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1 SICE-ICASE International Joint Conference 26 Oct , 26 in Bexco, Busan, Korea Fault Diagnosis of Bearings in Rotating Machinery Based on Vibration Power Signal Autocorrelation Alireza Sadoughi1 2, Soheil Tashakkor2, Mohammad Ebrahimi1, Esmaeil Rezaei1 Department of Electrical and computer Engineering, Isfahan University of Technology, Isfahan, Iran 2Department of Electrical Engineering, Malek Ashtar University of Technology, Shahinshahr, Iran ( sadoughigmut-es.ac.ir) Abstract: Since fault in a great number of bearings commences from a single point defect, research on this category of faults has shared a great deal in predictive diagnosis literature. Single point defects will cause certain characteristic fault frequencies to appear in machine vibration spectrum. In traditional methods, data extracted from frequency spectrum has been used to identify damaged bearing part. Because of impulsive nature of fault strikes, and complex modulations present in vibration signal, a simple spectrum analysis may result in erroneous conclusions. When a shaft rotates at constant speed, strikes due to a single point defect repeat at constant intervals. Each strike shows a high energy distribution around it. This paper considers the time intervals between successive impulses in auto-correlated vibration power signals. The most frequent interval between successive impulses determines the period of defective part. This period is related to fault frequency and therefore shows the defective part. A comparison of results extracted from the traditional and the proposed methods shows the efficiency improvement of the second method in respect of the first one. Keywords: Autocorrelation, Bearing, Diagnosis, fault, Intelligent, Vibration fault the frequency component related to each fault has been obtained by one of the following methods, the first is the traditional method of investigating frequency spectrum of signals by fast Fourier transform (FFT). The second is a novel approach based on evaluating the successive impulses in Autocorrelation of vibration power signal (square of the vibration signal). 1. INTRODUCTION Condition monitoring as a tool for maintenance planning is an integral part of modem manufacturing programs. Early prediction of bearing failure in machines saves both production time and raw materials. Considerable research has been focused on the early detection of bearings faults by monitoring the machine's vibration spectrum for the existence of specific harmonic frequencies generated by different bearing defects. Bearing faults can be categorized in two main groups, single point defects and generalized roughness. Single point defects produce fundamental frequencies depending on which surface of the bearing contains the fault, while roughness defects have broadband effects. So the diagnosing methods for these two groups are different [1]. Fault in a great number of bearings begins from a single point defect, therefore; research on this category of faults has shared a great deal in predictive diagnosis literature. Artificial neural networks have an essential role in recent works [2], [3], [4]. To design a diagnosing system with least error, researchers try to apply different signal processing methods and extract different time and frequency features to be used in neural network training [2]-[7]. Some works [5], [6] have used higher order spectra to detect the fault frequency from the modulated frequencies. This approach is useful when there is a simple modulation. However, in complex modulations it is hard to get a good result in this way. The present paper introduces a new approach in continuation to the former works done by the authors [8],[9].This research utilizes root mean square (rms) and kurtosis factor of vibration signal to distinguish between healthy and defective cases. To recognize the kind of /6/$1 26 ICASE 2. BEARING FAULT FREQUENCIES Due to single point defects, certain characteristic fault frequencies appear in machine vibration. These frequencies are predictable and depend on which surface of the bearing contains the fault. There are five basic frequencies that are used to describe the dynamic of bearing elements: Shaft rotation frequency (FS ), cage frequency (FC ), ball pass inner raceway frequency ( FBPI ), ball pass outer raceway frequency ( FBPO ), and ball rotational frequency ( FB) as shown in Fig. 1. These frequencies are given by: FC = Fs (1 - DbCosOlDc)/2 FBPI NBFs (1+ DbCosO DC)/2 = DbCosOlDc)/2 FB= (DCFs/Db)(1-D 2CoS 2ID7)/2 FBO =NBFs(1 (1) (2) (3) (4) Where, Db is the ball diameter, D is the bearing cage diameter measured from one ball center to the opposite ball center, and is the contact angle of the bearing. These frequencies have small amplitudes in healthy bearings. When a raceway fault occurs, the frequency associated with the defective part of bearing ( FBPO or FBPJ ) and its harmonics are excited. In ball 479

