Nonlinear Dyn
DOI 10.1007/s11071-016-3037-1
ORIGINAL PAPER
A new model for spall-rolling-element interaction
G. Kogan · J. Bortman · R. Klein
Received: 2 May 2016 / Accepted: 17 August 2016
© Springer Science+Business Media Dordrecht 2016
Abstract Evaluation of the spall size of a radially
loaded rolling-element bearing is required for the
assessment of the bearing damage severity and esti-
mation of its remaining useful life. A new multi-body,
nonlinear dynamic model of the interaction between the
rolling-element and a spalled outer race is presented.
The study focuses on the physics of rolling-element
contact in a broader range of spall sizes than has been
investigated to date, with intermittent contact between
rolling-element and the outer race, which is a relevant
defect size for diagnostics and prognosticsquery. The
analysis is performed in several time intervals accord-
ing to periods of rolling-element/race contact and peri-
ods when the rolling-element is not connected with the
outer race. An explicit expression of the spall size as
function of the time-to-impact has been developed by
considering radial load, shaft speed, and gravity. The
We gratefully acknowledge the invaluable support of the
Pearlstone Foundation.
G. Kogan · J. Bortman (B )
Pearlstone Center for Aeronautical Engineering Studies and
Laboratory for Mechanical Health Monitoring, Department
of Mechanical Engineering, Ben-Gurion University of the
Negev, P.O. Box 653, 8410501 Beer Sheva, Israel
e-mail: jacbort@gmail.com
G. Kogan
e-mail: ggkogan@gmail.com
R. Klein
R.K. Diagnostics, P.O. Box 101, 20103 Gilon,
D.N. Misgav, Israel
e-mail: renata.klein@rkdiagnostics.co.il
expression of the spall size was used in a sensitivity
study of the effect of parameters such as geometry and
radial load. The results obtained from the new model
are in good agreement with a well-established general
bearing model. The acceleration of the outer ring dur-
ing the rolling-element/spall interaction with intermit-
tent rolling-element race connection is a novel con-
tribution, which allows verification of the model from
direct observations using vibration sensors mounted on
the structure
Keywords Vibration response · Rolling-element
bearing · Nonlinear dynamics · Contact model · Spall
size · Localized surface defect
List of symbols
a
r
Radial acceleration
C
d
RE bearing clearance diameter
c Damping coefficient of each of the RE-
raceways contact
c
B
Damping coefficient of the bearing
c
RE
Damping coefficient of each RE
c
0
Speed of sound in a solid material
D
p
Bearing pitch diameter
d Spall depth
E Elasticity modulus
E Trailing edge relative to the outer ring
centre
F Force applied to the RE by the raceway
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