# A More Reliable Method for Monitoring the Condition of Three-Phase Induction Motors Based on Their Vibrations

Authors: R. Shnibha; A. Albarbar; A. Abouhnik; G. Ibrahim
Journal: ISRN Mechanical Engineering
 (2012)

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## Abstract

This paper is concerned with accurate, early, and reliable fault diagnosis using an enhanced vibration measurement technique based on short-time Fourier transform. The novelty of this work lies in detecting very low-phase imbalance-related faults. The energy contained within specified frequency bands centred on the rotor frequency and power supply frequency, and their sideband zones were calculated. The technique was firstly demonstrated by simulated signals and then verified by experimental measurements taken from two different-sized test rigs. The first one comprised a 1.1 kW variable speed three-phase induction motor with varying output load (no load, 25%, 50%, 75%, and 100% load). Two types of common faults were introduced: imbalance in one phase as the electrical fault and misalignment of load as the mechanical fault. The second test rig had a 3 kW three-phase induction motor again with varying load, and here the two seeded faults were: phase imbalance and one broken rotor bar. The measured energy levels in the test conditions were found to be affected by type of fault and fault severity. It is concluded that the proposed method offers a potentially reliable and computationally inexpensive condition monitoring tool which can be implemented with real-time monitoring systems.


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## Body

## 1. Introduction

Condition-monitoring and condition-based maintenance aim at increasing machine reliability, maintaining performance, reducing spare parts inventories, and reducing break-down maintenance. Induction motors are common prime movers and faults including winding faults, unbalanced stator and, broken rotor bars, eccentricity, and bearing faults have been extensively studied [1].All induction motors generate noise and vibration, and analysis of these can be used to give information on the condition of the motor. Noise and vibration in induction motors are caused by forces which are of magnetic, mechanical, and aerodynamic origin. The largest sources of vibration and noise in induction motors are the radial forces due to the air gap field because the air gap flux density distribution is a product of the resultant mmf wave and the total permeance wave. The resultant magneto motive force, mmf, also contains the effect of possible rotor or stator asymmetries, and the permeance wave depends on the variation of the air gap as the resulting magnetic forces also depend on these asymmetries. Thus by analysing the vibration signal of an induction motor, it is possible to detect various types of faults and asymmetries. There have been many practical demonstrations of the capability of vibration monitoring to detect a wide range of motor faults; these include shaft eccentricity/misalignment [2, 3], bearing faults [3], looseness [4], rotor imbalance [5], and broken rotor bar [3–6].The vibration of either the motor stator core or end caps can be easily monitored by an accelerometer which is usually directly mounted on the motor. Analysing the measured signal using conventional signal processing techniques such as fast Fourier transforms (FFTs) does not always achieve adequate results. When looking at a Fourier transform of a signal, it is impossible to tell when a particular event took place. In an effort to determine when and at what frequencies a signal event occurred, Darowicki and Zieliński [7] derived the short-time Fourier transform (STFT) based on application of a time window to localise the spectrum in the time domain.Jurado and Saenz [8] showed that the discrete STFT is suitable for harmonic analysis and by selecting a small window length was able to detect transients within noisy data. Arabaci and Bilgin [9] showed experimentally that using the STFT for fault diagnosis and classification in induction motors, where the faults were broken rotor bars and broken end rings, increased accuracy rates.


## 2. Conventional Methods and the Proposed Technique

### 2.1. The Proposed Method

Most condition monitoring to detect damage in the induction motor focuses on statistical analysis of the time-domain signal. RMS, crest factor (CF), and kurtosis are parameters that have been widely used. Each parameter has been defined in detail in [10, 11]. However, the method proposed here is based on using the STFT and subsequently calculating the energy contained within certain frequency bands and their sideband zones. Equation (1) mathematically expresses this novel method:
(1)TE=∫t1t2∫f1f2STFT(t,f)dfdt,
where TE is the total energy level in the frequency band, and f1 and f2 are the lower and upper frequency boundaries, respectively. In this study, integration is calculated using the trapezoid rule. As a first step, energy is calculated per unit time using MATLAB, obtaining numerical values for energy as a function of the time. In the second step the trapezoid rule is applied to find total energy of the signal spectrum. To help in understanding the first and second steps [12], the process is illustrated in Figure 1.Figure 1
Schematic representation of calculation of total energy.


