10 th International Symposium Topical Problems in the Field of Electrical and Power Engineering Pärnu, Estonia, January 10-15, 2011 Detection of broken rotor bars in three-phase squirrel-cage induction motor using fast Fourier transform Toomas Vaimann, Ants Kallaste Tallinn University of Technology toomas.vaimann@ttu.ee Abstract Induction motors have become the most used electrical motors in the world. They are rugged, easy to maintain, low in cost and good in performance. Those benefits have made induction motors very popular among users. During their exploitation period induction motors are exposed to various stresses that can become fatal to their performance and bring with them huge economic losses and safety risks for the people and companies using the motors. This has been the reason why there has been increasing interest in different condition monitoring and diagnostic systems in the past two decades. This paper analyses the diagnostic possibilities of three-phase squirrel-cage induction motor rotor faults through the implementation of fast Fourier transform. Keywords Induction motor, rotor faults, diagnostics, stator current, broken rotor bars, fast Fourier transform, FFT Introduction Induction motors are critical for many industrial processes because they are cost effective and robust in the sense of performance. They are also critical components in many commercially available equipment and industrial processes [1]. Furthermore, induction motors are often used in critical duty drives where a sudden failure can cause safety risks and economic expenses. Different failures can occur in electrical drives and one of the most common faults is the breaking of the rotor bars. The rotor failures are caused by a combination of various stresses that act in the rotor. These stresses can be electromagnetic, thermal, residual, dynamic, environmental and mechanical [2]. However, the induction motor rotor faults usually start from a small fracture or a high resistivity spot in the rotor bar [3]. When a fault like this increases the magnetic field becomes more and more asymmetrical due to the lack of induced currents in faulty rotor bars. This leads to local saturation in stator and rotor teeth near broken bars and unproportional distribution of magnetic field in the air gap. It can trigger several electromagnetic phenomena like increase of higher harmonic components, development of inverse magnetic field, torque pulsation, unbalanced magnetic pull etc. All these phenomena are undesired because they decrease the reliability of the induction motor and the whole drive. [4] ot only the number of the broken bars is important, but their position in the rotor cage has a very big role as well. As calculations have shown, the worst case of asymmetry is, when faulty bars are concentrated close together one by one under the same magnetic pole. Researches have verified that such case is also most probable in practice, because the increase of current is the highest in the bars near the broken one and so under highest thermal stress. When the same number of broken bars is situated under different poles the asymmetry is less expected. [4] Asymmetry of rotor cage winding due to some broken or cracked bars represents a significant part among several possible faults and must be detailed, considered and taken into account [5]. Another phenomenon that cannot be looked over is the induced rotor current. Resistance of broken bars is very high in comparison with the value of healthy rotor bars. This is very likely to cause unproportional distribution of rotor currents. Parts of the rotor currents, which are not able to flow in broken bars due to the high resistance, are flowing in bars, situated next to the broken ones. This leads to the increase of the current value in those bars. Although the currents of broken bars are flowing in adjacent bars, the entire sum of rotor currents is lower than in the case of healthy rotor. Too high current density leads to overheating in these bars and the fault propagates until the rotor cage is destroyed [4]. The main reasons for such faults is poor manufacturing, such as defective casting and poor jointing (Fig. 1). Another common reason is over current e.g. due to jam condition of the rotor [3], but there can be various reasons that will lead to cracking or broken rotor bars [6]: 1) Thermal stress due to over-load, non-uniform heat distribution, hot spot and arc. 2) Magnetic stresses due to electromagnetic forces, magnetic asymmetry forces, noises and electromagnetic vibrations. 52
