fault diagnosis of induction motors using signal processing based methods and optimal feature selection

공학박사 학위논문
최적 특징 선택과 신호처리기법을 이용한
유도전동기 고장 진단
Fault Diagnosis of Induction Motors using Signal
Processing based Methods and Optimal Feature
Selection


울산대학교 대학원
전기전자정보시스템공학부
웬 옥 투
최적 특징 선택과 신호처리기법을 이용한
유도전동기 고장 진단
Fault Diagnosis of Induction Motors using Signal
Processing based Methods and Optimal Feature
Selection
지도교수 이홍희
이 논문을공학박사학위 논문으로 제출함
2008 년 12 월
울산대학교 대학원
전기전자정보시스템공학부
웬 옥 투
Fault Diagnosis of Induction Motors using
Signal Processing based Methods and
Optimal Feature Selection
Ngoc-Tu Nguyen
A thesis submitted to the School of Electrical Engineering in fulfillment of the
thesis requirements for the degree of Doctor of Philosophy in the Graduate
School, University of Ulsan

December 2008

i
Abstract

Fault detection and diagnosis in rotating machines have been used widely in commercial
systems over the past few decades. Numerous works on machine conditions have been
implemented with the aid of the MCSA (Motor Current Signature Analysis) method, the
vibration-based methods, etc. The purpose of these methods is to detect and diagnose faults in
an early stage and therefore allow contingency plans to be put into place before the problems
worsen. The dynamic and vibratory behaviours of the machine, such as vibration, sound, and
temperature… are affected if the running condition is changed. The behaviours can be useful
indicators to detect problems within the machine as they vary abnormally from a standard when
a fault occurs. Of the many signals which can be measured, the vibration signal has been the
most useful to monitor the machine condition as in many cases the time domain vibration
signals are sufficient to diagnose and can be easily measured with accelerometers.

The signal processing methods for induction motor fault detection have recently received great
attention because they do not need a typical mathematical model. Many signal processing
diagnostic procedures have been studied in this work to identify faults of the machines. The
decision tree, support vector machine (SVM), artificial neural network (ANN), adaptive neuro-
fuzzy inference system (ANFIS), and k-nearest neighbour (K-NN) have been applied to
diagnose the condition of machines with rather high accuracy. These methods have used
vibration data as an indicator for monitoring the fault conditions. In this work, the vibration
data are measured in three dimensions to collect as much information as possible. Then an
optimal feature selection is proposed in this work for improving the classification performance
of the diagnostics system. The classification results have proved the efficiency of the proposed
optimal feature selection and the suitability of vibration data as an indicator for induction motor

fault diagnosis.









ii
Acknowledgements
University of Ulsan, Ulsan, Korea
School of Electrical Engineering
Ngoc-Tu Nguyen

This work has been carried out in Industrial Network and Power Electronics Laboratory,
School of Electrical Engineering, University of Ulsan. The work has been done during 2005-
2008 under the support of the Research Fund of University of Ulsan and the Network-based
Automation Research Center (NARC).

I would like to thank my supervisor of this work, Professor Hong-Hee Lee, for his helping and
interest in my research work that give me the opportunity to carry out this thesis. I would also
thank all people in my laboratory, especially Jeong-Min Kwon, for helping me greatly during
the research. Additionally, I wish to thank Huyndai Heavy Industries (HHI) for supporting the
faulty motors.

I would like to thank the examiners of this thesis, Professor
Young-Soo Suh, Professor Jin
Hur,

Professor Myeong-Jae Yi, and Professor Heung-Geun Kim for their valuable
comments and corrections.
















iii
Table of Contents

Abstract i
Acknowledgements ii
Table of Contents iii
List of Figures v
List of Tables vii
Abbreviations viii
1. Introduction
1.1 Background and motivation
1.2 Previous works

1.3 Objective and contribution
1.4 The structure of the thesis
1
1
3
6
7
2. Understanding the Basis of Induction Motor Faults
2.1 Bearing Damage
2.2 Electrical Induced Faults
2.3 Others
9
9
12
16
3. Methods for Fault Diagnosis of Induction Motor
3.1 FFT-based method
3.1.1 Case study 1 – Looseness case
3.1.2 Case study 2 – Stator winding fault
3.1.3 Case study 3 – Rub fault
3.1.4 Case study 4 – Unbalance Rotor
3.2 Model-based methods
3.3 Signal processing-based methods
3.3.1 ANFIS
3.3.2 K-Nearest Neighbor
3.3.3 Decision Tree
3.3.4 Random Forest
3.3.5 Support Vector Machine
23
23

