Third-order solution to the Navier-Stokes equation for two-dimensional hydrodynamic lubrication

The third-order solution of the film velocity and the film pressure in the two-dimensional hydrodynamic lubrication are solved from the Navier-Stokes equation by using the perturbation method. The calculation for the specific hydrodynamic inclined fixed pad thrust bearing shows that when the tilting angle θ of the bearing is more than 0.2 rad, the third-order solution gives more accurate results than the (classical) second-order solution, while for θ < 0.2 rad the second-order solution is sufficiently accurate. The calculation results also show that when θ < 0.075 rad, the fluid flow in the bearing can be considered as laminar and the Reynolds equation is correct for calculating the carried load and the friction coefficient of the bearing if the amplitude of the surface roughness is much smaller than the fluid film thickness. However, when θ > 0.1 rad, the fluid in the bearing should be considered as in the vortex flow and the solution to the Navier-Stokes equation is mandatory. The effect of the vortex flow is increased with increasing θ.