Abstract

Bearing fatigue life is significantly influenced by bearing clearance. Vibration monitoring of bearing clearance deviations can efficiently reveal bearing wear and give sufficient lead time for maintenance. This study investigates the dynamics of roller bearings utilizing the dimension theory with the support vector machine (SVM) technique for diagnosing the bearing clearance faults of revolving machines. The generation of local defects in rotating machines is closely related to the clearance behavior of the rotor-bearing system. A dynamic model of bearing with dimension theory by matrix method with SVM is developed for characteristics of bearing clearance considering the influence of local defects on the inner and outer bearings races. The characteristics of bearing internal radial clearance considering the impact of the defect on the bearing are analyzed. An experimental study has been performed to capture the vibration signature of radial clearance for different speeds and radial loads of the rotor. The rotor-bearing system equations are numerically integrated, and the results are validated with experimental findings. The collective effects among the four parameters (radial load, speed, defect size, radial clearance) are investigated in detail for the rotor-bearing system. The noisy signal is subsequently eliminated using the modulation signal bispectrum (MSB), and the peaks of the MSB results are represented by the bearing clearance indicator. The efficiency and reliability of the stated approach are evaluated using a specialized bearing test and a run-to-failure sugar centrifuge test. The results suggest that the proposed approach can detect a change in bearing clearance up to 40 µm.

References

1.
Cui
,
L.
,
Huang
,
J.
,
Zhang
,
F.
, and
Chu
,
F.
,
2019
, “
HVSRMS Localization Formula and Localization Law: Localization Diagnosis of a Ball Bearing Outer Ring Fault
,”
Mech. Syst. Signal Process
,
120
(
1
), pp.
608
629
.
2.
Yu
,
K.
,
Lin
,
T. R.
,
Ma
,
H.
,
Li
,
H.
, and
Zeng
,
J.
,
2020
, “
A Combined Polynomial Chirplet Transform and Synchroextracting Technique for Analyzing Nonstationary Signals of Rotating Machinery
,”
IEEE Trans. Instrum. Meas.
,
69
(
4
), pp.
1505
1518
.
3.
Rai
,
V. K.
, and
Mohanty
,
A. R.
,
2007
, “
Bearing Fault Diagnosis Using FFT of Intrinsic Mode Functions in Hilbert–Huang Transform
,”
Mech. Syst. Signal Process
,
21
(
6
), pp.
2607
2615
.
4.
Dick
,
P.
,
Carl
,
H.
,
Nader
,
S.
,
Alireza
,
M. A.
, and
Sarabjeet
,
S.
,
2015
, “
Analysis of Bearing Stiffness Variations Contact Forces and Vibrations in Radially Loaded Double Row Rolling Element Bearing With Raceway Defect
,”
Mech. Syst. Signal Process
,
51
(
1
), pp.
139
160
.
5.
Tandon
,
N.
, and
Choudhury
,
A.
,
1998
, “
A Theoretical Model to Predict Vibration Response of Rolling Bearings to Distributed Defects Under Radial Load
,”
ASME J. Vib. Acoust.
,
120
(
3
), pp.
214
220
.
6.
Goldman
,
P.
, and
Muszynska
,
A.
,
1991
, “
Analytical and Experimental Simulation of Loose Pedestal Dynamic Effects on a Rotating Machine Vibration Response
,”
Proceedings of the ASME 1991 Design Technical Conferences. 13th Biennial Conference on Mechanical Vibration and Noise: Rotating Machinery and Vehicle Dynamics
,
Miami, FL
,
Sept. 22–25
, Vol. 35, pp.
11
17
.
7.
Muszynska
,
A.
, and
Goldman
,
P.
,
1995
, “
Chaotic Responses of Unbalanced Rotor Bearing Stator Systems With Looseness or Rubs
,”
Chaos Soliton Fract.
,
5
(
9
), pp.
1683
1704
.
8.
Chu
,
F.
, and
Tang
,
Y.
,
2001
, “
Stability and Non-Linear Responses of a Rotor-Bearing System With Pedestal Looseness
,”
J. Sound Vib.
,
241
(
5
), pp.
879
893
.
9.
Wang
,
H. F.
,
Chen
,
G.
, and
Song
,
P. P.
,
2015
, “
Asynchronous Vibration Response Characteristics of Connectors With Looseness Fault and Its Verification
,”
J. Vibroeng.
,
17
(
7
), pp.
3551
3560
. www.extrica.com/article/15985
10.
Lee
,
S. M.
, and
Choi
,
Y. S.
,
2008
, “
Fault Diagnosis of Partial Rub and Looseness in Rotating Machinery Using Hilbert-Huang Transform
,”
J. Mech. Sci. Technol.
,
22
(
1
), pp.