2 sampled- through a low-pass filter to cancel unnecessary high frequencies. Numerous filters can be found in filter theory references. These filters differ in pass-band flatness of amplitude, phase delay, amplitude droop after cutoff frequency, and etc. The suitable filter for bearing fault diagnosis is Butterworth filter, which has flat amplitude response in pass-band region [ 1]. Z= r 4. FAULT DIAGNOSIS Numerous aspects of statistical and time features of vibration signal can be used in fault diagnosis. Maximum value, average, rms, variance, skewness, and kurtosis factors are among these aspects. In [8], [9], authors have obtained good results in distinguishing between healthy and faulty conditions by rms and kurtosis factors. Rms and kurtosis of a signal can be defined as: Fig. 1. Bearing structure and fundamental frequencies. defects, the defective portion comes in contact once with inner raceway and once with outer raceway per revolution, but one of these contacts may produce higher amplitudes so the frequencies 2FB or FB and their harmonics may appear in vibration spectrum. In many cases the above- mentioned frequencies are modulated with other present frequencies of system and result in a more complicated spectrum [2], [7] SOME NOTES ON SIGNAL SAMPLING AND PROCESSING For vibration characteristics identification, the vibration signal should be sampled, and then quantized. Number of quantizing levels q, and the length of digital word n are related by q = 2 n. Each bit increment in word length, increases the signal to noise ratio by about 6 decibels. This note should be considered in data acquisition card selection. Discrete Fourier Transform (DFT) is a useful method to distinguish existing frequencies in a sampled signal. Algorithms for fast computation of DFT by computer are called FFT. DFT transform of a time series XO, X1,..., XN_1 is defined as: N-1 X = EXk e j(2r N) N-1 Xrms = V (N (Xi-A) N-1 Kur = (,(xi i=o -p)4) I(N(T) (6) (7) Where xi is the sampled vibration signal,,u is the signal average, o- 2 is the variance, and N is the number of data points. An increase in vibration signal rms measured on bearing housing, shows an unusual condition, which can be due to a fault in the same bearing or any other defect in the mechanical set related to that bearing. Large values of kurtosis factor, show large peaks in a signal. Different defects in a bearing produce high peak impulses, which have high frequency components. These high frequency components decay rapidly as they go out of their source, therefore; a high value of kurtosis factor shows a defect at the measuring point. Kurtosis factor together with rms is a good indicator to distinguish between healthy and defective bearings, but none of them determines the kind of fault. To diagnose the fault category the frequency components relative to faults should be considered. One way to assess frequency components is to investigate the signal frequency spectrum and to determine the amplitude of the frequency related to each defect. In numerous practices, it was observed that the higher order harmonics related to fault frequency have considerable magnitude. Furthermore, small and gradual changes in shaft velocity or changes in bearing contact angle cause the energy of the related frequency to leak to nearby frequencies. In [2] and [5], authors have considered the energy distributed around the first harmonic of the fault frequencies. Due to impulsive nature of fault signals, it would be better to take into account some higher order harmonics too. Therefore, in order to design a diagnosing system, the energy distributed around first, second, and third harmonics is n = O,1,...,N-1 (5) k=o To determine frequency components by FFT, the sampling frequency should be adopted by considering the following rules. According to Nyquist sampling theorem, a band-limited signal x(t) with no frequency component higher than fh, can be uniquely determined by its samples if the sampling rate f5 is more than 2h. The frequency 2fh is commonly referred as the Nyquist frequency. If this rule does not hold, an overlap of spectrum repetition results in a distortion in the main signal spectrum which is referred to as aliasing. In practical applications, for signals with unlimited band, the sampling frequency is chosen about ten times the cutoff frequency (the frequency in which the amplitude has dropped by 3 dbs) [1]. It would be better to pass the signals -before being 471

3 computed by (8): 3 BW12 XF = E E PSD((kF + Af)T) (8) k=1 Af =-BW2 f:~ ~~~1AL I.- JI.U L Where F, can be FS X FBPO, FBPI, or FB, T is the sampling period, k is the number of harmonic, BW is the band width around the related frequency (which is considered 2 to 8 Hz in the present paper experiments), and PSD is the power spectrum density computed by Matlab software. In some cases, the frequencies related to faults modulate with other system frequencies and appear in other frequencies of the spectrum which are hard to be distinguished by the diagnosing system. Some works [5], [6] have used higher order spectra to extract the fault frequency from the modulated frequencies. This approach is useful when there is a simple modulation. However, in complex modulations it is hard to get a good result in this way. To overcome this weakness it has been referred to vibration time diagram to determine the fault frequency (or the period of impulses due to the fault, Dt). Figs. 2-a is a typical vibration signal of a bearing with defective inner raceway running at 192 rpm (the figure is obtained by the Lab. set introduced in section 5). Fundamental frequency FBPI of this bearing at shaft speed 192 rpm and its related fault impulse period, by,2-1 2 n (Xn )(Xn-j) I -14 (bi ~-2flkJkA faw kka& D12 14 D16 D18 2 D u 8< 6 - wl ~4 2.1 \j (d) Fig. 2. Bearing with inner raceway defect. (a) Vibration signal, (b) Vibration power signal, (c) Vibration power signal auto-correlation, (d) same as (c) but mean filtered. Impulses in Fig. 2-a show contacts between the defective part and