OF DIAGNOSTICS AIR GAP ECCENTRICITY IN CLOSEDLOOP DRIVE-CONNECTED INDUCTION MOTORS
A Dissertation Presented to The Academic Faculty by Xianghui Huang
In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in Electrical Engineering
School of Electrical and Computer Engineering Georgia Institute of Technology May 2005
DIAGNOSTICS OF AIR GAP ECCENTRICITY IN CLOSEDLOOP DRIVE-CONNECTED INDUCTION MOTORS
Approved by: Dr. T. G. Habetler, Chair School of Electrical and Computer Engineering Georgia Institute of Technology Dr. R. G. Harley School of Electrical and Computer Engineering Georgia Institute of Technology Dr. D. Divan School of Electrical and Computer Engineering Georgia Institute of Technology Date Approved: March 29, 2005
ACKNOWLEDGEMENT
During my Ph.D. study at Georgia Tech, I have been fortunate to receive valuable suggestions, guidance, and support from my mentors, colleagues, family, and friends. I am greatly appreciative to my advisor, Dr. Thomas Habetler, for his continual guidance and support. He has been a source of motivation and inspiration throughout the course of this work. I feel grateful to Dr. Ronald Harley, for his time and invaluable input into my research. I have benefited immensely from his knowledge and experience. I would also like to thank Dr. Deepak Divan, Dr. Russell Callen and Dr. Charles Ume for their time, input, and for serving on my thesis committee. I would like to acknowledge Eaton Corporation for providing the financial support necessary to conduct this work. I must also thank the machinists, Lorand Csizar and Louis Boulanger, who were always available and willing to help with the laboratory experimental setup. I wish to thank Dr. Jose Restrepo and my colleagues, Dr. Wiehan le Roux, Dr. Rangarajan Tallam, Dr. Ramzy Obaid, Dr. Dong-Myung Lee, Dr. Jason Stack, Dr. JungWook Park, Salman Mohagheghi, Satish Rajagopalan and Zhi Gao for their help and accompany throughout this study. I am deeply indebted to my grandmother, parents, sister, and brother for a lifetime of support, encouragement, and education. Lastly, I would like to thank my wife Yi Liu whose love, support and understanding has helped to make everything I have accomplished possible.
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TABLE OF CONTENTS
ACKNOWLEDGEMENT............................................................................................... iii LIST OF TABLES ........................................................................................................... vi LIST OF FIGURES ........................................................................................................ vii SUMMARY ...................................................................................................................... xi CHAPTER 1 INTRODUCTION AND OBJECTIVE OF RESEARCH .................... .1 1.1 1.2 1.3 1.4 1.5 Introduction................................................................................................ .1 Common Types of Induction Motor Faults ............................................... .2 Problem Statement ..................................................................................... .3 Objective of the Research .......................................................................... .6 Outline of the Dissertation ......................................................................... .7
CHAPTER 2 EXISTING METHODS IN INDUCTION MOTOR CONDITION MONITORING ...................................................................................... .10 2.1 2.2 2.3 2.4 2.5 2.6 Noise Monitoring ..................................................................................... .10 Torque Monitoring................................................................................... .11 Flux Monitoring....................................................................................... .13 Vibration Monitoring ............................................................................... .14 Current Monitoring .................................................................................. .15 Conclusions.............................................................................................. .22
CHAPTER 3 EXPERIMENTAL SETUP ................................................................... .24 3.1 3.2 3.3 Laboratory Test Equipment ..................................................................... .24 Implementation of Air Gap Eccentricity.................................................. .31 Conclusions.............................................................................................. .32
CHAPTER 4 DISTRIBUTION OF ECCENTRICITY-RELATED FAULT HARMONICS ........................................................................................ .33 4.1 4.2 4.3 4.4 4.5 Introduction.............................................................................................. .33 Effects of Drive Controllers..................................................................... .36 Effects of Mechanical Load ..................................................................... .39 Modeling Air Gap Eccentricity in Closed-Loop Drive-Connected Induction Motors...................................................................................... .41 Simulation Results ................................................................................... .53 iv
4.6 4.7
Experimental Results ............................................................................... .63 Conclusions.............................................................................................. .73
CHAPTER 5 DETECTION OF AIR GAP ECCENTRICITY USING AN ARTIFICIAL NEURAL NETWORK ................................................. .74 5.1 5.2 5.3 5.4 5.5 5.6 Introduction.............................................................................................. .74 Data Acquisition and Preprocessing ........................................................ .75 Feature Extraction.................................................................................... .78 Training and Testing of the Artificial Neural Network ........................... .79 Experimental Results ............................................................................... .80 Conclusions.............................................................................................. .95
CHAPTER 6 EFFECT OF AIR GAP ECCENTRICITY ON SURGE TEST DATA ...................................................................................................... .97 6.1 6.2 6.3 6.4 Introduction.............................................................................................. .97 Detection of Air Gap Eccentricity Using the Surge Test......................... .98 Experimental Results ............................................................................... .99 Conclusions............................................................................................ .105
CHAPTER 7 CONCLUSIONS, CONTRIBUTIONS, AND RECOMMENDATIONS..................................................................... .106 7.1 7.2 7.3 Conclusions............................................................................................ .106 Contributions.......................................................................................... .109 Recommendations.................................................................................. .110
REFERENCES.............................................................................................................. 112 VITA............................................................................................................................... 118
v
LIST OF TABLES
3.1 3.2
Parameters of the experimental induction motor.................................................... .26 Parameters of the experimental AC drive............................................................... .27
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LIST OF FIGURES
1.1 2.1
Static and dynamic eccentricity of induction motors................................................ .4 Stator current Parks vector .................................................................................... .16
3.1 Diagram of the experimental setup ......................................................................... .24 3.2 Experimental motor-drive system........................................................................... .25 3.3 AB 845S optical encoder ........................................................................................ .29 3.4 Principle of an optical encoder ............................................................................... .29 3.5 3.6 Data acquisition system .......................................................................................... .30 Components of induction motors............................................................................ .32
4.1 Block diagram of a speed-controlled, current-regulated, indirect field-oriented drive ........................................................................................................................ .37 4.2 Coupling between an induction motor and a mechanical load in case of rotor eccentricity.............................................................................................................. .40 4.3 4.4 4.5 Flow chart of the simulation program..................................................................... .43 2D model of an induction motor in simulation....................................................... .44 Lamination geometry of the motor in simulation ................................................... .44
4.6 Performance curve of the motor in simulation: torque vs. speed ........................... .45 4.7 Performance curve of the motor in simulation: current vs. speed .......................... .45 4.8 Performance curve of the motor in simulation: power vs. speed............................ .46 4.9 Performance curve of the motor in simulation: efficiency vs. speed...................... .46 4.10 Performance curve of the motor in simulation: power factor vs. speed ................. .47 4.11 Flow chart of Maxwell 2D...................................................................................... .48
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4.12 Flow chart of the drive control program ................................................................. .50 4.13 Design of current PI controller ............................................................................... .51 4.14 Design of speed PI controller.................................................................................. .53 4.15 Simulated speed vs. time for a healthy motor......................................................... .55 4.16 Simulated rotor position vs. time for a healthy motor ............................................ .55 4.17 Simulated torque vs. time for a healthy motor........................................................ .56 4.18 Simulated phase voltage vs. time for a healthy motor ............................................ .56 4.19 Simulated phase voltage vs. time for a healthy motor ............................................ .57 4.20 Simulated flux linkage vs. time for a healthy motor............................................... .57 4.21 Simulated regulation voltage vs. time for a healthy motor..................................... .58 4.22 Simulated regulation current vs. time for a healthy motor ..................................... .58 4.23 Simulated torque vs. time for a faulty motor with a mixed eccentricity rotor........ .60 4.24 Space vector spectral analysis for a faulty motor with a mixed eccentricity rotor . .60 4.25 Space vector spectral analysis for a faulty motor with a mixed eccentricity rotor and a position-varying load ........................................................................................... .61 4.26 Space vector spectral analysis for a faulty motor with a static eccentricity rotor... .62 4.27 Experimental setup of no-load test ......................................................................... .64 4.28 Experimental results of no-load test, 300 rpm and BW=25 rad/s (auto-tuning)... .64 4.29 Experimental results of no-load test, 1200 rpm and BW=25 rad/s (auto-tuning). .65 4.30 Experimental setup of load test............................................................................... .66 4.31 Experimental results of load test, 300 rpm and BW=16 rad/s (auto-tuning) ........ .66 4.32 Experimental results of load test,1200 rpm and BW=16 rad/s (auto-tuning) ....... .67 4.33 Experimental results of load test, 1200 rpm and BW=5 rad/s (manual)............... .68 4.34 Experimental results of load test, 1200 rpm and BW=5 rad/s (manual)............... .68
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4.35 Experimental setup of unbalanced disc test ............................................................ .70 4.36 Experimental results of unbalanced disc test, 300 rpm and BW=25 rad/s (autotuning) ..................................................................................................................... .70 4.37 Experimental results of unbalanced disc test, 600 rpm and BW=25 rad/s (autotuning) ..................................................................................................................... .71 4.38 Experimental results of unbalanced disc test, 1200 rpm and BW=25 rad/s (autotuning) ..................................................................................................................... .71 4.39 Harmonic magnitudes vs. speed in no-load test and load test ................................ .72 5.1 Relationship of three reference frames: a-b-c, - and d-q .................................... .77 5.2 Flow chart of reference frame transform in the data preprocessing phase ............. .78 5.3 Structure of the artificial neural network ................................................................ .82 5.4 The hyperbolic tangent sigmoid activation function .............................................. .83 5.5 The linear activation function ................................................................................. .83 5.6 Training process of the neural network .................................................................. .85 5.7 Training results of the neural network .................................................................... .85 5.8 Testing results of Type 1 neural network with the first set of validation data........ .86 5.9 Testing results of Type 1 neural network with the second set of validation data... .86 5.10 Slip-torque characteristics of the motor and load with ac-drives ........................... .88 5.11 Testing results of Type 2 neural network with the first set of validation data........ .89 5.12 Testing results of Type 2 neural network with the second set of validation data... .89 5.13 The logarithmic sigmoid activation function.......................................................... .90 5.14 Testing results of Type 3 neural network with the first set of validation data........ .92 5.15 Testing results of Type 3 neural network with the first set of validation data of a faulty motor shown in 3D ....................................................................................... .92 5.16 Testing results of Type 3 neural network with the first set of validation data of a healthy motor shown in 3D..................................................................................... .93
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5.17 Testing results of type 3 neural network with the first set of validation data of a faulty motor shown in 3D ....................................................................................... .93 5.18 Testing results of type 3 neural network with the first set of validation data of a healthy motor shown in 3Dt.................................................................................... .94 5.19 Testing results of type 3 neural network with the second set of validation data .... .94 5.20 Flow chart of the detection scheme using a neural network................................... .95 6.1 Equivalent circuit of the surge test.......................................................................... .98 6.2 Block diagram of the surge test setup ..................................................................... .99 6.3 Surge test experimental system............................................................................. .100 6.4 Surge waveform of induction motors ................................................................... .101 6.5 Surge test results of a healthy motor..................................................................... .103 6.6 Surge test results of a faulty motor with an eccentric rotor .................................. .103 6.7 Spectral analysis of a healthy motor ..................................................................... .104 6.8 Spectral analysis of a faulty motor with an eccentric rotor .................................. .104
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SUMMARY
The goal of this research is to develop a reliable, cost-effective detection scheme for air gap eccentricity in closed-loop drive-connected induction motors. A literature review of existing methods in motor condition monitoring is presented. The majority of existing detection methods deals with only line-fed motors, which is insufficient for the fault detection of closed-loop drive-connected induction motors. Analysis of existing methods identifies the motivation of this investigation. The development of the proposed detection scheme begins with an investigation of how the eccentricity-related fault harmonics distribute in a closed-loop motor-drive system. As motor voltage and current are modified by the converter, the appearance of the fault harmonics in the motor voltage and current is affected by the closed-loop speed and current feed-back controllers. Next, the effects on fault detection of the
misalignment associated with the mechanical load are discussed. The misalignment is caused by coupling an eccentric rotor with a mechanical load through a flexible coupling and results in a position-varying load torque that can change the distribution of fault harmonics. As a result of the above analysis, a sensorless detection method is proposed based on monitoring the space vector forms of stator voltage and current together, which ensures good detection sensitivity and reliability. One challenge in this investigation is that operating conditions of a driveconnected motor vary widely. The eccentricity-related harmonic amplitudes change
accordingly because of the mechanical resonance of a torsional spring system consisting of a motor and load. The relationship between fault harmonic amplitudes and operating
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conditions depends on many factors and cannot be formulated as strict analytical equations. Therefore, an artificial neural network is used to learn the complex
relationship and to test motor conditions. A series of simulations and laboratory experiments are conducted to verify the analysis and to test the performance of the proposed diagnostic scheme. The results validate that the diagnostic scheme is feasible over the entire range of operating conditions of experimental motors. The effect of air gap eccentricity on surge test data is analyzed. A new off-line method to detect rotor eccentricity faults using a surge tester is experimentally verified. The conclusions, contributions, and recommendations are summarized at the end.
