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Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts
American Journal of Mathematical and Computer Modelling
Volume 5, Issue 3, September 2020, Pages: 89-96
Received: Aug. 28, 2020; Accepted: Sep. 10, 2020; Published: Sep. 19, 2020
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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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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.
Density, Elastohydrodynamic, Surface Roughness, Thermal
To cite this article
Samuel Macharia Karimi, Mathew Ngugi Kinyanjui, Mark Kimathi, Surface Roughness and Density Effects in Thermal Elastohydrodynamic Lubrication Point Contacts, American Journal of Mathematical and Computer Modelling. Vol. 5, No. 3, 2020, pp. 89-96. doi: 10.11648/j.ajmcm.20200503.15
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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