other parts of bearing while the bearing rotates. The key note in diagnosing bearing fault is: Each fault strike produces a high energy distribution around the strike instant. If the amplitudes of these impulses are large enough, the period of the related defect can be determined by computing the time interval between successive impulses. But it is seen that some strikes have smaller amplitudes.therefore, to clarify these intervals, the square of vibration signal (vibration power) is auto-correlated. The discrete autocorrelation R at lagj for a discrete signal xn is E (a) U.12=LhLL.12 :=L[JSLLh FBPI = 262 Hz, Dt =.38 s = using (2), are: RxxU) i. (Fig.2-d), and then the successive peaks intervals Dts are obtained by using a computer program (see appendix). The most frequent value in Dt histogram shows the period of impulses due to the related fault and is used to indicate the fault type. 5. LABORATORY SET A laboratory set is prepared to examine theoretical results, which consists of a vibration sensor and its driver circuit, amplifying and filter circuits, a data acquisition card and a digital computer. To obtain the vibration of defective bearings an apparatus is made consisting of a shaft which two bearings are assembled (9) The above definition works for signals that are square summable, that is, of finite energy. Auto-correlation removes white noise from the signal, and also when there are some missed impulses in vibration signal; auto-correlation can detect the position of missed impulses. The latter property works better on squared vibration signal than the main vibration signal. Figs. 2-b and c show the vibration power signal, and vibration power signal auto-correlation of the bearing respectively, it is clear that the distance between the successive peaks is the period of inner raceway fault. To simplify the determination of successive impulses intervals, the last signal is filtered by a mean filter Fig. 3. Mounting structure for bearings and related motors. 4711

4 (a) networks. A neurocomputing approach to information processing involves a learning process within an artificial neural network that adaptively responds to inputs according to a learning rule [12]. This study uses MLP three layer feed forward neural networks in Matlab environment, which are learned by Levenberg-Marquardt algorithm. The functions applied in hidden layer and output layer are sigmoid (tansig) and linear (purelin) functions. Number of neurons in hidden layer has been selected by trial and error. There is no precise method to select the number of these neurons, but it should be greater than the total number of input and output vector components. In the first method, the input vector of the neural network consists of 4 frequency components according to (4) and two factors rms and kurtosis (according to (6) and (7)). The neural network has four outputs which in each case of healthy bearing, ball defect, inner raceway, and outer raceway defect, one of the outputs is "1" and the others are zero. Number of hidden neurons is 24 (selected by trial and error). In the second method, a neural network distinguishes between healthy and faulty conditions (with 7 neurons in hidden layer) and a computer program recognizes the fault class. The neural network has two inputs (rms and kurtosis) and two outputs (healthy and faulty). If the network diagnosed the bearing as faulty, the computer program would asses the fault class by calculating the most frequent interval between successive impulses. The number of vectors used for training is 4 for healthy bearing and 6 for defective bearings (2 for each fault class). Ninety vectors have been used to test the efficiency of designed networks (3 for healthy bearing, and 2 for each defect). None of the test vectors have been used in learning step. The results are shown in Table I. Although these results can be different for some other set of test vectors, but it can be concluded that the second proposed method has better efficiency in respect of the first method. The first method requires both filtered and unfiltered signals but the second method uses only unfiltered signal and therefore needs less hardware. (b) (c) Fig. 4. (a) Complete bearing (b) defective inner raceway (c) defective ball (d) defective outer raceway. on its ends and two housings to retain the bearings, accompanied by two induction machines working as motor and generator. By proper selection of pulleys and belts the shaft can rotate in different velocities. All of these parts are mounted on a frame (Fig. 3). The applied bearing can be easily disassembled. The complete bearing and its defective parts are shown in Fig. 4. Bearing has 28 balls in two rows, ball diameter is 7.9mm, inner raceway diameter is 35mm, and outer raceway diameter is 57mm. The vibration sensor is an accelerometer, with a bandwidth of more than 1 khz, the selected data acquisition card, is a 16-bit card with a maximum sampling rate of 25ks/s for all channels. The circuits consist of a current source to drive the vibration sensor and a low-pass 6th order Butterworth filter with a cut-off frequency of 1 khz. This circuit amplifies the signal too. 6. APPLYING NEURAL NETWORKS Neural networks can improve the fault detection rate. In addition to improved accuracy, it is also possible to detect and classify different types of faults using neural Table I. Results of correct diagnosing percentage for the two introduced methods 3 Method e > Frequency and time 2 domain components 224 time 77 domain components o Input vector components c K KulO lo lo lo xrms,kur,xfs x XF Kur XF XF

