JOURNAL OF CURRENT RESEARCH IN SCIENCE
ISSN 2322-5009
CODEN (USA): JCRSDJ
Available at www.jcrs010.com
JCRS
S (1), 2016: 771-780
A new diagnosis of severity broken rotor bar fault based modeling and image processing system
Hassan Divdel1, Mohammad Hosseinzadeh Moghaddam2, Ghafour Alipour3
1. Department of Electrical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2. Department of Computer Engineering, Hashtrood Branch, Islamic Azad University, Hashtrood,Iran
3. Department of Computer Engineering, Hashtrood Branch, Islamic Azad University, Hashtrood,Iran
Corresponding Author email: Hasan.divdel@gmail.com
K E Y W O R D S: fault based modeling, image processing, broken rotor bar, induction motor.
ABSTRACT: This paper proposes a new diagnosis of severity broken rotor bar fault based modeling and image
processing system approach. It is shown the rise of broken bars and load level increases harmonics of the stator
currents in the fault condition. Therefore, fully automatic pattern recognition methods are required to identify
induction motor severity broken rotor bar fault .this paper proposes a dynamic model to analyze broken rotor bar
fault in induction machines. In order to evaluate the ability of the proposed method several experiments are
performed and a sets of data are gathered before and after fault under noise condition. Simulations and experimental
results were performed to confirm the validity of the model.
Introduction
Induction motors are critical components of many industrial processes and are frequently integrated in commercially
available equipment. Safety, reliability, efficiency, and performance are some of the major concerns of induction motors
applications1. Although induction motors are reliable, they are subjected to some failures. Therefore, in the past two decades,
there has been substantial amount of research to provide new condition monitoring techniques for induction motors mostly
based on analyzing vibration signals, or other signals such as current, and hence a number of commercial tools are available in
this area1-7.
One of the most widely used techniques to obtain information on the health state of induction motors is based on the
processing of the stator line current. Typically in the motor fault diagnosis process, sensors are used to collect time domain
current signals2. In 1997, an adaptive statistical time-frequency method was used for the detection of bearing defects by stator
current analysis. The key idea in this method is to transform motor current into a time-frequency spectrum to capture the time
variation of the frequency components and to analyze the spectrum statistically to distinguish faulty conditions from the
normal operating condition of the motor. This method was used for broken rotor bar and bearing fault detection in 1999. In
recent years more advanced signal processing methods such as wavelet analysis and wavelet packet analysis have been used.
These methods require more computational effort and are not very successful in detecting defect location using motor current
signature analysis (MCSA). In order to overcome these problems, the idea of using park’s vector to precisely locate a fault and
at the same time to reduce the computational complexity was proposed by Angelo et al.3. That paper presents a dynamic model
suitable for computer simulation of induction machines in a healthy state and faulty state, Then based on the image processing
system identify rotor broken bars fault, as well as their correspondent severity and Finally to evaluate the ability of the
proposed method several experiments are performed, and a sets of data are gathered before and after fault under noise
condition. Simulations and experimental results were performed to confirm the validity of the model. This paper is organized
as follows: In Sec. II common faults of induction motors are listed. In the first part of Sec. II fault detection using stator phase
current signature is discussed. In the second part the symmetric model is introduced and in the next two part stator winding
fault and broken bars model are discussed. In the first part of Sec. III Concordia vector approach is introduced and in the next
two parts Pattern recognition approach and Image processing based systems are discussed. Finally the simulation results are
summarized in Sec. IV.
Problem Description
The common faults of induction motors can be classified as stator faults (inter-turn), rotor faults (broken rotor
bar/end-rings) and mechanical faults (bearing failures, air gap eccentricity). Approximately 40-50% of faults of induction
J. Curr. Res. Sci. Vol., S (1), 771-780, 2016
motors are bearing related faults, 30-40% are stator faults, and 5-10% are rotor faults8. Fig. 1 shows the general classification
of induction motors faults.
Fault Detection Using Stator Phase Current Signature
Stator phase current is measured directly using current transformer (CT) or current transducer, and then unwanted
high frequencies and noise components are filtered. For a certain time, depending on the selected frequency resolution, a
window of sampled points is recorded. The Fast Fourier transform (FFT) algorithm is then applied to obtain the stator current
spectrum or the signature. For a healthy motor this signature contains the fundamental supply frequency component and other
components are neglected. When a fault exists inside the motor some of frequency components magnitudes are increased with
respect to the fundamental component depending on fault type and severity. Thus, by identifying frequencies and magnitudes
of these components with respect to fundamental component, both fault type and severity can be addressed 8. This technique is
simple and requires only the measurement of one phase current. This reduces the cost of hardware and memory size required.
Fig. 2 and Fig. 3 show the effect of noise on the healthy and unhealthy motor respectively which the identification of noise
from the harmonics is difficult.
