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Fault detection of induction motor ball bearings.

INTRODUCTION

Among electric machines, three-phase induction motors have the highest application in industry and they consume between 40 and 50 percent of the produced electricity in industrial communities. Performance, reliability and efficiency are of the major concerns application of in induction motors [1]. Because most equipment that are set up with engine, have key role in industry. In the past two decades, extensive researches have been conducted to create new methods for monitoring the condition of induction motors based on analysis of vibrations signal fluctuations, flow, etc. [4-2]. There are also numerous commercial tools in this field.

Despite these tools, many factories encounter unexpected faults that cause useful life of the engine to reduce result in a lot of damages. Recent researches shows that more than 40% of damages in electrical machines are related to their ball bearings. Therefore, if process of creation progression of this type fault can be detected at early stages; damages (the cost of stopping the production line) can be avoided. Ball bearing faults are divided into two categories; one distributed faults like surface roughness, waviness, non-parallel rings, different sizes of case-shots, and other local faults such as gaps, holes and fines on rotating surfaces [5]. Created faults in ball bearings are usually local that exist in inner rings, outer rings, case-shots or cage. When case-shots pass through the bad points, consecutive hits are created in vibrations signal whose amplitude and frequency period is determined by rotation rate, fault location and dimensions of ball bearing. Accordingly, mostly vibration signal is used to fault detection of ball bearings [5-2]. Vibrations caused by bearings failure on the stator flow signal are modulated. And the flow signal can be easily measured to monitor status and control purposes. Therefore, in recent years, most researches have been driven to electric monitoring of motor with emphasis on the stator flow [6-8].

Theoretically, fault can be detected using FFT with regard to its related components' scope, but since created hit vibrations have relatively less energy and domain comparing noise and vibration caused by other Components from other parts of domain 2, they are often drowned in them.In order to overcome FFT problems and improve ratio of signal to noise and conduct more effective spectral analysis, some advanced techniques of signal processing have been used.

In recent years, more advanced techniques such as Short-Time Fourier Transform (STFT) [9], wavelet transform (WT) [10], and wavelet packet bearing [11-12], have been used for Fault detection of ball bearings. The methods have high computation volume; furthermore they need to an experienced and skilled person for the detection of system status [13]. In fact, an experienced person should recognize that if harmonics of the measured signal exist in normal circumstances or have been caused by the defect. To solve this problem, intelligent systems can be used. In this article, to solve these problems and making diagnosis process intelligent and faults isolation, a method is presented based on pattern recognition using neural networks. In this study, using the collected experimental data [14], the desired features are obtained by processing signal in time and frequency domains, for ball bearings in conditions of faultless, outer ring fault, inner ring fault and are given to teaching to neural network input. After teaching, neural network can classify faults well.

Frequencies of Fault Characteristics:

Local damage or wear causes consecutive periodic hits in vibration signal of engine body. Amplitude and frequency period of these hits are determined according to the rotation speed, fault location, and characteristic dimensions of ball bearings. These impulses are obtained by the relations (4)-(1), considering the part of ball bearing in which there is fault (5).

Fundamental Cage Frequency is obtained through the following relation:

([f.sub.c] - [f.sub.s]/2 (1 - d/D cos ([alpha])) (1)

Case shot Frequency is twice case shot frequency of rotation around itself and is obtained through the following relation:

([f.sub.bd] - D x [f.sub.s]/d (1 - [d.sup.2]/[D.sup.2] [cos.sup.2] ([alpha])) (2)

Also, the inner ring and outer ring fault frequency are obtained through the following relation, respectively:

([f.sub.od] = nx[f.sub.s]/2 x d (1 - d/D cos([alpha])) (3)

([f.sub.id] = nx[f.sub.s]/2(1 + d/D cos([alpha])) (4)

In these relations fs is rotation frequency, n is number of case shots, D is diameter of step, and d is Case shot diameters that are determined according to presented ball bearing characteristic in figure 1.

Therefore, with any part defective in ball bearing, we expect that a component is made in the spectrum of the vibration signals. Since the effect of fault is negligible at early stages and scope of created components by fault is so less compared to noise domain and vibrations caused by other parts of motor, faults cannot be detected easily by conventional methods of analyzing the spectrum, the need for more advanced methods of Signal processing is felt. These methods have high volume of calculations. In addition, need to an experience and skilled person for recognizing condition of system is very essential. To solve this problem, in this paper Intelligent systems are used.

Multilayer Perceptron Neural Network:

Multi-layer neural network consists of an input layer, an output layer and one or more hidden layers. Each layer consists of several neurons whose inputs are just connected to their previous layer, and outputs are connected to their next layer .A general sample is shown in Figure 2.