5 If this point is within the distance "w", "fpl" will be removed and "fp2" will be replaced by "fp 1", otherwise, "fp 1" will be considered as a peak. If no peak point found within distance "w", the routine explained in the former paragraph should be repeated. As Fig. 5 shows, the result of this flowchart will be stored in an array named "Dt", which contains the period of successive peaks in auto-correlated vibration power signal. The most frequent value in Dt represents the fault frequency. To find this value, we can simply calculate the Dt histogram. 7. CONCLUSION In this paper, theoretical prerequisite to analyze bearing vibration signal is introduced. According to the introduced notes, a laboratory set has been made which can effectively assess the bearing condition, by the aid of MLP neural networks. The factors rms and kurtosis effectively distinguish between healthy and defective conditions of bearing. To diagnose the fault class, the frequency related to the fault should be recognized. Two methods has been introduced, in the first method the signal spectrum has been used. The second method is a novel method based on evaluating time intervals between successive vibration impulses, which has better results compared to the first method. In both methods, the extracted signal features are used to train neural networks. In the first method the input vector of the ANN consist of four frequency components and two factors rms and kurtosis. In the second method the applied ANN distinguishes between healthy and faulty conditions with just rms and kurtosis as input, and a computer program determines the most frequent Dt, and therefore the defective part. The second method has shown better results in response to test data. APPENDIX: PEAK DETECTION [9] "Feature Extraction" is one of the most important subjects in using ANN's. "Feature" here refers to time intervals between successive peaks in Autocorrelation of vibration power signal (square of the vibration signal). To find maximum points of math functions, classical methods can be used. But when we are dealing with real sampled data - containing noise, harmonic, and non-harmonic components - more inventive methods should be used. Fig. 5 shows the flowchart used to find peaks. In this flowchart the array "data" is the autocorrelation of squared vibration signal, which is mean-filtered. "w" represents the minimum possible and meaningful distance between two successive peaks (that must be less than the period of the highest fault frequency) and "i" is an index indicating a sample under process. Referring to (1) to (4), it can be seen that inner raceway fault produces the highest characteristic frequency in respect of other fault frequencies. Thus we can define a rough equation to find a proper value for Find all of the positions in array "data" containing a flag. Calculate the distance between each two successive flags and store in array "Dt". I I~~En "w": w= 2k NBFs(1 + Db cos ODI ) bx 1 FBPI ~ (1) ~~~ Fig. 5. Flowchart for calculating time intervals between successive peaks in vibration power signal autocorrelation. where k E [.6,.9]. "fpl" and "fp2" are two temporary flags that will be put on peak point candidates. At the beginning, "fp 1" refers to the first data point as a peak. Now the second peak candidate should be found. "fp2" refers to the next data point with higher amplitude than the point of "fp 1". REFERENCES [1] J.R. Stack, T.G. Habetler, R.G. Harley, "Fault classification and fault signature production for rolling element bearings in electrical machines 4713

6 ,"IEEE Transactions on Industry Applications, vol. 4, pp , May/June 24. [2] B. Li, M.Y. Tipsuwan, Y. Hung, "Neural-network-based motor rolling bearing fault diagnosis," IEEE Transaction On Industrial Electronics, vol. 47, No. 5, pp , Oct 2. [3] H. OCAK, K.A. Loparo, "A new bearing fault detection and diagnosis scheme based on hidden markov modeling of vibration signals," Proceedings of the IEEE International Conjerence on Acoustics, Speech and Signal Processing, vol. 5, pp , May 21. [4] M.J. Devaney, L.Eren, "Detecting Motor Bearing Faults," IEEE Instrumentation & Measurement Magazine, pp. 3-35, Dec 24. [5] A.C. McCormick, A.K. Nandi, "Bispectral and trispectral features for machine condition diagnosis," IEE Proc. -Part VIS, vol. 146, No. 5, pp , Oct [6] J.R. Stack, R.G. Harley, T.G. Habetler, "An amplitude modulation detector for fault diagnosis in rolling element bearings," IEEE Transaction on Industrial Electronics, vol. 51 No. 5, pp , Oct 24. [7] B. Li, G. Goddu, M-Y Chow, "Detection of common motor bearing faults using frequency-domain vibration signals and a neural network based approach," Proc. of the American Control Conference, Philadelphia, Pennsylvania, pp , June [8] A. Sadoughi, S. Tashakor, M. Ebrahimi, "Intelligent diagnosis of bearing faults by using fretjjuency and time aspects of vi ration signal" The 14' Iranian Conference on Electrical Engineering, ICEE 26, Iran. [9] A. Sadoughi, S. Tashakor, M. Ebrahimi, "Intelligent fault diagnosing of bearings in rotating machinery (a novel approach)" XVII International Conference on Electrical Machines, ICEM26, Greece, to be published. [1] A.V. Oppenheim,R.W. Schafer, Discrete - Time Signal Processing, Prentic-Hall, [11] A.B. Williams,F.J. Taylor, Electronic Filter Design Hand Book,3r ed., [12] R.J. Schalkoff, Artificial Neural Network. McGraw-Hill 4714