over a sampling period that is sufficient to achieve the required fast Fourier transform. [9] Calculation of the fast Fourier algorithm was performed with MATLAB-software where computing of this transform can be done in a simple way. The MATLAB functions Y = fft(x) and y = ifft(x) implement the transform and inverse transform pair given for vectors of length by: X k ( j 1)( k 1) = x j ω (1) ( ) ( ) j= 1 Fig. 1. Defective casting of the rotor bar of an induction machine [3] 3) Residual stress from the fabrication process. 4) Dynamic stress due to rotor axial torque and centrifugal forces. 5) Circumferential stress due to wearing and pollution of rotor material by chemical materials and humidity. 6) Mechanical stress due to mechanical fatigue of different parts, bearing damage, loosened laminations etc. The biggest problem of those faults is that it is often not worth or possible to repair the rotor. However all of this can be avoided, when the motor is supervised by an appropriate condition monitoring or diagnostic system. 1 Fast Fourier Transform During the past twenty years there has been a continually increasing interest and investigation into induction motors fault detection and diagnosis. As this interest has grown, the literature has also grown. [7] Many different techniques can be found for the fault diagnostics of an induction motor rotor. All of them have their own benefits and drawbacks. In this case, fast Fourier transform was chosen to be a sufficient diagnostic method for induction motor broken rotor bars detection. Fourier analysis is very useful for many applications where the signals are stationary, as in diagnostic faults of electrical machines [8]. Its purpose is to monitor a single-phase stator current. This is accomplished by removing the 50 Hz excitation component through low-pass filtering and sampling the resulting signal. The single-phase current is sensed by a current transformer and sent to a 50 Hz notch filter where the fundamental component is reduced. The analog signal is then amplified and low-pass filtered. The filtering removes the undesirable high-frequency components that produce aliasing of the sampled signal while the amplification maximizes the use of the analog-to-digital converter input range. The analog-to-digital converter samples the filtered current signal at a predetermined sampling rate that is an integer multiple of 50 Hz. This is continued 1 j k ( 1)( 1) = ω (2) ( ) X( k) x j where 2π i k= 1 ω = e (3) is an th root of unity [10]. Equations 1 and 2 are known as fast Fourier transform algorithms, which have been developed from the discrete Fourier transform to reduce the amount of computations involved [11]. Induction motor faults detection, via fast Fourier transform based stator current signature analysis, could be improved by decreasing the current waveform distortions. After all, it is well known that motor current is a non-stationary signal, the properties of which vary with the time-varying normal operating conditions of the motor. As a result, it is difficult to differentiate fault conditions from the normal operating conditions of the motor using Fourier analysis. [8] The differentiation of faulty conditions of the motor will be easier, if the figures of healthy motor state are used as comparison material for the faulty rotor figures and peculiarities of local electrical network are noted. 2 Experimental setup and measurements Technical data of the tested induction motor (Fig. 2): U n = 177 V I n = 14.8 A n n = 1456 rpm T n = 20 m f = 50 Hz cosφ = 0.785 Fig. 2. Experimental setup for testing purposes Two different motor states were used for the measurements. First series of measurements were done with 53
a healthy rotor and the second series with a faulty rotor, containing seven broken bars, situated under the same magnetic pole next to each other (Fig. 3). Thus, the measurements provided two sets of results: one healthy set and one set with a faulty rotor in a very bad shape. Fig. 3. Magnetic field distribution in the cross section of a 3 kw induction motor at nominal load operating condition: left healthy rotor cage, right faulty rotor cage with seven broken bars (shaded) [12] To apply torque to the motor, an electromagnetic brake was used. As the nominal moment of the motor is 20 m and the length of the handle of the magnetic brake is 0.5 m, the measurements were taken from 0 40, when measured by the force sensor at the furthest point of the handle from the motor. The measurements were performed in two different series. In the first, a healthy rotor and in the second, a rotor with seven broken bars was used. During