Input layer processing functions are all linear, but in the hidden layers of nonlinear function Like sigmoid function, hyperbolic tangent, or any Continuous nonlinear and Differentiable function can be used. Usually to increase learning speed, excitation functions of Linear output layer neurons are selected.

In System modeling by multi-Layer neural networks, first network structure is defined as above, after defining structure network neurons should be configured in a way that by Applying input to the system, it gives outputs very close to the actual outputs of the system.

This work is called neural network training and its purpose is to adjust the weights in order to minimize the error between the network output and the output. In the following training method of Levenberg-Marquardt will be briefly discussed.

Training Algorithm of Levenberg-Marquardt:

This training algorithm is one of second order error function optimization methods for Training neural networks [15]. This method is an approximate of Newton's optimization method. For neural network training it is necessary that error function is quantified based On network parameters (Weights and bias s). According to Newton's method. Parameters change when training is:

[DELTA][x.bar] = -[[[[nabla].sup.2.sub.[x.bar]]E([x.bar])].sup.-1] [[[nabla].sub.[x.bar]]E([x.bar])] (5)

where [nabla] xE (x) 2 [nabla] is Hsien matrix, xE (x) error Function gradient with respect to vector of the network parameters, x.

by definition of sum of error squares, we have:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where P 'V = P.SL are n umber of training patterns and SL is the number of network outputs.

So we can write:

[[nabla].sub.[bar.x]] E([x.bar]) = [J.sup.T]([x.bar])[e.bar]([x.bar]) [[nabla].sup.2.sub.[bar.x]] E([x.bar]) = [J.sup.T]([x.bar])[J.bar]R([x.bar]) (7)

Where J (x) is Jacobian matrix and:

(8)

To avoid increasing the size of the calculations in Gauss-Newton method R (x) [congruent to] is assumed, so Hsien-matrix is obtained by this approximation:

[[nabla].sup.2] E([bar.x]) [congruent to] [J.sup.T] ([x.bar])J([x.bar]) (9)

To avoid the ill-condition of JTJ matrix, weights are obtained according to the modified method of Levenberg-Marquardt as following:

[x.bar](n+1) = [[x.bar](n) - [[J.sup.T] [x.bar](n)J[x.bar](n)+[[mu].sub.n]I].sup.-1] [[nabla].sub.[x.bar]] E([x.bar](n)) (10)

Where [[mu].sub.n] is Learning coefficient the more p., is smaller, the Training algorithm is closer to Gauss Newton.And the more [[mu].sub.n] is larger, the Training algorithm gets closer to Back propagation Learning with The fastest gradient With a very small step length.

Comparing Levenberg-Marquardt Back propagation Learning, this method needs more calculation for each training session. The convergence rate of this method is such that to reach a specific error, less time and fewer steps are required for Training

Collecting experimental data:

In all experiments, a 3-phase induction motor with specification of Four-pole 1400 rpm, 50 Hz, 380 V, 1/2 KW ratings (manufactured by Motogen) is used [15].

Both ball bearings of the fan and shaft end are 6205-2z. Usually, two methods are used for making fault on ball bearing and investigating its effect [5]. In this study for Simulation of different faults, some holes are made on Inner and outer end of the shaft ball bearing by spark. First, the experiments were conducted on safe ball bearing engines. We show this ball bearing with A. The second test for stimulating fault on the outer ring, a hole with diameter of 1 mm was created at the end of ball bearing. We show this by B. In figure 3 diagram of ball bearing with fault of outer ring is shown. In the third test for fault simulation on the inner ring, a hole with diameter of 1 mm on end shaft ball bearing. This ball bearing is shown by C.

If we go features of ball bearing 6205-2 bearing, its outer diameter is 52 and inner diameter is 25 mm. Therefore, bearing step diameter is obtained D=38.5. Also this ball bearing has 9 case shot whose diameter is approximately d=7.938 mm.

Given that cross angle, ([alpha]) is zero and engine is in idle mode and its speed is measured as (frm=24.96 1498 rpm) features of this fault of ball bearing are obtained according relations (1) to (4) and shown in table (1):

Table 1: frequency of fault characteristic in vibrations signal

Location of fault    frequency of fault characteristic

Outer ring           [f.sub.od] = 89.18 Hz
Inner ring           [f.sub.id] = 135.5 Hz
Cage                 [f.sub.c] = 9.9 Hz
Case shots           [f.sub.bd] = 116 Hz


Extraction of Time Domain Features:

In this part, data in all three phases are divided into 20 parts including 1024 sample after omitting D offset without overlapping.