2151
2162
.
11.
Lu
,
W.
, and
Chu
,
F.
,
2009
, “
Experimental Investigation of Pedestal Looseness in a Rotor-Bearing System
,”
Key Eng. Mater.
,
413
(
1
), pp.
599
605
.
12.
Nembhard
,
A. D.
,
Sinha
,
J. K.
, and
Yunusa-Kaltungo
,
A.
,
2015
, “
Experimental Observations in the Shaft Orbits of Relatively Flexible Machines With Different Rotor Related Faults
,”
Measurement
,
75
(
1
), pp.
320
337
.
13.
Chen
,
G.
,
2015
, “
Vibration Modelling and Verifications for Whole Aero-Engine
,”
J. Sound Vib.
,
349
(
4
), pp.
163
176
.
14.
Guo
,
Y.
, and
Parker
,
R. G.
,
2012
, “
Dynamic Analysis of Planetary Gears With Bearing Clearance
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
4
), p.
041002
.
15.
Tiwari
,
M.
,
Gupta
,
K.
, and
Prakash
,
O.
,
2000
, “
Effect of Radial Internal Clearance of a Ball Bearing on the Dynamics of a Balanced Horizontal Rotor
,”
J. Sound Vib.
,
238
(
5
), pp.
723
756
.
16.
Rathore
,
M. S.
, and
Harsha
,
S. P.
,
2023
, “
Fault Diagnostics and Faulty Pattern Analysis of High-Speed Roller Bearings Using Deep Convolutional Neural Network
,”
ASME J. Nondestr. Eval.
,
6
(
2
), p.
021006
.
17.
Ehrich
,
F. F.
,
1988
, “
“High Order Subharmonic Response of High Speed Rotors in Bearing Clearance
,”
ASME J. Vib. Acoust.
,
110
(
1
), pp.
9
16
.
18.
Wilkes
,
J. C.
,
Wade
,
J.
,
Rimpel
,
A.
,
Moore
,
J.
,
Swanson
,
E.
,
Grieco
,
J.
, and
Brady
,
J.
,
2018
, “
Impact of Bearing Clearance on Measured Stiffness and Damping Coefficients and Thermal Performance of a High-Stiffness Generation 3 Foil Journal Bearing
,”
ASME J. Eng. Gas Turbines Power
,
140
(
7
), p.
072503
.
19.
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
.
20.
Smolík
,
L.
,
Hajžman
,
M.
, and
Byrtus
,
M.
,
2017
, “
Investigation of Bearing Clearance Effects in Dynamics of Turbochargers
,”
Int. J. Mech. Sci.
,
127
(
1
), pp.
62
72
.
21.
Choi
,
S.
, and
Noah
,
S. T.
,
1994
, “
Mode-Locking and Chaos in a Jeffcott Rotor With Bearing Clearances
,”
ASME J. Appl. Mech.
,
61
(
1
), pp.
131
138
.
22.
Yang
,
Y.
,
Dejie
,
Y.
, and
Junsheng
,
C.
,
2007
, “
A Fault Diagnosis Approach for Roller Bearing Based on IMF Envelope Spectrum and SVM
,”
Measurement
,
40
(
9–10
), pp.
943
950
.
23.
Yongbo
,
L.
,
Minqiang
,
X.
,
Wei
,
Y.
, and
Wenhu
,
H.
,
2016
, “
A New Rolling Bearing Fault Diagnosis Method Based on Multiscale Permutation Entropy and Improved Support Vector Machine Based Binary Tree
,”
Measurement
,
77
(
1
), pp.
80
94
.
24.
Hung
,
L. A.
,
Cheng
,
J.
,
Yang
,
Y.
, and
Truong
,
T. K.
,
2013
, “
The Support Vector Machine Parameter Optimization Method Based on Artificial Chemical Reaction Optimization Algorithm and Its Application to Roller Bearing Fault Diagnosis
,”
J. Vib. Control
,
21
(
12
), pp.
2434
2445
.
25.
Juhamatti
,
S.
,
Daniel
,
S.
,
Jan
,
L.
, and
Allan
,
T.
,
2019
, “
Detection and Identification of Windmill Bearing Faults Using a One-Class Support Vector Machine (SVM)
,”
Measurement
,
137
(
1
), pp.
287
301
.
26.
Widodo
,
A.
,
Kim
,
Y. E.
,
Son
,
D. J.
,
Yang
,
B. S.
,
Tan
,
C. A.
,
Dong
,
S. G.
,
Byeong
,
K. C.
, and
Mathew
,
J.
