Closure in Elastohydrodynamic Line Contact,” J. Mech. Eng. Sci., 16(4), pp. 276–278. [CrossRef]
Mostofi, A. , and Gohar, R. , 1983, “ Elastohydrodynamic Lubrication of Finite Line Contacts,” ASME J. Lubr. Technol., 105(4), pp. 598–604. [CrossRef]
Park, T.-J. , and Kim, K.-W. , 1998, “ Elastohydrodynamic Lubrication of Finite Line Contacts,” Wear, 223, pp. 102–109. [CrossRef]
Park, T.-J. , 2013, “ Elastohydrodynamic Lubrication Analysis of a Lundberg Profile-Type Cylindrical Roller,” J. Korean Soc. Tribol. Lubr. Eng., 29(6), pp. 353–359.
Liu, X. , and Yang, P. , 2002, “ Analysis of the Thermal Elastohydrodynamic Lubrication of a Finite Line Contact,” Tribol. Int., 35(3), pp. 137–144.
Zhu, D. , Wang, J. , Ren, N. , and Wang, Q. J. , 2012, “ Mixed Elastohydrodynamic Lubrication in Finite Roller Contacts Involving Realistic Geometry and Surface Roughness,” ASME J. Tribol., 134(1), p. 011504. [CrossRef]
He, T. , Wang, J. , Wang, Z. , and Zhu, D. , 2015, “ Simulation of Plasto-Elastohydrodynamic Lubrication in Line Contacts of Infinite and Finite Length,” ASME J. Tribol., 137(4), p. 041505. [CrossRef]
Hetenyi, M. , 1970, “ A General Solution for the Elastic Quarter Space,” ASME J. Appl. Mech., 37(1), pp. 70–76. [CrossRef]
Keer, L. M. , Lee, J. C. , and Mura, T. , 1983, “ Hetenyis Elastic Quarter Space Problem Revisited,” Int. J. Solids Struct., 19(6), pp. 497–508. [CrossRef]
Keer, L. M. , Lee, J. C. , and Mura, T. , 1984, “ A Contact Problem for the Elastic Quarter Space,” Int. J. Solids Struct., 20(5), pp. 513–524. [CrossRef]
Hanson, M. T. , and Keer, L. M. , 1990, “ A Simplified Analysis for an Elastic Quarter-Space,” Q. J. Mech. Appl. Math., 43(4), pp. 561–587. [CrossRef]
Yu, C. C. , Keer, L. M. , and Moran, B. , 1996, “ Elastic-Plastic Rolling-Sliding Contact on a Quarter Space,” Wear, 191(1–2), pp. 219–225. [CrossRef]
Guilbault, R. , 2011, “ A Fast Correction for Elastic Quarter-Space Applied to 3D Modeling of Edge Contact Problems,” ASME J. Tribol., 133(3), p. 031402. [CrossRef]
Najjari, M. , and Guilbault, R. , 2014, “ Modeling the Edge Contact Effect of Finite Contact Lines on Subsurface Stresses,” Tribol. Int., 77, pp. 78–85. [CrossRef]
Najjari, M. , and Guilbault, R. , 2014, “ Edge Contact Effect on Thermal Elastohydrodynamic Lubrication of Finite Contact Lines,” Tribol. Int., 71, pp. 50–61. [CrossRef]
Zhang, Z. M. , Wang, W. , and Wong, P. L. , 2013, “ An Explicit Solution for the Elastic Quarter-Space Problem in Matrix Formulation,” Int. J. Solids Struct., 50(6), pp. 976–980. [CrossRef]
Zhang, H. , Wang, W. , Zhang, S. , and Zhao, Z. , 2015, “ Modeling of Finite-Length Line Contact Problem With Consideration of Two Free-End Surfaces,” ASME J. Tribol., 138(2), p. 021402. [CrossRef]
Liu, S. B. , Wang, Q. , and Liu, G. , 2000, “ A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses,” Wear, 243(1–2), pp. 101–111. [CrossRef]
Love, A. E. H. , 1929, “ The Stress Produced in a Semi-Infinite Solid by Pressure on Part of the Boundary,” Philos. Trans. R. Soc. London, 228(1929), pp. 377–420. [CrossRef]
Hu, Y.-Z. , and Zhu, D. , 2000, “ A Full Numerical Solution to the Mixed Lubrication in Point Contacts,” ASME J. Tribol., 122(1), pp. 1–9. [CrossRef]
Wang, W. Z. , Wang, H. , Liu, Y. C. , Hu, Y. Z. , and Zhu, D. , 2003, “ A Comparative Study of the Methods for Calculation of Surface Elastic Deformation,” Proc. Inst. Mech. Eng. Part J, 217(2), pp. 145–154. [CrossRef]
Liu, Y. C. , Wang, Q. J. , Wang, W. Z. , Hu, Y. Z. , and Zhu, D. , 2006, “ Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts,” ASME J. Tribol., 128(3), pp. 641–653. [CrossRef]
Zhu, D. , 2007, “ On Some Aspects of Numerical Solutions of Thin-Film and Mixed Elastohydrodynamic Lubrication,” Proc. Inst. Mech. Eng. Part J., 221(5), pp. 561–579. [CrossRef]
Lundberg, v. G. , 1939, “ Elastische Beruhrung Zweierhalbraume,” Forchung Auf Dem Gebiete Des IngenieurWesen, 10(5), pp. 201–211. [CrossRef]
Johnson, K. L. , 1987, Contact Mechanics, Cambridge University Press, London.
Johns, P. M. , and Gohar, R. , 1981, “ Roller Bearings Under Radial and Eccentric Loads,” Tribol. Int., 14(3), pp. 131–136. [CrossRef]
Fujiwara, H. , and Kawase, T. , 2006, “ Logarithmic Profile of Rollers in Roller Bearing and Optimization of the Profile,” Trans. Jpn. Soc. Mech. Eng. C, 72(721), pp. 3022–3029. [CrossRef]
Sun, H. Y. , Chen, X. Y. , Liu, C. H. , and Yang, P. R. , 2008, “ Study on Thermal EHL Performance of Lundberg Profile Rollers and the Modification of Its Crowning Value,” Tribology, 28(1), pp. 68–72. http://en.cnki.com.cn/Article_en/CJFDTOTAL-MCXX200801012.htm
Fujiwara, H. , Kobayashi, T. , Kawase, T. , and Yamauchi, K. , 2010, “ Optimized Logarithmic Roller Crowning Design of Cylindrical Roller Bearings and Its Experimental Demonstration,” Tribol. Trans., 53(6), pp. 909–916. [CrossRef]

