Transient Response Solution Applying ADI Scheme to Boltzmann Flow-Modified Reynolds Equation Averaged With Respect to Surface Roughness

Abstract

A numerical calculation methodology applying the alternating direction implicit (ADI) scheme is derived for the solution to the averaged Reynolds equation in volving flow factors resulting from Boltzmann molecular free flow. This methodology features the transformation of the dependent variable in the Reynolds equation from the pressure to the product of the averaged pressure times the averaged spacing, in combination with the determination of the flow factor using averaged spacing. This technique can be used to obtain the dynamic characteristics of compressible lubricating films incurring surface roughness effects under rarefaction conditions. In applying this method to a head slider in practical use, transient responses resulting from the slider flying over a bump and incurring surface roughness effects are compared for three roughness pattern cases. Longitudinal roughness effects are found to appear in the transient response with regard to a simultaneous decrease in the natural frequency and in the damping speed. Conversely, moving transverse roughness affects the response inversely, and stationary transverse roughness influences it only slightly.