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Optimized Short Bearing Theory for Squeeze Film Dampers

[+] Author Affiliations
Stephen L. Edney

Rolls-Royce Corporation, Indianapolis, IN

Paper No. GT2009-59283, pp. 735-742; 8 pages
doi:10.1115/GT2009-59283
From:
  • ASME Turbo Expo 2009: Power for Land, Sea, and Air
  • Volume 6: Structures and Dynamics, Parts A and B
  • Orlando, Florida, USA, June 8–12, 2009
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-4887-6 | eISBN: 978-0-7918-3849-5
  • Copyright © 2009 by Rolls-Royce

abstract

It is well established that classical short bearing theory can be applied to assess squeeze film dampers whirling in circular centered orbits. This theory yields accurate values for the stiffness and damping coefficients for designs with small length-to-diameter (L/D) ratios (typically less than 0.5) whirling at amplitudes of less than half the damper radial clearance. For L/D ratio designs above 0.5 and/or whirling amplitudes approaching the damper radial clearance, the short bearing theory increasingly overestimates the stiffness and damping coefficients that stretch its applicability for some designs. There are two limitations with the classical theory that compromise the solution at high L/D ratios and large whirling amplitudes. The first is that as the L/D ratio increases, the unrestricted end flow assumption that forms the basis of the short bearing theory introduces increasingly larger errors. The second is that as the whirling amplitude approaches the damper radial clearance, the stiffness and damping coefficients approach infinity much more rapidly than those from a full solution of the governing lubrication equation. The ideal method for determining more exact values is to numerically solve the full lubrication equation, although not everyone has access to such a code. An alternative approach is to use the expressions presented in this paper that are derived from an optimized solution of the short bearing theory that appreciably reduces the errors introduced at high L/D ratios and whirling amplitudes approaching the damper radial clearance. The optimized solution yields a simple closed form correction factor based on Galerkin’s method that minimizes these errors over the positive pressure region of the oil film. This analytic correction factor increases the accuracy of the short bearing theory for all whirling amplitudes and extends the applicability of the closed form solution to larger L/D ratio damper designs. The simple closed form expressions presented herein apply to a damper whirling in a circular centered orbit for both a partial pi-film cavitated model and a full-film uncaviated model. Examples are given that demonstrate the optimized solution yields stiffness and damping values that are significantly closer to the numerical solution for L/D ratio designs up to 1.0 and/or whirling amplitudes approaching the damper radial clearance.

Copyright © 2009 by Rolls-Royce
Topics: Bearings , Dampers

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