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CHAPTER 1
INTRODUCTION AND OBJECTIVE OF RESEARCH
1.1 Introduction
Electrical machines are a necessary part of our daily life. As important elements in electromechanical energy conversion, they are used in many fields, such as power generation, the paper industry, oil fields, manufacturing, etc. Among electrical machines, induction motors are the most widely used in industry because of their rugged configuration, low cost, and versatility. With their great contributions, induction motors are called the workhorse of industry. Because of natural aging processes and other factors in practical applications, induction motors are subject to various faults. Those faults disturb the safe operation of motors, threaten normal manufacturing, and can result in substantial cost penalties. The field of motor condition monitoring recognizes those problems, and more and more relative research is being devoted to it by industry and academia. With condition
monitoring, an incipient fault can be detected at an early stage. Appropriate maintenance can then be scheduled at a planned downtime, avoiding a costly emergency. This reduces downtime expense and reduces the occurrence of catastrophic failures. With the rapid developments in digital signal processing and power electronic devices, variable-speed induction motor applications have become common. AC drives can provide qualified control performance with a comparatively low price like DC drives. However, the use of AC drives adds significant challenges to fault detection. Unlike traditional condition monitoring methods dealing with main or line-fed induction motors, 1
more sophisticated techniques are required for sensitive and reliable fault detection of closed-loop drive-connected induction motors.
1.2
Common Types of Induction Motor Faults
There are several types of faults that may occur in induction motors. According to a survey by EPRI in 1982, about 41% of all induction motor failures are caused by bearing faults, 37% by stator faults, 10% by rotor faults, and 12% by miscellaneous faults [1]. Bearing faults are categorized as inner race faults and outer race faults by the location of occurrences. The most common causes of bearing faults include
contamination of lubricant, loss of lubricant, over-loading, and excess heating. The ultimate result is either extreme vibration leading to catastrophic failure, or a complete seizure of the bearing [52]. Stator faults are basically caused by a breakdown of winding insulation, which may result from excess thermal or voltage stress, mechanical vibration, or even an abrasion between the stator and rotor. The weakness of winding insulation may further result in a turn-to-turn short circuit and eventually a winding-to-ground short circuit [53]. There are two types of rotor faults. One is associated with the rotor itself, such as a bar defect or bar breakage. This type of fault occurs from thermal stresses, hot spots, or fatigue stresses during transient operations such as startup, especially in large motors. A broken bar changes torque significantly and is dangerous to the safe and consistent operation of electric machines [54].
2
The second type of rotor fault is related to air gap eccentricity.
Air gap
eccentricity is a common effect arising from a range of mechanical problems in induction motors such as load unbalance or shaft misalignment. Long-term load unbalance can cause damage of the bearings and the bearing housing, which will influence air gap symmetry. Shaft misalignment means horizontal, vertical, or radial misalignment With shaft misalignment, the rotor will be
between a shaft and its coupled load.
displaced from its normal position because of a constant radial force.
1.3
Problem Statement
The research in detecting air gap eccentricity of induction motors began in the 20th century. Existing detection schemes are classified by the type of monitoring
parameters. Examples of monitoring parameters include torque, flux, vibration signal, and stator current. Depending on whether the minimum air gap is spatially fixed or not, air gap eccentricity is described as being either static or dynamic. For static eccentricity, the rotor shifts from its normal position at the center of the stator and rotates around its own center. For dynamic eccentricity, the rotor shifts from its normal position, but still rotates around the center of the stator. Figure 1.1 illustrates the different cases of eccentricity. Air gap eccentricity may result from the assembly and manufacturing processes. For example, static eccentricity is caused by manufacturing tolerances between the center of the stator bore and bearing centers. Dynamic eccentricity in a new motor is controlled by the total indicated reading (TIR) of the rotor [4, 5, 6].
3
a healthy motor
static eccentricity
dynamic eccentricity
mixed eccentricity
Figure 1.1. Static and dynamic eccentricity of induction motors.
In addition to flaws in the assembly and manufacturing processes, air gap eccentricity is also caused by external mechanical problems in induction motors, such as load unbalance, loose mounting, or shaft misalignment. These mechanical problems cause a radial unbalanced force on the rotor, which pulls the rotor from its normal position and generates a non-uniform air gap. detected by monitoring the air gap [15, 54]. In practice, all three-phase induction motors contain inherent static and dynamic eccentricity. They exist simultaneously in practice and are referred to as mixed These mechanical problems can be
eccentricity [2, 18, 19, 28]. Air gap eccentricity causes a ripple torque, which further 4
leads to speed pulsations, vibrations, acoustic noise, and even an abrasion between the stator and rotor. Therefore, it is critical to detect air gap eccentricity as early as possible. Among existing methods in induction motor condition monitoring, motor current signal analysis (MCSA) is the most commonly used technique. The advantages of this scheme include low cost and easy operation. In most applications, the stator current of an induction motor is readily available to protect machines against destructive over-currents, ground currents, etc. Therefore, an MCSA scheme can be implemented at no additional cost. For this reason, MCSA is often referred to as sensorless condition monitoring. Several industrial case studies based on MCSA are reported in the literature [4, 6, 9, 19], but the majority of the previous work deals only with line-fed induction motors. The use of a motor drive adds several significant challenges to fault detection above and beyond those faced by conventional line-fed machines. First, the motor and drive operate in a closed-loop fashion. Therefore, their behavior is coupled and their fault signatures interact. Second, since the source of energy to the motor is not a sine wave voltage, the drive controllers modify the motor terminal quantities such as the current and voltage. In a line-fed motor, any change in air gap modulates the induced stator voltage and therefore shows up as harmonics in stator current. However, in a converter-fed motor, any closed-loop speed or current feed-back controller also affects the appearance of fault harmonics. Third, with an AC drive, the mechanical speed of an induction motor can vary widely. This changes the operating condition and eccentricityrelated harmonic amplitudes. It is difficult or even impossible to formulate these
relationships as strict analytical equations because they depend on several factors, such as installation, motor size, etc. In addition, it is impossible to measure fault harmonic
5
amplitudes corresponding to all the operating conditions since speed or load may change continuously. With the above problems, MCSA may no longer be sufficient because of the reduced sensitivity. Meanwhile, operating conditions must be considered in the fault detection [14, 47]. Together with the above problems in the diagnostics of induction motors in a closed-loop system, new detection techniques become possible. For example, in a linefed machine, only motor terminal quantities, such as the stator current, are available for sensorless condition monitoring. However, in a drive-connected motor, many additional parameters of the motor and drive are readily available. These parameters contain fault signature information and can be used in developing an efficient and sensorless detection scheme.
1.4
Objective of the Research
This research focuses on the detection of air gap eccentricity in a three-phase induction motor supplied by a speed-controlled, current-regulated, indirect field-oriented drive. The objective is to design a practical detection scheme that can be adopted in future commercial drives. Based on the discussion in Section 1.3, the detection scheme should meet the following requirements. First, it should be reliable and sensitive, which allows faults to be detected at an early stage before a catastrophic failure occurs. Second, the operation of the diagnostic scheme should require a minimum amount of expert knowledge. Although some commercial condition monitoring tools are on the market, most of them
6
provide only information such as the values of certain parameters or graphics of data, whose interpretation needs an experienced engineer. Too much expert knowledge
involvement limits the applications of condition monitoring in practical applications, since in most cases experts are not available. An ideal condition monitoring tool should simply tell operators the condition of electrical machines. While it may not be able to predict the exact amount of remaining life, it is possible to notify operators when a potential fault is present so appropriate maintenance can be scheduled. Third, the
diagnostic scheme should be cost effective. To have a detection scheme implemented in practical applications, avoiding expensive sensors and invasive operation is necessary. This research proposes a detection scheme that is sensorless and intelligent and uses only readily available parameters. In the following chapters, the principles of this detection scheme are described. Simulation and experimental results demonstrate that the proposed scheme provides a reliable and accurate prediction about motor conditions over the entire range of operating conditions of experimental motors.
1.5
Outline of the Dissertation
A literature survey and review of previous work in induction motor condition monitoring is presented in Chapter 2. This chapter familiarizes readers with the research topic. The limitations of existing detection methods are analyzed in detail to clarify the motivation of this research. Chapter 3 introduces the experimental setup. It describes the experimental
equipment, such as the induction motor, load system, vector-controlled drive, and data
7
acquisition system. Furthermore, it explains the methods used to implement air gap eccentricity in induction motors. Chapter 4 investigates the distribution of eccentricity-related fault harmonics between the stator voltage and current under the influences of drive controllers and mechanical load. First, a brief description of eccentricity-related fault harmonics in a closed-loop system is introduced. It helps understanding basic differences between fault detection for a line-fed induction motor and a drive-connected induction motor. Next, the effects of drive controllers on the distribution of fault harmonics are investigated, and a preliminary sensorless detection scheme is proposed. Finally, the influence of the The
mechanical load on the distribution of the fault harmonics is investigated.
preliminary detection scheme is modified to ensure good detection sensitivity and reliability. A direct time-stepping coupled finite element analysis (FEA) model is used to simulate air gap eccentricity in a closed-loop drive-connected induction motor. The model incorporates the effects of magnetic nonlinearity and space harmonics because of the machine magnetic circuit topology and winding layouts. Simulation and
experimental results are presented to support the analysis and feasibility of the proposed detection method. Based on the above analysis, Chapter 5 introduces a new detection scheme of air gap eccentricity using an artificial neural network (ANN). With a neural network, the variation of eccentricity-related harmonic amplitudes with changing operating conditions is incorporated into the fault detection. The performance of this detection scheme is tested over the entire range of operating conditions of experimental motors.
8
Chapter 6 investigates the effects of air gap eccentricity on surge test data. The experimental results show that air gap eccentricity can be unobtrusively observed in surge waveforms. With this observation, a new off-line method to detect rotor eccentricity faults in induction motors is proposed and experimentally validated. Conclusions, contributions, and recommendations are discussed in Chapter 7.
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CHAPTER 2
EXISTING METHODS IN INDUCTION MOTOR CONDITION MONITORING
This chapter reviews and summarizes existing methods in induction motor condition monitoring. The aim of this chapter is to provide theoretical foundations and to clarify the motivation of this research.
2.1
Noise Monitoring
Acoustic noise from air gap eccentricity in induction motors can be used for fault detection. Noise monitoring is accomplished by measuring and analyzing the acoustic noise spectrum. An example of using this method to detect air gap eccentricity is given in [42]. Ellison and Yang verified from a test carried out in an anechoic chamber that slot harmonics in the acoustic noise spectra from a small power induction motor were functions of static eccentricity. However, the application of noise measurements in a plant is not practical because of the noisy background from other machines operating in the vicinity. This noise reduces the accuracy of fault detection using this method [22, 49].
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2.2
Torque Monitoring
Almost all motor faults cause harmonics with special frequencies in the air gap torque. However, air gap torque cannot be measured directly. From the input terminals, the instantaneous power includes the charging and discharging energy in the windings. Therefore, the instantaneous power cannot represent the instantaneous torque. From the output terminals, the rotor, shaft, and mechanical load of a rotating machine constitute a torsional spring system that has its own natural frequency. The attenuations of the components of air gap torque transmitted through the torsional spring system are different for different harmonic orders of torque components. Generally, the waveform of the air gap torque curve is different from the torque measured at the shaft [16, 17]. Hsu [16] proposed a special method to detect cracked rotor bars, and stator unbalance caused by winding defects and unbalanced stator voltages using air gap torque. The air gap torque was presented by measurable motor terminal quantities as
Torque[ Nm] =
p 3
{(i A i B )
[v
CA
R (i C i A )]dt
(i C i A ) [v AB R(i A i B )]dt}
(2.1)
where i A , iB , and iC are three-phase line currents of an induction motor, vCA and v AB are line-to-line voltages, R is half of the line-to-line resistance, and p is the number of polepairs. Frequencies of major torque harmonics associated with the above defects in
induction motors are discussed for three extreme cases:
11
Under normal operation: Angular frequency of torque=0 (2.2)
With a single-phase stator: Angular frequency of torque = 2 s (2.3)
With a single-phase rotor: Angular frequency of torque = 2s s (2 .4)
where s is the supply frequency in rad/s, and s is the slip.
Therefore, the fault
condition can be identified by monitoring the special harmonics in the air gap torque. However, in equation (2.1) it is assumed that the magnetic paths of the three phases are identical. It is well known that only the interaction between stator currents and fluxes produced by rotor currents alone yields torque. Although the interactions between stator currents and fluxes produced by the same stator currents do not produce torque, those stator currents can affect the saturation of magnetic paths. Once the leakage reactances and magnetic paths of the three phases become asymmetrical, errors are induced and the calculation of air gap torque in equation (2.1) is no longer accurate [17]. Kral [33] proposed a current model and a voltage model to estimate the electromagnetic torque of an induction motor, which is called the Vienna Monitoring Method. The difference between the estimated torques from those two models gives an indication of the existence of broken bars.
