In this paper the nonlinear dynamic responses of a rigid rotor supported by ball bearings due to surface waviness of bearing races are analyzed. A mathematical formulation has been derived with consideration of the nonlinear springs and nonlinear damping at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running surface waviness on the nonlinear vibrations of rotor bearing system is investigated. The results are mainly presented in time and frequency domains are shown in time-displacement, fast Fourier transformation, and Poincaré maps. The results predict discrete spectrum with specific frequency components for each order of waviness at the inner and outer races, also the excited frequency and waviness order relationships have been set up to prognosis the race defect on these bearing components. Numerical results obtained from the simulation are validated with respect to those of prior researchers.

References

References
1.
Gustafson
,
O. G.
,
Tallian
,
T.
,
Fukata
,
S.
, and
Tamura
,
H.
, 1963, “
Research Report on Study of the Vibration Characteristics of Bearings
,” Reg: 585 14, 4223, December, Report: AL 631 023,
SKF Ind., Inc
.
2.
Sunnersjo
,
C. S.
, 1978, “
Varying Compliance Vibrations of Rolling Bearings
,”
J. Sound Vib.
,
58
, pp.
363
373
.
3.
Meyer
,
L. D.
,
Ahlgran
,
F. F.
, and
Weichbrodt
,
B.
, 1980, “
An Analytical Model for Ball Bearing Vibrations to Predict Vibration Response to Distributed Defects
,”
ASME J. Mech. Des.
,
102
, pp.
205
210
.
4.
El-Sayed
,
H. R.
, 1980, “
Stiffness of Deep-Groove Ball Bearings
,”
Wear
,
63
, pp.
89
94
.
5.
Tamura
,
H.
, and
Tsuda
,
Y.
, 1980, “
On the Spring Characteristics of Ball Bearing (Extreme Characteristics With Many Balls)
,”
Bull. Jpn. Soc. Mech. Eng.
,
23
, pp.
961
969
.
6.
Sayles
,
R. S.
and
Poon
,
S.Y.
, 1981, “
Surface Topography and Rolling Element Vibration
,”
Precis. Eng.
,
3
(
3
), pp.
137
144
.
7.
Wardle
,
F. P.
and
Poon
,
S.Y.
, 1983, “
Rolling Bearing Noise, Cause and Cure
,”
Chat. Mech. Eng.
, July/August, pp.
36
40
.
8.
Wardle
,
F. P.
, 1988, “
Vibration Forces Produced By Waviness of the Rolling Surfaces of Thrust Loaded Ball Bearings, Part I: Theory. Part II: Experimental Validation
,”
Proc. Inst. Mech. Eng.
,
202
(
C5
), pp.
305
319
.
9.
Rahnejat
,
H.
, and
Gohar
,
R.
, “
The Vibrations of Radial Ball Bearings
,”
Proc. Inst. Mech. Eng.
,
199
(
C3
), pp.
181
193
.
10.
Kankar
,
P. K.
,
Sharma
,
Satish
,
C.
, and
Harsha
,
S. P.
, 2011, “
Fault Diagnosis of High Speed Rolling Element Bearings Due to Localized Defects using Response Surface Method
,”
ASME J. Dyn. Syst., Meas., Control
,
133
, p.
031007
.
11.
Yhland
,
E. M.
, 1992, “
A Linear Theory of Vibration Caused By Ball Bearings With Form Errors Operating at Moderate Speeds
,”
ASME J. Tribol.
,
114
, pp.
348
359
.
12.
Aktürk
,
N.
, and
Gohar
,
R.
, 1998, “
The Effect of Ball Size Variation on Vibrations Associated With Ball Bearings
,”
Proc. Inst. Mech. Eng.
,
212
, pp.
101
110
.
13.
Aktürk
,
N.
, 1999, “
The Effect of Waviness on Vibrations Associated With Ball Bearings
,”
ASME J. Tribol.
,
121
, pp.
667
677
.
14.
Harsha
,
S. P.
,
Sandeep
,
K.
, and
Prakash
,
R.
, 2004, “
Non-linear Dynamic Behaviors of Rolling Element Bearings Due to Surface Waviness
,”
J. Sound Vib.
,
272
, pp.
557
580
.
15.
Harsha
,
S. P.
, 2006, “
Nonlinear Dynamic Analysis of a High-Speed Rotor Supported By Rolling Element Bearings
,”
J. Sound Vib.
,
290
, pp.
65
100
.
16.
Brändlein
,
J.
,
Eschmann
,
P.
,
Hasbargen
,
L.
, and
Weigand
,
K.
,
Ball and Roller Bearings: Theory, Design and Application
, (
Wiley
,
New York
, 1999).
17.
Harris
,
T. A.
,
Rolling Bearing Analysis
(Wiley
,
New York
, 1991).
You do not currently have access to this content.