Comparative Investigation of Diagnostic Media for Induction Motors: A Case of Rotor Cage Faults

Transcription

1 1092 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 47, NO. 5, OCTOBER 2000 Comparative Investigation of Diagnostic Media for Induction Motors: A Case of Rotor Cage Faults Andrzej M. Trzynadlowski, Fellow, IEEE, and Ewen Ritchie, Member, IEEE Abstract Results of a comparative experimental investigation of various media for noninvasive diagnosis of rotor faults in induction motors are presented. Stator voltages and currents in an induction motor were measured, recorded, and employed for computation of the partial and total input powers and of the estimated torque. Waveforms of the current, partial powers and, total power, and estimated torque were subsequently analyzed using the Fast Fourier Transform. Several rotor cage faults of increasing severity were studied with various load levels. The partial input power was observed to exhibit the highest sensitivity to rotor faults. This medium is also the most reliable, as it includes a multiplicity of fault-induced spectral components. Index Terms Diagnostic media, fault diagnosis, induction motors, rotor faults. A theoretical discussion of the diagnostic potential of these media is presented briefly. The experimental arrangement is described and the results are presented and discussed. The paper concludes on the relative usefulness and reliability of the five diagnostic media studied when attempting to identify a faulty rotor cage. II. THEORETICAL BACKGROUND For a hypothetical ideal motor supplied from a balanced three-phase source of sinusoidal voltages and driving a constant load, the following waveforms of selected stator voltages and currents may be assumed: I. INTRODUCTION NONINVASIVE diagnosis of electric machine faults has attracted a vivid interest of researchers, due to both the high importance of this issue as well as the abundance of improved hardware and software tools for signal processing. Various approaches to fault detection have been reported in the literature. Use of the machine intelligence systems [1] [3], and spectral analysis ( signature analysis ) of a selected motor variable, usually the stator current [4], [5], are the most common approaches. The motor variable indicative of faults in the motor is referred to as a diagnostic medium. Published studies on diagnostic media other than the current dealt with the input power and the estimated torque [6] [8]. This paper reports results of research on sensitivity of various diagnostic media. Specifically, their spectral response to bar and ring breakage in the rotor cage of an induction motor supplied directly from the power system was investigated experimentally. The diagnostic media studied included the following: 1) line current, in phase of the supply line; 2) partial input power, calculated as a product of the line-to-line voltage and line current ; 3) partial input power, calculated as a product of the line-to-line voltage and line current in phase of the supply line; 4) total input power, a sum of and ; 5) estimated torque of the motor. Manuscript received January 15, 1999; revised August 3, Abstract published on the Internet July 1, This paper was presented at the 1999 IEEE Industry Applications Society Annual Meeting, Phoenix, AZ, October 3 7, A. M. Trzynadlowski is with the Department of Electrical Engineering, University of Nevada, Reno, NV USA ( chin@ee.unr.edu). E. Ritchie is with the Institute of Energy Technology, Aalborg University, DK-9220 Aalborg East, Denmark. Publisher Item Identifier S (00) (1) (2) where, rms values of the line-to-line voltage and line current, respectively; supply frequency in radians per second; power-factor angle. Multiplying by and by yields partial instantaneous input powers and given by and The two partial powers add up to the total instantaneous input power, expressed by the well-known formula Thus, in an ideal motor, the total instantaneous input power is constant and it is equal to the average real power supplied to the motor. This approach to determination of the total input power corresponds to the popular two-wattmeter method of power measurement. (3) (4) (5) (6) (7) /00$ IEEE

