0
Research Papers: Elastohydrodynamic Lubrication

An Efficient Numerical Model of Elastohydrodynamic Lubrication for Transversely Isotropic Materials

[+] Author and Article Information
Zhanjiang Wang

Tribology Research Institute,
Department of Mechanical Engineering,
Southwest Jiaotong University,
Chengdu 610031, China
e-mail: wangzhanjiang001@gmail.com

Yinxian Zhang

Tribology Research Institute,
Department of Mechanical Engineering,
Southwest Jiaotong University,
Chengdu 610031, China

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received April 8, 2019; final manuscript received May 22, 2019; published online June 12, 2019. Assoc. Editor: Yonggang Meng.

J. Tribol 141(9), 091501 (Jun 12, 2019) (11 pages) Paper No: TRIB-19-1157; doi: 10.1115/1.4043902 History: Received April 08, 2019; Accepted May 22, 2019

An elastohydrodynamic lubrication model for a rigid ball in contact with a transversely isotropic half-space is constructed. Reynolds equation, film thickness equation, and load balance equation are solved using the finite difference method, where the surface vertical displacement or deformation of transversely isotropic half-space is considered through the film thickness equation. The numerical methods are verified by comparing the displacements and stresses with those from Hertzian analytical solutions. Furthermore, the effects of elastic moduli, entertainment velocities, and lubricants on fluid pressure, film thickness, and von Mises stress are analyzed and discussed under a constant load. Finally, the modified Hamrock–Dowson equations for transversely isotropic materials to calculate central film thickness and minimum film thickness are proposed and validated.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge.
Kurokawa, M., Uchiyama, Y., Iwai, T., and Nagai, S., 2003, “Performance of Plastic Gear Made of Carbon Fiber Reinforced Polyamide 12,” Wear, 254(5–6), pp. 468–473. [CrossRef]
Senthilvelan, S., and Gnanamoorthy, R., 2006, “Damping Characteristics of Unreinforced, Glass and Carbon Fiber Reinforced Nylon 6/6 Spur Gears,” Polym. Test, 25(1), pp. 56–62. [CrossRef]
Kim, S. S., Park, D. C., and Lee, D. G., 2004, “Characteristics of Carbon Fiber Phenolic Composite for Journal Bearing Materials,” Compos. Struct., 66(1–4), pp. 359–366. [CrossRef]
Wang, A., Lin, R., Stark, C., and Dumbleton, J. H., 1999, “Suitability and Limitations of Carbon Fiber Reinforced PEEK Composites as Bearing Surfaces for Total Joint Replacements,” Wear, 225–229(2), pp. 724–727. [CrossRef]
Lovell, M., 1988, “Analysis of Contact Between Transversely Isotropic Coated Surfaces: Development of Stress and Displacement Relationships Using FEM,” Wear, 214(2), pp. 165–174. [CrossRef]
Kuo, C. H., and Keer, L. M., 1992, “Contact Stress Analysis of a Layered Transversely Isotropic Half-Space,” ASME J. Tribol., 114(2), pp. 253–261. [CrossRef]
Lovell, M. R., and Khonsari, M. M., 1999, “On the Frictional Characteristics of Ball Bearings Coated With Solid Lubricants,” ASME J. Tribol., 121(4), pp. 761–767. [CrossRef]
Shi, Z., and Ramalingam, S., 2001, “Thermal and Mechanical Stresses in Transversely Isotropic Coatings,” Surf. Coat. Technol., 138(2–3), pp. 173–184. [CrossRef]
Lovell, M., and Morrow, C., 2006, “Contact Analysis of Anisotropic Coatings With Application to Ball Bearings,” Tribol. Trans., 49(1), pp. 33–38. [CrossRef]
Elliott, H. A., and Mott, N. F., 1948, “Three-Dimensional Stress Distributions in Hexagonal Aeolotropic Crystals,” Math. Proc. Cambridge Philos. Soc., 44(4), pp. 522–533. [CrossRef]
Pan, Y. C., and Chou, T. W., 1976, “Point Force Solution for an Infinite Transversely Isotropic Solid,” ASME J. Appl. Mech., 43(4), pp. 608–612. [CrossRef]
Pan, Y. C., and Chou, T. W., 1979, “Green’s Function Solutions for Semi-Infinite Transversely Isotropic Materials,” Int. J. Eng. Sci., 17(5), pp. 545–551. [CrossRef]
Lin, W., Kuo, C. H., and Keer, L. M., 1991, “Analysis of a Transversely Isotropic Half Space Under Normal and Tangential Loadings,” ASME J. Tribol., 113(2), pp. 335–338. [CrossRef]
Hanson, M. T., 1992, “The Elastic Field for Spherical Hertzian Contact Including Sliding Friction for Transverse Isotropy,” ASME J. Tribol., 114(3), pp. 606–611. [CrossRef]
Hanson, M. T., 1994, “The Elastic Field for an Upright or Tilted Sliding Circular Flat Punch on a Transversely Isotropic Half Space,” Int. J. Solids Struct., 31(4), pp. 567–586. [CrossRef]
Ding, H. J., Hou, P. F., and Guo, F. L., 2000, “The Elastic and Electric Fields for Three-Dimensional Contact for Transversely Isotropic Piezoelectric Materials,” Int. J. Solids Struct., 37(23), pp. 3201–3229. [CrossRef]
Ding, H., Chen, W., and Zhang, L., 2006, Elasticity of Transversely Isotropic Materials, Springer, Dordrecht, The Netherlands.
Chen, C. Y., Tseng, Y. F., Chu, L. M., and Li, W. L., 2013, “Soft EHL for Transversely Isotropic Materials,” Tribol. Int., 67, pp. 240–253. [CrossRef]
Chu, L. M., Chen, C. Y., Tee, C. K., Chen, Q. D., and Li, W. L., 2013, “Elastohydrodynamic Lubrication Analysis for Transversely Isotropic Coating Layer,” ASME J. Tribol., 136(3), p. 031502. [CrossRef]
Turner, J. R., 1980, “Contact on a Transversely Isotropic Half-Space, or Between Two Transversely Isotropic Bodies,” Int. J. Solids Struct., 16(5), pp. 409–419. [CrossRef]
Liu, S., 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]
Ahmadi, N., 1982, “Non-Hertzian Normal and Tangential Loading of Elastic Bodies in Contact,” Ph.D. dissertation, Northwestern University, Evanston, IL.
Sackfield, A., and Hills, D. A., 1991, “The Stress Field Induced by Uniform or Hertzian Shear Tractions Over a Rectangular Uniform Contact Patch,” ASME J. Tribol., 113(1), pp. 220–222. [CrossRef]
Liu, S., and Wang, Q., 2002, “Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm,” ASME J. Tribol., 124(1), pp. 36–45. [CrossRef]
Wang, W. Z., Chen, H., Hu, Y. Z., and Wang, H., 2006, “Effect of Surface Roughness on Mixed Lubrication Characteristic,” Tribol. Int., 39(6), pp. 522–527. [CrossRef]
Wang, Z., Yu, C., and Wang, Q., 2014, “Model for Elastohydrodynamic Lubrication of Multilayered Materials,” ASME J. Tribol., 137(1), p. 011501. [CrossRef]
Wang, Z., Zhu, D., and Wang, Q., 2014, “Elastohydrodynamic Lubrication of Inhomogeneous Materials Using the Equivalent Inclusion Method,” ASME J. Tribol., 136(2), p. 021501. [CrossRef]
Hamrock, B. J., and Dowson, D., 1977, “Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part III—Fully Flooded Results,” ASME J. Lubr. Technol., 99(2), pp. 264–276. [CrossRef]
Bair, S., 2007, High Pressure Rheology for Quantitative Elastohydrodynamics, Elsevier, Amsterdam, The Netherlands.
Dowson, D., and Higginson, G. R., 1966, Elastohydrodynamic Lubrication: The Fundamentals of Roller and Gear Lubrication, Pergamon, New York.
Ai, X., 1993, “Numerical Analyses of Elastohydrodynamically Lubricated Line and Point Contacts With Rough Surfaces by Using Semi-System and Multigrid Methods,” Ph.D. dissertation, Northwestern University, Evanston, IL.
Liu, Y., Wang, Q., Wang, W., Hu, Y., 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]