Figures

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Fig. 1

Schematic plot for finite-length space problem

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Fig. 2

The loading condition of the three half-spaces for overlapping: (a) the three parts of horizontal half-space, (b) the vertical half-space, and (c) the reversed vertical half-space

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Fig. 3

The variation of shear stresses-normal stresses ratiowith γ for coincident end condition: R41 and R51 represent τxy-max/σyy-max and τyz-max/σyy-max, respectively

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Fig. 4

Schematic diagram of contact model in the present paper (x = 0 plane)

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Fig. 5

Flowchart for solving finite-length space EHL problem

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Fig. 6

Pressure and film thickness with different mesh densities: (a) profiles along the y-direction at x = 0 and (b) profiles along the x-direction at y = 0.5Lf

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Fig. 7

Comparison of pressure and film thickness between finite-length space and half-space when e = 1.2ah: (a) profiles along the y-direction at x = 0 and (b) profiles along the x-direction at y = 0.5 Lf

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Fig. 8

Comparison of pressure (in z = 0 plane) and von Mises stress (in x = 0 plane) between finite-length space and half-space when e = 1.2ah

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Fig. 9

Comparison of overall film thickness of finite-length space and half-space when e = 1.2ah (half domain is plotted)

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Fig. 10

Comparison of pressure and film thickness between finite-length space and half-space when e = 2ah: (a) profiles along the y-direction at x = 0 and (b) profiles along the x-direction at y = 0.5Lf

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Fig. 11

Comparison of pressure (in z = 0 plane) and von Mises stress (in x = 0 plane) between finite-length space and half-space when e = 2ah

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Fig. 12

Comparison of pressure and film thickness between finite-length space and half-space when e = 2ah, W = 8000 N: (a) profiles along the y-direction at x = 0 and (b) profiles along the x-direction at y = 0.5Lf

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Fig. 13

Comparison of pressure and film thickness between finite-length space and half-space when e = 2ah, U = 4.3 m/s: (a) profiles along the y-direction at x = 0 and (b) profiles along the x-direction at y = 0.5Lf

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Fig. 14

Comparison of pressure and film thickness between finite-length space and half-space for tapered rollers: (a) profiles along the y-direction at x = 0 and (b) profiles along the x-direction at y = 0.5Lf

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Fig. 15

Comparison of pressure (in z = 0 plane) and von Mises stress (in x = 0 plane) between finite-length space and half-space when β = 20 deg

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Fig. 16

Comparison of pressure (in z = 0 plane) and von Mises stress (in x = 0 plane) between finite-length space and half-space when β = 30 deg

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Fig. 17

Comparison of pressure and film thickness between finite-length space and half-space for Lundberg profile rollers when δ = 1.0: (a) profiles along the y-direction at x = 0 and (b) profiles along the x-direction at y = 0.5Lf

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Fig. 18

Comparison of pressure (in z = 0 plane) and von Mises stress (in x = 0 plane) between finite-length space and half-space when δ = 1.0

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Fig. 19

The pressure profiles (along the y-axis) and von Mises stress contours (in x = 0 plane) in half-space with different δ

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Fig. 20

The pressure profiles (along the y-axis) and von Mises stress contours (in x = 0 plane) in finite-length space with different δ

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