2 TRZYNADLOWSKI AND RITCHIE: INVESTIGATION OF DIAGNOSTIC MEDIA FOR INDUCTION MOTORS 1093 Fig. 1. Experimental setup. Fig. 3. Spectrum of line current: fault 1, s = 0:06. Fig. 2. Spectrum of line-to-line voltage. When an abnormality, such as the rotor cage fault, motor-load shaft misalignment, broken teeth in the load gearbox, or vibration, develops in the drive system, the current, torque, and speed of the motor are affected, typically, in a periodic manner. In the case of periodic disturbances, all three line currents, and are simultaneously modulated with the fundamental frequency of the fault-induced oscillation of motor variables. Thus, currents in phases and of the supply line may now be expressed as Fig. 4. Spectrum of partial power p : fault 1, s =0:06. sideband components at frequencies. Corresponding expressions for the partial powers are (8) (9) where denotes the modulation depth (modulation index) and. The value of the modulation index depends on the severity of the abnormality. Substituting (3) in (8) yields and (11) (12) (10) indicating that the spectrum of stator current contains, apart from the fundamental equal to the supply frequency,two Clearly, in addition to the fundamental, here equal, and sideband components, at, the partial powers have a fourth spectral component, directly at, subsequently called a characteristic component. This component is characteristic of the abnormality, not of the motor.

3 1094 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 47, NO. 5, OCTOBER 2000 Fig. 5. Spectrum of partial power p : fault 1, s = 0:06. Fig. 7. Spectrum of estimated torque: fault 1, s =0:06. Fig. 6. Spectrum of total power: fault 1, s =0:06. The total input power, given by (13) has only the dc and characteristic components. Note that amplitude of the characteristic component is different for each of the powers studied. Specifically, if, the largest characteristic component is that of, while for it is the characteristic component of that has the highest value. Throughout the whole range of the possible power-factor angle of induction motors, the characteristic component of is greater than that of. This indicates to be the monitored power (this is only valid for the positive phase sequence assumed in (1) (4) and for an induction machine working as a motor). In practice, the current is modulated with respect to not only the amplitude but also the phase, and the modulation process is more complex than that described by (9), but the derived equations, (10) (13), provide an adequate basis for qualitative assessment of individual diagnostic media. Fig. 8. Spectrum of line current: fault 1, s =0:02. The developed torque of the induction motor is roughly proportional to, therefore, similar spectral makeup of these two variables can be expected. Since direct torque measurements are impractical, the estimated torque was used as a diagnostic medium. Here, this torque was calculated as (14) where number of poles;, direct and quadrature components of the stator flux vector, respectively;, components of the stator current vector. The stator flux vector was computed from and the vector of the stator voltage as (15)

4 TRZYNADLOWSKI AND RITCHIE: INVESTIGATION OF DIAGNOSTIC MEDIA FOR INDUCTION MOTORS 1095 Fig. 9. Spectrum of partial power: fault 1, s = 0:02. Fig. 11. Spectrum of partial power: fault 2, s =0:06. Fig. 10. Spectrum of partial power: fault 3, s =0:06. where denotes the stator resistance and the and components of the initial stator flux vector were selected so that and had no dc component (offset). III. EXPERIMENTAL SETUP In the experiments, a 1.1-kW 400-V, 50-Hz two-pole induction motor with the stator resistance of 8.8 /ph was used. As shown in Fig. 1, it was supplied directly from the power line and equipped with voltage, current, and speed sensors. The load, a dc generator with a resistive load, allowed setting the desired torque. Recorded data were subsequently processed using the Matlab software package. The Fast Fourier Transform (FFT) was computed and the power spectra were plotted. Faults of various severity were produced in the 16-bar rotor. The following cases were studied experimentally: 1) healthy rotor; 2) one bar partly broken; 3) one bar broken; 4) two bars broken; 5) three bars broken; and 6) both a bar and the end ring broken. For Fig. 12. Spectrum of partial power: fault 4, s =0:06. each case, voltage and current measurements were taken for the motor operating with various values of slip. For each variable, 2 values were recorded, with the sampling frequency of 4096 Hz. For the purpose of this study, only cases 3)-6), subsequently called fault 1, fault 2, fault 3, and fault 4, respectively, were considered, each with three slip values: 0.02, 0.04, and Advantage was taken from the well-known fact that a rotor cage fault results in sideband harmonics of the stator current that differ from the fundamental by even multiples of the slip frequency [9]. Hence, for example, for the supply frequency of 50 Hz and slip of 0.04, sideband components closest to the 50-Hz fundamental may be expected in the power spectrum of current at ( ) Hz, that is, at 46 Hz and 54 Hz. Power spectra were determined in the per-unit format, with a logarithmic amplitude scale. As the base value of total power and torque, the amplitude of the dc component was used. The amplitude of the fundamental, 50-Hz, component was chosen as the base value for voltage and current. Spectra of the partial