23
24
24
25
25
26
26
27
29
32
33
4. Vibration Measurements 36
5. Experimental Results
5.1 Genetic Algorithm
5.2 Feature Selection
41
41
41

iv
5.2.1 Genetic algorithm based feature selection
5.2.2 Principal Component Analysis
5.3 Some Experimental Results
5.3.1 K-Nearest Neighbor
5.3.2 Decision Tree
5.3.2.1 Decision Tree using PCA based feature extraction
5.3.2 2 Decision Tree using GA based feature selection
5.3.3 Random Forest
5.3.4 Support Vector Machine
5.3.5 ANFIS

5.4 Summary
42
44
47
47
51
51
54
58
62
65
71
6. Conclusions 74
References 75
Publications 79

v
List of Figures

Fig. 1 Typical causes for machine failures.
Fig. 2 Bearing structural defects.
Fig. 3 Ball bearing geometry.
Fig. 4 Bearing time-domain vibration signals and FFT spectrum, (a) normal, and (b) defective
bearing.
Fig. 5 Frequency domain and time domain vibration signals of a rotor unbalance case in three
directions.
Fig. 6 Frequency domain and time domain vibration signals of a stator unbalance case in three
directions.
Fig. 7 Frequency domain and time domain vibration signals of a rub case in three directions.
Fig. 8 Frequency domain and time domain vibration signals of a distortion case in three
directions.
Fig. 9 Frequency domain and time domain vibration signals of a misalignment case in three
directions.
Fig. 10 Vibration spectrums (a) in radial direction (b) in axial direction.
Fig. 11 Vibration spectrums of case study 2
Fig. 12 Vibration spectrums (a) in radial direction (b) in axial direction
Fig. 13 Vibration spectrums in radial direction.
Fig. 14 General model based fault detection scheme.
Fig. 15 An adaptive network-based fuzzy inference system
Fig. 16 An example of a k-NN classification. The test pattern x can be classified either as

positive or negative class.
Fig. 17. Typical structure of a decision tree.
Fig. 18. Hyperplanes for the SVM trained with two-class samples.
Fig. 19 Experimental setup.
Fig. 20 Accelerometer (a) is used in this work and induced faults (b) rotor unbalance, (c)
bearing damage and (d) sensor measuring position.
Fig. 21 Time signal waveforms in 3 dimensions (Horizontal-Axial-Vertical): (a) Bearing
damage (b) Bearing looseness (c) Rotor unbalance (d) Stator fault (e) Normal condition.
Fig. 22 GA process.
Fig. 23 Weighted values of 18 features given by the genetic algorithm.
Fig. 24 (a) Normal bearing (horizontal, axial, and vertical); (b) Defective bearing time signals.

vi
Fig.25 Extracted features, (-, blue) normal and ( , red) defective bearing.
Fig.26 The projection of the training data on the first three axes.
Fig. 27 Classification results of the conventional k-NN (-, square) and proposed k-NN ( ,
triangle) according to k; (a) evaluated with three, (b) four, (c) five, (d) six, and (e)
seven features (vertical axis is the average accuracy, horizontal axis is k).
Fig. 28 Decision tree without feature extraction.
Fig. 29 PCA-based decision tree with 9 new features.
Fig. 30 PCA-based decision tree with 4 new features.
Fig. 31 Decision tree with all features.
Fig. 32 Decision tree with 3 selected features.
Fig. 33 RF classification result of case 1. The test data classification error is 7.506%.
Fig. 34 RF classification result of case 2. The test data classification error is 7.748%.
Fig. 35 RF classification result of case 3. The test data classification error is 4.843%.
Fig. 36 RF classification result of case 4. The test data classification error is 4.358%.
Fig. 37 RF classification result of case 5. The test data classification error is 5.327%.
Fig. 38 Some bearing training patterns, defective (-) and normal ( ).
Fig. 39 Input membership functions (training with 150 epochs) (a) before training, (b) after

training, and (c) targets and ANFIS system output.
Fig. 40 Input membership functions (training with 80 epochs), (a) before training, (b) after
training, and (c) targets and ANFIS system output.