12
2.3
Flux Monitoring
Air gap flux of induction motors contains rich harmonics. A flux monitoring scheme can give reliable and accurate information about electrical machine conditions. Any change in air gap, winding, voltage, and current can be reflected in the harmonic spectra. Verma and Natarajan [43] studied the change of air gap flux as a function of static eccentricity. Binns and Barnard [44] monitored air gap flux and core vibration together, and concluded that the use of the two signals provided useful information for machine analysis. But this research only identified the parameters that were certainly functions of air gap eccentricity, rather than directed to the development of on-line diagnostics [49]. Thomson, Rankin, and Dorrell [49] analyzed the respective relationships among air gap flux, stator current, vibration signal, and air gap eccentricity by strict analytical equations. They derived the frequencies of eccentricity-related harmonics in the air gap flux to be
f ecc = f1 [( R nd )
1 s nw ] p 1 s ) p
(2.5)
f ecc = f1 f m = f 1 (1
(2.6)
where equation (2.5) is for static or dynamic eccentricity alone, and equation (2.6) is for mixed eccentricity, f1 is the supply frequency, R is the number of rotor bars, nd is the eccentricity index that is equal to zero for static eccentricity and one for dynamic eccentricity, n w is equal to 1, 3, 5, which is always chosen as one since these
13
harmonics are the largest and easiest to monitor, f m is the rotor mechanical frequency, s is the slip, and p is the number of pole-pairs. Air gap flux can be measured by search coils installed in the stator core. Because of the enclosed structure of induction motors, this operation requires the disconnection of induction motors from the main supply before dismantling. As such, this is neither practical nor economical for the motors that are already in service. In addition, because of the small air gap in most induction motors, installation of search coils may require significant design modifications that may not be easy to implement and certainly would be expensive.
2.4
Vibration Monitoring
Extensive work has been done in the detection of motor faults by monitoring unbalanced magnetic pull and vibration. The basic idea is that different mechanical faults create unique harmonics with different frequencies and power levels in the vibration signal. Thus, the vibration signal is first collected via a vibration sensor mounted on the stator frame, and then its spectrum is calculated using the fast Fourier transform (FFT). Specific harmonics are then monitored to determine the corresponding motor faults. Cameron, Thomson, and Dow [49] verified that air gap eccentricity resulted in vibratory harmonics at frequencies of f m , 2 f m , 3 f m , or 4 f m . Riley, Lin, Habetler, and Kliman [45, 46] identified that there was a monotonic relationship between RMS vibration sum and RMS current sum at a given frequency. This is because the
14
mechanical vibration modulates air gap at that particular frequency. Those frequency components then show up in inductances and therefore in stator current. The major weakness of vibration-based condition monitoring is its cost. The vibration sensor, especially the accelerometer, is expensive, and the acquisition of the vibration signal requires a significant investment.
2.5
Current Monitoring
The most economically attractive technology in induction motor condition monitoring is stator current monitoring. In most applications, the stator current of an induction motor is readily available since it is used to protect machines from destructive over-currents, ground current, etc. Therefore, current monitoring is a sensorless detection method that can be implemented without any extra hardware. There are three current monitoring methods: current Parks vector, zero-sequence and negative-sequence current monitoring, and current spectral analysis. The basic idea of current Parks vector is that in three-phase induction motors, the connection to stator windings usually does not use a neutral. For a Y-connection
induction motor, the stator current has no zero-sequence component. A two-dimensional representation of the three-phase currents, referred to as current Parks vector, can then be regarded as a description of motor conditions. Under ideal conditions, balanced threephase currents lead to a Parks vector that is a circular pattern centered at the origin of coordinates, as shown in Figure 2.1. Therefore, by monitoring the deviation of current
15
Parks vector, the motor condition can be predicted and the presence of a fault can be detected.
5
iq (A)
4
3
iq
2
1 0
id
-1
-2
-3
-4
-5
-5
-4
-3
-2
-1
0
1
2
3
4
5
id (A)
Figure 2.1. Stator current Parks vector of a healthy motor.
Cardoso and Saraiva [30, 31] used the Parks vector of the stator current to detect air gap eccentricity. Mendes and Cardoso [32] detected faults in voltage-sourced
inverters using the current Parks vector. Nejjari and Benbouzid [29] analyzed the deviation in the pattern of current Parks vector to diagnosis the supply voltage unbalance of induction motors. However, this method ignores the non-idealities of electrical
machines and inherent unbalance of supply voltages. In addition, it is difficult to isolate different faults using this method alone, since different faults may cause a similar deviation in the current Parks vector. The zero-sequence and negative-sequence currents can be monitored to detect stator winding faults of electrical machines. Stator winding faults, such as turn-to-turn short circuit, can cause an asymmetrical electromagnetic field in electrical machines. This can create zero-sequence and negative-sequence currents, which cannot be observed in a symmetrical and healthy three-phase electrical machine. Similar to the current
16
Parks vector, this method is vulnerable to unbalanced voltages. Tallam, Habetler, and Harley [13, 53] monitored the negative-sequence voltage to detect a turn-to-turn short circuit in a closed-loop drive-connected induction motor. A neural network was used to learn and to estimate the negative-sequence voltage of a healthy motor, which is used as the threshold. This helped to reduce the effects of machine non-ideality and unbalanced supply voltage. According to [13], most of the turn-to-turn short circuit-related fault signatures exist in the stator voltage because of the regulation of the drive controllers. However, the influence of mechanical load was neglected. In practice, the distribution of fault information between the stator voltage and current depends on drive controllers, as well as mechanical load and operating conditions. Monitoring either stator current or voltage alone cannot ensure an accurate prediction of motor conditions. Current spectral analysis, or MCSA, is the most commonly used method in the detection of rotor faults of induction motors. Broken bars cause special harmonics at the frequency given by equation (2.7) in the stator current [12, 21].
f bar = f1 (1 2 s )
(2.7)
where f1 is the fundamental frequency of supply voltage, and s is the slip. Bellini et al. [12] investigated the impact of a closed-loop controller on the diagnostics of broken bars in induction motors. They proposed the use of the flux control current in a rotor-flux
e e oriented synchronous reference frame, ids , as the diagnostic index. They assumed ids to
be independent of control parameters and to depend on only the degree of asymmetry.
e But in their research, only a proportional speed controller was considered. Actually, ids
17
e is also affected by iqs , the torque control current. When an integral speed controller is
e present, ids becomes dependent on the speed bandwidth and therefore it is not the case e e that ids depends only on the asymmetry. Furthermore, the fault harmonics in ids are e e much smaller than those in iqs in a field-oriented drive because the reference I qs is the
e e output of a speed controller, while the reference I ds is a constant. The parameter iqs
e contains larger fault harmonics because of speed feedback. Monitoring ids alone reduces
the detection sensitivity. As discussed in Section 2.3, the air gap eccentricity results in flux harmonics at the frequencies given by equations (2.5) and (2.6). As these harmonic fluxes move relative to the stator, they induce corresponding current harmonics at the same frequencies in a stationary stator winding [49]. Therefore, those current harmonics can provide an indication of motor health. The voltage equations modeling an ideal induction machine in a stationary reference frame, assuming no neutral connection, are
d v qs = Rs i qs + dt qs v = R i + d s ds ds ds dt 0 = R i + d r qr r dr qr dt d 0 = Rr idr + r qr + dr dt
(2.8)
18
where v qs and v ds are stator voltages, Rs and Rr are stator and rotor resistances,
iqs , ids , i qr and idr are stator and rotor currents, and r is the rotor electrical velocity in
rad/s. The stator and rotor flux linkages are given by
qs ds qr dr
= Ls iqs + Lm iqr = Ls ids + Lm idr = Lr iqr + Lm iqs = Lr idr + Lm ids
(2.9)
where Ls and Lr represent the stator and rotor self inductances, and Lm represents the mutual inductance. If the stator voltage is assumed to vary sinusoidally in a line-
connected induction motor and the stator copper losses are neglected, then it can be seen from equation (2.8) that the stator flux linkages oscillate at the fundamental frequency f1 . Since the stator flux linkages vary at a single frequency, equation (2.9) implies that any variation in the mutual inductance caused by air gap asymmetry may result in corresponding harmonics in the stator current. Thomson [4, 5] verified that the use of the current spectrum was successful in diagnosing air gap eccentricity problems in large, high-voltage, three-phase induction motors. Benbouzid [23, 24] investigated the efficacy of current spectral analysis on induction motor fault detection. The frequency signatures of some asymmetrical motor faults, including air gap eccentricity, broken bars, shaft speed oscillation, rotor asymmetry, and bearing failure, were identified. His work verified the feasibility of current spectral analysis. Besides induction motors, current spectral analysis was applied to other types of electrical machines too. For example, Le Roux [60] monitored the 19
current harmonic component at the rotating frequency (0.5 harmonic) to detect the rotor faults of a permanent magnet synchronous machine. Schoen and Habetler [7, 8] investigated the effects of a position-varying load torque on the detection of air gap eccentricity. The torque oscillations were found to cause the same harmonics as eccentricity. These harmonics are always much larger than eccentricity-related fault harmonics. It is therefore impossible to separate torque
oscillations and eccentricity unless the angular position of the eccentricity fault with respect to the load torque characteristic is known [7, 8]. In current spectral analysis, the actual harmonics measured from a running machine are always compared with known values (thresholds) obtained from a healthy motor. In practical applications, the thresholds change with motor operating conditions. Therefore, Obaid [14] proposed tracking the normal values of a healthy motor at different load conditions. For each load condition, a corresponding threshold was determined and compared with the on-line measurement to determine the motor condition. Besides the traditional FFT technique in spectral analysis, other techniques in advanced digital signal processing and pattern recognition were applied to motor condition monitoring as well. Yazici and Kliman [11] monitored stator current and applied the short-time Fourier transform (STFT) to detect broken bars and bearing faults in induction motors. Their experimental results supported the advantages of STFT than the traditional FFT because of the non-stationary stator current in practical applications. Kliman and Song [65] used a wavelet analysis of the stator current to remotely monitor DC motor sparking. However, it is difficult to determine suitable wavelet functions if the motor operating conditions change frequently, as in a vector-controlled drive. Haji and
20
Toliyat [63, 64] used a Bayes minimum error classifier to detect eccentricity and broken bars in induction motors. They assumed that the fault signature had a normal distribution density function. However, the distribution parameters had to be determined empirically. Unlike direct measurement, in model-based parameter estimation, the thresholds of a healthy motor can be calculated by simulation. Toliyat [62] used the Winding Function Approach (WFA) to simulate an induction motor. The basic idea is to replace the squirrel-cage rotor by n independent loops, where n is the number of rotor bars. Then, the inductances of the n rotor loops and m stator phases can be calculated from the MMF, permeance, and air gap. Once the inductances are known, motor current and torque can be calculated. The WFA was applied to detect air gap eccentricity fault in induction motors [18, 19, 20] and in a synchronous machine [61]. Nandi [18] simulated a threephase induction motor using the WFA and found that rotor slot and other eccentricityrelated harmonics in stator current depended on the structure of rotor cage. In order to observe static or dynamic eccentricity-related components in stator current, the number of rotor bars R needs to be equal to
R = 2 p[3(m q ) r ] k
(2.10)
where (m q ) =0, 1, 2, 3, and r=0 or 1, k=1 or 2. The finite element analysis is another popular method to simulate electrical machines. Thomson and Barbour [3, 6] used the FEA to predict the level of static eccentricity in three-phase induction motors. Their investigation showed that those
predictions were much closer to the measured values in comparison to previous attempts
21
using the classical MMF and permeance wave approach. Demerdash and Bangura [26] calculated eccentricity-related current harmonics of a squirrel-cage induction motor using a time-stepping coupled finite element state-space method. In their research, the authors calculated the electromagnetic field of an induction motor by FEA at each step in rotation. However, they only considered a motor supplied by an open-loop v/f adjustable-speed drive. For all model-based parameter estimations, diagnostic reliability heavily depends on the accuracy of the model. However, in most applications, accurate parameter It limits the
information for the electrical machines or drives is not available.
implementation of model-based parameter estimation in practical applications. Rapidly evolving computing power and continual progress in ANN technology provide new tools for detection automation. Many different ANN-based detection
methods were developed and implemented [34-41]. References [36, 37] proposed the use of a fuzzy or neural/fuzzy system to detect motor insulation problem. Such a system helps to give exact reasons for an abnormal phenomenon. But it is difficult to establish suitable fuzzy rules. References [35, 38] used a self-organizing map (SOM) to detect faults by distinguishing a fault pattern from an acquired normal pattern. But it is difficult to find an effective induction rule. That is, although a deviation pattern appears, it is hard to decide whether it is due to the expected fault.
