Determination of the static performance of finite elasto-hydrodynamic journal bearings lubricated by magnetic fluids with couple stresses

Abstract

This study concerns the theoretical determination of static performance of finite elasto- hydrodynamic journal bearings lubricated by ferro-fluids with couple stresses. The Reynolds equation that takes into account magneto elasto-hydrodynamics is derived by use of continuity and momentum equations. The equation has been integrated locally across the film thickness and an equation for the pressure gradient obtained as a function of film thickness and total mass flow rate of lubricant, now the modified Reynolds equation. The modified Reynolds equation obtained is solved simultaneously with the energy equation numerically by the finite difference technique since they are highly non- linear. The pressure and temperature profiles are obtained. The numerical scheme used is implemented in MATLAB software version 7.14.0.739, so as to obtain the approximate solutions where these solutions are represented in tables and graphs. Based on the micro-continuum theory, and by taking into account the couple stresses due to the microstructure additives, the effects of couple stresses on the performance of a finite elasto-hydrodynamic journal bearings were studied. The results were obtained by varying various flow parameters, notably couple stress parameter, magnetic coefficient and eccentricity ratio. From the results it was found that the magnetic lubrication gives higher pressure distribution. The results have also shown that lubricants with couple stresses compared with Newtonian lubricants increase the pressure especially at high eccentricity ratios. Thus it can be concluded that magnetic fluids lubricants with couple stresses are better than Newtonian fluids. The results provide engineers with useful information to design machine elements and bearing systems with a higher life expectancy and efficiency.