Numerical Solution of Elastohydrodynamic Lubrication for Sliding/Rolling Bearing for Non-newtonian Lubricant
American Journal of Applied Mathematics
Volume 8, Issue 5, October 2020, Pages: 257-264
Received: Aug. 12, 2020;
Accepted: Sep. 3, 2020;
Published: Sep. 11, 2020
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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
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.
Samuel Macharia Karimi,
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.
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