2.6
Conclusions
This chapter presented a review of existing induction motor condition monitoring methods. It has been a broadly accepted requirement that a diagnostic scheme should be
22
non-invasive and capable of detecting faults accurately at low cost. MCSA has become a widely used method because its monitoring parameter is a motor terminal quantity that is easily accessible. The other broadly accepted requirement is that the diagnostic scheme should require a minimum amount of expert knowledge. Relatively little research has been done to detect air gap eccentricity faults in closed-loop drive-connected induction motors. Specifically, no work has been done to comprehensively analyze the effects of closed-loop drive controllers and the mechanical load on the detection of air gap eccentricity in induction motors. In this research, these effects will be analyzed in detail, and then a sensorless and reliable diagnostic scheme will be proposed. Its feasibility will be validated experimentally.
23
CHAPTER 3
EXPERIMENTAL SETUP
To study air gap eccentricity and to test the proposed diagnostic scheme, an experimental setup is designed and built. Experimental results are used to explain test phenomena and to support the analysis in the following chapters. Therefore, it is
important to describe the experimental setup at the beginning of this thesis.
3.1
Laboratory Test Equipment
This test setup consists of an induction motor, a commercial vector-controlled drive, a mechanical load, and a data acquisition system. The complete experimental setup is shown in Figures 3.1 and 3.2.
Data Acquisition Personal Computer A B C Feedback Speed Vector Control Drive Induction Motor
DC Dynamometer
Load
Field
Figure 3.1. Diagram of the experimental setup.
24
Figure 3.2. Experimental motor-drive system.
3.1.1
Motor and load Three induction motors are used in this research. One is a healthy motor, and the
other two motors contain static and mixed rotor eccentricity, respectively. All motors are 7.5 Hp, four-pole, three-phase induction motors. The main parameters of these motors are shown in Table 3.1. The mechanical load consists of a DC dynamometer and a resistor bank. The dynamometer is a 10 Hp, 60 Amp, 3600 rpm, DC machine and is controlled by an adjustable 125 V DC supply, connected to its shunt field winding to vary the load on the test motor. The output of the DC dynamometer is connected to resistor banks, and the generated DC power is dissipated as heat.
25
Table 3.1. Parameters of experimental induction motor
HP RPM R1 (ohm @25C) L1 (mH) Lm (mH) # of stator slots
7.5 1755 0.174 1.3783 52.7742 48
Volt Ampere R2 (ohm @25C) L2 (mH)
Air gap length (in)
230 18.2 0.1597 1.7592 0.014 40
# of rotor bars
This mechanical load is actually a linear load, in which the load torque varies linearly with speed, and load power varies with speed squared, according to equations (3.1) and (3.2)
Tload =
(k k i )
2 a f f
m
Ra + R L
(3.1)
Pload =
(k k
a
f
i f m )
2
Ra + R L
(3.2)
where k a , k f are design constants of the DC dynamometer, i f is the field current, m is the mechanical speed, Ra is the armature resistance of the DC dynamometer, RL is the load resistance, and Pload is the output power. Therefore, the load can be changed in three ways: varying motor speed, switching on/off the resistance bank, and adjusting field current. With i f and m fixed, the load power is increased when load resistance RL is reduced, and the largest load power is reached when RL is equal to the armature resistance Ra . 26
3.1.2 Vector-controlled drive In the experiments, the induction motors are fed from a 460 V AC power supply through a commercial vector-controlled drive. Its main parameters are shown in Table 3.2.
Table 3.2. Parameters of the experimental AC drive
Input Volt Current Bandwidth Output Frequency
380-480 VAC 2000 rad/s
Drive Hp Speed Bandwidth 0-250 Hz
20 0-30 rad/s
The experimental AC drive is a high-performance, microprocessor-based, fieldoriented AC drive. It is designed to be a low-cost drive for stand-alone applications and is user friendly besides having an easy-to-use start up sequence for simple, out-of-box installation. The micro-controlled field-oriented current loop has a fixed bandwidth of 2000 rad/s, which is not accessible to users. The customized parameters pertinent to the experiments in this research include reference speed and bandwidth of a digital speed loop. Before starting up, the drive goes through auto-tuning. Auto-tuning is a procedure that involves running a group of tests on the motor/drive combination. Some of the tests check the drive hardware, while others configure drive parameters to maximize the performance of the attached motor. The experimental AC drive uses auto-tuning to determine leakage inductance, stator resistance, flux current, and load inertia. All these parameters are then used to tune speed and current PI controllers. The drive also includes a user interface, through which users can control electric motors remotely. The
experimental AC drive can work either in the speed-control or in the torque-control mode,
27
where the reference torque is calculated by a speed PI controller or fed from external control devices. In this research, the drive is always used in the speed-control mode. Indirect field orientation requires a feed-back speed from an encoder mounted on the shaft. The experimental AC drive provides an optional board for the encoder
interface. Motor speed is measured through an Allen-Bradley 845S incremental optical encoder installed on the motor shaft, as shown in Figure 3.3. Principles of an optical encoder are illustrated in Figure 3.4. The encoder is constructed with a light source, a sensor, a rotary disc, and a stationary mask. The rotary disk has alternate opaque and transparent sectors. As the disc rotates with shaft, the mask periodically passes and blocks light. The output signal from the sensor is used to decide the speed and direction of rotation.
3.1.3
Data acquisition and storage Two types of signals are collected in the experiments: stator current and stator
voltage via current sensors LEM LA-55P and voltage sensors LEM LV-25P, respectively. By appropriately choosing the measuring resistance, the ratios of current and voltage sensors are adjusted to be 10:1 and 100:1, respectively. Two phase currents and two line-to-line voltages are measured. Because the experimental motors do not have a neutral connection, the remaining third phase can be calculated from these two phase signals. Each of the signals measured is anti-alias low-pass filtered, amplified, and then simultaneously sampled through four channels of a data acquisition (DAQ) board and stored directly into a desktop computer. The whole system is shown in Figure 3.5.
28
Figure 3.3. AB 845S optical encoder.
Rotary disk Light source
Stationary disk
Sensor
Figure 3.4: Principle of an optical encoder
29
Figure 3.5: Data acquisition system
Experimental data are acquired by a National Instruments SCXITM integrated measurement system. This system is composed of an SCXITM-1305 AC/DC coupling BNC terminal block, an SCXITM-1141 module, and an SCXITM-1000 chassis. The
SCXITM-1305 block has eight BNC connectors and one SMB connector. Signal sources can be configured as either floating or ground referenced, and either AC or DC coupled. The SCXITM-1141 module has eight elliptic low-pass filters and eight differential-input amplifiers. The DAQ board PCI-6025E, cabled to the SCXITM-1141 module, reads the signal from each channel. The data acquisition process is controlled and monitored using National Instruments LabVIEWTM software. Once the data acquisition is complete, a Matlab program is used to process and analyze the data.
30
3.2 3.2.1
Implementation of Air Gap Eccentricity
Implementing static eccentricity As given in Table 3.1, the normal air gap between the stator and rotor in the
experimental induction motors is small, which is 0.014 in (0.0356 cm). The small air gap makes it very difficult to implement rotor eccentricity. For example, at the beginning of the experiments, if there was air gap eccentricity, the rotor was always pulled onto the stator once the motor was energized because of the unbalanced magnetic pull (UMP). To solve this problem, the rotor has to be uniformly machined to 0.039 in (0.099 cm) to increase the air gap. The parts of an induction motor are shown in Figure 3.6. The static eccentricity is created by first machining the bearing housing of one end bell eccentrically, and then inserting a 0.010 in (0.0254 cm) offset shim between the housing and the bearing [19, 28, 48]. In this way 25.6% static eccentricity is created.
3.2.2
Implementing dynamic eccentricity Dynamic eccentricity is also created inside experimental motors in order to
generate mixed eccentricity. Dynamic eccentricity is created by first machining the shaft under the bearing eccentrically, and then inserting a 0.015 in (0.0381 cm) offset sleeve between the bearing and the shaft. The degree of dynamic eccentricity is 38.4%.
31
Figure 3.6. Components of induction motors.
3.3
Conclusions
This chapter introduced the experimental setup used in the experiments of this investigation. The experimental equipment was introduced. Methods used to implement static eccentricity and dynamic eccentricity were also described.
32
CHAPTER 4
DISTRIBUTION OF ECCENTRICITY-RELATED FAULT HARMONICS
This chapter first describes eccentricity-related fault harmonics in a closed-loop motor-drive system. The effects of the drive controllers and the mechanical load on the distribution of fault harmonics between stator voltage and current are analyzed next. Finally, the analysis is verified by simulation and experiments.
4.1
Introduction
Vector-controlled drives calculate motor variables in a synchronous reference frame. In a synchronous frame, an induction motor can be modeled as
e e v qds = rs iqds + j s e + qds
de qds dt
(4.1)
Tem =
3 pLm e e dr iqs Lr
(4.2)
J eq
d m = Tem Tload dt
(4.3)
e e where v qds is the stator voltage space vector, i qds is the stator current space vector, e is qds
the stator flux linkage space vector, e is the rotor flux linkage space vector, s is the qds
33
synchronous electrical angular speed, Tem is the electromagnetic torque, p is the number of pole-pairs, J eq is the equivalent load inertia, m is the mechanical speed, and Tload is the load torque. With eccentricity, the air gap between the rotor and stator becomes nonuniform, which can be approximated by [49, 55]
g = g 0 [1 s cos d cos( m t )]
(4.4)
where g 0 is the normal air gap length, s is the degree of static eccentricity, d is the degree of dynamic eccentricity, m is the mechanical speed, t is time, and is the angle measured from a base point. Air gap permeance is defined as
P=
A
g
=
A g 0 [1 s cos d cos( m t )]
(4.5)
where is the air gap permeability, and A is the air gap area. Since d and s are small, equation (4.5) can be approximated as
P=
A
g
=
A
g0
[1 + s cos + d cos( m t )]
(4.6)
Then, the field flux linkage is calculated as
34
= n d = n
g
MMF dA
(4.7)
where MMF is the field magnetomotive force, and n is the turns function. In equation (4.2), eccentricity causes ripple torque, while in equation (4.3), the ripple torque, in turn, leads to a speed pulsation. Equations (4.4-4.7) show that air gap eccentricity results in harmonics in field flux linkage. With speed feedback and controller action, the
eccentricity-related fault harmonics spread to the controller variables and the motor supply voltage. All the variables in the motor and drive contain fault information. To be precise, for speed, electromagnetic torque, and the controller variables in a synchronous reference frame, the frequency of the main mixed eccentricity-related harmonics is given by equation (4.8), and the frequency of the main static eccentricityrelated harmonics is given by equation (4.9)
f ecc = f m = f1
1 s p 1 s nw 1] p
(4.8)
f ecc = f1[( R nd )
(4.9)
For motor terminal quantities in a stationary reference frame, the above harmonics are located at frequencies given by equations (4.10) and (4.11), respectively
f ecc = f1 (1
1 s ) p 1 s nw ] p
(4.10)
f ecc = f1 [( R nd )
(4.11)
35
4.2
Effects of Drive Controllers
A typical vector-controlled drive has two control loops, each with a PI controller, an inner current loop, and an outer speed loop, as shown in Figure 4.1. The vectorcontrolled drive calculates the spatial angular position of rotor flux from the feed-back speed and stator current. Then, the d-axis is aligned with the rotor flux, which is referred to as field-orientation. In this way, sinusoidal variables are modulated to be DC, and the steady state error can be efficiently eliminated using PI controllers. Furthermore, the
e motor torque can be controlled by adjusting the decoupled flux current, ids , and the e torque current, iqs , so that vector-controlled drives can emulate the operation of DC
drives. Because of its special configuration, a vector-controlled drive is also called a speed-controlled, current-regulated, indirect field-oriented drive. The PI controller functions like a low-pass filter, and the bandwidth determines its regulation ability. The controller generates an effective control signal only when the input signal is inside its bandwidth. In practice, the speed bandwidth, BW, is usually up to a few Hz because of the limited current capacity of the drive. The current PI controller forms the inner loop and its bandwidth, BWI, is much larger. Therefore, the cascade controllers are able to respond correctly to smooth out the error [13, 56]. Regarding equations (4.8) and (4.9), there are three possible relationships between the controller bandwidths and the eccentricity-related frequencies:
36
* m
PI
* I ds
* I qs
PI PI
s
e vqs
PWM VSI IM
m
e vds
i
e qs
e i ds
abc qd
IFO
m
Figure 4.1. Block diagram of a speed-controlled, current-regulated, indirect field-oriented drive.
Case 1:
BWI > 2 f ecc > BW
In this case, the speed pulsation resulting from air gap eccentricity is beyond the bandwidth of the speed controller, and the regulation ability of the speed controller is therefore weak. Ideally, the output of the speed controller, which is the reference torque current, contains only low-level eccentricity-related harmonics. The reference flux
current is always a constant value except for operation in field weakening. On the other hand, the regulation ability of the current controller is relatively strong. They force the actual stator current to track the references to contain low-level harmonics as well. Consequently, according to equation (4.1), through flux linkage, the harmonics in the non-uniform air gap will cause larger fault harmonics in the stator voltage. The fault harmonics in voltage or current are defined large or small with respect to the fundamental component and noise. Because the fault harmonics always have small magnitudes, larger harmonics are easier to monitor, and therefore detection reliability and sensitivity are improved. 37
Case 2:
BWI > BW > 2 f ecc
In this situation, the regulation abilities of both the speed and current PI controllers are strong. The fault signal in the feed-back speed makes the speed PI controller output a corresponding control signal. Hence, the harmonic level of the motor current becomes higher. However, it is not a common case in practice since the speed bandwidth is fixed after installation. Its variation is limited even when adjusted manually.
