Investigations of Slip Effect on the Performance of Micro Gas Bearings and Stability of Micro Rotor-Bearing Systems

Hai Huang,Guang Meng,Jieyu Chen

doi:10.3390/s7081399

Abstract

Incorporating the velocity slip effect of the gas flow at the solid boundary, theperformance and dynamic response of a micro gas-bearing-rotor system are investigated inthis paper. For the characteristic length scale of the micro gas bearing, the gas flow in thebearing resides in the slip regime rather than in the continuum regime. The modifiedReynolds equations of different slip models are presented. Gas pressure distribution and loadcarrying capacity are obtained by solving the Reynolds equations with finite differentmethod (FDM). Comparing results from different models, it is found that the second orderslip model agrees reasonably well with the benchmarked solutions obtained from thelinearized Boltzmann equation. Therefore, dynamic coefficients derived from the secondorder slip model are employed to evaluate the linear dynamic stability and vibrationcharacteristics of the system. Compared with the continuum flow model, the slip effectreduces dynamic coefficients of the micro gas bearing, and the threshold speed for stableoperation is consequently raised. Also, dynamic analysis shows that the system responseschange with variation of the operating parameters including the eccentricity ratio, therotational speed, and the unbalance ratio.

Highlights

In an attempt to address the ever rising demand for high performance compact power source, a new branch of micro-electro-mechanical system called power MEMS has recently been defined[1, 2]
The high speed rotor dynamic characteristic of the micro rotor-bearing system is a major concern in the mechanical design of micro motors and such kind of power MEMS
By comparison of performances of the micro gas bearing such as flow rate, gas pressure distribution, load carrying capacity and attitude angle derived from different models, the slip effect on the performances of the bearing is discussed and the second order slip model is chosen to evaluate dynamic characteristics of the system

Summary

Introduction

Wang[7] analyzed the bifurcation of a rotor supported by a self-acting gas journal bearing, and the analysis focused on the dynamic behavior of the rotor-bearing system In these researches, the lubricated gas film was mostly treated as continuum flow, and effects of the micro fluid mechanics have not been considered. Y.H Sun[12] presented analytical investigations of slip flow between the flying head and disk in the hard disk drive These researchers mainly focused on the micro fluid mechanics, and few attentions have been paid to the performance of the micro journal bearing. By comparison of performances of the micro gas bearing such as flow rate, gas pressure distribution, load carrying capacity and attitude angle derived from different models, the slip effect on the performances of the bearing is discussed and the second order slip model is chosen to evaluate dynamic characteristics of the system. The stability of the micro rotor system is compromised and the threshold speed for stable operation is pushed upwards

Slip model and Reynolds equation

Steady-state performance

Motion equations and the linear threshold speed

Findings

Conclusions