Induction Motor Bearing Fault Identification Using Vibration Measurement Raj Kumar Patel, Sanjay Agrawal and
Abstract—Condition monitoring and fault diagnosis of equipment and processes are of great concern in industries. Early fault detection in machineries can save money in emergency maintenance cost. Therefore, it is necessary to fault detection of various parts of the machine. In this paper we present the detection of running speed frequency and bearing defect frequencies of an induction motor using vibration data through the wavelet transform and the Hilbert transform. Bearing defect frequencies are frequencies at which roller elements pass over a defect point. The analysis result shows that the proposed method can diagnose faulty bearing. Index Terms—Discrete wavelet transform, Hilbert transform, Power spectrum, Rolling ball bearing, Spectrum.
I. INTRODUCTION
I
N induction motor ball bearings are among the most important part which need to monitor. According to the motor Reliability working group and investigation carried by the Electric Power Research Institute, the most common failure mode of an induction motor is bearing failure followed by stator winding failures, and rotor failures. Therefore, proper monitoring of bearing condition is highly cost effective in reducing capital cost. Vibration monitoring is the most widely used and reliable method to detect, and distinguish defects in ball bearings. In most machine fault diagnosis and prognosis system, the vibration of the induction machine bearings is directly measured by an accelerometer and conducted typically following phases: data acquisition, feature extraction and fault detection or identification. When localized damage in a bearing surface strikes another surface, impact vibrations are generated. The signature of a damaged bearing consists of exponentially decaying ringing that occurs periodically at the characteristic defect frequency [1]. For a particular bearing geometry, inner raceway, outer raceway and rolling element fault generate vibration spectra
Navin Chandra Joshi
with unique frequency components. These frequencies known as defect frequencies are function of the running speed of the motor and the pitch diameter to ball diameter ratio of the bearing. The difficulty in the detection of the defect lies in the fact that, the signature of a defective bearing is spread across a wide frequency band and hence can be easily masked by noise and low frequency effects. Fourier transform (FT) was used to perform such analysis [2]-[4]. If the level of random vibration and noise are high, the result may mislead about actual condition of the bearings so that noise and random vibration may be suppressed from the vibration signal using signal processing technique such as filtering, averaging, correlation, convolution, etc. Advance signal processing methods, including wavelet transform (WT) and Hilbert transformation (HT), have been presented to extract vibration features in recent years [5]-[9]. When a local fault exists in a ball bearing, the surface is locally affected and the vibration signals exhibit modulation [10]. Therefore, it is necessary to implement filtering and demodulation so as to obtain fault sensitive features from the raw signals. At present, the Hilbert transform has been widely used as a demodulation method in vibration-based fault diagnosis [11]-[12]. It has a quick algorithm and can extract the envelope of the vibration signal. In addition, WT which can provide the useful information from vibration signal in time domain with different bands of frequencies [12]-[14], which can be treated as band-pass filters. Further we can calculate the energy of each signal components and select the higher energy signal component for the envelope detection. This paper is organized as follows. In section II, wavelet and Hilbert transforms are briefly introduced. Section III a method is proposed for detection of bearing fault. In section IV, the real vibration data of induction machine bearing is used and evaluate the proposed method. II.
THEORETICAL BACKGROUND
A. Wavelet Transform Raj Kumar Patel, M.Tech student in Department of Electrical Engineering, National Institute of Technology, Hamirpur-177005, India (email:
[email protected]). Sanjay Agrawal, M.Tech student in Department of Electrical Engineering, National Institute of Technology, Hamirpur-177005, India (e-mail:
[email protected]). Navin Chandra Joshi, M.Tech student in Department of Electrical Engineering, National Institute of Technology, Hamirpur-177005, India (email:
[email protected]).
