Ball-bearing rotor systems are key components of rotating machinery. In this work, a new dynamic modeling method for ball-bearing rotor systems is proposed based on rigid body element (RBE). First, the concept of RBE is given, and then the rotor is divided into several discrete RBEs. Every two adjacent RBEs are connected by imaginary springs, whose stiffness is calculated according to properties of the RBEs. Second, all the parts of rolling ball bearings (i.e., outer ring, inner ring, ball, and cage) are considered as RBEs, and Gupta's model is employed to model bearings which include radial clearance, waviness, pedestal effect, etc. Finally, the rotor and all the rolling ball bearings are coupled to develop a dynamic model of the ball-bearing rotor system. The vibration responses of the ball-bearing rotor system can be calculated by solving dynamic equations of each RBE. The proposed method is verified with both simulation and experiment. The RBE model of the rotor is compared with its finite element (FE) model first, and numerical simulation shows the validity of the RBE model. Then, experiments are conducted on a rotor test rig which is supported with two rolling ball bearings as well. Good agreements between measurement and simulation show the ability of the model to predict the dynamic behavior of ball-bearing rotor systems.

References

References
1.
Jones
,
A. B.
,
1960
, “
A General Theory of Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions
,”
ASME J. Basic Eng.
,
82
(
21
), pp.
309
320
.
2.
Harris
,
T. A.
, and
Kotzalas
,
M. N.
,
2007
,
Rolling Bearing Analysis: Essential Concepts of Bearing Technology
,
Taylor and Francis
,
Boca Raton, FL
.
3.
Harris
,
T. A.
, and
Kotzalas
,
M. N.
,
2007
,
Rolling Bearing Analysis: Advanced Concepts of Bearing Technology
,
Taylor and Francis
,
Boca Raton, FL
.
4.
Walters
,
C. T.
,
1969
, “
Study of the Behavior of High-Speed Angular-Contact Ball Bearings Under Dynamic Load
,” Final Report on Contract Report No. NAS 8-21255, May 12.
5.
Walters
,
C. T.
,
1971
,“
The Dynamics of Ball Bearings
,”
ASME J. Lubr. Technol.
,
93
(
1
), pp.
1
10
.
6.
Gupta
,
P. K.
,
1979
, “
Dynamics of Rolling-Element Bearings—Part III: Ball Bearing Analysis
,”
ASME J. Lubr. Technol.
,
101
(
3
), pp.
312
318
.
7.
Gupta
,
P. K.
,
1984
,
Advanced Dynamic of Rolling Elements
,
Springer
,
New York.
8.
Weinzapfel
,
N.
, and
Sadeghi
,
F.
,
2009
, “
A Discrete Element Approach for Modeling Cage Flexibility in Ball Bearing Dynamics Simulations
,”
ASME J. Tribol.
,
131
(
2
), p.
021102
.
9.
Ashtekar
,
A.
, and
Sadeghi
,
F.
, “
A New Approach for Including Cage Flexibility in Dynamic Bearing Models by Using Combined Explicit Finite and Discrete Element Methods
,”
ASME J. Tribol.
,
134
(
4
), p.
041502
.
10.
Jain
,
S.
, and
Hunt
,
H.
,
2011
, “
A Dynamic Model to Predict the Occurrence of Skidding in Wind-Turbine Bearings
,”
J. Phys.: Conf. Ser.
,
350
, p.
012027
.
11.
Tu
,
W.
,
Shao
,
Y.
, and
Mechefske
,
C. K.
,
2012
, “
An Analytical Model to Investigate Skidding in Rolling Element Bearings During Acceleration
,”
J. Mech. Sci. Technol.
,
26
(
8
), pp.
2451
2458
.
12.
Singh
,
S.
,
Köpke
,
U. G.
,
Howard
,
C. Q.
, and
Petersen
,
D.
,
2014
, “
Analyses of Contact Forces and Vibration Response for a Defective Rolling Element Bearing Using an Explicit Dynamics Finite Element Model
,”
J. Sound Vib.
,
333
(
21
), pp.
5356
5377
.
13.
Kogan
,
G.
,
Klein
,
R.
,
Kushnirsky
,
A.
, and
Bortman
,
J.
,
2015
, “
Toward a 3D Dynamic Model of a Faulty Duplex Ball Bearing
,”
Mech. Syst. Sig. Process.
,
54–55
, pp.
243
258
.
14.
Liu
,
J.
, and
Shao
,
Y.
,
2015
, “
A New Dynamic Model for Vibration Analysis of a Ball Bearing Due to a Localized Surface Defect Considering Edge Topographies
,”
Nonlinear Dyn.
,
79
(
2
), pp.
1329
1351
.
15.
Ahmadi
,
A. M.
,
Petersen
,
D.
, and
Howard
,
C.
,
2015
, “
A Nonlinear Dynamic Vibration Model of Defective Bearings–The Importance of Modelling the Finite Size of Rolling Elements
,”
Mech. Syst. Sig. Process.
,
52–53
, pp.
309
326
.
16.
Vakharia
,
V.