vii
List of Tables

Table 1: Time-domain features
Table 2: The 10 largest weight features
Table 3: The conventional k-NN classifier performance before and after feature selection
Table 4: The weighted k-NN classifier performance before and after feature selection
Table 5: Performance for the SVM classifier
Table 6: Compare the performance of normal decision tree and PCA based decision tree
Table 7: k-NN classifier performance before and after feature selection
Table 8: Decision tree performance before and after feature selection
Table 9: SVM classifier performances before and after feature selections

Table 10: Decision tree (DT) performances before and after feature selections
Table 11: Performance comparison for SVM classifier (under the same condition)
Table 12: Local optimum parameters are obtained from GA algorithm
Table 13: Performance comparison on multi faults diagnosis
Table 14: The main advantages and disadvantages of classifiers



















viii
Abbreviations

ANFIS adaptive neuro-fuzzy inference systems
ANN artificial neural network
BP back-propagation

DT decision tree
F feature
FFT fast Fourier transform
GA genetic algorithm
ICA independent component analysis
K-NN k nearest neighbors
MCSA motor current signature analysis
PCA principal component analysis
SVM support vector machine
X rotating frequency






- 1 -
1. Introduction

1.1 Background and motivation
Major rotating machinery may have very high cost, once machinery is shut-down then not only
affect the financial losses but also human lives. Therefore, maintenance of rotating machine is an
important factor to minimize the losses and keep the machine in good condition. In recent years,
diagnostic techniques have changed to increase the performance of rotating machine fault detection.
That because induction motors are becoming an increasingly important aspect of industrial
processes. The purpose of monitor condition or diagnosis of induction motor is to detect and
diagnose faults in an early stage and therefore allow contingency plans to be put into place before
the problems worsen. It can be achieved either manually or on the basis of the expert system.

The machines are designed to generate mechanical power from an energy source or convert

mechanical power to electrical power, etc. They therefore create forced vibration and dynamic
stresses when are operated. The dynamic and vibratory behaviours of the machine, such as
vibration, sound, and temperature, are affected if the running condition is changed. Then, these
behaviors can be useful indicators to detect problems within the machine as they vary abnormally
from a standard when a fault occurs. For electrical machinery, the abnormal vibratory behaviors
can be caused by either mechanical or electromagnetic defects. The latter can be isolated by
removing power then the vibration caused by electrical or magnetic defects will disappear.
Vibration caused by electrical problems can be analyzed to determine the nature of the defect. For
example, a defect such as stator winding fault produces two times line frequency component. A
broken rotor bar produces 1X component with two times slip frequency sidebands.

The quality and effectiveness of a diagnosis procedure is most often limited by the availability of
capable and skilled personnel. With the equipments becoming more and more complex,
maintenance personnel have to help setup and establish the maintenance program. They may also
assess the condition of the machine by comparing acquired data with healthy data. Based on their
knowledge of machinery and working experience, they will be able to determine whether an
abnormal symptom is due to a defect, or to a change in operating condition. However, this task is
difficult even for experts because of a great amount of machinery knowledge and the influence of
the environmental noises. A major problem with rotating machinery is, they run smoothly for a


- 2 -
long time and then suddenly develop a defect. The defect may slowly increase and deteriorate the
condition of the machine or suddenly develop into a shutdown condition. It is difficult and also too
expensive for the industry to employ maintenance personnel dealing with machinery problems and
wait for an opportunity to diagnose an impending problem that may occur in the machine. That is
when intelligent classification systems have been developed to assist the machine fault diagnosis
tasks by processing the fault data. Up to now, there are many algorithms have been studied for this
goal.

With the knowledge of the machine behavior based on its design and operation that can be
collected over time, it is possible to perform a diagnostic analysis of the machine under trouble.
Instead of using maintenance experts, an expert system using the knowledge-base of the machine
can be used, so that the diagnostic decision can be quickly given whenever a fault occurs without
employing the experts. Most machine fault diagnosis systems utilize the expert system, which is
mainly based on vibration symptoms or stator currents. The principle of this method is the fact that
the fault inside the machine structure can be visible as distinct frequency components in the
spectrum. The expert system can operate based on previously defined knowledge-base. It basically
consists of two parts, the data or knowledge-base and the inference engine, which is the diagnosis
part. The knowledge-base will be in general based on experience in carrying a particular task and
be gathered in a period of time. An expert system can only be good if it possesses a good
knowledge-base. When a problem is sensed in the machine, the symptoms can be measured or
observed and using the knowledge-base, the inference engine can applied to identify the possible
defects.

