Stokes Roughness Effects on Hydrodynamic Lubrication. Part I—Comparison Between Incompressible and Compressible Lubricating Films

A perturbation method for the Navier-Stokes equations is presented for analyzing Stokes roughness effects on hydrodynamic lubrication in both incompressible and compressible films. The solution is obtained from direct numerical calculation by using an actual rough spacing, without applying the currently accepted assumption that the roughness height should be small. The roughness wavelength and height influences on flow rate, load carrying capacity and frictional force are clarified. Secondary quantities induced by Stokes effects are found to be proportional to wavenumber n squared for sufficiently large n values, so that the amount of the Stokes effect can be determined by the spacing to wavelength squared ratio. A significant difference between incompressible and compressible films is that Stokes roughness increases the flow resistance of and then enhances the load carrying capacity of incompressible films, while it inversely affects compressible films. The compressibility with respect to secondary pressure induced by the Stokes effects can be neglected for any compressibility number, no matter how large, as long as the local compressibility number, defined by the wavelength, is small.