Each of these parts that are introduced in the following are processed: effective value (rms) variance ([[sigma].sup.2]), skweness, Normalized third central of torque([[gamma].sub.3]), Kurtosis, Normalized third central of torque([[gamma].sub.4]), normalized Sixth-order central of torque ([gamma]6) that are obtained by following relations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

in These relations E represents the expected value of function. In figure 4 extracted features of vibration signals are shown. All these features are normalized within [0, +1] except normalized third central of torque (skweness) which are normalized in [0, +1]. For normalization, each feature is divided by difference maximum and minimum.

Extraction of Frequency Domain Features:

For identifying fault type, usually frequency components are used. Therefore, a plan of computing emitted energy around harmonic is as input for neural network. In this plan, vibration signal spectrum is calculated and energy around fault components is given to neural network as input [16]. For this purpose, 96900 samples of each signal is selected an according to envelope detecting method, after passing 4 KHz2. filter Power Spectrum or Power Spectral Density of square signal is computed. Then, emitted energy around frequency of rotation and related frequencies to fault are obtained. Therefore, spectrum domain for frequencies fid 'fod' fs and fb are as following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

Time field frequency features that are used include mean, domain, maximum and vibration signal Kurtosis coefficient. therefore features that are used as neural netwok input are as following:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

These data Is given to neural network as input after normalization between [-1, +1].

Designing MLP Neural Network for Separating Modes of Safe, Outer Ring Fault and Inner Ring Fault:

In this part the aim is separating safe and faulty ball bearings in two modes of outer ring fault and inner ring fault. Features of time and frequency field introduced in three modes are obtained in all three modes. Two outputs are considered for network and each of these modes are distinguished with a target vector. Safe mode: [[0 0].sup.T]., outer ring fault: [[0 1].sup.T] and inner ring fault [[1 0].sup.T]. of course an output with components -1,0,+1 can also be considered. To get the appropriate network we act in this way: First, network is considered with a hidden layer and is taught by Levenberg-Marquardt algorithm that is faster than other algorithms.

If appropriate responses are not obtained with cells increasing in a layer, number of hidden layers is increased. In the following firs faults are classified by time and frequency field Features presented in reference (16). Then time field features presented are used, results in both modes are compared.

Using Time and Frequency Domain Features:

In order to design an appropriate network, first a three-layer network with 5 input, 2 cells in middle layer and 2 cells in output layer are considered, then number of cells and hidden layers is changed so that optimized number of cells and hidden layers are obtained. Number of samples that are used for training in this part is 40 samples related to outer ring fault, 40 samples related to inner ring fault. For measuring efficiency of designed network this number of samples is used too; and none of training test samples are used.

In figure 5 error change curve for different networks and in figure 6 response of neural designed network number 2 to test data are shown. Detection Accuracy percent of each network is brought in table 2.

Using Time Domain Features:

Number of samples that are used for training in this part is 20 samples related to outer ring fault, 20 samples related to inner ring fault. For measuring efficiency of designed network 20 samples for safe mode an 40 samples for fault ones are used; and none of training test samples are used.

First, structure of network is considered as this: 5 cells in input layer, 2 cells in middle layer and 2 cells in output layer. Then number of cells and hidden layers are changed so that optimal number of cells and hidden layers are obtained. In figure 7 error change curve for different networks and in figure 8 responses of neural network designed number 2 to test data are shown. Results of detection Accuracy Percent for each mode are brought in table 3.

As it is observed, detection Accuracy Percent of safe modes and inner ring is 100% in all cases. But with change of hidden layer cells number and also number of hidden layers, detection Accuracy Percent of outer ring fault is 100% in just one mode. Another important point which is seen in network number 5 is that with increasing layers number and hidden cells, not only the responses did not get better but also they got worse.

Conclusion:

In this article first principle of fault detection in ball bearings was offered. For making the process of fault detection intelligent, using algorithms of pattern recognition based on neural networks were proposed. In order to examine accuracy of the proposed method, an experiment set was designed and appropriate data was collected in three modes of safe, outer ring fault and inner ring fault. In the following a neural network using time and frequency field features and another network using time filed features was designed. The results showed that using time field features, better or similar results can be obtained with less volume of calculations compared with using time sand frequency features.

Since getting time field features is simpler and has less calculations volume, using time filed features for classifying faults of ball bearings is recommended.

ARTICLE INFO

Article history:

Received 11 January 2014

Received in revised form 2 February 2014

Accepted 12 April 2014

Available online 15 May 2014

REFERENCES

[1] Benbouzid, M.E.H., 1999. "Bibliography on induction motors faults detection and diagnosis," IEEE Trans. Energy Conversion, 14(4).

[2] Thomson, W.T., 1999. "A review of on-line condition monitoring techniques for three-phase squirrel cage induction motors--Past present and future," in IEEE SDEMPED'99, Spain, pp: 3-18.

