American Journal of Mathematical and Computer Modelling

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Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts

Received: 28 August 2020    Accepted: 10 September 2020    Published: 19 September 2020
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Abstract

Elastohydrodynamic lubrication is a type of lubrication which most machine elements such as bearings operate. Density changes, thermal and surface roughness effects are also key factors in bearings, working under heavy loads and high speeds. Previous research has focused on smooth surfaces where density and thermal effects have been neglected. The present study intends to model the effect of surface roughness and density on thermal elastohydrodynamic lubrication for sliding-rolling bearing using non-Newtonian lubricant. The surface roughness is incorporated into the film thickness equation while the non-Newtonian nature of the lubricant is incorporated into the Reynolds and energy equation by using the Eyring model. The changes in compressibility of the lubricant is given by the lubricant’s density equation. The energy equation is solved simultaneously with the Reynolds-Eyring equation, film thickness, density and viscosity of lubricant equations. The equations are then discretized using the finite difference numerical method and are solved simultaneously in Matlab together with their boundary conditions. It is noted that an increase in surface roughness results to a reduction in the film thickness and an increase in both temperature and pressure. Increase in temperature lowers the density of the lubricant while increase in pressure leads to an increase in density. It is also noted that an increase in the density of the lubricant leads to an increase in the film thickness. The temperature profile shows that as the load in the bearing is increased, the temperature of the lubricant also increases.

DOI 10.11648/j.ajmcm.20200503.15
Published in American Journal of Mathematical and Computer Modelling (Volume 5, Issue 3, September 2020)
Page(s) 89-96
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Density, Elastohydrodynamic, Surface Roughness, Thermal

References
[1] Dowson, D., Higginson, G. R. and Whitaker, A. V. (1962). Elasto-Hydrodynamic Lubrication: A Survey of Isothermal Solutions. J. Mech. Eng. Sci., 4, 121–162.
[2] Gohar, R. and Cameron, A. (1963). Optical Measurement of Oil Film Thickness under Elasto-Hydrodynamic Lubrication. Nature, 200, 458–459.
[3] Lord, J. and Larsson, R. (2001). Effects of slide-roll ratio and lubricant properties on elastohydrodynamic lubrication film thickness and traction. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol., 215, 301–308.
[4] Bair, S. (2005). Shear thinning correction for rolling/sliding elastohydrodynamic film thickness. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol., 219, 69–74.
[5] Kumar, P. and Khonsari, M. M. (2008). EHL circular contact film thickness correction factor for shear-thinning fluids. J. Tribol., 130, 041506–041513.
[6] K. N. Mistry, and M. Priest, “Prediction of the Lubrication Regimes and Friction of Piston Ring Assembly of an I. C Engine Considering the Effect of Surface Roughness,” Proceeding of 33rd Leeds–Lyon Symposium on Tribology, 12th-15th September 2006.
[7] Venner, C. H. and Napel, W. E. T. (1992). Surface roughness effects in an EHL line contact. ASME Journal of Tribology, 114, 616-622.
[8] Kumar, P. and Kumar, N. (2014). Surface Roughness Effects in Pure Sliding EHL Line Contacts with Carreau-Type Shear-Thinning Lubricants. Mechanical and Mechatronics Engineering, 8 (6): 311-319.
[9] Bujurke, N. M., Naduvinamani, N. B. and Basti D. P. (2007). Effect of surface roughness on the squeeze film lubrication between curved annular plates. Industrial Lubrication and Tribology, 59 (4): 178-185.
[10] Nadivinamani, N. B., Thasneem, S. F. and Jamal, S. (2010). Effect of roughness on hydrodynamic squeeze films between porous rectangular plates, Tribology International, 43: 2145-2151.
[11] Kondo, S., Sayles, R. S. and Lowe, M. J. S. (2006). A combined optical-ultrasonic method of establishing the compressibility of high-pressure oil and grease films entrapped in a ball on flat contact. Journal of Tribology, 128 (1): 155-167.
[12] Stahl, J. and Jacobson, O. (2003). Compressibility of lubricants at high pressure. Tribology Transactions, 46 (4): 592-599.
[13] Prasad, D. and Sinha, P. (1988). Non-uniform temperature in non-Newtonian compressible fluid film lubrication of rollers. ASME Journal of Tribology, 110 (4): 653-658.
[14] Moraru, L. and Keith, T. G. (2007). Lobatto point quadrature for thermal lubrication problems involving compressible lubricants: EHL applications. Journal of Tribology, 129 (1): 194-198.
[15] Chu, L., Hsu, H., Lin, J. and Chang, Y. (2009). Inverse approach for calculating temperature in EHL of line contacts. Tribology International, 42 (8): 1154-1162.
[16] Mishra, P. C (2014). Analysis of a Rough Elliptic Bore Journal Bearing using Expectancy Model of Roughness Characterization. Tribology in Industry, 36 (2), 211-219.
[17] Liu, Y., Wang, J., Krupka, I., Hartl, M. and Bair, S. (2008). The shear thinning elastohydrodynamic film thickness of a two-component mixture. Journal of Tribology, 130 (2): 1-7.
[18] Kumar, P., Bair, S., and Khonsari, M. (2008). Full EHL simulations using the actual Ree-Eyring model for shear-thinning lubricants. Journal of Tribology, 131 (1): 1-6.
[19] Shettar, B. M., Hiremath, P. S. and Bujurke, N. M. (2016), Jacobian-free Newton Multigrid method for Elastohydrodynamic line contact with grease as lubricant. International Journal of Computational Engineering Research 6 (8): 2250-3005.
[20] Srikanth, D. V., Kaushal, K. C. and Chenna, K. R. (2012). Determination of a large tilting pad thrust bearing angular stiffness. Tribology International 47: 69–76.
[21] Vishwanath, B. A. and Ashwini, K. (2013). Surface roughness effect on thermohydrodynamic analysis of journal bearings lubricated with couple stress fluids. Nonlinear Engineering, Volume 8, Issue 1: 397–406.
[22] Almqvist, T. and Larsson, R. (2002). The Navier-Stokes approach for thermal EHL line contact solutions. Tribology International, 35: 163-170.
Author Information
  • Institute of Basic Sciences, Technology and Innovation, Pan African University, Nairobi, Kenya

  • Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Department of Mathematics, Statistics and Actuarial Science, Machakos University, Machakos, Kenya

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  • APA Style

    Samuel Macharia Karimi, Mathew Ngugi Kinyanjui, Mark Kimathi. (2020). Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts. American Journal of Mathematical and Computer Modelling, 5(3), 89-96. https://doi.org/10.11648/j.ajmcm.20200503.15

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    ACS Style

    Samuel Macharia Karimi; Mathew Ngugi Kinyanjui; Mark Kimathi. Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts. Am. J. Math. Comput. Model. 2020, 5(3), 89-96. doi: 10.11648/j.ajmcm.20200503.15

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    AMA Style

    Samuel Macharia Karimi, Mathew Ngugi Kinyanjui, Mark Kimathi. Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts. Am J Math Comput Model. 2020;5(3):89-96. doi: 10.11648/j.ajmcm.20200503.15

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  • @article{10.11648/j.ajmcm.20200503.15,
      author = {Samuel Macharia Karimi and Mathew Ngugi Kinyanjui and Mark Kimathi},
      title = {Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts},
      journal = {American Journal of Mathematical and Computer Modelling},
      volume = {5},
      number = {3},
      pages = {89-96},
      doi = {10.11648/j.ajmcm.20200503.15},
      url = {https://doi.org/10.11648/j.ajmcm.20200503.15},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmcm.20200503.15},
      abstract = {Elastohydrodynamic lubrication is a type of lubrication which most machine elements such as bearings operate. Density changes, thermal and surface roughness effects are also key factors in bearings, working under heavy loads and high speeds. Previous research has focused on smooth surfaces where density and thermal effects have been neglected. The present study intends to model the effect of surface roughness and density on thermal elastohydrodynamic lubrication for sliding-rolling bearing using non-Newtonian lubricant. The surface roughness is incorporated into the film thickness equation while the non-Newtonian nature of the lubricant is incorporated into the Reynolds and energy equation by using the Eyring model. The changes in compressibility of the lubricant is given by the lubricant’s density equation. The energy equation is solved simultaneously with the Reynolds-Eyring equation, film thickness, density and viscosity of lubricant equations. The equations are then discretized using the finite difference numerical method and are solved simultaneously in Matlab together with their boundary conditions. It is noted that an increase in surface roughness results to a reduction in the film thickness and an increase in both temperature and pressure. Increase in temperature lowers the density of the lubricant while increase in pressure leads to an increase in density. It is also noted that an increase in the density of the lubricant leads to an increase in the film thickness. The temperature profile shows that as the load in the bearing is increased, the temperature of the lubricant also increases.},
     year = {2020}
    }
    

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  • TY  - JOUR
    T1  - Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts
    AU  - Samuel Macharia Karimi
    AU  - Mathew Ngugi Kinyanjui
    AU  - Mark Kimathi
    Y1  - 2020/09/19
    PY  - 2020
    N1  - https://doi.org/10.11648/j.ajmcm.20200503.15
    DO  - 10.11648/j.ajmcm.20200503.15
    T2  - American Journal of Mathematical and Computer Modelling
    JF  - American Journal of Mathematical and Computer Modelling
    JO  - American Journal of Mathematical and Computer Modelling
    SP  - 89
    EP  - 96
    PB  - Science Publishing Group
    SN  - 2578-8280
    UR  - https://doi.org/10.11648/j.ajmcm.20200503.15
    AB  - Elastohydrodynamic lubrication is a type of lubrication which most machine elements such as bearings operate. Density changes, thermal and surface roughness effects are also key factors in bearings, working under heavy loads and high speeds. Previous research has focused on smooth surfaces where density and thermal effects have been neglected. The present study intends to model the effect of surface roughness and density on thermal elastohydrodynamic lubrication for sliding-rolling bearing using non-Newtonian lubricant. The surface roughness is incorporated into the film thickness equation while the non-Newtonian nature of the lubricant is incorporated into the Reynolds and energy equation by using the Eyring model. The changes in compressibility of the lubricant is given by the lubricant’s density equation. The energy equation is solved simultaneously with the Reynolds-Eyring equation, film thickness, density and viscosity of lubricant equations. The equations are then discretized using the finite difference numerical method and are solved simultaneously in Matlab together with their boundary conditions. It is noted that an increase in surface roughness results to a reduction in the film thickness and an increase in both temperature and pressure. Increase in temperature lowers the density of the lubricant while increase in pressure leads to an increase in density. It is also noted that an increase in the density of the lubricant leads to an increase in the film thickness. The temperature profile shows that as the load in the bearing is increased, the temperature of the lubricant also increases.
    VL  - 5
    IS  - 3
    ER  - 

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