978-1-4673-0455-9/12/$31.00 ©2012 IEEE
The use of wavelet transform is particularly appropriate since it gives information about the signal both in frequency and time domains. The continuous wavelet transform (CWT) of a finite energy time domain signal with wavelet is defined as [15]. (1)
and
(6) (2)
Where t is the time, is the wave or mother wavelet and it has two characteristic parameter namely, is the scale and b is the location or space, which vary continuously. Here the space parameter, “ ”, controls the position of the wavelet in time and a small scale parameter corresponds to a highfrequency component. This means that the parameter “ ” varies for different frequencies. The parameters “ ” and “ ” take discrete values and can perform discrete wavelet transform (DWT). The DWT employs a dyadic grid and orthonormal wavelet basis functions and exhibits zero redundancy. The DWT compute the wavelet coefficients at discrete intervals (integer power of two) of time and scales [18], that is and , where m and n are integers. Therefore the discrete wavelet function and scaling function can be defined as follows:
Where and are the time and transformation parameters respectively. Because of the possible singularity at , the integral is to be considered as a Cauchy principle value. The Hilbert Transform is equivalent to an interesting kind of filter, in which the amplitudes of the spectral components are left unchanged, but there are phase shifted by . In machinery fault detection, modulation on caused by local faults is inevitable in collected signals. In order to identify fault related signatures, demodulation is necessary step, and it can be accomplished by forming a complex value time domain analytic signal with and That is (7) Where ,
(3) (4)
S. Mallat introduced an efficient algorithm to perform the DWT known as the Multi-resolution analysis (MRA) [18]. MRA can decompose signals at different level. The ability of signal decomposition can decompose a variety of different frequency components of the mixed-signal intertwined into different sub-band signals, which can be effectively applied to signal analysis and reconstruction, signal and noise separation, feature extraction, and so on. For example, if is the sampling frequency then the approximation of level DWT decomposition corresponds to the frequency band and the detail covers the frequency range
and ; is the envelope of which representation estimate of the modulation in the signal. III. THE PROPOSED METHOD FOR ROLLING BEARING FAULT IDENTIFICATION
A. Rolling Bearing Failure Behaviour For a particular bearing geometry, inner raceway, outer raceway and rolling element faults generate vibration spectra with unique frequency components, called bearing defect frequencies, and these frequencies are linear function of the running speed of the motor. The formulae for various defect frequencies are as follows [19].
. Fundamental train frequency
In MRA, signal is passing through high-pass and low-pass filters, from which the original signal can be reconstructed. The low frequency sub-band is called as „approximation ‟ and the high frequency sub-band by „detail ‟. Thus, at three levels signal can be reconstructed as .
(5)
B. Hilbert Transform The HT, as a kind of integral transformation, plays a significant role in vibration analysis [16]. One of the common ways it can be used as a direct examination of a vibration instantaneous attributes frequency, phase and amplitude. It allows rather complex signals and systems to be analysed in the time domain. The HT of function f (t) is defined by an integral transform:
Ball spin frequency Outer raceway frequency Inner raceway frequency Where, , , are the revolution per second of IR or the shaft, Ball diameter, pitch diameter and contact angle respectively. Manufacturer often provide these defect frequencies in the bearing sheet.
B. The Proposed Method For the proper identification of bearing defect frequencies, from the vibration signal measured by accelerometer, used two techniques DWT and HT. First one is quadratic sub band filtering technique that can decompose the captured signal up to three decomposition levels, using mother wavelet “db10” of Daubechies family. After decomposition of signal into detail
and approximation coefficient, signal was reconstructed and calculates the energy of detail reconstructed signal using Parsavel‟s theorem of each level, later one provides a means of signal demodulation. In this proposed method, the selection of detail reconstruction signal for HT is based on the higher energy contain by that detail reconstructed signal. To make the signals comparable regardless of difference in magnitude, the signals are normalised by using following equation (8) Where is reprocessed signal, and the mean value and standard deviation of respectively. When a local fault exists in the bearing, there is modulation in the signal. To reduce the impact of modulation, the Hilbert transform was performed on higher energy detail reconstructed signals using (6) and (7), and the corresponding analytical signals and their envelopes, , can be obtained. th Here, is the envelope signal of the j detail reconstructed signal after the Hilbert transform. To identify the existence of defect frequency components (such as BS, IR, OR, FTF) of the bearing, perform the spectrum analysis of A flow chart of the bearing defect frequencies identification based on wavelet and the Hilbert transform as shown in Fig. 2.
