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

Hai Huang*, Guang Meng, and Jieyu Chen State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 DongChuan Road, Shanghai, 200240, People Republic of China); E-mails: huanghai2003@gmail.com; gmeng@sjtu.edu.cn * Author to whom correspondence should be addressed: huanghai2003@gmail.com Received: 27 June 2007 / Accepted: 2 August 2007 / Published: 3 August 2007 Abstract: Incorporating the velocity slip effect of the gas flow at the solid boundary, the performance and dynamic response of a micro gas-bearing-rotor system are investigated in this paper. For the characteristic length scale of the micro gas bearing, the gas flow in the bearing resides in the slip regime rather than in the continuum regime. The modified Reynolds equations of different slip models are presented. Gas pressure distribution and load carrying capacity are obtained by solving the Reynolds equations with finite different method (FDM). Comparing results from different models, it is found that the second order slip model agrees reasonably well with the benchmarked solutions obtained from the linearized Boltzmann equation. Therefore, dynamic coefficients derived from the second order slip model are employed to evaluate the linear dynamic stability and vibration characteristics of the system. Compared with the continuum flow model, the slip effect reduces dynamic coefficients of the micro gas bearing, and the threshold speed for stable operation is consequently raised. Also, dynamic analysis shows that the system responses change with variation of the operating parameters including the eccentricity ratio, the rotational speed, and the unbalance ratio. Keywords: MEMS, Micro rotor, Micro gas bearing, Velocity slip, Mechanical performance, Stability, Dynamical response.