5 1096 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 47, NO. 5, OCTOBER 2000 TABLE I AMPLITUDES OF MAIN SPECTRAL COMPONENTS (db) power were computed in two versions, with both the dc component and the fundamental, 100-Hz, component taken as the reference. IV. EXPERIMENTAL RESULTS To exemplify the results, selected spectra are shown. The spectrum of voltage in Fig. 2 contains a relatively large fifth harmonic. Spectra of all diagnostic media with fault 1 (one broken bar) are shown in Figs. 3 7, for, and, respectively. For these, the motor was loaded to give a slip of 0.06, that is, a slip frequency of 3 Hz. Spectra of the partial input powers were plotted here with respect to the value 0 db of dc component as base. It may be seen that the spectral components coincide with the predicted values, that is, 6 Hz (2 3 Hz) for the powers and torque, 44 Hz (50 Hz 2 3 Hz) and 56 Hz (50 Hz 2 3 Hz) for the current, and 94 Hz (100 Hz 2 3 Hz) and 106 Hz (100 Hz 2 3 Hz) for the partial powers. Secondary components, representing even and higher than two multiples of the slip frequency, are also visible. As expected, the partial power exhibits greater amplitudes of spectral components than. Consequently, will subsequently be the only partial power considered as a diagnostic medium. Concerning the sideband components, those to the right of the fundamental are barely discernible, and do not seem to be of practical value for fault diagnosis. In contrast, the components to the left of the fundamental are prominent in all the spectra presented. The 50-Hz component in the spectra of the powers is the result of unbalanced voltages. In the spectrum of torque, the same component is additionally accentuated by the estimation process, involving integration and requiring an accurate value of the stator resistance. Clearly, the diagnosis of rotor faults is easier under high load conditions, since on no load the rotor cage hardly carries any current. This is especially true for the current signature analysis, as seen in Fig. 8, illustrating the 0.02 case. The powers, particularly the partial power, have an attraction at low slip values, as shown in Fig. 9, which depicts the spectrum of partial power for fault 1 at slip of Although the sideband components are indiscernible, the characteristic components at 2 and 4 Hz are very prominent. However, in all fairness, it should be noted that

6 TRZYNADLOWSKI AND RITCHIE: INVESTIGATION OF DIAGNOSTIC MEDIA FOR INDUCTION MOTORS 1097 TABLE II RESOLUTION OF MAIN SPECTRAL COMPONENTS (db) the often poor resolution of the sideband components demonstrated in this study may result more from the way the FFT is computed than from the underlying physical phenomena. As was predicted, the fault-related spectral components tend to grow in amplitude with the extent of the fault. This is illustrated in Fig. 10, which shows the spectrum of partial power for fault 3 and with the slip of Similar spectra for faults 2 and 4 are shown in Figs. 11 and 12, respectively. Comparing these spectra, it may be seen that from the point of view of spectral effects, fault 4 (one broken bar and broken end ring) ranks in severity between fault 1 (one broken bar) and fault 2 (two broken bars). V. DISCUSSION OF THE RESULTS Amplitudes of the spectral components related to the double slip frequency are summarized in Table I for all the spectra obtained in the course of this study. Consistently, the most reliable fault indication was obtained from the lowest frequency components, that is, the sideband in the spectrum of current and the characteristic component, directly at, in the spectra of all the remaining variables. Taking an average amplitude of the most pronounced component for each medium, the following ranking, from the most to least sensitive, results: 1) partial power referred to the dc component: db; 2) estimated torque: db; 3) total power: db; 4) partial power referred to the fundamental: db; 5) current: db. The high amplitude of spectral components indicative of the fault is not the only quality expected from a good diagnostic medium. Consider, for instance, the sideband component in the spectrum of partial power in Fig. 11, which exhibits a relatively large amplitude of db. However, at about 4 db only, its local resolution, that is, the difference between the peak and the closest minimum, is poor. In a noisy spectrum, such a component could easily be overlooked. Therefore, the local resolution of fault-related spectral components is important, too. The impact of the employed methods of measurement and spectrum computing on this factor needs further studies. The local resolution of individual spectral components from Table I is given