[3] Singh, G.K., Sa'ad Ahmed Saleh Al Kazzaz, 2003. "Induction machine drive condition monitoring and diagnostic research survey," Journal of electric power research, 64: 145-158.

[4] Nandi, S., H.A. Toliat, X. Li, 2005. "Condition monitoring and fault diagnosis of electrical motors-A Review," IEEE Trans. Energy Conversion, 20(4).

[5] Tandon, N. and A. Choudhury, 1999. "A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings," Journal of Tribology International, 32(8): 469-480.

[6] Schoen, R.R., T.G. Habetler, F. Kamran, R.G. Bartheld, 1995. "Motor Bearing damage detection using stator current monitoring," IEEE Trans. Industry Applications, 32(6): 1274-1279.

[7] Benbouzid, M.E.H., 2000. "A review of induction motors signature analysis as a medium for faults detection," IEEE Trans. Industrial Electronics, 47(5): 984-993.

[8] Benbouzid, M.E.H., 2003. "What stator current processing-based technique to use for induction motor rotor faults diagnosis?" IEEE Trans. Energy Conversion, 18(2): 238-244.

[9] Yazici, B., G.B. Kliman, 1999. "An adaptive statistical time frequency method for detection of broken bars and bearing faults in motors," IEEE Trans. On Industry App., 35(2).

[10] Prabhakar, S., A.R. Mohanty, A.S Sekhar, 2002. "Application of discrete wavelet transform for detection of ball bearing race faults," Journal of Tribology International, 35(12): 793-800.

[11] Zarei, J., J. Poshtan, 2007. "Bearing fault detection using wavelet packet transform of induction motor stator current," Journal of Tribology International, 40(5): 763-769.

[12] Nikolaou, N.G., I.A. Antoniadis, 2002. "Rolling element bearing fault diagnosis using wavelet packets," Journal of NDT&E, 35(3): 197-205.

[13] Haji, M., H.A. Toliyat, 2001. "Pattern recognition-a technique for induction machines rotor broken bar detection," IEEE Trans. Energy Conversion, 16(4): 312-317.

[14] Zarei, J., 2005. Induction Motor Bearings Fault Detection using Stator Current Analysis Compared to Vibration Analysis, Msc Thesis, Iran University of Science and Technology, IRAN, (in Persian language).

[15] Hagan, M.T., M.B. Menhaj, 1994. "Training feed forward networks with the Marquardt algorithm," IEEE Trans. On Neural Networks, 5(6): 989-993.

[16] Li, B., M. Chow, Y. Tipsuwan, J.C. Hung, 2000. "Neural network based motor rolling bearing fault diagnosis," IEEE Trans. Industrial Electronics, 47(5): 1060-1068.

(1) Javad Haddadnia, (2) Omid Rahmani Seryasat, (3) Hamidreza Rabiee

(1) Associate Professor, Electrical and Computer Engineering Department, Hakim Sabzevari University, Sabzevar, Iran.

(2,3) Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran.

Corresponding Author: Omid Rahmani Seryasat, Associate Professor, Electrical and Computer Engineering Department, Hakim Sabzevari University, Sabzevar, Iran.

E-mail: Omid.seryasat@gmail.com

Table 2: Comparison of network with number of cells and hidden
layers Different from using time and frequency domain features

Network    Network      Safe      Outer Ring
Number     Structure              Fault

1          [5 2 2]      97.5 %    100 %
2          [5 4 2]      97.5 %    100 %
3          [5 7 2]      97.5 %    100 %
4          [5 5 3 2]    97.5 %    100 %
5          [5 10 5 2]   97.5 %    100 %

Network    Inner Ring   Detection
Number     Fault        Accuracy Mean

1          100 %        91.16 %
2          100 %        91.16 %
3          100 %        91.16 %
4          100 %        91.16 %
5          100 %        91.16

Table 2: Comparison of network with number of cells and hidden
layers Different from using time domain features

Network    Network      Safe    Outer Ring
Number     Structure            Fault

1          [5 2 2]      100 %   85 %
2          [5 4 2]      100 %   100 %
3          [5 7 2]      100 %   90 %
4          [5 5 3 2]    100 %   90 %
5          [5 10 5 2]   0 %     0 %

Network    Inner Ring   Detection
Number     Fault        Accuracy Mean

1          100 %        93.33 %
2          100 %        100 %
3          100 %        96.66 %
4          100 %        96.66 %
5          0 %          0 %
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Author:Haddadnia, Javad; Seryasat, Omid Rahmani; Rabiee, Hamidreza
Publication:Advances in Environmental Biology
Geographic Code:7IRAN
Date:Apr 15, 2014
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