Combined Effect of Rarefaction and Effective Viscosity on Micro-Elasto-Aerodynamic Lubrication Performance of Gas Microbearings.

Yao Wu,Lihua Yang,Tengfei Xu,Haoliang Xu

doi:10.3390/mi10100657

Abstract

Elastic deformation and gaseous rarefaction effects are of great importance to the static and dynamic characteristics of gas microbearings. Based on the effective viscosity model of Veijola, the governing equations can be solved by the partial derivative method, finite element procedure, and relaxed iterative algorithm. The numerical results showed that the maximum gas pressure is relatively lower compared to a microbearing with a rigid liner at a local pressure peak region, owing to the film thickness of two converging-diverging profiles and the existence of bimodal pressure inside the elastic microbearing liner. However, the effect of bearing flexibility provides a marginal increase in the load capacity on account of the integral area of pressure distribution is larger than the rigid bearing liner. The friction coefficient and direct stiffness coefficients increase as the elastic modulus decreases while the direct damping coefficients become smaller at high eccentricity ratios and bearing numbers. Since the Poiseuille flow rate increases in connection with an increasing Knudsen number, the effective viscosity of the lubricant leads to a decreased load carrying capacity, friction coefficient, and direct stiffness coefficient, which produces an increase in the direct damping coefficients.

Highlights

For applications involving micro-electromechanical systems (MEMS) microfluidic devices with high power efficiency and density, such as micro gas turbines, microgenerators, micromotors, medical devices, and hard disk drives (HDDs), there has been great interest in micro gas journal bearings
Based on the Veijola’s effective viscosity formula [6,7], the compressible lubricant viscosity is influenced by the Knudsen number Kn, which characterizes the degree of gas rarefaction
The modified Reynolds equation incorporating the Poiseuille flow rate for rarefied gas are solved simultaneously with three-dimensional elasticity equations to predict the film pressure distribution and the elastic deformation of the bearing liner; the results are compared with those obtained from the rigid microbearing, which ignores the effective viscosity in ultra-thin gas film lubrication

Summary

Introduction

For applications involving micro-electromechanical systems (MEMS) microfluidic devices with high power efficiency and density, such as micro gas turbines, microgenerators, micromotors, medical devices, and hard disk drives (HDDs), there has been great interest in micro gas journal bearings. The modified Reynolds equation incorporating the Poiseuille flow rate for rarefied gas are solved simultaneously with three-dimensional elasticity equations to predict the film pressure distribution and the elastic deformation of the bearing liner; the results are compared with those obtained from the rigid microbearing, which ignores the effective viscosity in ultra-thin gas film lubrication. Important information, such as the dynamic characteristics in microbearing with an elastic liner and the effective viscosity of the gas lubricant is of practical importance in the bearing design to improve the microbearing-rotor system stability

Governing Equations

Elastic Deformation and Fluid Film Thickness

Results and Discussion