Symmetric Model
The voltage equations which describe the induction machines are established5. Some of the machines inductance
which are functions of the rotor speed, where upon the coefficients of the differential equations (voltage equations) which
describe the behavior of these machines, are time-varying except when the rotor is stalled. A change of variables described by
Eq. (5) is often used to reduce the complexity of differential equations. So the voltage
, the flux
and the current
can
be expressed in arbitrary reference frame. The equations for the stator and rotor flux are:
,
(1)
,
(2)
,
(3)
.
(4)
The subscript indicates the variables, the parameters and transformation associated with rotor circuit. The machine
electromagnetic torque (
, the load torque (
and the rotor velocity (
are related as,
.
(5)
Where is the rotor inertia and
is a damping coefficient associated to the mechanical rotational system of the
machine and mechanical load. The differential equations derived above can be solved by the fourth-order Runge-kutta method.
The stator and rotor currents can be obtained from:
,
(6)
,
(7)
,
(8)
.
(9)
Where
,
,
,
,
,
.
The parameters and
are stator and rotor self-inductance,
and
are stator and rotor leakage inductances and
is mutual inductance. The expression for the electromagnetic torque in terms of arbitrary reference frame for a p-pole
machine may be expressed as:
(
).
(10)
Stator winding fault
In this section, a model of induction motor which includes short circuit is applied, Leakage inductance of the winding
which is shorted, is obtained by the following equations, in these equations is the ratio of short period2.
(
,
(11)
,
(12)
),
,
,
,
(13)
(14)
(15)
(16)
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.
Where
,
,
,
(17)
,
,
,
and
.
Broken Bars Model Of Induction Motors
Fig. 4 shows a broken rotor bar in an induction motor which in such cases With regard to fault machine models, many
researchers have developed methods for the analysis of the steady state and dynamic behavior that are able to introduce a
specific fault. The dynamic models give the solution as instantaneous values from which the signal components can be
computed under quasi-steady state. With respect to simulate the defect of bar breaks, a defect resistance is added to the
corresponding element of the rotor matrix ,
[ ] [ ] [ ].
(18)
Solutions
Concordia Vector Approach
In three-phase induction motors, the connection to the main does not usually use the neutral, Therefore, the mains
current has no homopolar component. A two-dimensional (2-D) representation is based on the current Concordia vector,
sometimes erroneously called Park vector. The current Concordia vector components, (
are functions of mains phase
variables which are:
√
√
√
,
(19)
.
(20)
In ideal conditions, these-phase currents lead to a Concordia vector with the following components,
√
√
√
,
(21)
√
.
(22)
Where
is the supply phase current maximum value and
is the supply frequency. Fig. 5 shows the overall
structure of the stator currents acquisition that are transformed into equivalents two-phase using the Concordia conversion.
Pattern Recognition Approach
Most of the common methods used to identify and classify a faulty induction motor are based on the analysis of the
stator currents. The proposed approach also uses the analysis of stator currents, however, in this methodology the problem is
converted into a pattern recognition analysis. Thus, considering a three-phase induction motor without neutral connection,
ideal conditions for the motor and an unbalanced voltage supply, the stator currents are given by Eq. (23), where , and
denote the three stator currents,
their maximum value, their frequency, their phase angle and denotes time,
(
) .
(23)
(
)
In the proposed approach the currents are recognized as typical patterns for each faulty mode. This is accomplished
by analyzing them in a 2-D current state space by using Concordia vector approach. For a healthy motor the corresponding
current pattern is a circle centered at the origin of the coordinates of expression (23) where R denotes its radius so,
.
(24)
For an induction motor working in a faulty mode, the previous pattern is no longer valid. So, with some rotor broken bars the
current pattern is no longer a circle but a donut pattern is obtained.
{
Image Processing Based System
In order to implement the proposed pattern recognition based fault detection algorithm, a feature-based recognition
procedure of the stator current pattern, independent of their shape, size and orientation must be obtained. The key point to
solve this problem is to find efficient invariant features. Particular attention is paid to visual-based features obtained in the
image processing system.
The proposed image-processing algorithm is divided into three steps: the stator current Park transformation, the image
composition, and the feature extraction. The inputs for the image processing based system are the three-phase stator currents
and the output is the identification of the motor working condition. In the image composition step, the three-phase stator
current vector is converted into a binary image contour.
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The last step of image-processing algorithm is the features extraction. Once a digital image has been segmented,
measurements can be performed to scrutinize the shape and size of the spatial pattern in the image. Several image analysis
applications commonly employ geometric features10.
The proposed methodology uses an effective algorithm, based on visual features, for induction motor fault detection.
In the feature extraction step the key features used for fault diagnosis are: contour section of the object, region orientation, and
severity index. Assume that the pixels in the digital image are piecewise constant and that the dimension of the bounded region
image for each object is denoted by
, where
and express, respectively the number of rows and columns. In these
conditions the contour section is obtained using the following algorithm:
In the nearest
⁄ line of the digital image, start the search from the 1st column until the first point which belongs to the
region contour is found.
