Preliminary analysis on the preload influence on the behavior of offset half gas bearings

Technical Paper
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Abstract

This paper deals with a preliminary computational analysis of the influence of the preload factor on the performance characteristics of gas-lubricated offset half bearings. A finite element procedure is devised to solve the lubrication equations rendered by a linearized perturbation method applied on the compressible Reynolds equation. High-order shape functions are employed in the fluid domain modeling to avoid numerical instabilities in the equation solver. Steady-state and dynamic performance characteristics of gas bearings with different values of preload are predicted at several operating conditions. Curves of the bearing characteristics are rendered to show the influence of the preload on the performance of offset half gas bearings at high speeds.

Keywords

Gas-lubricated bearings Offset half bearings Offset-halves bearings Noncircular bearings Non-cylindrical bearings 

List of Symbols

c

Bearing radial clearance (m)

Cij

Damping coefficients (N s/m)

\( \bar{C}_{ij} \)

Dimensionless damping coefficients

D

Bearing diameter (m)

e

Journal eccentricity (m)

Fi

Fluid film reaction force (N)

h

Fluid film thickness (m)

ho

Zeroth-order film thickness (m)

hσ

First-order film thickness (m/m)

Kij

Stiffness coefficients (N/m)

\( \bar{K}_{ij} \)

Dimensionless stiffness coefficients

L

Bearing length (m)

m

Preload factor, dimensionless

p

Hydrodynamic pressure (Pa)

po

Zeroth-order pressure (Pa)

pσ

First-order pressure (Pa/m)

pa

Ambient pressure (Pa)

QL

Side leakage flow (kg/s)

R

Journal radius (m)

RB

Bearing radius (m)

S

Sommerfeld number, dimensionless (\( S = \mu \cdot \varOmega \cdot D \cdot L \cdot R^{2} /(2 \cdot \pi \cdot W \cdot c^{2} ) \))

W

Bearing external load (N)

U

Surface speed (m/s)

Z

Dynamic Impedance (N/m)

\( \dot{m} \)

Mass flow rate (kg/s)

α

Radial clearance ratio, dimensionless (α = cmin/cmax)

Δe

Perturbation on the journal position (m)

ε

Eccentricity ratio, dimensionless

φ

Journal attitude angle (rad)

θ

Circumferential coordinate (rad)

Γe

Finite element boundary

Λ

Bearing or speed number, dimensionless (\( \varLambda = {{6\mu \cdot \varOmega \cdot R^{2} } \mathord{\left/ {\vphantom {{6\mu \cdot \varOmega \cdot R^{2} } {\left( {p_{a} \cdot c^{2} } \right)}}} \right. \kern-0pt} {\left( {p_{a} \cdot c^{2} } \right)}} \))

μ

Dynamic viscosity (Pa s)

ρ

Mass density (kg/m3)

σ

Frequency number, dimensionless (\( \sigma = {{2\varLambda \omega } \mathord{\left/ {\vphantom {{2\varLambda \omega } \varOmega }} \right. \kern-0pt} \varOmega } \))

ω

Excitation frequency (rad/s)

Ω

Rotational speed (rad/s)

Ωe

Finite element domain

ψje

Shape functions

Notes

Acknowledgements

The author wishes to express his sincere thanks to Prof. Dr.-Ing. Georg Jacobs, head of the Institut für Maschinenelemente und Maschinengestaltung (IME) from RWTH Aachen University, and to Dipl.-Ing. Gero Burghardt, leader of the Tribology Group at IME, for their support during the development of this work.

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Departamento de Engenharia MecânicaUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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