all these tests four different values were measured: U a first phase voltage, U b second phase voltage, I a first phase current, I b second phase current. Measurements were done while applying different torques. Torque values were chosen so that the torque would rise step by step: starting from 0 m, continuing with 5; 10; 15 and ending at 20 m, being the nominal moment of the motor. All of those measurements were performed in two different time bases (10 and 100 ms). Two different time bases were chosen in order to have more data before starting the analysis. This gave the opportunity to make the transforms in that time base, which is visually more traceable. A four-channel oscilloscope was used to obtain the oscillations of current and voltage at all the values mentioned before and results were saved as MATLAB files. All together 80 files were produced using all four channels of the oscilloscope, two different time bases, two different motor states and five different torque values. 3 Analysis According to the literature, fast Fourier transform should provide a good technique for finding out whether a rotor is healthy or not. The graph shows peaks of current in different frequencies and harmonics, so there should be a difference between the graphs of a healthy rotor current and the current of the rotor with seven broken bars. In addition, the amplitude of the current should be different according to the torque applied to the motor. Figures that were plotted result from the measurements done with the time base of 100 ms, considering more periods of the measured signal available for the analysis. That yields better results. For better comparison graphs of both rotor states and different torques were plotted (Figs. 4 and 5). First observation from these graphs would be that the amplitude rises as more torque is applied to the motor. This can be particularly well observed at the peak of the first harmonic (50 Hz). At the beginning of the test when torque is set to 0 m, it can be noted that the current amplitude stays at 0.55 units in the case of healthy rotor, whereas at 20 m the amplitude has risen to almost 0.9 units. It can also be seen that in the case of the faulty rotor, the amplitude is always higher than in the healthy motor state, whichever the applied torque to the motor is. Second biggest change in those graphs is the development of peaks at different frequencies. Some unexpected peaks can be seen even on the healthy rotor graphs, but these should not be considered relevant as they are not significantly big and are most likely arising as a result of the non-ideal sine waves that occur in the line voltage. On the other hand, on the faulty rotor figures, some of the peaks are significantly larger and are certainly caused by the broken bars in the squirrel-cage rotor of the induction motor that was tested. There are different peaks that vary in size and shape at 75 Hz and 100 Hz margins. The largest and the most viewable is the peak at the third harmonic (150 Hz) which changes substantially in shape when more torque is applied to the motor. According to the plotted graphs and literature about using fast Fourier transform to analyze the state of induction motors, it can be stated that in the case that is shown on Fig. 5 there is obviously some problems in the motor and it can indeed be faulty. All of the described factors can be considered a proof that the fast Fourier transform can be used as an indicator for a possibly faulty motor and broken rotor bars for diagnostic purposes. Conclusion All the measurements and analyses were done in laboratory conditions but it should be taken into account that the voltage supply during the measurements was not ideal in view that it was not perfectly sinusoidal. This provides an explanation to the figures that appear not exactly the same as in the literature describing the methods and not always quite the same as expected. on-ideal sine waves have an effect on the outcomes of the current figures and some unexpected peaks and curves in the graphs. 54
Fig. 4. Stator current spectra of a healthy squirrelcage rotor with applied torque values of 0 m; 5 m; 10 m; 15 m; 20 m Fig. 5. Stator current spectra of a faulty squirrelcage rotor (seven broken bars) with applied torque values of 0 m; 5 m; 10 m; 15 m; 20 m 55
