Transient Response of Rotor on
Rolling Element Bearings with Clearance
David P. Fleming
Brian T. Murphy
NASA Glenn Research Center
RMA, Inc.
Cleveland, OH 44135, USA
7701 Baja Cove
David.P.Fleming@nasa.gov
Austin, TX 78759,
USA
bmurphy@xlrotor.com
J. V. Poplawski
Jerzy T.
Sawicki
J. V. Poplawski and
Associates
Cleveland State University
Bethlehem, PA 18018, USA
Cleveland, OH 44115, USA.
Jvpoplawski@aol.com
j.sawicki@csuohio.edu
Published: May 2007
Abstract
Internal clearance
in rolling element bearings is usually present to allow for radial
and axial growth of the rotor-bearing system and to accommodate
bearing fit-up. The presence of this clearance also introduces a
"dead band" into the load-deflection behavior of the bearing.
Previous studies demonstrated that the presence of dead band
clearance might have a significant effect on synchronous rotor
response. In this work, the authors investigate transient response
of a rotor supported on rolling element bearings with internal
clearance. In addition, the stiffness of the bearings varies
nonlinearly with bearing deflection and with speed. Bearing
properties were accurately calculated with a state of the art
rolling bearing analysis code. The subsequent rotordynamics analysis
shows that for rapid acceleration rates the maximum response
amplitude may be less than predicted by steady-state analysis. The
presence of clearance may shift the critical speed location to lower
speed values. The rotor vibration response exhibits subharmonic
components which are more prominent with bearing clearance.
Full Text (PDF)
Introduction
Response of all but
very flexible rotors depends strongly on bearing properties. When
bearings are nonlinear, accurate rotor response calculations require
use of bearing properties for the precise conditions encountered,
rather than average properties. While fluid film bearings are often
reasonably linear for small deflections (although there is usually a
strong speed dependence), rolling-element bearings have a much less
linear force-displacement relationship. Two aspects of rolling
element bearings contribute further to nonlinearity. First, the
bearings are often fabricated with internal clearance, or deadband.
For example, in a 25 mm bore deep-groove ball bearing, the internal
radial clearance (IRC) is typically between 4 and 13 μm. (For
rotordynamic purposes it is most convenient to use bearing radial
clearance as is done herein. However, bearing engineers more
typically use internal diametral
clearance (IDC), which is twice the internal
radial clearance). Second, at speed, centrifugal forces move the
rolling elements outward, increasing the clearance between the inner
race and the rolling elements.
The rotordynamic software
XLRotor was used to perform all numerical integrations. XLRotor was
selected because it enables the use of user-defined routines for
nonlinear elements. For this study, a Microsoft Excel Visual Basic
Macro was written which computes the bearing reaction force as a
function of both speed and deflection via a curve fit of the COBRA
data. For transient analysis, XLRotor provides several
different numerical integration schemes, all of which are implicit
and unconditionally stable. These types of integration schemes
permit efficient integration of the full unreduced system of
differential equations.
Fig 1: Sketch of Rotor
Fig 2: Critical Speed map
Fig
3: The Rotor response over a speed range from 10000 rpm to 80000 rpm
for these values of internal radial clearance and four acceleration
rates with the rotor axis vertical (i.e., no gravity load on the
bearings)
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