Power Law Fluid Model for Thermal Elastohydrodynamic Lubrication
Samuel Macharia Karimi *
Department of Education, Arts and Social Sciences, Zetech University, 2768-00200, Nairobi, Kenya.
Duncan Kioi Gathungu
Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Juja, 62000-00200, Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
The aim of this paper is to analyse thermal elastohydrodynamic lubrication (TEHL) line contact of rolling a bearing using a non-Newtonian uid that is described by the power law model. The performance characteristics of the rolling bearing are determined for various index for dilatant, Newtonian and pseudo plastic uids. The one-dimensional Reynolds and energy equations are both modied to incorporate the non-Newtonian nature of the lubricant. The coupled system of governing equations are discretized using the finite difference method and solved simultaneously. The results show that the pressure, film thickness and temperature for dilatant uids increased with increase in the ow index as compared to pseudo plastic uids. The in uence of thermal effects on pressure and lm thickness is more significant compared with that under isothermal elastohydrodynamic lubrication especially on the case of dilatant uids. The viscosity of the lubricant increases with increase in pressure and reduces with increment in temperature. The surface roughness in the bearing surface increases the lm thickness of the lubricant. The uid pressure, film thickness and temperature increases with increase in the bearing speed. To truly re ect the characteristics of EHL models, thermal effects should be considered.
Keywords: Elastohydrodynamic, power law, film thickness, thermal