data is acquired using accelerometers, which are attached in to the housing with magnetic basis. Digital data us sampled at 12,000 samples per second and recorded using 16 channel DAT recorders. Motor bearings were seeded with faults using electro-discharge machining (EDM). In this paper, four set of data were obtain from experiment system: 1. Under normal condition. 2. With inner raceway fault. 3. With outer raceway fault. 4. With a ball element fault. The selected fault is 0.5334 mm in diameter on full load and speed during the experiment near to 1754 rpm. The time domain vibration signals considered for the analysis are collected for four different condition of the bearing at full load is shown in Fig. 2(a), 2(b), 2(c), 2(d). B. Experimental Result Listed in Table I, II shows the specification and the main defect frequencies based on geometric structure of the bearing respectively [19]. The vibration data analyzed for this case is for a faulty bearing located at the drive end side at full load. In order to evaluate the proposed method, FFT is taken of raw signal with inner race defect is shown in Fig. 3 and find that, it is very difficult to identify the defect frequency so that, the proposed method applied to the bearing vibration data and result shown in Fig. 4 to Fig. 7. The location of the frequencies peaks can be used to distinguish between normal and abnormal behaviors. The shaft rotating frequency is about 29 Hz on full load so that at normal condition the only peaks exist at multiple integral of shaft rotation frequency as shown in Fig. 4. From Fig. 5, it can be seen that the dominating frequency are 158 Hz and its multiple integral which is identified as the IR. Such a frequency indicates the existence of a localized defect on inner raceway. 0.25 0.2 0.15
Amplitude
0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Time (sec)
Fig. 2. (a) Vibrartion signal of normal condition 3
2
result and discussion
A. Description of Experiment Vibration signals provided by the CWRU (Case Western Reserve University) bearing data center [20], collected a 2 HP motor fixed in a test stand is used for investigation. Vibration
Amplitude
1
Fig. 1. Flow chart for identification of defect frequencies
0
-1
-2
-3 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time (sec)
Fig. 2. (b) Vibrartion signal of Inner race defect condition
0.4
0.45
0.5
spectrum indicates that the fault localized in ball of the bearing.
6
4
5
16
Amplitude
2
x 10
raw signal 0
14
-2
12 -4
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Time (sec)
Fig. 2. (c) Vibrartion signal of Outer race defect condition
Amplitude
10 -6 0
8
6 0.5
4
0.4 0.3
2
X: 444 Y: 1.161e+005
Amplitude
0.2 0.1
0 0
1000
2000
0
3000
4000
5000
6000
frequency f/Hz
-0.1
Fig. 3. Power spectrum of Inner race defect bearing raw vibration signal -0.2 -0.3 -0.4 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
500
0.5
Time (sec)
Normal
450
Fig. 2. (d) Vibrartion signal of rolling element defect condition
400
Specification
Value
Number of rolling element, N
9
spectrum P/W
350
TABLE I BALL BEARING SPECIFICATION
300 250 200
fr
150
Diameter of rolling element, Bd
X: 29.3 Y: 146.2
7.940 mm
Pitch diameter of bearing, Pd
39.039 mm
Contact angle, θ
0
100
2*fr
50 0 0
200
400
600
800
1000
frequency f/Hz
Fig. 4. Power spectrum of ball bearing vibration signal at normal condition TABLE II CHARACTERISTICS OF BALL BEARING
Defect Frequencies Running speed frequency,
Value
500
29.23 Hz
450
IR
400
Fundamental train frequency,
IR Defect
X: 157.5 Y: 418.9
11.64 Hz 68.89 Hz
Outer raceway frequency,
104.76 Hz
Inner raceway frequency,
158.34 Hz
spectrum P/W
350
Ball spin frequency,
300 fr 250
2*IR
200 BS IR+fr
150 100
As shown in Fig. 6, the dominating frequency exists at 105 Hz and its multiple integral can be identified as the OR. The existence of such frequency component in the spectrum indicates that the rolling bearing developed a localized defect on its outer raceway. Figure. 7, shows the dominating frequency at 99 Hz, This frequency is identified as BF+fr and also exist at BF+2*fr, BF+3*fr. The existence of such frequency component in the
IR-fr
3*IR 50 0 0
200
400
600
800
1000
frequency f/Hz
Fig. 5. Power spectrum of bearing vibration signal at inner raceway defected condition.
[3] 1000 OR Defect
900
OR
[4]
800
spectrum P/W
700
fr
X: 104.7 Y: 788.5
[5]
600 OR-fr
[6]
500 400 OR+fr
300
[7] 2*OR
200
3*OR
100 0 0
200
400
[8] 600
800
1000
frequency f/Hz
Fig. 6. Power spectrum of bearing vibration signal at outer raceway defected condition.
[9]
[10]
500 Ball Defect
450
[11]
400
spectrum P/W
350 300
[12]
250 200 150
X: 99.61 Y: 134.3
fr 100
[13]
BS+fr BS+2*fr
[14]
50 0 0
200
400
600
800
1000
frequency f/Hz
[15]
Fig. 7. Power spectrum of bearing vibration signal at ball defected condition.