The condition monitoring techniques have changed over years as the machines became more
sophisticated with increasing capacities and speeds. Such techniques are initially done by recording
the time domain signal and then using some procedures to extract the certain components, i.e.
frequency components or statistical characteristics. Then the diagnostic processes are applied using
that processed data. In the past, these consume time and depend on the experience of operating
experts. In recent years with the development of microprocessors, personal computers and analog
to digital converters, diagnostic process through computer programs is becoming a standard
practice. The real time condition monitoring and diagnosis are becoming the realistic and effective
techniques.


- 3 -

The work deals with some basics of understanding of induction motor faults, signal based
processing methods for monitoring the condition of induction motor, the optimal feature selection

using distance based criterion is considered to remove the irrelevant and redundant information in
data set. The thesis will be limited to vibration condition monitoring, through there could be some
other useful indicators, for example, stator current.
Since the most common faults of induction motors are rotor faults, stator faults, and bearing faults,
four types of faults are simulated and classified in this work, namely, bearing looseness, bearing
damage, rotor unbalance, and stator fault.

1.2 Previous works
In recent years, rotating machine fault diagnostic technology continues to grow rapidly. Many kind
of intelligent diagnostic methods have been developed, such as artificial neural network, fuzzy
technology, decision tree, adaptive network-based fuzzy inference system, support vector machine,
k-nearest neighbour, etc. Those methods can use different machine condition indicator, such as
current, voltage, speed, efficiency, temperature and vibrations. Fault detection based on machine
current or voltage relies on interpretation of the frequency components in the spectrum. But it only
can diagnose the electrical related and certain mechanical problems, such as broken rotor bar,
broken rotor end ring, eccentricity, stator windings or power supply problems, bearing defects.
Nowadays, a principal tool for diagnosing machinery problems has been the vibration analysis.
That because the physical movement or motion of a rotating machine is normally referred to as
vibration. Almost common machine faults can be detected by analyzing the vibration data.

The classification methods can be divided into three groups: signal processing based methods,
model based methods, and FFT based methods.
The FFT based methods are relied on the following principles:
- The machine problems have distinct frequency components that can be isolated and identified.
- The FFT signature of a machine is compared over time, a problem can be detected if there are
some changes in the FFT pattern, i.e. the amplitude of each frequency component will remain
constant until there is a change in the operation dynamics of the machine.
However, an increase or decrease in amplitude may indicate degradation of the machine, but is not
always caused by a problem. Variation in load, operation, and other normal changes also generate

- 4 -
a change in the amplitude of one or more frequency components within the FFT signature.
Therefore, it is important for FFT based method that the knowledge of machine faults be clearly
understood. Motor current signature analysis (MCSA) is a typical FFT based method which
analyses the frequency components of stator current signals. The fundamentals of MCSA are
illustrated via industrial case histories (W. T. Thomson et al. 2003 [21]). But the FFT based
method is required operator persons with expert knowledge to make the final decision to either
immediately repair the motor or let it run and prepare for a rectified plan.

In order to replace the role of experts, the model and signal processing based methods have been
developed to keep checking the data signatures continuously. The signal processing based methods
for fault detection have recently received great attention because it does not need a typical
mathematical model. Many signal processing diagnostic procedures have been introduced to
identify faults of the machines. The decision tree is proposed to diagnose the rotating machine and
bearing condition (V. Sugumaran et al. 2007 [1], W. Sun et al. 2007 [2], B. S. Yang et al. 2000 [3],
D. S. Lim et al. 2000 [4]). The support vector machine (Y. Yang et al. 2007 [5], A. Widodo et al.
2007 [6, 8], J. Yang et al. 2007 [7], A. Rojas et al. 2006 [9]), artificial neural network (B. Samata
et al. 2003, 2006 [10, 11], L. B. Jack et al. 2002 [12], B. Li et al. 2000 [13], A. Saxena et al. 2007
[14]), adaptive neuron-fuzzy inference system (Y. Lei et al. 2007 [15], Z. Ye et al. 2006 [16]), and
fuzzy logic (T. Lindh et al. 2004 [18]) have been applied to diagnose the condition of machines
with rather high accuracy. Most of the methods have used vibration data as an indicator for
monitoring the fault conditions. In addition to these signal processing methods, which are based on
characteristic analysis in the time or frequency domains, the model based methods are another way
to diagnose machine fault. The model based fault detection for an induction motor is based on
analytical redundancy (C. Combastel et al. 2002 [23], K. Kim et al. 2002 [24]). Due to the
availability of the mathematical model, it is possible to model the electrical behaviour of an
induction motor and is widely used to detect electrically related faults such as the rotor bar and
stator winding faults. However, this method requires an accurate mathematical model and is
difficult to compensate for the uncertainties in practical applications. Further, not all faults can be