,
2009
, “
Fault Diagnosis of Low Speed Bearing Based on Relevance Vector Machine and Support Vector Machine
,”
Expert Syst. Appl.
,
36
(
3
), pp.
7252
7261
.
27.
Saimurugan
,
M.
,
Ramachandran
,
K. I.
,
Sugumaran
,
V.
, and
Sakthivel
,
N. R.
,
2011
, “
Multi Component Fault Diagnosis of Rotational Mechanical System Based on Decision Tree and Support Vector Machine
,”
Mech. Syst. Signal Process
,
38
(
4
), pp.
3819
3826
.
28.
Widodo
,
A.
, and
Yang
,
B. S.
,
2007
, “
Support Vector Machine in Machine Condition Monitoring and Fault Diagnosis
,”
Mech. Syst. Sig. Process.
,
21
(
6
), pp.
2560
2574
.
29.
Kumar
,
A.
, and
Kumar
,
R.
,
2017
, “
Time-Frequency Analysis and Support Vector Machine in Automatic Detection of Defect From Vibration Signal of Centrifugal Pump
,”
Measurement
,
108
(
1
), pp.
119
133
.
30.
Liu
,
R.
,
Yang
,
B.
,
Zhang
,
X.
,
Wang
,
S.
, and
Chen
,
X.
,
2016
, “
Time-Frequency Atoms-Driven Support Vector Machine Method for Bearings Incipient Fault Diagnosis
,”
Mech. Syst. Signal Process
,
75
(
1
), pp.
345
370
.
31.
Yang
,
J.
,
Youyun
,
Z.
, and
Yongsheng
,
Z.
,
2007
, “
Intelligent Fault Diagnosis of Rolling Element Bearing Based on SVMs and Fractal Dimension
,”
Mech. Syst. Signal Process
,
21
(
5
), pp.
2012
2024
.
32.
Fan
,
Y.
,
Chao
,
Z.
,
Yu
,
X.
,
Jianguo
,
W.
, and
Fengshou
,
G.
,
2020
, “
A Bearing Fault Diagnosis Using a Support Vector Machine Optimised by the Self-Regulating Particle Swarm
,”
Shock Vib.
,
2020
(
1
), pp.
1
11
.
33.
Yoshimoto
,
S.
,
Yamamoto
,
M.
, and
Toda
,
K.
,
2007
, “
Numerical Calculations of Pressure Distribution in the Bearing Clearance of Circular Aerostatic Thrust Bearings With a Single Air Supply Inlet
,”
ASME J. Tribol.
,
129
(
2
), pp.
384
390
.
34.
Wang
,
J.
,
Xu
,
M.
,
Zhang
,
C.
,
Huang
,
B.
, and
Gu
,
F.
,
2020
, “
Online Bearing Clearance Monitoring Based on an Accurate Vibration Analysis
,”
Energies
,
13
(
2
), p.
389
.
35.
Dawoud
,
M.
,
Beitler
,
S.
, and
Schwarze
,
H.
,
2023
, “
Slip Characteristics in Cylindrical Roller Bearings—Part III: Influence of Bearing Clearance on the Roller and Set Slip
,”
ASME J. Tribol.
,
145
(
2
), p.
021205
.
36.
Fingerle
,
A.
,
Hochrein
,
J.
,
Otto
,
M.
, and
Stahl
,
K.
,
2020
, “
Theoretical Study on the Influence of Planet Gear Rim Thickness and Bearing Clearance on Calculated Bearing Life
,”
ASME J. Mech. Des.
,
142
(
3
), p.
031102
.
37.
Childs
,
D. W.
,
2003
, “
Twice-Running-Speed Response Due to Elliptical Bearing Clearances
,”
ASME J. Vib. Acoust.
,
125
(
1
), pp.
64
67
.
38.
Taylor
,
E. S.
,
1975
, “
Dimensional Analysis for Engineers
,”
J. Fluid Mech.
,
68
(
2
), p.
416
.
39.
Desavale
,
R. G.
,
Kanai
,
R. A.
,
Chavan
,
S. P.
,
Venkatachalam
,
R.
, and
Jadhav
,
P. M.
,
2015
, “
Vibration Characteristics Diagnosis of Roller Bearing Using the New Empirical Model
,”
ASME J. Tribol.
,
138
(
1
), p.
011103
.
40.
Desavale
,
R. G.
,
2019
, “
Dynamics Characteristic and Diagnosis of a Rotor-Bearing's System Through a Dimensional Analysis Approach: An Experimental Study
,”
ASME J. Comput. Nonlinear Dyn.