IV. CONCLUSION This paper has presented an approach for identification of bearing defect frequencies at full load. The approach takes advantage of the merits of DWT and HT to extract the features from bearing vibration signal of an induction motor. The experimental bearing results obtained have shown this proposed method can be used for bearing fault detection and diagnosis.
[16]
[17] [18] [19] [20]
V. ACKNOWLEDGMENT The authors would like to thank Professor L. A. Laparo of Case Western Reserve University for providing access to the bearing data sheet. VI. REFERENCES [1]
[2]
S. Wadhwani, S. P. Gupta and V. Kumar, “ Wavelet based vibration monitoring for detection of faults in ball bearings of rotating machines,” Journal Inst. Eng. (India) -EL, vol. 86, pp. 77-81, 2005. B. Yazıcı, G.B. Kliman, “An adaptive statistical time-frequencymethod for detection of broken bars and bearing faults in motors using stator current,” IEEE Trans. Ind. Appl., vol. 35, no. 2, pp. 442–452, 1999.
S. Seker, “Determination of air-gap eccentricityin electric motors using coherence analysis,” IEEE Power Eng. Rev, vol. 20, no. 7, pp. 48-50, 2000. S. Seker, E. Ayaz, “A study on condition monitoring for induction motors under the accelerated aging processes,” IEEE Power Eng. Rev., vol., 22, no. 7, 2002. N.G. Nikolaou, I.A. Antoniadis, “Rolling element bearing fault diagnosis using wavelet packets,” NDT& E International,vol. 35, pp. 197-205, 2002. Michael Feldman, “Hilbert transform in vibration analysis- A tutorial review”, Mechanical Systems and Signal Processing, vol. 25, pp. 735802, 2011. G.K. Singh , Saleh Al Kazzaz Sa‟ad Ahmed, “Vibration signal analysis using wavelet transform for isolation and identification of electrical faults in induction machine”, Electric Power Systems Research, vol. 68, pp. 119-136, 2004. Serhat Seker, Emine Ayaz, “Feature extraction related to bearing damage in electric motors bywavelet analysis”, Electric Power Systems Research, vol. 65, pp. 197-221, 2003. Hasan Ocak, Kenneth A. Loparo, “Estimation of the running speed and bearing defect frequencies of an induction motor from vibration data”, Mechanical Systems and Signal Processing, vol. 18, pp. 515-533, 2004. J. Antoni, and R.B. Randall, “Differential diagnosis of gear and bearing faults”, Journal of Vibration and Acoustics, vol.124, no.2, pp.65- 171, 2002. D. Wang, Q. Miao, X. Fan, and H.Z. Huang, “Rolling element bearing fault detection using an improved combination of Hilbert and wavelet transforms.” Journal of Mechanical Science and Technology, vol.23, no.12, pp. 3292-3301, 2009. Y. Qin, S. Qin, and Y. Mao, “Reasearch on iterated Hilbert transform and its application in mechanical faults diagnosis,” Mechanical Sustem and Signal Processing, vol.22, no.8, pp. 1967-1980, 2008. D. Wang, Q. Miao, and R. Kang, “Robust health evaluation of gearbox subject to tooth failure with wavelet decomposition,” Journal of Sound and Vibration, vol.324, no.3-5, pp. 1141-1157, 2009. G. Niu, A. Widodo, J.D. Son, B.S. Yang, D.H. Hwang, and D.S. Kang, “Decision-level fusion based on wavelet decomposition for induction motor fault diagnosis using transient current signal,” Expert Systems with Applications, vol.35, no.3, pp. 918-928, 2008. F. Al-Badour, M. Sunar, L. Cheded,” Vibration analysis of rotating machinery using time-frequency analysis and wavelet technique”, Mechanical System and Signal Processing, vol. 25, pp. 2083-2101, 2011. Michael Feldman, “Time-varying vibration decomposition and analysis based on the Hilbert transform,” Journal of Sound and Vibration, vol. 295, pp. 518-530, 2006. A. Mertins, Signal analysis: wavelets, filter banks, time-frequency transforms and applications. John Wiley & sons Ltd; 1999. S. Mallat, Awavelet Tour of Signal Processing, Academic Press, New York, 1997. V. Wowk, “Machinery Vibration, Measurement and Analysis, McGrawHill, New York, 1991. Case Western Reserve University, Bearing data center [online], Available:URL:http://www.eecs.cwru.edu/laboratory/bearing/download. htm, 2011.