simulated by the model; however, for such cases, signal processing can be applied to design the
model. The FFT based signal processing technique (H. S. Lim et al. 2006 [25]) is used in
combination with a model-based method to estimate fault features, and while this is an effective
method, it is applied only for two-condition situations.


- 5 -

Decision tree is concerned as a diagnostic tool in [1-4]. B. S. Yang et al. 2000 [3] and D. S. Lim et
al. 2000 [4] have been developed decision trees for motor fault diagnosis based on Sohre’s cause-
result matrix [43]. However, those systems can only be operated by experts and the input data can
not imported without considering of maintenance personnel. Those systems can give the high
reliability but need a great amount of machine knowledge. W. Sun et al. 2007 [2] have recently
developed decision tree using PCA algorithm. In that research, the authors use PCA to reduce
features after data collection, preprocessing and feature extraction. Then, C4.5 is trained by using
the samples to generate a decision tree model. But even PCA is an effective technique to reduce
data dimension, but sometimes it can remove some useful information in the dataset. Together with
a linear classification method as decision tree, k-nearest neighbour has also recently been applied
successfully for fault diagnosis of induction motor (R. Casimir et al. 2006 [29]) with stator current
and voltage features.

The support vector machine (Y. Yang et al. 2007 [5], A. Widodo et al. 2007 [6, 8], J. Yang et al.
2007 [7], A. Rojas et al. 2006 [9]) is applied successfully to diagnose the motor and bearing
condition with many data processing techniques such as fractal dimension, IMF envelope spectrum,
independent component analysis, nonlinear feature extraction. Support vector machine in those
researches has classification performance that outperforms many other methods. In this work,
support vector machine is also studied with the proposed optimal feature selection.

Artificial neural network (B. Samata et al. 2003, 2006 [10, 11]) has been applied to fault bearing
detection using time-domain features. Genetic algorithm is used to select the characteristic

parameters of the classifier and the input feature. L. B. Jack et al. 2002 [12], B. Li et al. 2000 [13],
A. Saxena et al. 2007 [14] have investigated neural network for applying to intelligent fault
diagnosis of rotating machine. However, the neural network model basically has poor
generalization ability, so that it can not predict the novel samples well. Fuzzy logic (T. Lindh et al.
2004 [18], G. Goddu et al. 1998 [19]) has been applied to bearing fault classification because it can
mimic human decisions. But it is difficult to tune its parameters in order to maximize the reliability
of the system. Combining the power of artificial neural network and fuzzy logic, adaptive neuron-
fuzzy inference system (Y. Lei et al. 2007 [15], Z. Ye et al. 2006 [16]) has been introduced for
machine fault diagnosis with good classification performance.


- 6 -

Although many classification algorithms are available for study, the research comparison (G. Niu
et al. 2007 [26]) shows no single algorithm has the best performance in all cases. Taking this into
account, some special data processing can be considered to guarantee good classification results.
Many methods have been suggested for data preparation; two common ones are feature selection
and feature extraction. Further, principal component analysis (PCA) and independent component
analysis (ICA) are two popular feature extraction techniques used to decrease data dimensions by
extracting as much information as possible from a given data set. In addition, decision tree using
the PCA technique for fault diagnosis have been shown to provide encouraging results (W. Sun et
al. 2007 [2]); however, for the purpose of feature selection, distance criterion has been effectively
used in many research studies, although it should be noted that some researchers have used GA to
choose the most appreciated features in a feature set (B. Samanta et al. 2003, 2006 [10, 11], Y. Lei
et al. 2007 [15]). Selection of the highest qualified features can help to improve system
performance as well as remove useless features that can spoil the performance of a diagnosis.

