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Research Papers: Hydrodynamic Lubrication

Linear Stability Analysis of the Herringbone Groove Journal Bearings in Microsystems: Consideration of Gas Rarefaction Effects

[+] Author and Article Information
Wang-Long Li1

Institute of Nanotechnology and Microsystems Engineering, Center for Micro/Nano Science and Technology, National Cheng Kung University, No. 1, University Road, Tainan 701, Taiwanli.dragonpuff@gmail.com

Rui-Wen Shen

Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan

1

Corresponding author.

J. Tribol 131(4), 041705 (Sep 23, 2009) (8 pages) doi:10.1115/1.3201872 History: Received January 09, 2009; Revised July 14, 2009; Published September 23, 2009

The dynamic performance of the herringbone groove journal bearings (HGJBs) with the effects of gas rarefaction taken into account is considered for applications in microsystems. Two important parameters (the Knudsen number Kn and the tangential momentum accommodation coefficients, TMACs or the accommodation coefficients, ACs) that affect gas rarefaction significantly are considered. Small variations in film thickness and pressure from the equilibrium state are substituted into the transient modified molecular gas lubrication (MMGL) equation, which considers effects of gas rarefactions with the Poiseuille and Couette flow rate correctors. The gas film in the rotor-bearing system is modeled as stiffness and damping elements with coefficients dependent on the exciting frequency. The dynamic coefficients are then obtained by solving the linearized MMGL equations. The equations of motion of the rotor as well as the dynamic coefficients are performed for the present linear stability analysis. Due to the exciting frequency-dependent nature of the dynamic coefficients, an iterative method with the golden section technique is introduced in the linear stability analysis of rotor-bearing systems. The critical mass parameters and the related threshold speed are computed and discussed. The results of this study prove that HGJBs in microsystems can operate at concentric conditions at very high speeds.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of herringbone grooves

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Figure 2

(a) Comparison of dimensionless critical mass parameters with those by Vleugels (15), (b) comparison of dimensionless load capacities with those by Vleugels (15), and (c) comparison of dimensionless stiffness coefficients with those by Vleugels (15)

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Figure 3

Stability map plotted as functions of bearing numbers for various eccentricity ratios

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Figure 4

Stability map plotted as functions of bearing numbers for various groove depth ratios

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Figure 5

Stability map plotted as functions of bearing numbers for various groove numbers

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Figure 6

(a) Stability map plotted as functions of inverse Knudsen numbers for various eccentricity ratios for Λ=1.0, (b) stability map plotted as functions of inverse Knudsen numbers for various eccentricity ratios for Λ=10, and (c) stability map plotted as functions of inverse Knudsen numbers for various eccentricity ratios for Λ=100

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Figure 7

(a) Stability map plotted as functions of ACs for various combinations of ACs at Λ=1.0, (b) stability map plotted as functions of ACs for various combinations of ACs at Λ=10, and (c) stability map plotted as functions of ACs for various combinations of ACs at Λ=100

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