Case 3:
2 f ecc > BWI > BW
In this case, the regulation abilities of both the speed and current controllers are weak. The fault harmonics in the feedback speed are filtered by both the speed and current PI controllers. Only low-level harmonics exist in the motor voltage. This is equivalent to a line-fed motor, which means that most fault information exists in the stator current.
In most cases, except for operation at a very low speed, the mixed eccentricity of equation (4.8) always matches the first case, and the static eccentricity of equation (4.9) matches the third case. To detect mixed eccentricity, it is necessary to focus on Since voltage harmonics are larger than current
monitoring voltage harmonics.
harmonics, the detection is more sensitive and reliable. This explains why MCSA may be insufficient to detect rotor eccentricity in a closed-loop drive-connected induction motor. Similarly, when detecting static eccentricity, one should focus on monitoring current harmonics.
38
4.3
Effects of Mechanical Load
In practice, an induction motor is typically coupled to a mechanical load through a flexible coupling. At an early stage of rotor eccentricity faults, the shaft of the motor shifts from its normal position, while the shaft of the mechanical load is still fixed. The coupling between these two shafts actually allows a misalignment, as shown in Figure 4.2. In rotation, the misalignment leads to a position-varying load torque given by
Tload = TL + k sin( m t )
(4.12)
where TL is a constant load, k is the amplitude of the load oscillation caused by misalignment, and m is the mechanical speed that is equal to 2f 1 (1 s ) / p .
To
compensate for this exterior load oscillation, the controllers command the motor to generate a corresponding torque component according to equation (4.2). Therefore, the special frequency components caused by the misalignment are at the same frequency as the eccentricity-related fault harmonics and overlap with each other [7, 8]. As torque is proportional to current using vector control, this misalignment increases the current harmonics and may even make the current harmonics larger than the voltage harmonics.
39
induction motor
mechanical load
coupling
Figure 4.2. Coupling between an induction motor and a mechanical load in case of rotor eccentricity.
In summary, the distribution of eccentricity-related fault harmonics between the stator voltage and current depends on the drive as well as the mechanical load. Either voltage or current may contain larger fault harmonics. Reliable fault detection cannot be achieved based on just monitoring one parameter. In addition, in some applications, especially small induction motors, the actual motor terminal voltages are not readily available.
e Instead, the voltage space vector, v qds , which is available in the drive
controllers, can be used as the monitoring parameter.
Therefore, a combination of
e e monitoring voltage and current space vectors together, i.e., v qds and i qds , is able to ensure
good detection sensitivity and reliability. Since both space vectors are readily available in the drive controllers, this diagnostic scheme is sensorless and will not add any extra cost to the existing instrumentation system of the drive.
40
4.4
Modeling Air Gap Eccentricity in Closed-Loop Drive-Connected Induction Motors Introduction
4.4.1
Two methods are commonly used to simulate air gap eccentricity in induction motors: the winding function approach (WFA) and finite element analysis (FEA) [3, 1820, 26]. The idea of the WFA is first to model the air gap asymmetry by equation (4.4). Inductances of stator and rotor windings can then be calculated from the air gap, the turn function, the winding function, and the air gap area. Substituting the inductances into voltage and flux linkage equations, (2.8) and (2.9), which model an induction motor, any fault signal in the motor terminal quantities can be calculated. Once the inductances are determined, the simulation can be done by any computational software, such as Matlab or Simulink. Readers can refer to the references [18-20] for more detail of this
simulation method. The weakness of WFA is its accuracy. For example, WFA cannot simulate magnetic nonlinearities in the stator or rotor. Generally, the nonlinearities can only be approximated by Carters coefficient. In addition, it is impossible to analyze an air gap asymmetry caused by stator slots and rotor bars, since the surfaces of stator and rotor are treated as smooth and circular in WFA. FEA is another common simulation method for air gap eccentricity in electrical machines [3, 26]. FEA can incorporate the effects of magnetic nonlinearities and space harmonics because of machine magnetic circuit topology and winding layouts. The basic idea of FEA is to divide the whole motor, including the stator, rotor, shaft, and air gap, into triangle or rectangular finite elements (FE). In each FE, the partial differential
41
equations that model the motor are replaced by linear interpolation functions. The linear interpolation functions within all FEs are solved together with the boundary conditions. Today, more and more commercial FEA software packages are on the market. They usually provide a friendly user interface so that customers no longer necessarily spend time writing their own code for analyzing a motor. Once several motor design
parameters are determined, a motor model can be built up and numerical analysis can be conducted. In this research work, Ansoft Maxwell 2D software is used to simulate air gap eccentricity in a closed-loop drive-connected induction motor.
4.4.2 Finite element analysis of induction motors
The flow chart of the simulation program is shown in Figure 4.3. First, an induction motor is designed using Ansoft RMxrpt, which is electrical machine design software. The user must decide the design parameters. The RMxprt can then design the motor, calculate performance curves, output winding layout, and create a corresponding FEA model. The user-input design parameters include motor rated power, rated voltage, rated frequency, number of poles, stator material, number of stator slots, size of slots, stator winding layout, rotor material, number of rotor bars, size of bars, shaft material, and the size of the shaft. The main outputs from RMxprt include stator resistance, stator leakage reactance, rotor resistance, rotor leakage reactance, magnetic reactance, rotor lamination geometry, and various motor performance curves.
42
Design of an IM using RMxprt
FEA using EMpulse
Transient simulation of IM using MAXWELL 2D
Transient simulation of drive using Use Control Program
Postprocess of the simulation results
Figure 4.3. Flow chart of the simulation program.
In this research, a 70.87 kW, 460 V, two-pole, three-phase induction motor is designed using Ansoft RMxrpt. The 2D model of this motor can be seen in Figure 4.4. The shaft is the red center circle. The green cylinder, with the inner diameter the same as the diameter of the shaft, is the rotor material. The outer green cylinder is the stator. The lamination geometry of the motor is shown in Figure 4.5. The stator has 36 slots with a double-layer, 60o spread distribution winding. One pole pitch is 18 slots, since this is a two-pole machine. Each coil spans 16 slots, making this winding short-pitched by two slots. The coil sides belonging to the same phase have the same color, as seen in Figure 4.4. For example, the coil sides belonging to the a-
43
phase are all red, while the a-phase returning coil sides are orange. The motor has a squirrel-cage rotor with a total of 25 bars. The magnetic nonlinearities are simulated by defining the stator and rotor as nonlinear materials. Skewing is not considered. The typical performance curves of this induction motor are shown in Figures 4.6 to 4.10.
Rotor
Stator
Rotor bar
Shaft
Stator slot
Figure 4.4. 2-D model of the simulation motor.
Figure 4.5. Lamination geometry of the simulation motor.
44
200 180 160 140 Output Torque (N.m) 120 100 80 60 40 20 0 0 500 1000 1500 2000 2500 Speed (rpm) 3000 3500 4000
Figure 4.6. Performance curve of the motor in simulation: torque vs. speed.
250
200
Input Current (A)
150
100
50
0
0
500
1000
1500
2000 2500 Speed (rpm)
3000
3500
4000
Figure 4.7. Performance curve of the motor in simulation: current vs. speed.
45
6
x 10
4
5
4 Output Power (W)
3
2
1
0
0
500
1000
1500
2000 2500 Speed (rpm)
3000
3500
4000
Figure 4.8. Performance curve of the motor in simulation: power vs. speed.
1
0.5 Efficiency 0 -0.5 0
500
1000
1500
2000 2500 Speed (rpm)
3000
3500
4000
Figure 4.9. Performance curve of the motor in simulation: efficiency vs. speed.
46
1 0.9 0.8 0.7 Power Factor 0.6 0.5 0.4 0.3 0.2 0.1 0 0 500 1000 1500 2000 2500 Speed (rpm) 3000 3500 4000
Figure 4.10. Performance curve of the motor in simulation: power factor vs. speed.
Once the motor is designed and a corresponding FEA model is created, the finite element analysis can be conducted in Maxwell 2D. To do this, material properties and excitation source need to be decided first. Then, Maxwell 2D works as follows, as shown in Figure 4.11: To create the required finite element mesh, either automatically or from userdefined seeding requirements; To iteratively calculate the desired field solution and special quantities of interest, including force, torque, current, and speed; With EMpulse, to simulate the transient motion of the system; To allow customers to analyze, manipulate, and display field solutions. Maxwell 2D uses a software package called EMpulse to solve two-dimensional electromagnetic problems. EMpulse is a time-domain analysis software package that
47
solves coupled non-linear electromagnetic field, circuit, and motion problems using a time-stepping finite element approach. Air gap eccentricity can be implemented in
simulation by moving the rotor and its rotational from center their normal positions.
Select solver and drawing type
Draw geometry model, which can be optionally completed by RMxprt
Assign material properties
Assign boundary conditions and sources
Set up solution and motion criteria
Generate solution
Inspect solutions, view solution information, display field plots, and manipulate basic field quantities
Figure 4.11. Flow chart of Maxwell 2D.
48
4.4.3
Modeling vector-controlled drives
EMpulse has the capability to interact with an external control program. This program can be written in any language such as Fortran, C, C++, Pascal. The only requirement is that the program must be compiled into an executable program. In this research, the vector-controlled drive shown in Figure 4.1 is simulated by a control program written in C language. The flow chart of this program is shown in Figure 4.12. At the first time step, EMpulse reads the values specified in Maxwell 2D material manager, boundary manager, and solve setup modules. After solving for the fields, EMpulse writes mechanical speed and stator current data to a file named solution.ctl and then calls the control program. The control program calculates the control variables and then writes the supply voltage data into a file called user.ctl. EMpulse reads the values from this file for the simulation of the next step. Once EMpulse finishes solving the fields, it copies the values from solution.ctl to a file called previous.ctl. Thus, the control program has access to the solutions of both the current time step and the previous time step [27, 59]. Switching harmonics in PWM are mainly located at
f h = ( jm f k ) f 1
(4.13)
where f1 is the fundamental frequency, m f is the frequency modulation ratio, and j , k are integers. Compared with equations (4.8) and (4.9), switching harmonics have much higher frequency than eccentricity-related harmonics. Therefore, in the simulation, the PWM voltage-sourced inverter is assumed ideal to save simulation time and memory.
49
Initialize integral controllers
Read speed and current data from solution.ctl file
Calculate reference torque current I_qs of speed PI controller
Park transform of stator current; calculate slip frequency, angle, and Flux_dr
Park transform of stator voltage; write voltage data into user.ctl file; update integral controllers
Calculate reference voltages V_qs and V_ds of speed PI controllers
Figure 4.12. Flow chart of the drive control program.
The field orientation in vector control is calculated from the feed-back speed and stator current according to equations (4.14) to (4.16).
e = dr
R r Lm e i ds Rr + L r P
e Rr Lm iqs
(4.14)
s s =
Lr e dr
(4.15)
50
s = s s + r = s s + p m
(4.16)
where P is a derivative operator, Rr is the rotor resistance, Lm is the magnetic inductance, Lr is the rotor inductance, and r is the rotor electrical speed in rad/s. Parameters, such as Lm , Rr , the rotor time constant r = Lr Rr , and the reference flux
* current, I ds , are determined by the auto-tuning function of the drive. Particularly, r is * calculated from a single phase excitation test, Rr from a DC current test, Lm and I ds
from a no-load test. In the simulation, all the parameters are calculated in RMxprt. The proportional and integral gains of the speed and current PI controllers are calculated from bandwidth (BW) and phase margin (PM) [56]. The design should begin from the inner current loop and work toward the outer speed loop.
* i qs
k
e i qs
pI
k + iI s
' vqs
1 R
s
+ s ( L
s
L 2 m ) L r
Figure 4.13. Design of current PI controller.
As shown in Figure 4.13, the open-loop transfer function of the current loop is
G I ,OL ( s ) = (k pI +
k iI ) s
1 L2 R s + s ( Ls m ) Lr
(4.17)
51
where Rs is the stator resistance, and Ls is the stator reactance. The bandwidth and phase margin are equal to
G I ,OL ( jBW I ) = 1 G I ,OL ( jBW I ) = 180 + PM
(4.18) (4.19)
Therefore, the integral and proportional gains are calculated to be
k iI = BWI
L2 2 R + [ BWI ( Ls m )] Lr
2 s
L2 tan 2 {PM I + tan 1 [ BWI ( Ls m ) / Rs ]} + 1 Lr 2
(4.20)
k pI
k iI L2 1 = tan{PM I + tan [ BWI ( Ls m ) / Rs ]} BWI Lr 2
(4.21)
Since the current loop has a much larger bandwidth than the speed loop, once designed, the current loop can be considered an ideal transfer block in the design of the speed PI controller. The design of the speed loop is shown in Figure 4.14. Similarly, the integral and proportional gains can be calculated from bandwidth and phase margin as follows:
k i =
BW2 J eq L2 * p m ids 1 + tan 2 ( PM ) Lr
(4.22)
52
k p =
k i tan( PM ) BW
(4.23)
* m
k p
k + i s
1
* i qs
L2 p m I de s* 2 Lr
1 sJ eq
m
Figure 4.14. Design of speed PI controller.