There are some drawbacks for the stator current spectral analysis of three-phased squirrel-cage motors in order to detect broken rotor bars when using the fast Fourier transform. One of them is that the resolution of the obtained figure of fast Fourier transform is directly related to the length of the sampling time. In order to get fine and correctly readable figures, the motor has to be in steady-state during the sampling of the signal. It is however often not possible to keep the motor in a steady state during a prolonged sampling time. Attention should be paid to the fact that it is difficult to differentiate fault conditions from the normal operating conditions of the motor using only fast Fourier transform, due to variability of properties of the non-stationary motor current signal. It is essential to know the characteristics of the tested motor under normal operating conditions, as well as the peculiarities of the local electrical network where the motor is being tested. Another drawback of this kind of diagnosis is that the computational power required for the analysis is rather large. Without appropriate knowledge and software it is not possible to make all the transformations and graphs so easily. The benefit is that on-line monitoring makes the detection of a fault easy. If all the procedures are done correctly, then the faults will appear on the graphs. Also, when the drive is monitored, the faults of the rotor will be detected on an early stage. When using that kind of monitoring it will not be necessary to stop the motor of running in its stage of work. All the needed procedures can be done without changing the working cycle. However, in general it is certainly possible to decide on the motor rotor state using only the signals of the stator current and analyzing them through fast Fourier transform. The differences are very clearly shown in the figures and the faulty motor is noticeable. Still it would be the best if the fast Fourier transform figures could be proved by some other diagnostic method that is used simultaneously or in cooperation with the fast Fourier transform. These tests and analysis that are presented in this paper are based on the measurements performed on a healthy motor and a motor in a very bad shape. For future tests it is necessary to analyse similar diagnostic possibilities on motors with smaller faults as well. This would show if such diagnosis is relevant in cases not as severe as described here. Acknowledgement This paper is based on the measurements and analysis of induction motor rotor faults performed in Ljubljana University, Faculty of Electrical Engineering, under supervision and help of Prof. Dr. Vanja Ambrožič, Dr. Mitja emec and Mr. Klemen Drobnič. References 1. Kim K., Parlos A., Bharadwaj R., Sensorless Fault Diagnosis of Induction Motors, IEEE Transactions on Industrial Electronics, vol. 50, no. 5, October 2003, pp. 1038 1051. 2. Bonnett A., Soukup G., Cause and Analysis of Stator and Rotor Failures in Three-Phase Squirrel-Cage Induction Motor, IEEE Transactions on Industry Applications, vol. 28, no. 4, July/August 1992, pp. 921 937. 3. Lindh, T., On the condition monitoring of induction machines. Lappeenranta: Lappeenranta University of Technology, 2003. 148 p. 4. Fišer R., Ferkolj S., Calculation of Magnetic Field Asymmetry of Induction Motor with Rotor Faults, Proceedings of the 1998 IEEE Mediterranean Electrotechnical Conference, Tel Aviv (Israel), vol. 2, pp.1175 1179. 5. Belmans R., Hameyer K., Different Approaches to the Preventive Maintenance of Induction Motors, Proceedings of International Conference on Electrical Machines ICEM 96, Vigo (Spain), 10.-12. September 1996, vol. 2, pp. 423 428. 6. Faiz J., Ebrahimi B., Sharifian M., Time Stepping Finite Element Analysis of Broken Bars Fault in a Three-Phase Squirrel-Cage Induction Motor, Progress in Electromagnetic Research, PIER 68, 2007, pp. 53 70. 7. Benbouzid M., Bibliography on Induction Motors Faults Detection and Diagnosis, IEEE Transactions on Energy Conversion, December 1999, vol. 14, no. 4, pp. 1065 1074. 8. Benbouzid M., Kliman G., What Stator Current Processing-Based Technique to Use for Induction Motor Rotor Faults Diagnosis, IEEE Transactions on Energy Conversion, vol. 18, no. 2, June 2003, pp. 238 244. 9. Benbouzid M., A Review of Induction Motors Signature Analysis as a Medium for Faults Detection, Proceedings of the 1998 International Conference of the IEEE Industrial Electronics Society, Aachen (Germany), vol. 4, pp. 1908 1913. 10. MathWorks: http://www.mathworks.com/help/techdoc/ref/fft. html 11. Ingle V., Proakis J., Digital Signal Processing Using MATLAB, 2nd edition. Toronto: Thompson, 2007. 605 p. 12. Fišer R., Ferkolj S., Application of a Finite Element Method to Predict Damaged Induction Motor Performance, IEEE Transactions on Magnetics, vol. 37, no. 5, September 2001, pp. 3635 3639. 56