High-Speed Gas Bearings for Micro-Turbomachinery

  • Zoltán S. Spakovszky
Part of the MEMS Reference Shelf book series (MEMSRS)


The mechanical design and architecture of high-speed rotating machinery, independent of size or scale, are strongly governed by the rotordynamic behavior of the spool and its bearing arrangement. Large-scale gas turbine engines yield multi-spool shaft constructions where the rolling contact bearings are close to the centerline of the engine supporting the shaft and disk assemblies as shown in Fig. 6.1 on the left.


Journal Bearing Thrust Bearing Labyrinth Seal Rotor Unbalance Bearing Clearance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



rotor imbalance


area, area ratio




angular damping coefficient


journal bearing clearance, coefficient

C,\(\tilde {C}\)

damping coefficient


friction coefficient


orifice diameter


rotor diameter, orifice diameter


hydraulic diameter


bearing diameter times rotor speed in mm-rpm


dynamic eccentricity


unit vector


force, function


Green’s function


thrust-bearing gap or clearance


diametral moment of inertia


polar moment of inertia

k, K



journal bearing length, orifice length

\(\dot m\)

mass flow


mass of rotor disk


Mach number, moment

n, N

harmonic number, number of




hydrostatic differential pressure across journal bearing

q, Q

specific flow rate, flow rate


radial coordinate, radial location of orifices


rotor radius, radius of thrust-bearing pad, specific gas constant


Reynolds number


whirl-ratio Ω W N


Laplace variable





u, \({\overline{U}}\)

velocity, mean axial velocity due to hydrostatic flow

v, V



whirl number = k v /k p


axial location, parameter


plenum circumferential angle


reduced frequency ωL/\({\overline{U}}\)


ratio of axial flow-through time and viscous diffusion time

βx, βy

Euler angles




rotor normalized radial eccentricity




ratio of specific heats


bearing number


dynamic imbalance


dynamic viscosity


kinematic viscosity


frequency, stagnation pressure loss coefficient


journal bearing inlet stagnation pressure loss coefficient


rotor speed


natural frequency


rotor speed at onset of whirl instability



ρ, ρd

fluid density, rotor disk density


wall shear stress


characteristic viscous diffusion time


flow-through time of axial hydrostatic flow


damping ratio, non-dimensional hydrodynamic moment




cross-coupled hydrodynamic


direct-coupled hydrostatic




hydrodynamic pumping action


hydrodynamic viscous effect


critical, singular condition




nominal, equilibrium condition






total or stagnation







The work described in this chapter has resulted from contributions of a number of individuals, many of whom are co-authors of the referenced papers. It has been a pleasure working with the students and members of the bearing team of the microengine project. In particular the author would like to mention his gratitude to Dr. L. Liu, Dr. C.J. Teo, Dr. S. Jacobson, and Dr. F. Ehrich. The editorial help by Ms. D. Park is gratefully acknowledged.


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Zoltán S. Spakovszky
    • 1
  1. 1.Gas Turbine LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

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