,
Gupta
,
V. K.
, and
Kankar
,
P. K.
,
2015
, “
Nonlinear Dynamic Analysis of Ball Bearings Due to Varying Number of Balls and Centrifugal Force
,” 9th
IFToMM
International Conference on Rotor Dynamics Mechanisms and Machine Science
, Vol.
21
, pp.
1831
1840
.
17.
Zhang
,
X.
,
Han
,
Q.
,
Peng
,
Z.
, and
Chu
,
F.
,
2014
, “
A New Nonlinear Dynamic Model of the Rotor-Bearing System Considering Preload and Varying Contact Angle of the Bearing
,”
Commun. Nonlinear Sci. Numer. Simul.
,
22
(
1–3
), pp.
821
841
.
18.
He
,
C.
,
Xu
,
H. Y.
, and
Zhang
,
Y. Q.
,
2015
, “
Analysis of the Nonlinear Dynamic Response of Gyroscope Rotor System Considered Elasto-Hydrodynamic Lubrication
,”
3rd International Conference on Mechatronics, Robotics and Automation
, pp.
727
731
.
19.
Hou
,
L.
,
Chen
,
Y. S.
,
Cao
,
Q. J.
, and
Zhang
,
Z. Y.
,
2015
, “
Turning Maneuver Caused Response in an Aircraft Rotor-Ball Bearing System
,”
Nonlinear Dyn.
,
79
(
1
), pp.
229
240
.
20.
Babu
,
C. K.
,
Tandon
,
N.
, and
Pandey
,
R. K.
,
2012
, “
Vibration Modeling of a Rigid Rotor Supported on the Lubricated Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races
,”
ASME J. Vib. Acoust.
,
134
(
1
), p.
011006
.
21.
Babu
,
C. K.
,
Tandon
,
N.
, and
Pandey
,
R. K.
,
2014
, “
Nonlinear Vibration Analysis of an Elastic Rotor Supported on Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races
,”
ASME J. Vib. Acoust.
,
136
(
4
), p.
044503
.
22.
Gupta
,
T. C.
,
Gupta
,
K.
, and
Sehgal
,
D. K.
,
2011
, “
Instability and Chaos of a Flexible Rotor Ball Bearing System: An Investigation on the Influence of Rotating Imbalance and Bearing Clearance
,”
ASME J. Eng Gas Turbines Power
,
133
(
8
), p.
082501
.
23.
Gupta
,
T. C.
, and
Gupta
,
K.
,
2013
, “
Correlation of Parameters to Instability and Chaos of a Horizontal Flexible Rotor Ball Bearing System
,”
ASME
Paper No. GT2013-95308.
24.
Gupta
,
T. C.
, and
Gupta
,
K.
,
2014
, “
Modeling of Flexible Coupling to Connect Misaligned Flexible Rotors Supported on Ball Bearings
,”
ASME
Paper No. GT2014-26891.
25.
Cao
,
Y.
, and
Altintas
,
Y.
,
2004
, “
A General Method for the Modeling of Spindle-Bearing System
,”
ASME J. Mech. Des.
,
126
(
6
), pp.
1089
1104
.
26.
Cao
,
H.
,
Holkup
,
T.
, and
Altintas
,
Y.
,
2011
, “
A Comparative Study on the Dynamics of High Speed Spindles With Respect to Different Preload Mechanisms
,”
Int. J. Adv. Manuf. Technol.
,
57
(
9–12
), pp.
871
883
.
27.
Cao
,
H.
,
Niu
,
L.
, and
He
,
Z.
,
2012
, “
Method for Vibration Response Simulation and Sensor Placement Optimization of a Machine Tool Spindle System With a Bearing Defect
,”
Sensors
,
12
(
7
), pp.
8732
8754
.
28.
Cao
,
H.
,
Holkup
,
T.
,
Chen
,
X.
, and
He
,
Z.
,
2012
, “
Study on Characteristic Variations of High-Speed Spindles Induced by Centrifugal Expansion Deformations
,”
J. Vibroeng.
,
14
(
3
), pp.
1278
1291
.
29.
Kurvinen
,
E.
,
Sopanen
,
J.
, and
Mikkola
,
A.
,
2015
, “
Ball Bearing Model Performance on Various Sized Rotors With and Without Centrifugal and Gyroscopic Forces
,”
Mech. Mach. Theory
,
90
, pp.
240
260
.
30.
Li
,
Y.
,
Cao
,
H.
,
Niu
,
L.
, and
Jin
,
X.
,
2015
, “
A General Method for the Dynamic Modeling of Ball-bearing Rotor Systems
,”
ASME J. Manuf. Sci. Eng.
,
137
(
2
), p.
021016
.
31.
Niu
,
L.
,
Cao
,
H.
,
He
,
Z.
, and
Li
,
Y.
,
2014
, “
Dynamic Modeling and Vibration Response Simulation for High Speed Rolling Ball Bearings With Localized Defects in Raceways
,”
ASME J. Manuf. Sci. Eng.
,
136
(
4
), p.
041015
.
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