Sage Journals: Discover world-class research

Abstract

The unbalance response of micro gas bearing-rotor system is calculated using the fourth-order Runge–Kutta method based on the motion equation of the rotor, in which the nonlinear gas film force is obtained from solving the modified Reynolds equation using the alternating direction implication algorithm. The study shows that the proper eccentric mass of the rotor can improve the stability of micro gas bearing-rotor system. Compared with the result without considering the gas rarefaction effect, the stability threshold speed of micro rotor system considering the gas rarefaction effect is increased. Meanwhile for the same mass eccentricity, the peak value emerges at the lower rotation speed, which shows that the unbalance eccentric mass will influence the motion of micro rotor system more greatly when the gas rarefaction effect is taken into account.

Keywords

Micro gas bearing-rotor system unbalance response Reynolds equation alternating direction implication algorithm rarefaction effect

Get full access to this article

View all access options for this article.

References

Epstein

. Millimeter-scale, micro-electro-mechanical systems gas turbine engines. J Eng Gas Turbines Power 2004; 126: 205–226.

Liu LX. Theory for hydrostatic gas journal bearings for micro-electro-mechanical systems. PhD Thesis, Massachusetts Institute of Technology, USA, 2005.

Meng

Zhang

W-M

Huang

. Micro-rotor dynamics for micro-electro-mechanical systems (MEMS). Chaos Soliton Fract 2009; 40: 538–562.

Orr DJ. Macroscale investigation of high speed gas bearing for MEMS devices. PhD Thesis, Massachusetts Institute of Technology, USA, 2000.

Piekos E.S. Numerical simulation of gas-lubricated journal bearings for microfabricated machines. PhD Thesis, Massachusetts Institute of Technology, USA, 2000.

Teo CJ. MEMS turbomachinery rotordynamics: Modeling, design and testing. PhD Thesis, Massachusetts Institute of Technology, USA, 2006.

Teo

Liu

. High-speed operation of a gas-bearing supported MEMS-air turbine. J Tribol 2009; 131: 032001.

Kim

Lee

Bryant

. Hydrodynamic performance of gas microbearings. J Tribol 2004; 126: 711–718.

Lee

Kwak

Kim

. Numerical prediction of slip flow effect on gas-lubricated journal bearings for MEMS/MST-based micro-rotating machinery. Tribol Int 2005; 38: 89–96.

10.

Zhang

Zhou

Meng

. Performance and stability analysis of gas-lubricated journal bearings in MEMS. Tribol Int 2011; 44: 887–897.

11.

Zhang

Wang

Liu

. Influence of temperature on nonlinear dynamic characteristics of spiral-grooved gas-lubricated thrust bearing-rotor systems for microengine. Tribol Int 2013; 61: 138–143.

12.

Zhang

Wang

Zhang

. Non-linear dynamic analysis of the ultra-short micro gas journal bearing-rotor systems considering viscous friction effects. Nonlinear Dyn 2013; 73: 751–765.

13.

Yang Q, Liu Y and Zhang H. Study on the solution of Reynolds equation for micro gas bearings using the alternating-direction implication algorithm. In: Sixth international conference on nonlinear mechanics (ICNM-6), Shanghai, 2013, pp.137–140.

14.

Fukui

Kaneko

. Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: First report-derivation of a generalized lubrication equation including thermal creep flow. J Tribol 1988; 110: 253–262.

15.

Fukui

Kaneko

. A database for interpolation of Poiseuille flow rates for high Knudsen number lubrication problems. J Tribol 1990; 112: 78–83.

16.

Sun

Chan

Liu

. A slip model for gas lubrication based on an effective viscosity concept. Proc IMechE, Part J: J Engineering Tribology 2003; 217: 187–196.

17.

Zhang

Zhu

Yang

. Characteristics of micro gas journal bearings based on effective viscosity. J Tribol 2009; 131: 041707.

18.

Peaceman

Rachford

. The numerical solution of parabolic and elliptic differential equations. J Soc Ind Appl Math 1955; 3: 28–41.

19.

Temperton

. Algorithms for the solution of cyclic tridiagonal systems. J Comput Phys 1975; 19: 317–323.

20.

Gad

Kaneko

. Performance characteristics for gas-lubricated bump-type foil thrust bearing. Proc IMechE, Part J: J Engineering Tribology 2015; 229: 746–762.

Unbalance response of micro gas bearing-rotor system considering rarefaction effect

Abstract

Keywords

Get full access to this article

References