Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts

Samuel Macharia Karimi; Mathew Ngugi Kinyanjui; Mark Kimathi

doi:doi:10.11648/j.ajmcm.20200503.15

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Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts

Samuel Macharia Karimi, Mathew Ngugi Kinyanjui, Mark Kimathi

Published in American Journal of Mathematical and Computer Modelling (Volume 5, Issue 3)

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.

Published in	American Journal of Mathematical and Computer Modelling (Volume 5, Issue 3)
DOI	10.11648/j.ajmcm.20200503.15
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), 2020. Published by Science Publishing Group

Keywords

Density, Elastohydrodynamic, Surface Roughness, Thermal

References

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[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.
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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://article.sciencepublishinggroup.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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Author Information

Samuel Macharia Karimi

Institute of Basic Sciences, Technology and Innovation, Pan African University, Nairobi, Kenya
Mathew Ngugi Kinyanjui

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

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://article.sciencepublishinggroup.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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