,
14
(
2
), p.
014501
. doi.org/10.1115/1.4041828
41.
Lazovic
,
T.
,
Ristivojevic
,
M.
, and
Mitrovic
,
R.
,
2008
, “
Mathematical Model of Load Distribution in Rolling Bearing
,”
FME Trans.
,
36
(
1
), pp.
189
196
.
42.
Yang
,
R.
,
Jin
,
Y.
,
Hou
,
L.
, and
Chen
,
Y.
,
2017
, “
Study for Ball Bearing Outer Race Characteristic Defect Frequency Based on Nonlinear Dynamics Analysis
,”
Nonlinear Dyn.
,
90
(
2
), pp.
781
796
.
43.
Choudhury
,
A.
, and
Tandon
,
N.
,
2006
, “
Vibration Response of Rolling Element Bearing in a Rotor Bearing System to a Local Defect Under Radial Load
,”
ASME J. Tribol.
,
128
(
2
), pp.
252
261
.
44.
Wu
,
T. Y.
,
Chung
,
Y. L.
, and
Liu
,
C. H.
,
2010
, “
Looseness Diagnosis of Rotating Machinery Via Vibration Analysis Through Hilbert–Huang Transform Approach
,”
ASME J. Vib. Acoust.
,
132
(
1
), p.
031005
.
45.
Huang
,
B.
,
Feng
,
G.
,
Tang
,
X.
,
Gu
,
J. X.
,
Xu
,
G.
,
Cattley
,
R.
,
Gu
,
F.
, and
Ball
,
A. D.
,
2019
, “
A Performance Evaluation of Two Bispectrum Analysis Methods Applied to Electrical Current Signals for Monitoring Induction Motor-Driven Systems
,”
Energies
,
12
(
8
), p.
1438
.
46.
Tian
,
X.
,
Gu
,
J. X.
,
Rehab
,
I.
,
Abdalla
,
G. M.
,
Gu
,
F.
, and
Ball
,
A. D.
,
2018
, “
A Robust Detector for Rolling Element Bearing Condition Monitoring Based on the Modulation Signal Bispectrum and Its Performance Evaluation Against the Kurtogram
,”
Mech. Syst. Signal Process.
,
100
(
1
), pp.
167
187
.
47.
Guo
,
J.
,
Zhen
,
D.
,
Li
,
H.
,
Shi
,
Z.
,
Gu
,
F.
, and
Ball
,
A. D.
,
2019
, “
Fault Feature Extraction for Rolling Element Bearing Diagnosis Based on a Multi-stage Noise Reduction Method
,”
Measurement
,
139
(
1
), pp.
226
235
.
48.
Rehab
,
I.
,
Tiana
,
X.
,
Hu
,
N.
,
Yan
,
T.
,
Zhang
,
R.
,
Gu
,
F.
, and
Ball
,
A. D.
,
2016
, “
A Study of Two Bispectral Features From Envelope Signals for Bearing Fault Diagnosis
,”
Proceedings of the 1st International Conference on Maintenance Engineering
,
Manchester, UK
,
Aug. 30–31
, pp.
1
8
.
49.
You
,
K. J.
,
Noh
,
G. J.
, and
Shin
,
H. C.
,
2016
, “
Spectral Gini Index for Quantifying the Depth of Consciousness
,”
Comput. Intell. Neurosci.
,
16
(
1
), pp.
1
12
.
50.
Miao
,
Y.
,
Zhao
,
M.
, and
Lin
,
J.
,
2017
, “
Improvement of Kurtosis-Guided-Grams Via Gini Index for Bearing Fault Feature Identification
,”
Meas. Sci. Technol.
,
28
(
1
), pp.
125001
12
.
51.
Jagadeesha
,
T.
,
Salunkhe
,
V. G.
,
Desavale
,
R. G.
,
Patil
,
P. B.
,
Kumbhar
,
M. B.
, and
Koli
,
A. R.
,
2021
, “Investigation of Crack Detection Technique in a Rotating Shaft by Using Vibration Measurement,”
Advances in Industrial Automation and Smart Manufacturing. Lecture Notes in Mechanical Engineering
,
A.
Arockiarajan
,
M.
Duraiselvam
, and
R.
Raju
, eds.,
Springer
,
Singapore
.
52.
Kumbhar
,
M. B.
,
Salunkhe
,
V. G.
, and
Borgaonkar
,
A. V.
,
2020
, “
Mathematical Modeling and Experimental Evaluation of an Air Spring–Air Damper Dynamic Vibration Absorber
,”
J. Vib. Eng. Technol.
,
9
(
1
), pp.
781
789
.
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