7 1098 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 47, NO. 5, OCTOBER 2000 in Table II. Based on the average local resolution of the most prominent spectral component, the ranking of the media is as follows: 1) total power: 33.2 db; 2) partial power referred to the fundamental: 29.5 db; 3) partial power referred to the dc component: 29.3 db; 4) estimated torque: 25.4 db; 5) current: 12.7 db. As an overall indicator of quality, the sum of the average amplitude and local resolution may be used. This indicator yields the following final ranking of the diagnostic media considered: 1) partial power referred to the dc component: 12.6 db; 2) total power: 6.8 db; 3) partial power referred to the fundamental: 3.0 db; 4) estimated torque: db; 5) current: db. The stator current, which is popularly used in the practice of motor diagnosis, has been assessed here as the least useful diagnostic medium. The dominant rationale behind the choice of stator current as diagnostic medium is that the stator voltage, unaffected by the conditions of drive system, adds no pertinent information. However, multiplication of corresponding current and voltage samples seems to enhance the fault-warning signals. The instantaneous powers, both total and partial, appear to be better suited for diagnosis of rotor abnormalities than the stator current. The winner, the partial power, provides an additional advantage as it is the only medium characterized by both sideband and characteristic components. Although the sideband component is often insignificant, the other,, sideband component may be employed for verification of the characteristic component in noisy spectra. This diagnostic medium has already been promoted in [7] and [10]. However, no comparative investigations have been reported, and the extent of experiments is significantly greater here. Although it is a valid diagnostic medium, the estimated torque seems to offer no advantage over the instantaneous power, which is determined with a greater degree of accuracy. Theoretically, just after the rotor current, which is inaccessible for direct sensing, the developed torque is the diagnostic medium most affected by rotor faults. In reality, the developed torque is also inaccessible, while inaccuracies in the computation of the estimated torque compromise the usefulness of this medium. VI. CONCLUSION Extensive experiments carried out on an induction motor with various rotor faults and under various load conditions have shown the usefulness of the total and partial instantaneous power as diagnostic media for rotor faults in induction machines. The stator current, which is regularly used in motor signature analysis, yielded inferior results. The experiments were carried out on a motor supplied directly from the 50-Hz line. However, should the motor be fed from a pulsewidth modulation inverter, the spectra of the diagnostic media are unlikely to change significantly at the low frequency range considered. Switching frequencies in modern inverters, typically in the range of 2 20 khz, are greater from the output frequencies by more than one order of magnitude. Thus, the switching-related spectral components are well above the frequency range of interest to the fault diagnosis. This claim will be a subject of further study. If a motor is supplied from an inverter operating in the square-wave mode, the resultant harmonics appear at integer multiples of. Generally, spectral components at multiples of the supply frequency, which can be observed in most of the spectra presented, are ignored in algorithms for detection of mechanical abnormalities in the drive system. Only frequencies related to the rotational frequency are of interest here. As an aside, it should be mentioned that spectral components coinciding with the supply frequency or its multiples may indicate electrical faults in the stator which, however, are out of the scope of this paper. The study was limited to rotor faults only. Therefore, any extension of the ranking of the individual diagnostic media would be inappropriate. It is conceivable that the fault sensitivity of each medium depends on the type of fault present, and more research is certainly needed. Hopefully, the results presented will enhance the understanding of the application of various variables to the diagnosis of abnormalities in induction motor drives. REFERENCES [1] M. Y. Chow, R. N. Sharp, and J. C. Hung, On the application and design of artificial neural networks for motor fault detection Parts I and II, IEEE Trans. Ind. Electron., vol. 40, pp , Apr [2] R. R. Schoen, B. K. Lin, T. G. Habetler, J. H. Schlag, and S. Farag, Unsupervised, on-line system for induction motor fault detection using stator current monitoring, IEEE Trans. Ind. Applicat., vol. 31, pp , Nov./Dec [3] B. Li, G. Goddu, and M. Y. Chow, Knowledge based technique to enhance the performance of neural network based motor fault detectors, in Proc. IEEE IECON 97, New Orleans, LA, 1997, pp [4] G. B. Kliman and J. Stein, Methods of motor current signature analysis, Elect. Mach. Power Syst., vol. 20, no. 5, pp , [5] A. M. Trzynadlowski, Detection of mechanical abnormalities in induction motors by electric measurements, Int. J. of Rotating Mach., vol. 5, no. 1, pp , [6] R. Maier, Protection of squirrel-cage induction motor utilizing instantaneous power and phase information, IEEE Trans. Ind. Applicat., vol. 28, pp , Mar./Apr [7] S. F. Legowski, S. Ula, and A. M. Trzynadlowski, Instantaneous stator power as a medium for the signature analysis of induction motors, IEEE Trans. Ind. Applicat., vol. 32, pp , July/Aug [8] J. S. Hsu, Monitoring of defects in induction motors through air-gap torque observation, IEEE Trans. Ind. Applicat., vol. 31, pp , Sept./Oct [9] P. Vas, Parameter Estimation, Condition Monitoring, and Diagnosis of Electrical Machines. Oxford, U.K.: Oxford Univ. Press, [10] A. M. Trzynadlowski, M. Ghassemzadeh, and S. F. Legowski, Diagnostics of mechanical abnormalities in induction motors using instantaneous electric power, IEEE Trans. Energy Conversion, vol. 14, pp , Dec