1.3 Objective and contribution
The work focuses in signal processing based methods with optimal feature selection. In this work,
the data for signal processing based methods is obtained from time domain vibration signals. To

improve the classification performance, an optimal feature selection is required that reduces the
data dimension and removes the irrelevant and redundant information in the data. For these
purposes, principal component analysis, and GA have been introduced. For data preprocessing,
there are two ways to apply: feature selection and feature extraction. The feature extraction
methods such as PCA (or ICA) can be used to extract useful information, although these
approaches both require alteration of the original data. Conversely, feature selection is a technique
that selects a small subset within a dataset and does not change the original data. If all the data are
used as input of the classifier, they may make the classification processes become slower and
reduce the system performance. Therefore, the most difficult task for improving the system
performance of the proposed methods is to select proper important features. Here, we propose a
simple selection method based on distance criterion and GA that provides high efficient method for
classifying an induction motor fault. Feature extraction using PCA methods is also tested and
applied to bearing fault detection.



- 7 -
Vibration data measurements can be a useful motor fault indicator. A tri-axial accelerometer is
installed to collect the vibration signals in x, y, and z directions. The efficiency of vibration
measurements as a fault indicator has been verified in the thesis. Tri axial vibration data can make
extending the range of target without caring of direction of vibration amplitude due to motor
installation.

Another goal of this work is the evaluation of signal processing based methods with applying the
proposed optimal features and vibration data, such as k-nearest neighbor, support vector machine,
decision tree, random forest, etc. The vibration data with optimal feature selection are applied to
these methods and obtained promising results.

1.4 The structure of the thesis
The first part shows some introduction of fault condition monitoring techniques. The rapid

development and importance of the machine fault diagnosis over years and the goal of this work
are introduced briefly. The second part describes some basis knowledge of machine failures such as
bearing damage, stator unbalance and rotor unbalance. As the availability of accurate sensors and
fast computers, many techniques have been studied to analyze the machine condition. The third
part of this thesis introduces some methods for rotating machine fault diagnosis: decision tree,
SVM, K-NN, random forest, etc. The next part shows the experimental setup and diagnosed results
of signal processing based methods. Finally are the conclusions and given future works.

Chapter 1 is above briefly introduction.

Chapter 2 presents the basic knowledge of induction motor faults, such as bearing faults, electrical
induced faults and the other faults. It also shows the time-domain signals and their FFT in three
directions. Some descriptions and characteristics of the faults are discussed.

Chapter 3 introduces methods that are used for diagnosing induction motor faults. FFT based
method, model based methods, and signal processing based methods are discussed.

Chapter 4 presents the measurement and experimental setup used in this work. The data set are
formed by 18 time-domain vibration signal features.


- 8 -

Chapter 5 shows some results of signal processing based methods. It also compares the
classification performances with and without using feature selection.

Chapter 6 concludes the thesis and gives some suggestions for future work.

- 9 -
2. The Basic Knowledge of Induction Motor Faults

The design and operating characteristics of a machine determine both the type of defects and the

vibration response to those defects. Vibration analysis is difficult without a working knowledge of
these characteristics. The condition of the machine will affect the vibration response of the machine
on the shaft, bearings, housing, foundation, etc. There are many causes that generate the failure as
shown in Fig.1 and these causes should be removed as fast as possible to have the machine working
in a good condition.
Bearing re lated
faults
41%
Stator rel ated faults
37%
Rotor related faults
10%
Other s
12%
Beari ng related faults
Stator related faults
Rotor re lated faul ts
Others

Fig. 1 Typical causes for machine failures.

About 41% of failures are caused by bearing problems, 37% by stator, 10% by rotor, and 12% by
other problems. The symptoms of the machine and the causes are related to each other, the more
we know how to analyze the symptoms, the more we can find ways to identify the causes.
Therefore, understanding the basis knowledge of machine faults is necessary for the fault detection
of induction motor. A good maintenance practice requires a good understanding of the causes in the
machine.

2.1 Bearing Damage
Rolling-elements bearings are the most common cause of machine failure. The dynamic

performance of motor bearing is highly influential on the performance of the entire motor system.


- 10 -
Therefore, an early detection of their damage is advantageous in keeping the downtime of a
machine to a minimum. Faulty bearing can cause the system to function incorrectly, and cause
vibration increase at some specific frequencies that result from bearing defects depend on the
defect, the bearing geometry, and speed of rotation. These frequencies are fundamental cage
frequency, ball pass outer raceway frequency, ball pass inner raceway frequency, and ball rotating
frequency.



Fig. 2 Bearing structural defects.