It is noted that the above calculations use the Park transform given by
2 4 a cos( da ) cos( da ) cos( da ) d 2 3 3 b q = 3 sin( ) sin( 2 ) sin( 4 ) c da da da 3 3
(4.24)
where da is the angle between the d-axis and stator a-axis. With different values of da , the above integral and proportional gains will take on different forms.
4.5
Simulation Results
Four sets of simulation results are introduced: one for a healthy motor, one for a motor with a mixed rotor eccentricity fault, one for a motor with eccentricity and a position-varying load torque, and one for a motor with static eccentricity. In all four simulations, the reference speed is changed step-wise from zero to 3000 rpm at zero
53
seconds. The speed and current bandwidths of the drive are equal to 16 rad/s and 2000 rad/s, respectively.
4.5.1. Simulation of a healthy motor
In this simulation, a healthy induction motor drives a linear load whose torque is equal to 0.02n , where n is the motor speed in rpm. The simulation results are shown in Figures 4.15 to 4.22. Figures 4.15 and 4.16 demonstrate the motor start-up from standstill to a steady speed of 3000 rpm in around 1.5 sec. In Figure 4.17, the torque reaches a steady state value of 60 Nm, which is equal to the load torque. In Figures 4.18 to 4.20, the stator voltage, current, and flux linkage are shown to be symmetrical for a healthy three-phase induction motor. The controller variables, such as the flux and torque currents, and d-q reference voltages, are shown in Figures 4.21 and 4.22. They are modulated to be DC values in the synchronous reference frame. The controller variables contain harmonics even for a healthy motor because of the effects of stator slots, rotor bars, and nonsinusoidal windings.
54
3500 speed 3000 2500 2000 speed (Rpm) 1500 1000 500 0 -500
0
0.5
1
1.5 time (sec)
2
2.5
3
Figure 4.15. Simulated speed vs. time for a healthy motor.
400 rotor angular position 350 300 250 speed (Rpm) 200 150 100 50 0
0
0.5
1
1.5 time (sec)
2
2.5
3
Figure 4.16. Simulated rotor position vs. time for a healthy motor.
55
70 torque 60 50 40 torque (N-m) 30 20 10 0 -10
0
0.5
1
1.5 time (sec)
2
2.5
3
Figure 4.17. Simulated torque vs. time for a healthy motor.
400 300 200 voltage (V) 100 0 -100 -200 -300 -400 -500
v a v b v c
0.05
0.1
0.15
0.2
0.25 0.3 time (sec)
0.35
0.4
0.45
0.5
Figure 4.18. Simulated phase voltage vs. time for a healthy motor.
56
50 40 30 20 10 0 -10 -20 -30 -40 -50 0 0.5 1 1.5 time (sec) 2 2.5 3 ia ib ic
current (A)
Figure 4.19. Simulated phase current vs. time for a healthy motor.
1.5 lambdaa lambdab 1 lambdac
0.5 current (A)
0
-0.5
-1
-1.5
0
0.5
1
1.5 time (sec)
2
2.5
3
Figure 4.20. Simulated flux linkage vs. time for a healthy motor.
57
600 500 400 300 voltage (V) 200 100 0 -100 -200 -300 vsd vsq
0
0.5
1
1.5 time (sec)
2
2.5
3
Figure 4.21. Simulated regulation voltage vs. time for a healthy motor.
60 isd isq 50
40 current (A)
30
20
10
0
0
0.5
1
1.5 time (sec)
2
2.5
3
Figure 4.22. Simulated regulation current vs. time for a healthy motor.
58
4.5.2. Simulation of a motor with a mixed eccentric rotor
In the second simulation, a mixed eccentricity rotor is created by moving the rotor to left from its normal position by 10% of the normal air gap, and its rotational center right by 30% of the normal air gap. The motor is still driving the same load, whose torque is equal to 0.02n , where n is the motor speed in rpm. The simulation results are shown in Figures. 4.23 and 4.24. Compared to Figure 4.17, the torque contains more oscillation spikes in Figure 4.23 because of air gap eccentricity. After the motor reaches a steady state, the stator voltage and current space vectors are analyzed in the frequency domain. As shown in Figure 4.24, the eccentricity-related frequency is located at 50 Hz in the synchronous reference frame according to equation (4.8). The harmonic amplitudes are normalized to the fundamentals so that the harmonic level can be easily identified. In this simulation, the current harmonic is 0.031%, and the voltage harmonic is 0.12%. The stator voltage harmonic is almost fives times that of the current harmonic because of the influence of speed and current PI controllers.
59
70 torque 60 50 40 torque (N-m) 30 20 10 0 -10
0
0.5
1
1.5 time (sec)
2
2.5
3
Figure 4.23. Simulated torque vs. time for a faulty motor with a mixed eccentric rotor.
Harmonic amplitude (%)
0.08 0.06 0.04 0.02 0 10 20 30 40 50 60 Frequency (Hz) 70 80 90
iqd
100
Harmonic amplitude (%)
0.25 0.2 0.15 0.1 0.05 0 10 20 30 40 50 60 Frequency (Hz) 70 80 90
vqd
100
Figure 4.24. Space vector spectral analyses for faulty motor with a mixed eccentric rotor.
60
4.5.3. Simulation of a motor with mixed eccentricity and a position-varying load
The influence of the mechanical load is evaluated in this simulation. Besides air gap eccentricity, the load torque is set to 0.02n + 10 sin( m ) for the sake of simulating a position-varying load caused by misalignment, where m is the rotor position. The spectra of the voltage and current space vectors are shown in Figure 4.25. To
compensate for the position-varying load, the motor is commanded to generate a corresponding torque. The current and voltage harmonics therefore increase to 0.39% and 0.35%, respectively. Compared to the results in the second simulation, the current harmonic now becomes larger than the voltage harmonic.
Harmonic amplitude (%)
0.5 0.4 0.3 0.2 0.1 0 10 20 30 40 50 60 Frequency (Hz) 70 80 90
iqd
Harmonic amplitude (%)
0.5 0.4 0.3 0.2 0.1 0 10 20 30 40 50 60 Frequency (Hz) 70 80 90
vqd
Figure 4.25. Space vector spectral analyses for a faulty motor with mixed eccentricity and a positionvarying load.
61
4.5.4
Simulation of a motor with a static eccentric rotor
Although the focus of this investigation is mixed eccentricity, a motor with static eccentricity is simulated to verify the analysis in Section 4.2. Static eccentricity is created by moving the rotor and its rotational center left from the center of the stator by 30% of the normal air gap. The load torque is still equal to 0.02n . The spectra of the voltage and current space vectors are shown in Figure 4.26. The eccentricity-related frequencies are located at 1250 Hz and 1144.4 Hz in the synchronous reference frame according to equation (4.9). The current harmonics are 0.081% and 0.028%, while the voltage harmonics are 0.045% and 0.015%, respectively. For static eccentricity, the drive-connected induction motor responds like a line-fed motor. Therefore, more fault information exists in the stator current.
Harmonic amplitude (%)
0.1 0.08 0.06 0.04 0.02 0 1120 0.06 1140 1160 1180 1200 1220 Frequency (Hz) 1240 1260 1280
iqd
1300
Harmonic amplitude (%)
vqd 0.04 0.02 0 1120
1140
1160
1180
1200 1220 1240 Frequency (Hz)
1260
1280
1300
Figure 4.26. Space vector spectral analyses for a faulty motor with a static eccentric rotor.
62
4.6
Experimental Results
Four experiments are conducted to verify the analysis of the effects of drive controllers and the mechanical load on fault detection. Air gap eccentricity is
implemented, as described in Chapter 3. Current bandwidth of the drive is equal to 2000 rad/s, and speed bandwidth is determined by the auto-tuning function of the drive.
4.6.1
No-load test
The motor is supplied by the converter, but not coupled to any load, as shown in Figure 4.27. This test is designed to specifically investigate the effects of the drive controllers. The speed bandwidth is set to 25 rad/s by the auto-tuning feature. As shown in Figures 4.28 and 4.29, when the motor is running at speeds of 300 rpm and 1200 rpm, the frequency of eccentricity-related harmonics is located at 5 Hz and 20 Hz in the synchronous reference frame, respectively. The frequency is shown on the x-axis, and the y-axis is the harmonic amplitudes normalized to the fundamentals. For the operation at 300 rpm, the current and voltage harmonics are 0.001 and 0.0055, respectively. For the operation at 1200 rpm, the current and voltage harmonics are 0.0009 and 0.0013, respectively. According to the analysis in Section 4.2, the converter controllers push more fault information into the voltage. Therefore, voltage harmonics are larger than current harmonics for operation at both 300 rpm and 1200 rpm.
63
Figure 4.27. Experimental setup of no-load test.
x 10 2 Normalized iqd 1.5 1 0.5 0 4 x 10 6 4 2 0
-3
iqd
4.2
-3
4.4
4.6
4.8 5 5.2 Frequency (Hz)
5.4
5.6
5.8
6
vqd
Normalized vqd
4.2
4.4
4.6
4.8 5 5.2 Frequency (Hz)
5.4
5.6
5.8
6
Figure 4.28. Experimental results of no-load test, 300 rpm and BW=25 rad/s (auto-tuning).
64
x 10 10 Normalized iqd
-4
iqd
5
0 10 x 10 15 Normalized vqd 10 5 0 12 14 16 18 20 22 Frequency (Hz) 24 26 28 30
-4
12
14
16
18 20 22 Frequency (Hz)
24
26
28
30
vqd
Figure 4.29. Experimental results of no-load test, 1200 rpm and BW=25 rad/s (auto-tuning).
4.6.2 Motor loaded with a speed controller bandwidth equal to 16 rad/s (load test)
In the second experiment, the motor is used to drive a DC dynamometer, as shown in Figure 4.30. The output of the dynamometer is connected to resistor banks. The field voltage of the dynamometer is adjusted to 100 V. Because of the air gap eccentricity of the motor, the connection between the motor and dynamometer compose a misalignment. Compared to the first test, since the total inertia of the motor and load increases, the speed bandwidth is reduced to 16 rad/s after auto-tuning. As shown in Figures 4.31 and 4.32, although the motor still runs at 300 and 1200 rpm, the distribution of fault signals between the stator voltage and current is different in comparison to Figures 4.28 and 4.29. For the operation at 300 rpm, the current and voltage harmonics are 0.0295 and 0.027, respectively. For the operation at 1200 rpm, the current and voltage harmonics are 0.014 and 0.0077, respectively. The position-varying load caused 65
by a misalignment has a dominant influence on the distribution of fault harmonics, and now the current harmonics become larger.
Figure 4.30. Experimental setup of load test.
iqd Normalized iqd 0.03 0.02 0.01 0 3 3.5 4 4.5 5 5.5 Frequency (Hz) 6 6.5
vqd Normalized vqd 0.03 0.02 0.01 0 3 3.5 4 4.5 5 5.5 Frequency (Hz) 6 6.5 7
Figure 4.31 Experimental results of load test, 300 rpm and BW=16 rad/s (auto-tuning).
66
x 10 15 Normalized iqd 10 5 0
-3
iqd
10 x 10 8 Normalized vqd 6 4 2 0 10
-3
15
20 Frequency (Hz)
25
30
35
vqd
15
20 Frequency (Hz)
25
30
Figure 4.32 Experimental results of load test, 1200 rpm and BW=16 rad/s (auto-tuning).
4.6.3 Motor loaded with a speed controller bandwidth equal to 5 rad/s (load test)
In some applications, the speed bandwidth may be adjusted manually to achieve the required operational performance. For example, a lower speed bandwidth helps to avoid cogging but results in a slower response. In the third experiment, the motor still drives the same mechanical load as that in the second experiment. However, the speed bandwidth is manually reduced to 5 rad/s. Experimental results for the operation at 1200 rpm are shown in Figures 4.33 and 4.34. In both the synchronous and stationary
reference frames, the voltage harmonics are larger than the current harmonics, as expected. This is because the reduced speed bandwidth limits the ability of drive
controllers to compensate for the load oscillation caused by a misalignment. Therefore, the voltage harmonics can remain large.
