Gaseous slip flow in micro-bearings with random rough surface

Abstract

The strongly coupling effects of rarefaction, compressibility and roughness are taken into account to investigate the flow characteristics of the gas bearing in micro-electro-mechanical systems (MEMS). The bearing surface is described by a random rough surface model with the fractal geometry. A modified Reynold's equation incorporating the velocity slip on the rough wall and the effective viscosity is developed. It can be used for a wide range of Knudsen numbers in the slip flow and transition regimes. Effects of Knudsen number, bearing number, Mach number, geometry parameters and roughness parameters on the flow characteristics, including pressure distribution, load carrying capacity, streamwise location of the load carrying capacity, velocity profile, and Poiseuille number, are studied and discussed analytically and numerically. The results show that surface roughness influences not only pressure distribution and load carrying capacity but also velocity distribution and friction factor (Poiseuille number) of the compressible rarefied gas flow in micro-bearings. It is indicated that the coupling effects of rarefaction, compressibility and random roughness are of great significance in the analysis and design of the gas bearings, and should be comprehensively considered in the slip flow and transition regimes for MEMS and micro-fluidic devices.