1 Dynamic characteristics of grooved air bearings in microsystems L-M Chu 1 , W-L Li 2∗ , R-W Shen 3 , and T-I Tsai 3 1 Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung County,Taiwan, Republic of China 2 Institute of Nanotechnology and Microsystems Engineering, Center for Micro/Nano Science andTechnology, National Cheng Kung University,Tainan,Taiwan, Republic of China 3 Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung,Taiwan, Republic of China The manuscript was received on 23 August 2008 and was accepted after revision for publication on 6 January 2009. DOI: 10.1243/13506501JET517 Abstract: The performance of grooved air bearings in microsystems is analysed and discussed. The modified molecular gas lubrication (MMGL) equation is utilized as the governing equation for the gas film to include the effect of gas rarefaction. The gas rarefaction is significantly affected by two important parameters (Knudsen numbers (Kn) and accommodation coefficients (ACs)). The Poiseuille and Couette flow rate correctors (Q P and Q C ) are introduced in the MMGL equation to extend the lubrication theory (compressible Reynolds equation) for arbitrary Kn and tangential momentum accommodation coefficients or ACs. At a specific operating condition, the transient MMGL equation is linearized by small variations in film thickness and pressure. The linearized MMGL equation is then solved by finite-element method to obtain the dynamic pressure distri- butions. Therefore, the dynamic coefficients (stiffness and damping coefficients) are obtained by integrating the dynamic pressure over the bearing surfaces. Keywords: modified molecular gas lubrication, Knudsen number, tangential momentum accommodation coefficient, dynamic coefficient 1 INTRODUCTION The applications of gas bearings in microsystems become important due to the requirement of their better and feasible features as compared with the current conventional ball bearings and oil-lubricated bearings. To improve the instability nature of plain journal bearings operating in concentric or nearly con- centric conditions, bearing surfaces with grooves are applied to pump the lubricant inward, and to prevent the whirl instability. There are many configurations of grooves on bearing surfaces, i.e. the herringbone, ∗ Corresponding author: Center for Micro/Nano Science and Tech- nology, Institute of Nanotechnology and Microsystems Engineering, National Cheng Kung University, No. 1, University Road, Tainan, Taiwan 701, Republic of China. email: wlli@mail.ncku.edu.tw, dragon@mail.mina.ncku.edu.tw spiral, and helical grooves. Herringbone groove jour- nal bearings are widely used in many applications (in rotating disc spindles and microbearings) due to their better dynamic performance and self-sealing charac- teristics in concentric or nearly concentric operating conditions [1]. Traditionally, the compressible Reynolds equation is introduced as the governing equation in modelling the gas lubricating film. The complexity of herringbone configurations and the gap discontinuity make some difficulty in solving the Reynolds equation. The nar- row groove theory (NGT) [2], which assumed infinite number of grooves, is introduced to approximate and to simplify the physical model of grooved bearings. However, the NGT is questionable as small number of grooves (the groove is not ‘narrow’ enough) is on the bearing. Additional numerical procedure is needed to solve the limitation in geometry. The NGT overesti- mates the load capacity of herringbone groove journal JET517 © IMechE 2009 Proc. IMechE Vol. 223 Part J: J. Engineering Tribology