67
6 Normalized iqd 5 4 3 2
x 10
-4
iqd
10 x 10 10 Normalized vqd 8 6 4 10
-4
12
14
16
18 20 22 Frequency (Hz)
24
26
28
30
vqd
12
14
16
18 20 22 Frequency (Hz)
24
26
28
30
Figure 4.33. Experimental results of load test, 1200 rpm and BW=5 rad/s (manual).
x 10 6 5 Normalized ia 4 3 2 1
-3
ia
10 x 10 5 Normalized vab 4 3 2 1 10
-3
20
30
40 50 Frequency (HZ)
60
70
80
vab
20
30
40 50 Frequency (HZ)
60
70
80
Figure 4.34. Experimental results of load test, 1200 rpm and BW=5 rad/s (manual).
68
4.6.4
Unbalanced disc test
A disc with holes is mounted on the motor shaft between the motor and flexible coupling. By placing bolts into the holes of the disc, an unbalance is created. By moving the bolts further from the center of the disc, a load unbalance is increased. This causes slight air gap eccentricity since there is a force pushing the rotor outwards in the radial direction. However, this also creates a position-varying load torque. Since the motor is no longer coupled to a dynamometer, the total inertia of the motor and load decreases and the speed bandwidth is then increased to 25 rad/s after auto-tuning. When the motor is running at 300 rpm, 600 rpm, and 1200 rpm, the main eccentricity-related frequency is located at 5 Hz, 10 Hz, and 20 Hz, respectively. As shown in Figures 4.36 to 4.38, the voltage harmonics are 0.00135, 0.005, and 0.00148, while current harmonics are 0.0011, 0.0008, and 0.00064, respectively. The voltage harmonics remain larger than the current harmonics. This is because, although there is a load oscillation on the motor, the load oscillation is not large enough to reverse the distribution of fault signals between the stator voltage and current. These results prove once again that the distribution of fault harmonics depends on both the drive controllers and the mechanical load. Reliable fault detection cannot be achieved by monitoring either voltage or current alone.
69
Figure 4.35. Experimental setup of unbalanced disc test.
x 10 15 10 5
-4
iqd
Normalized iqd
4 20 Normalized vqd 15 10 5 0 x 10
-3
4.2
4.4
4.6
4.8 5 5.2 Frequency (Hz)
5.4
5.6
5.8
6
vqd
4.2
4.4
4.6
4.8 5 5.2 Frequency (Hz)
5.4
5.6
5.8
6
Figure 4.36. Experimental results of unbalanced disc test, 300 rpm and BW=25 rad/s (auto-tuning).
70
x 10 10 Normalized iqd 8 6 4 2 6 6 Normalized vqd 5 4 3 2 1 x 10
-4
iqd
7
-3
8
9
10 11 Frequency (Hz)
12
13
14
vqd
7
8
9
10 11 Frequency (Hz)
12
13
14
Figure 4.37. Experimental results of unbalanced disc test, 600 rpm and BW=25 rad/s (auto-tuning).
8 Normalized iqd 6 4 2
x 10
-4
iqd
10 x 10 15 Normalized vqd
-4
12
14
16
18 20 22 Frequency (Hz)
24
26
28
30
vqd
10
5 10 12 14 16 18 20 22 Frequency (Hz) 24 26 28 30
Figure 4.38. Experimental results of unbalanced disc test, 1200 rpm and BW=25 rad/s (auto-tuning).
71
The first and second experiments are conducted at several different speeds, and the results are shown in Figure 4.39. The upper diagram in Figure 4.39 refers to the noload test and shows that the voltage harmonics remain larger than the current harmonics, as shown in Figures 4.28 and 4.29. Without the mechanical load, the distribution of fault harmonics is basically determined by the drive controllers. However, in the lower
diagram corresponding to the load test, the current contains larger harmonics because of the misalignment associated with the mechanical load. The distribution of fault
harmonics strongly depends on the operating conditions. Monitoring voltage and current harmonics together is able to ensure good detection reliability and sensitivity.
x 10
-3
6 Normalized harmonic amplitudes
No-load test vqd iqd
4
2
0 200 0.03 Normalized harmonic amplitudes
400
600
800
1000 1200 Speed (rpm) Linear load test
1400
1600
1800
vqd iqd 0.02
0.01
0 200
400
600
800
1000 1200 Speed (rpm)
1400
1600
1800
Figure 4.39. Harmonic magnitudes vs. speed in no-load test and load test.
72
4.7
Conclusions
This chapter analyzed the effects of drive controllers and mechanical load on the distribution of fault harmonics between the stator voltage and current. It showed that the distribution of fault harmonics strongly depended on the operating conditions. Under some operating conditions, current harmonics were much smaller than voltage harmonics, in which traditional MCSA monitoring only stator current was insufficient to provide reliable and sensitive detection. Regarding practical limits, a detection scheme was proposed based on monitoring fault harmonics in both the voltage and current space vectors together. This detection scheme is sensorless and can be implemented at no additional cost. A direct time-stepping coupled finite element analysis model was then introduced to simulate air gap eccentricity in a closed-loop drive-connected induction motor. This model could simulate the effects of magnetic nonlinearities and space harmonics because of the machine magnetic circuit topology and winding layouts. Experiments were conducted. The simulation and experimental results validated the analysis of the distribution of fault harmonics and the feasibility of the proposed detection scheme.
73
CHAPTER 5
DETECTION OF AIR GAP ECCENTRICITY USING AN ARTIFICIAL NEURAL NETWORK
5.1 Introduction
With an adjustable speed drive, motor operating conditions, such as speed and mechanical load, vary widely. The amplitudes of fault harmonics change with operating conditions accordingly, as shown in Figure 4.39. The fault harmonic amplitudes change with speed as the motor and mechanical load form a torsional spring system. This torsional spring system has its own natural frequency and resonates with different amplitudes at different operating conditions. The resonance modifies the air gap and consequently the eccentricity-related fault harmonics. The resonance depends on several factors, such as the inertia of the motor and its mechanical load. If the load is composed of multiple parts connected together by compliant couplings, the resonance also depends on each inertial part, the inter-connection, and installation [57]. The relationship
between the fault harmonic amplitudes and operating conditions is too complex to be formulated as strict analytical equations. Furthermore, it is even impossible to measure fault harmonic amplitudes corresponding to all operating conditions experimentally, since the speed and load may change continuously. To monitor motor conditions, actual measurements on a running motor need to be compared with thresholds obtained on a healthy motor [3, 6, 10]. The thresholds are eccentricity-related harmonic amplitudes of the healthy motor. The relationship between thresholds and operating conditions is therefore necessary in order to establish a reliable
74
condition monitoring system. This investigation proposes the use of an artificial neural network to learn this complex relationship through training. Once the training is
complete, the neural network can estimate the corresponding eccentricity-related harmonic amplitudes for other operating conditions. If the training is based on the experimental data of a healthy motor, the estimations can be used as thresholds to assess the motor condition. Compared with traditional methods such as a look-up table, the neural network provides more accurate estimation because of its non-linear interpolation. Meanwhile, the neural network does not require large memory storage, because it is usually composed of only a few neurons. The detection algorithm consists of four steps: data acquisition and preprocessing, feature extraction, threshold calculation, and fault detection. The neural network is used in the third and fourth steps. Experimental results are included to verify the feasibility of this detection scheme.
5.2
Data Acquisition and Preprocessing
The most effective method for analyzing data in the frequency domain is the Fourier transform. The discrete Fourier transform (DFT) is typically used for discrete sampling systems. A common requirement of spectrum analysis using the Fourier
transform is that the signal, x, is stationary. However, in the detection, the frequency and magnitudes of the stator voltage and current of a drive-connected induction motor always change. They are non-stationary.
75
To improve the accuracy of spectrum analysis, the short time Fourier transform (STFT) is developed [11]. The STFT partitions the sampled data with a sliding window of a short width. In each window, the signal is assumed stationary and is analyzed in the frequency domain using the DFT. For most variable speed applications in industry, excluding servo motors, assuming a steady state of 1-2 seconds is reasonable since the mechanical system usually has a large inertia time constant. In this investigation, the window is selected to be 2 seconds at a sampling rate of 20 kHz. This window provides enough resolution in the spectrum analysis for speeds higher than 150 rpm. Several indices can be used to determine whether there is a variation of operating condition in each window. For example, if changes in the frequency or magnitude of the fundamental current remain less than preset tolerances, the collected data is considered stationary. The experimental AC drive used in this research does not provide access to the controller parameters, such as the voltage and current space vectors. The space vectors are calculated from two line-to-line voltages and two phase currents measured at motor terminals. The experimental motor does not have a neutral. The third phase can be calculated from the two phase measurement, and then three-phase currents are transformed into - reference frame according to
1 1 a 1 2 2 2 b = 3 3 3 c 0 2 2
(5.1)
where a, b, and c are the currents in a three-phase reference frame, and and are the currents in a two-phase reference frame. The - reference frame is actually a stationary 76
reference frame parallel to the rotational, synchronous d-q reference frame oriented to the rotor flux, as shown in Figure 5.1.
b
q
e iqds
i
d
a
c
Figure 5.1. Relationship of three reference frames: a-b-c, -, and d-q.
e The current space vector, iqds , and its phase angle, i , with respect to the
stationary -axis are first calculated from i and i . The d-axis is first assumed to
e coincide with iqds , and the phase angle between the d-axis and -axis is equal to i
initially. The actual phase angle of the rotor flux is defined as , which is also the actual
e phase angle of the d-axis in a field-oriented frame. Since the current phasor iqds rotates
synchronously with the d-q reference frame, i and are stationary relative to each other. There is a constant phase angle between them. The experimental AC drive provides the value of the actual reference flux current,
* e I ds , which can be read from the user interface. It is a constant value. The quantity ids is
e * calculated by changing angle i . Whenever I ds (the average value of ids ) becomes equal
^
77
* to the given I ds , the field orientation is achieved. The process for the above calculation is
shown in Figure 5.2.
ia , ib , ic i , i , = tan 1 (i / i )
in a stationary reference frame
Decide angle increment and error tolerance of flux current I_ds
* , I ds
Current Park Transfrom from stationary frame to synchronous frame
e e i , i ids , iqs
* * e I ds average(ids ) < I ds
no
= +
yes
Voltage Park Transform from stationary frame to synchronous frame
e e va , vb , vc vds , vqs
End
Figure 5.2. Flow chart of reference frame transform in the data preprocessing phase
5.3
Feature Extraction
e e Once the spectra of the stator voltage and current space vectors, v qds and i qds , are
calculated, the parameters can be analyzed in the frequency domain. To reduce the large amount of spectral information to a usable level, a frequency filter is used to extract feature components pertinent to the detection of air gap eccentricity. This filter is a 78
window centered at the eccentricity-related frequency given by equation (4.8), with a width of 2 Hz and amplitude of one. The feature components can be calculated in several ways, for example, averaging all the FFT components within that window, or selecting the maximum component within that window as used in this investigation. The
maximum components are denoted as v f ecc and i f ecc for the voltage and current, respectively.
5.4
Training and Testing of the Artificial Neural Network
After the feature components of the stator voltage and current space vectors are extracted, an artificial neural network is used to learn the relationship between the feature components and operating conditions and to predict motor conditions. A neural network is composed of simple processing elements (PE) operating in parallel. The network function is determined largely by the connections between elements. A neural network can be trained to perform a particular function by adjusting the values of the connections (weights) between each element. This investigation uses a supervised three-layer feed-forward network that uses back-propagation as a training algorithm. The input layer represents the system inputs. The single hidden layer provides the learning capability of the network. The output layer consists of one neuron y that is an estimation of (v f ecc + i f ecc ) . The neural network is first trained with samples of a healthy motor. Once the training is complete, the weights are frozen and the neural network represents the relationship between operating conditions and eccentricity-related harmonic magnitudes of a healthy motor. 79 Once air gap
^
eccentricity sets in, the amplitudes of the measured eccentricity-related harmonics y of the stator voltage and current space vectors will become continuously larger than y of the healthy motor predicted by the neural network. Various techniques can be utilized to train the neural network to learn harmonic amplitudes, y = v f ecc + i f ecc , corresponding to different operating conditions. The basic idea is to adjust the weights to minimize the mean square error (MSE) between neural network outputs y and actual measurements y . The structure of the neural network is determined heuristically. For example, it is known that signal y is affected by operating conditions. However, the parameters
^
representing operating conditions need to be determined and sent to the inputs. The activation functions need to be selected based on the property of fault harmonics. The process to determine the neural network is explained below.
5.5
Experimental Results
The neural network training data are collected on a healthy motor when the speed changes from 150 rpm to 1755 rpm (motor nameplate speed) at intervals of 25 rpm, while the field voltage of the dynamometer changes from 90 V to 125 V at intervals of 5 V. There are a total of 520 operating points. Two sets of validation data are collected on both a healthy and a faulty motor. The first set of validation data is sampled when the speed is equal to {150, 300, 450, 600, 750, 900, 1050, 1200, 1350, 1500, 1650, 1755 rpm}, while the field voltage for each
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speed is set equal to {90, 95, 100, 105, 110, 115, 120, 125 V}, giving a total of 96 points. The second set of validation data is sampled when the speed is equal to {600, 712, 887, 900, 1037, 1189, 1200, 1362, 1500, and 1563 rpm}, while the field for each speed voltage is set equal to {90, 95, 100, 105, 110, 115, 120 V}, giving a total of 70 points. The first set of validation data is collected at the same speed as the training data to validate the learning ability of the neural network. The second set of validation data is collected at different speeds to validate the ability of the neural network to interpolate. Three types of neural networks are trained and tested with above experimental data.