Figures

Grahic Jump Location
Fig. 1

Model of EHL contact with transversely isotropic materials

Grahic Jump Location
Fig. 2

Comparisons of the results from present solutions and those from analytical solutions: (a) dimensionless surface normal displacements and (b) and (c) dimensionless surface normal stresses along the x-axis and z-axis, respectively

Grahic Jump Location
Fig. 3

Dimensionless fluid pressure and film thickness along the x-axis with lubricant 1 for cases 1–4 at entertainment velocities: (a) U = 1 m/s and (b) U = 10 m/s

Grahic Jump Location
Fig. 4

Contour plots of dimensionless film thickness for cases 1–4 with lubricant 1 at entertainment velocity U = 1 m/s: (a) case 1, (b) case 2, (c) case 3, and (d) case 4

Grahic Jump Location
Fig. 5

Dimensionless fluid pressure and film thickness (a), and surface deformation in the z direction along the x-axis (b), for lubrication 1 at entertainment velocity U = 1 m/s for various E3

Grahic Jump Location
Fig. 6

Dimensionless fluid pressure and film thickness (a), and surface deformation in the z direction along the x-axis (b), for lubrication 1 at entertainment velocity U = 1 m/s for various G13

Grahic Jump Location
Fig. 7

Central film thickness and minimum film thickness of cases 1–4 for lubricant 1 at various entertainment velocities U

Grahic Jump Location
Fig. 8

Dimensionless fluid pressure and film thickness along the x-axis for different lubricants at entertainment velocity U = 1 m/s: (a) case 1, (b) case 2, (c) case 3, and (d) case 4

Grahic Jump Location
Fig. 9

Contour plots of dimensionless von Mises stress in the xz plane with lubricant 1 for the cases 1–4 at different entertainment velocities U = 1 m/s and U = 10 m/s: (a) case 1, (b) case 2, (c) case 3, and (d) case 4

Grahic Jump Location
Fig. 10

Central film thickness and minimum film thickness obtained from numerical solutions and Hamrock–Dowson equations for case 3 at various entertainment velocities with different lubricants: (a) lubricant 1 and (b) lubricant 2

Grahic Jump Location
Fig. 11

Central film thickness and minimum film thickness obtained from numerical solutions and Hamrock–Dowson equations with lubricant 1 at different entertainment velocities U = 1 m/s and U = 10 m/s: (a) E1 = 100 GPa, G13 = 38.46 GPa, various E3 and (b) E1 = 100 GPa, E3 = 100 GPa, various G13

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In