Volume 8, Issue 5, October 2020, Page: 257-264
Numerical Solution of Elastohydrodynamic Lubrication for Sliding/Rolling Bearing for Non-newtonian Lubricant
Samuel Macharia Karimi, Pan African University, Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya
Mark Kimathi, Department of Mathematics, Statistics and Actuarial Science, Machakos University, Machakos, Kenya
Mathew Ngugi Kinyanjui, Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Received: Aug. 12, 2020;       Accepted: Sep. 3, 2020;       Published: Sep. 11, 2020
DOI: 10.11648/j.ajam.20200805.13      View  12      Downloads  28
There is always a demand in the industry sector to increase the efficiency of machine components to reduce wear and tear. This paper presents the numerical solution to the study of Elastohydrodynamic lubrication point contact for sliding/rolling bearing where the viscosity of the lubricant is non-Newtonian. The assumption that a lubricant is Newtonian reduces validation of the model hence the Reynolds-Eyring model in this research will incorporate the non-Newtonian nature of the lubricant of the bearing. The mathematical model comprises of Reynold-Eyring equation, film thickness, load balance, lubricant viscosity and lubricant density equations together with their boundary conditions. The Reynolds-Eyring equation governing the flow is non-linear hence the finite difference method numerical technique is used to discretize it together with the other two dimensional equations. These equations are solved simultaneously and Matlab software is used simulate the results. The film thickness and pressure profiles with various loads and speeds are presented. The findings note that an increase in load lowers the pressure and film thickness while an increase in the speed results to a direct increase in pressure and film thickness. A pressure spike is also noted at the exit of the bearing.
Elastohydrodynamic, Thermal, Eyring, Non-newtonian
To cite this article
Samuel Macharia Karimi, Mark Kimathi, Mathew Ngugi Kinyanjui, Numerical Solution of Elastohydrodynamic Lubrication for Sliding/Rolling Bearing for Non-newtonian Lubricant, American Journal of Applied Mathematics. Vol. 8, No. 5, 2020, pp. 257-264. doi: 10.11648/j.ajam.20200805.13
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
C. E. Googyer, "Adaptive numerical methods for elastohydrodynamic lubrication”, PhD thesis, The University of Leeds School of Computing, May 2001.
A. F. Koura, M. E. Elhady and M. S. Metwally, "Numerical solution of Reynolds equation using differential transform method”, International Journal of Advanced Research (IJAR), vol. (6), pp. 729-737, 2018.
D. Dowson, "Modelling of elastohydrodynamic lubrication of real solids by real lubricants", Meccanica, vol. 33, pp. 47-58, 1998.
H. Liu, K. Mao, C. Zhu, X. Xu, and M. Liu, "Parametric studies of spur gear lubrication performance considering dynamic loads”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, May 9, 2012.
Y. -Q. Wang and X.-J. Yi, "Non-Newtonian transient thermoelastohydrodynamic lubrication analysis of an involute spur gear”, Lubrication Science, vol. 22, pp. 465-478, 2010.
H. Liu, "Lubricated Contact Analysis of a Spur Gear Pair with Dynamic Loads”, PHD Thesis, School of Engineering, University of Warwick April 2013.
H. Lu, M. Berzins, C. E. Goodyer, and P. K. Jimack, "High order discontinuous Galerkin method for elastohydrodynamic lubrication line contact problems”, Communications in Numerical Methods in Engineering, vol. 21, pp. 643-650, 2005.
T. Almqvist and R. Larsson, "Thermal transient rough EHL line contact simulations by aid of computational fluid dynamics”, Tribology International, vol. 41, pp. 683-693, 2008.
M. Berzins, C. E. Goodyer and P. Jimack, " High order discontinuous Galerkin method for elastohydrodynamic lubrication line contact”, Communications in Numerical Methods in Engineering, vol. 00, pp. 1-6, 2000.
Y. Liu, Q. J. Wang, S. Bair, and P. Vergne, "A quantitative solution for the full shear thinning EHL point contact problem including traction”, Tribology Letters, vol. 28 (2):171-181, 2007.
D. V. Srikanth, A. N. Kaushal, K. B. Chaturvedi et al., "Determination of a large tilting pad thrust bearing angular stiffness”, Tribology International, 47, 69-76, 2012.
P. R. Kiogora, M. N. Kinyanjui, D. M. Theuri, "A Conservative Scheme Model of an Inclined Pad Thrust Bearing”, International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 3, Issue 1, January 2014.
P. R. Kiogora, M. N. Kinyanjui, D. M. Theuri, "Numerical Solution of the Momentum and Energy Equations of an Inclined Pad Thrust Bearing”, International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 3, Issue 3, May 2014.
V. Petrone, A. Senatore and V. D’Agostino, "Effect of an Improved Yasutomi Pressure-Viscosity Relationship on the Elastohydrodynamic Line Contact Problem”, International Scholarly Research Notices, vol. 2013, pp. 1-7, 2013.
J. S. Issa and W. Habchi, “Influence of Realistic Lubricant Density-Pressure Dependence on the Stiffness of Elastohydrodynamic Lubricated Contacts”, Journal of Tribology, vol. 142 (3), pp. 1-20, 2019.
S. Jadhav, G. D. Thakre and S. C. Sharma, “Numerical modeling of elastohydrodynamic lubrication of line contact lubricated with micropolar fluid”, J Braz. Soc. Mech. Sci. Eng., vol. 40, 326 (2018).
A. Al-Hamood, Friction and thermal behaviour in elastohydrodynamic lubrication power transmission contacts, PhD thesis, Cardiff University, institute of Mechanics and Advance material, 2015.
K. Chen, L. Zenga, Z. Wu and F. Zheng, “Elastohydrodynamic lubrication in point contact on the surfaces of particle-reinforced composite”, AIP Advances, vol. 8 (4), 2018.
T. Almqvist, Numerical simulation of elastohydrodynamic and hydrodynamic lubrication using Navier-stokes and Reynolds equation, Department of mechanical engineering, Lulea University, Sweden, 2001.
P. Chaomleffel, G. Dalmaz and V. Philippe, “Experimental Results and Analytical Predictions of EHL Film Thickness”, 33rd Leeds Lyon Symposium on Tribology “Tribology at the Interface”, Sep 2006, Leeds, United.
J. Makala, G. Dalmaz, B. Villechaise and J. Chaomleffel, “Experimental investigations of elastohydrodynamic point contacts lubricated with a traction fluid”, International Tribology Conference Tribology: Voyaging into the New Millennium, Nagasaki, 2000.
Browse journals by subject