The coordinates of the first point are
.
The coordinates of the last point are
.
Continue search of the contour points until reaching the column (
.
The last contour point will have the coordinates
.
The region contour section will then be given by Eq. (25).
.
(25)
The severity index for the rotor broken bars are given by Eq. (26), where
and
denote the maximum and
minimum values of the contour section respectively. Those severity indexes assume values between zero and one, being the
absence of any fault reported by a zero severity index ( =0).
(26)
The
and
values are obtained computing the distances between the center of the closed contour and the two contour
and (
points (
,
), so
(27)
.
(28)
When the contour section is a straight line, the two contour points are equal and a zero severity index is obtained for
the rotor broken bars. Fig. 6 shows the flow chart of the proposed algorithm.
Simulation results
Defect resistance effect on the pattern of the stator current
The simulation results of the induction motor with and without fault were obtained using the Matlab/Simulink
environment. The broken bars model implement with considering the different levels severity fault. Fig. 7 shows the obtained
2-D stator current pattern for a healthy motor. After applying the image processing based system, the computed severity
indexes are very close to zero, denoting a healthy motor. The obtained contour section was one and the contour region pattern
a circle. Figs. (8-10) show the obtained 2-D stator current pattern for a faulty motor by adding a defect resistance with a
different level of severity fault (
. In this condition, due to small rotor asymmetries which
force a small unbalance in the line currents, after applying the image processing based, the computed severity indexes based on
severity fault are: 0.02840, 0.0709, 0.1134.
Stator Winding Fault Effect On The Pattern Of The Stator Current
The simulation results of the induction motor in state of healthy and stator winding fault with open each phases has
been done Computing software. Fault Severity Index In state without fault value 0.228 obtained. With the opening of each of
the phases, of this index is obtained equal to 0.8005. However, this index does not provide information on the type of phase
fault. Another index the orientation is used to detect the phase fault. The pattern of the stator current (dq) for this type of fault
is ellipse of shape.
Experimental Results
The data on the three-phase stator currents measured in January 2006 in normal rotor speed of 1450 rpm to 1469 rpm
and second time three-phase stator currents in the rotor pierced twice speed of 1460 rpm with a sampling frequency of 12kHz
and velocity measured with light Telemetry .Due to an imbalance in network voltage and presence of noise a 2-D stator current
(d-q) pattern for healthy motor is shown in Fig. (5). So for detect the curve of healthy and faulty motor, severity index analysis
was used. The severity index analysis based image processing system According to Fig. (5) after image processing based
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system, the severity index computed 0.1768, and a 2-D stator current (d-q) pattern for faulty motor is shown in Fig. (6) and the
severity index computed 0.2114.
Figure 1: Induction motor’s faults classification.
Figure 2: The stator current spectrum of healthy motor.
Figure 3: The stator current spectrum of faulty motor (broken bar rotor).
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Figure 4: broken bar rotor induction motor.
Figure 5: Overall structure of the stator currents acquisition.
Figure 6: Flow chart of the proposed Image processing based algorithm.
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Figure 7: Current d-q Vector pattern for the healthy motor (
=0.005) - simulation results.
Figure 8: Current d-q Vector pattern for the faulty motor (broken rotor,
=0.05) - simulation results.
Figure 9: Current d-q Vector pattern for the faulty motor (broken rotor,
=0.1) - simulation results.
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Figur. 10: Current d-q Vector pattern for the faulty motor (broken rotor,
=0.15) - simulation results.
Figure 11: Current d-q Vector pattern for the faulty motor.
Figure . 12: Current d-q Vector pattern for the faulty motor- short circuit phase A.
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Figure 13: Current d-q Vector pattern for the faulty motor- short circuit phase B.
Figure 14: Current d-q Vector pattern for the faulty motor- short circuit phase C.
Figure 15: Current d-q Vector pattern for the healthy motor- experimental results.
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Figure 16: Current d-q Vector pattern for the faulty motor (broken bar rotor)- experimental results.
Conclusion
In this paper an image processing based classifier for detection and diagnosis of induction motor rotor fault was
presented. In order to implement the proposed pattern recognition based fault detection algorithm, a feature-based recognition
procedure of the stator current pattern, independent of their shape, size and orientation must be obtained. The key to solve this
problem is to find efficient in variants features. Particular attention is paid to visual-based features obtained in the image
processing system. This system is based on the obtained stator currents and the correspondent Clark-Concordia transformation.
This results in a circular or an elliptic pattern, of the Clark-Concordia stator currents. From the obtained current patterns it was
used an image processing algorithm to identify if there is a motor fault. Several simulation and experimental results have been
presented. From these results it was possible to verify that the proposed image based classifier can effectively be used for the
diagnosis of induction motors.
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