Ball pass outer raceway frequency f
outer
appears when the rolling elements are not on the best road
and can be calculated as:

1cos
2
r
outer c
f
BD
fnfn
PD
θ
⎛⎞

== −
⎜⎟
⎝⎠
(1)

Ball pass inner raceway frequency f
inner
appears when the shaft is not ideally circular:

()
1cos
2
r
inner r c
f
BD
fnffn
PD
θ
⎛⎞
=−= +
⎜⎟
⎝⎠
(2)

Ball rotating frequency f
ball
appears if a rolling element is not circular but has edges:

Outer race

Inner race
Balls
Cage


- 11 -
2
2
2
1cos
2
r
ball c
fPD BD
fnf
BD PD
θ
⎛⎞
== −
⎜⎟
⎝⎠
(3)

Fundamental cage frequency f
c
appears when one rolling element has larger or less diameter:

1cos
2
r

cage c
f
BD
ff
PD
θ
⎛⎞
== −
⎜⎟
⎝⎠
(4)

Where θ is contact angle of bearing.
f
r
is the rotating frequency.
n is number of balls.
PD is the pitch diameter of bearing.
BD is the ball diameter.








Fig. 3 Ball bearing geometry.

If bearing geometry is not available, the inner raceway and outer raceway frequencies can be

approximated as 60% and 40% of the number of balls multiplied by the running speed, respectively.
This approximation is possible because the ratio of ball diameter to pitch diameter is relatively
constant for the bearings.

Time domain vibration signals and their FFTs are shown in Fig. 4 for normal and faulty bearing
(6206Z bearing type).

Pitch Diameter (PD)
Ball Diameter (PB)


- 12 -


Fig. 4 Bearing time-domain vibration signals and FFT spectrum, (a) normal, and (b) defective
bearing.

2.2 Electrical Induced Faults
Electrical faults are rotor problems, stator related problems. These faults produce vibration at 1X or
2 times of line frequency. The common feature is the amplitude will disappear when turn off the
power.
When stator damage or phase unbalance appears, vibration will be produced at 2 times of line
frequency. When rotor problems such as broken rotor bar or broken end-ring occurs, the 2 times of
slip frequency component and sidebands occur.

Rotor Unbalance
0 100 200 300 400 500 600 700 800 900 1000
0
2
4

6
8
10
12
14
16
18
Frequency (Hz)
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-100
-80
-60
-40
-20
0
20
40
60
80
Time (1/20000 sec)
Vibration (mV)
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-40
-30
-20
-10
0
10
20
30

40
Time (1/20000 sec)
Vibration (mV)
0 100 200 300 400 500 600 700 800 900 1000
0
2
4
6
8
10
12
Frequency (Hz)
(a)
(b)


- 13 -
0 50 100 150 200
0
1
2
3
4
5
6
7
8
H radial (Hz)
mV
0 50 100 150 200

0
1
2
3
4
5
6
7
8
A axial (Hz)
mV
0 50 100 150 200
0
1
2
3
4
5
6
7
8
V radial (Hz)
mV
0 500 1000 1500 2000 2500
-50
-40
-30
-20
-10
0

10
20
30
40
50
H radial
t/20000 sec
mV
0 500 1000 1500 2000 2500
-30
-20
-10
0
10
20
30
A axial
t/20000 sec
mV
0 500 1000 1500 2000 2500
-150
-100
-50
0
50
100
150
V radial
t/20000 sec
mV

Rotor unbalance is the major problem in most of the rotation machines. Pure unbalance vibrations
always occur at the rotor speed (1X). It is identified by a predominant 1X component in the
frequency domain. The particular characteristic of this fault is the amplitude increases with speed.
Rotor unbalance can be caused by broken rotor bars, broken rotor end ring, eccentricity, etc. The
rotor unbalance time domain signals and their frequency domain are shown in Fig. 5.
The motor parameters as follow: 5Hp, 220/380V, 4 poles, running frequency is 29.9 Hz.

















Fig. 5 Frequency domain and time domain vibration signals of a rotor unbalance case in three
directions.

Stator Unbalance
Stator faults are occurred in the stator core or in the stator windings. Stator winding faults can be
due to insulation damage, thermal damage caused by over current, or due to bad installation, etc.
Stator unbalance time domain signals and their frequency domain are shown in Fig. 6. Motor

parameters as follow: 3.7 kW, 4 poles, 220/380 V, voltage drop in 1 phase = 37 V, line frequency
is 60 Hz.
1X
1X
1X