5.5.1. Type 1 neural network
The structure of the first neural network is shown in Figure 5.3. The output of the network is y , the sum of the eccentricity-related harmonics of the stator voltage and current space vectors, each normalized to their respective fundamental values. The neural network has two inputs: the motor speed and the fundamental frequency of the stator current, both normalized to the nameplate values of the motor. parameters actually determine the slip according to These two
^
s = 1
p m 60 f 1
(5.2)
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where s is the slip, p is the number of pole-pairs, m is the speed, and f1 is the fundamental frequency. One value for slip corresponds to one point at the mechanical characteristic of the induction motor.
measured value
y = (v f ecc + i f ecc )
m
estimated value
+
f1
y = (v f ecc + i
f ecc
)
-
e mean iqs
( )
update weights train
detection
Figure 5.3. Structure of the artificial neural network.
The neurons in the hidden layer use the hyperbolic tangent sigmoid activation function and the output neuron uses a linear activation function, as shown by Figures 5.4 and 5.5. Their mathematical definitions are given by
f ( n) =
2 1 (1 + e 2 n )
(5.3) (5.4)
f ( n) = n
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hyperbolic tangent sigmoid activation function 1 0.8 0.6 0.4 0.2 f(n) 0 -0.2 -0.4 -0.6 -0.8 -1 -5 -4 -3 -2 -1 0 n 1 2 3 4 5
Figure 5.4. The hyperbolic tangent sigmoid activation function.
linear activation function 5 4 3 2 1 f(n) 0 -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 0 n 1 2 3 4 5
Figure 5.5. The linear activation function.
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The training is complete after 2000 epochs. The training results are shown in Figures 5.6 and 5.7. Figure 5.6 shows that the training error is stable after 1400 epochs. The weights are then frozen and the 520 data points in the training set are passed through the neural network to verify y for this small training error, as illustrated in Figure 5.7. Because of the error, it is necessary to conduct the testing at several different operating conditions rather than at only one point. An air gap eccentricity fault is determined only when measurements are consistently larger than estimated thresholds. In this way, the effect of estimation errors in fault detection is reduced. The eccentricity fault is now introduced and the faulty motor is operated at 96 operating points that are included in the training set of 520. The results appear in Figure 5.8. The upper diagram corresponds to the validation data collected on a faulty motor, while the lower one corresponds to the validation data collected on a healthy motor. In the upper diagram, y is compared with 1.2 y , which is the estimated threshold of a 20% margin above the healthy motor values. Since y remains consistently larger than the estimated threshold, the eccentricity fault can be detected. In the lower diagram, y is compared with y to verify the learning ability of the neural network. The experimental measurements y are equal to estimations y at most operating points.
^ ^ ^ ^ ^
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10
0
10
-1
10 Mean square error
-2
10
-3
10
-4
10
-5
10
-6
10
-7
0
200
400
600
800 1000 1200 1400 1600 1800 2000 Epochs
Figure 5.6. Training process of the neural network.
0.014 y NN Est. y 0.012 Sum of harmonic amplitudes (%)
0.01
0.008
0.006
0.004
0.002
0
0
100
200
300 Operating point
400
500
600
Figure 5.7. Training results of the neural network.
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ANN testing result on a faulty motor 0.06 Normalized vqd+iqd 0.04
Measured y NN estimated 1.2y
0.02
0
0
10
20
40 50 60 70 Operating conditions ANN testing result on a healthy motor
30
80
90
100
0.015 Normalized vqd+iqd
Measured y NN estimated y
0.01
0.005
0
0
10
20
30
40 50 60 Operating conditions
70
80
90
100
Figure 5.8. Experimental results of Type 1 neural network with the first set of validation data.
ANN testing result on a faulty motor 0.1 Normalized vqd+iqd 0.08 0.06 0.04 0.02 0 0 x 10
-3
Measured y NN estimated 1.2y
10
30 40 50 Operating conditions ANN testing result on a healthy motor
20
60
70
8 Normalized vqd+iqd 6 4 2 0
Measured y NN estimated y
0
10
20
30 40 Operating conditions
50
60
70
Figure 5.9. Experimental results of Type 1 neural network with the second set of validation data.
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The experimental results of the second set of validation data are shown in Figure 5.9. Now the faulty motor is operated at different points than the training set of 520. The neural network cannot detect the faulty motor because the estimated threshold becomes larger than the measurement at point 66. The experimental results of the healthy motor are shown in the lower diagram of Figure 5.9. There are errors between y and y because the speeds of the test data and the training data are different. However, the errors will not cause a wrong prediction of mistaking the healthy motor as a faulty motor since
y
^
is not consistently larger than y .
^
5.5.2. Type 2 neural network
With AC drives, the fundamental frequencies of the voltage and current change with speed. This variation changes the slip-torque characteristic of an induction motor, as shown in Figure 5.10. The linear load used in this investigation intersects the different motor curves at different operating points in Figure 5.10. Thus, the two inputs of the Type 1 neural network in Section 5.5.1 are not enough to represent an operating condition since they can decide only the slip. The Type 2 neural network has three input
components: the speed, the fundamental frequency of the stator current, and the q-axis
e torque current i qs , all normalized to the nameplate values. Again, the first two inputs
e determine the slip. Since the output torque is proportional to i qs in the vector control, the
torque is determined by the third input. Now the neural network is able to identify an operating point by torque and slip together.
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0 0.1 0.2 0.3 0.4 Slip 0.5 0.6 0.7 0.8 0.9 1 0 20 40 60 80 100 120 Torque (N.m) 140 motor at f1 motor at f2 motor at f3 mechanical load 160 180 200
Figure 5.10. Slip-torque characteristics of the motor and load with AC drives.
Once again, the neural network is trained and tested. The experimental results are shown in Figures 5.11 and 5.12. In Figure 5.11, the performance of neural network is tested by the first set of validation data. The neural network distinguishes the faulty motor from the healthy motor, as it does for the Type 1 neural network. However, compared to Figure 5.9, the Type 2 neural network corrects the wrong estimation at point 66 made by the Type 1 neural network tested with the second set of validation data, as shown in the upper diagram of Figure 5.12. Measurements y become consistently larger than estimations y and the motor is predicted to be faulty. This proves that the third
e input i qs helps improving the performance of the neural network.
^
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ANN testing result on a faulty motor 0.15 Normalized vqd+iqd 0.1 0.05 0 -0.05 Measured y NN estimated 1.2y
0
10
20
40 50 60 70 Operating conditions ANN testing result on a healthy motor
30
80
90
100
0.015 Normalized vqd+iqd Measured y NN estimated y 0.01
0.005
0
0
10
20
30
40 50 60 Operating conditions
70
80
90
100
Figure 5.11. Testing results of Type 2 neural network with the first set of validation data.
ANN testing result on a faulty motor 0.05 Normalized vqd+iqd 0.04 0.03 0.02 0.01 0 0 x 10
-3
Measured y NN estimated 1.2y
10
30 40 50 Operating conditions ANN testing result on a healthy motor
20
60
70
8 Normalized vqd+iqd 6 4 2 0
Measured y NN estimated y
0
10
20
30 40 Operating conditions
50
60
70
Figure 5.12. Testing results of Type 2 neural network with the second set of validation data.
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5.5.3. Type 3 neural network
The training data y = v fecc + i fecc collected on a healthy motor have small magnitudes. In the Type 3 neural network, y is scaled by a preset constant (e.g., 100) to fall within the range of the sigmoid functions, which improves the performance of the neural network. In addition, as shown in the upper diagram of Figures 5.11 and 5.12, the neural network gives negative estimations y at some operating conditions for a faulty motor. However, the actual eccentricity-related harmonics are always larger than zero. Negative outputs should be avoided to prevent the weights from being updated in the wrong direction. The linear activation function of the output neuron is therefore replaced by a logarithmic sigmoid activation function of equation (5.5) whose output is always positive as shown in Figure 5.13.
^
f ( n) =
1 (1 + e n )
(5.5)
logarithmic sigmoid activation function 1 0.9 0.8 0.7 0.6 f(n) 0.5 0.4 0.3 0.2 0.1 0 -5 -4 -3 -2 -1 0 n 1 2 3 4 5
Figure 5.13. The logarithmic sigmoid activation function.
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The testing results are shown in Figures 5.14 to 5.19. Figures 5.14 and 5.19 show the experimental results with the first and second sets of validation data in 2-D, respectively. They support that the neural network can detect the faulty motor correctly, same as the Type 1 and Type 2 neural networks. However, the negative output from the neural network is now eliminated. Figures 5.15 and 5.16 give the same testing results as the first set of validation data in 3D by plotting the estimation against field voltage and speed. In Figure 5.15, the measurement surface for the faulty motor remains above the estimation surface for the healthy motor. However, the two surfaces exchange their positions in Figures 5.16 since the measurement surface and estimation surface both apply to a healthy motor. Figures 5.17 and 5.18 confirm the diagnostic performance of the neural network when the motor runs from low to full speed and light to full load. The two different patterns given by the neural network can be distinguished by software. It is clear that the Type 3 neural network is feasible for detecting rotor eccentricity faults over the entire range of operating conditions of the experimental induction motors, including those conditions where it has not been trained. In practice, it is unlikely that a motor drive could be taken from no-load to full load, at many different speeds, simply to train the neural network. Figure 5.20 explains how this can be overcome by simply training with a data set gathered during the first few hours or days after commissioning [53]. After this training, the training data changes only when a new operating condition appears. Once new data is added into the training set, the neural network is trained again.
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ANN testing result on a faulty motor 6 Normalized vqd+iqd
Measured y NN estimated 1.2y
4
2
0
0
10
20
40 50 60 70 Operating conditions ANN testing result on a healthy motor
30
80
90
100
1.5 Normalized vqd+iqd
Measured y NN estimated y
1
0.5
0
0
10
20
30
40 50 60 Operating conditions
70
80
90
100
Figure 5.14. Testing results of Type 3 neural network with the first set of validation data.
Figure 5.15: Testing results of Type 3 neural network with the first set of validation data on a faulty motor shown in 3D.
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Figure 5.16: Testing results of Type 3 neural network with the first set of validation data on a healthy motor shown in 3D.
Figure 5.17: Testing results of Type 3 neural network with the first set of validation data on a faulty motor shown in 3D.
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Figure 5.18: Testing results of Type 3 neural network with the first set of validation data on a healthy motor shown in 3D.
Faulty motor 5 Normalized vqd+iqd 4 3 2 1 0 0 10 20 30 40 Operating conditions Healthy motor 50 60 70 Measured y NN estimated 1.2y
0.8 Normalized vqd+iqd 0.6 0.4 0.2 0 Measured y NN estimated y 0 10 20 30 40 Operating conditions 50 60 70
Figure 5.19: Testing results of Type 3 neural network with the second set of validation data.
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Start
DAQ training
Enough data?
N
Y Training
Testing N
Measurement > threshold
Training
N
New operating condition?
Y
Update training data
Y Count times testing N
Times > limit
Y Trigger alarm
End
Figure 5.20. Flow chart of the detection scheme including updating processes
5.6
Conclusions
This chapter described a detection scheme with the use of an artificial neural network. The detection was based on monitoring the fault harmonics of the stator voltage and current space vectors together. The artificial neural network was used to learn the complex relationship between fault harmonic amplitudes and operating conditions. Once the learning was complete, the neural network could estimate the thresholds corresponding to different operating conditions, which was then used to predict motor conditions. The design process of the neural network was illustrated. The training and testing results showed that the Type 3
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neural network gave the best performance. The experimental results validated that the Type 3 neural network was feasible for fault detection over the entire range of operating conditions of the experimental motors.
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CHAPTER 6
EFFECT OF AIR GAP ECCENTRICITY ON SURGE TEST DATA
6.1 Introduction
In many cases, an inexpensive and reliable off-line method for eccentricity detection can be useful, especially for routine and detailed maintenance. On-line
methods are typically based on monitoring special frequency components in motor stator voltage and current, and require data sampled with high resolution and noise immunity. This chapter illustrates the relationship between air gap eccentricity and surge test waveforms that are commonly used for detecting stator winding insulation problems. Air gap eccentricity makes surge waveform rotor-position dependent. In this way the
eccentricity can be clearly seen without any spectral analysis of voltage or current, but still in a completely unobtrusive manner. In this way eccentricity can be detected with minimal noise interference and a high degree of reliability using test equipment that many users already have on hand. Surge testing is performed with an impulse generator, which contains an oscilloscope-type display to observe the surge waveform in progress. In general, the impulse generator consists of a capacitor and a controllable switch. The capacitor is first charged to a high DC vol...