An analysis of the Different Parameters influence on the Microbearing load carrying capacity

Abstract

An analytical solution for the two-dimensional non-isothermal compressible gas flow in a slider micro-bearing is presented in this paper. It is shear-driven subsonic slip gas flow. In view of the fact that a fluid flow in a micro system is rarefied, the model takes into account this influence. The slip gas flow is defined by the continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and the temperature jump Maxwell-Smoluchowski first order boundary conditions. Knudsen number is in the range of 0-10-1, which corresponds to the continuum and slip gas flow. The analytical solutions of the pressure, velocity and temperature are obtained. The results are of the order of Navier-Stokes equations, i.e., O(Kn) and they agree well with those found in the open literature. The solutions enable analysis of the relevant parameters influences on the load carrying capacity of the micro-bearing. Hence, the influences of the flow conditions expressed by Mach, Reynolds and Knudsen numbers, the ratio of the inlet to outlet heights, bearing number, as well as temperature field are investigated. Moreover, obtained analytical solutions comprise second order effects for gas flows in micro-systems such as inertia and dissipation which enabled the assessment of their impact on the load carrying capacity of the micro-bearing, i.e. estimation of the calculations safety when these effects are neglected.