8 TRZYNADLOWSKI AND RITCHIE: INVESTIGATION OF DIAGNOSTIC MEDIA FOR INDUCTION MOTORS 1099 Andrzej M. Trzynadlowski (M 83 SM 86 F 99) received the M.S. degree in electrical engineering, the M.S. degree in electronics, and the Ph.D. degree in electrical engineering from the Technical University of Wroclaw, Wroclaw, Poland, in 1964, 1969, and 1974, respectively. From 1966 to 1979, he was a member of the faculty of the Technical University of Wroclaw. He was later with the University of Salahuddin, Iraq, University of Texas, Arlington, and University of Wyoming. Since 1987, he has been with the University of Nevada, Reno, where he is currently a Professor of Electrical Engineering. In 1997, he spent seven months at Aalborg University, Denmark, as the Danfoss Visiting Professor. In 1998, he was a Summer Faculty Research Fellow at the Naval Surface Warfare Center, Annapolis, MD. He has authored or coauthored more than 120 publications on power electronics and electric drive systems, and is the holder of 11 patents. He is the author of The Field Orientation Principle in Control of Induction Motors (Amsterdam, The Netherlands: Kluwer, 1994) and Introduction to Modern Power Electronics (New York: Wiley, 1998). His next book, Control of Induction Motors, will be published shortly. Dr. Trzynadlowski is an Associate Editor of the IEEE TRANSACTIONS ON POWER ELECTRONICS and IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and a member of the Industrial Drives and Industrial Power Converter Committees of the IEEE Industry Applications Society (IAS). He was the recipient of the 1992 IAS Myron Zucker Grant. He is listed in Who s Who in the World. Ewen Ritchie (M 98) was born in Glasgow, U.K. He received the B.Tech. degree, with honors, from the University of Bradford, Bradford, U.K., in He was a Development Engineer with the Special Machines and Equipment Division, English Electric Company, from 1966 to 1973, and with Scragg Power Drives from 1973 to He was a Development Engineer with Thrige Titan from 1976 to 1979, ASEA from 1979 to 1983, and Electrolux Elmotor from 1983 to Since 1987, he has been an Associate Professor in the Institute of Energy Technology, Aalborg University, Aalborg East, Denmark. In 1991, he spent three months at Ondo State University, Ado Ekiti, Nigeria. His research areas are electrical machines, dynamic modeling in connection with transient disturbances, controlled operation and fault diagnosis, electrical machine design, and magnetic materials. He has supervised five Ph.D. candidates. He is a Member of the Editorial Board of Electromotion Magazine Mr. Ritchie is the Honorary Treasurer of the Danish Magnetic Association.