### 2.2. Numerical Simulation

Conventional analysis, using statistical parameters and the Fourier transform of a periodic, stationary, and deterministic signal, cannot take into account the temporal variation of the spectral characteristics of a nonstationary signal. Consider the two signals shown in Figure2. The first signal is represented in (2):
(2)f1(t)=sin(2π·25t)+sin(2π·90t)+sin(2π·150t).
This signal contains three sinusoids of equal amplitudes and frequencies 25, 90, and 150 Hz; therefore, it can be described as a stationary signal. Figure 2(a) represents a 1000 ms period of this signal, and its frequency spectrum is shown in Figure 2(b).Time- and frequency-domain representations of the two signalsf1 and f2. (a) f1 in time domain, (b) f1 in frequency domain, (c) f2 in time domain, and (d) f2 in frequency domain.
(a)
(b)
(c)
(d)A nonstationary signalf2 contains the same frequency components as f1 but in three discrete and different time intervals. A 1000 ms length of this signal is plotted in Figure 2(c), and its spectrum is plotted in Figure 2(d). The time interval from 0 to 350 ms contains a 25 Hz sinusoid, the interval from 350 to 700 ms contains a 90 Hz sinusoid, and the interval from 700 to 1000 ms contains a 150 Hz sinusoid as described in (3).Consider(3)f2(t)={sin(2π*25t),0≤t≤350,sin(2π*90t),350≤t≤700,sin(2π*150t),350≤t≤1000.
Consider the signals represented by (2) and (3) and presented in Figure 2. Both signals are composed of the same three frequency components, but while f1(t) shown in Figure 2(a) contains all three signals for the entire time interval, f2(t) shown in Figure 2(c) contains the individual components for different time intervals. The time-domain representations are completely different. However, the frequency domains shown in Figures 2(b) and 2(d) obtained using the FFT are essentially identical because the FFT does not provide information on the time when spectral components are present. In this sense the FFT is not a suitable technique for nonstationary signals.To accurately represent the frequency information contained in a nonstationary signal, a transform that presents both time and frequency information is needed to produce a signal spectrum in the time-frequency domain, preferably in a manner which plots the amplitudes against time and frequency as shown in Figure3.Time- and frequency-domain representations of the two signalsf1 and f2: (a) f1 time domain, (b) f1 time frequency-domain, (c) f2 time domain, and (d) f2 time-frequency domain.
(a)
(b)
(c)
(d)Using such a technique to analyse transient, nonstationary, and vibration signals emitted by electromechanical machinery theoretically enables every event observed in the time-frequency domain to be linked to its source. Provided that the sources can be separated in the frequency domain it should be possible to quantify the vibration energy associated with each event. This energy can then be evaluated with respect to that obtained for a healthy machine.An efficient time-frequency method should(1)
analyse the frequencies associated with each source of excitation,(2)
identify at each point of the structure the response to each source of excitation, and(3)
measure the contribution of each source of excitation in terms of its energy.


## 2.1. The Proposed Method

Most condition monitoring to detect damage in the induction motor focuses on statistical analysis of the time-domain signal. RMS, crest factor (CF), and kurtosis are parameters that have been widely used. Each parameter has been defined in detail in [10, 11]. However, the method proposed here is based on using the STFT and subsequently calculating the energy contained within certain frequency bands and their sideband zones. Equation (1) mathematically expresses this novel method:
(1)TE=∫t1t2∫f1f2STFT(t,f)dfdt,
where TE is the total energy level in the frequency band, and f1 and f2 are the lower and upper frequency boundaries, respectively. In this study, integration is calculated using the trapezoid rule. As a first step, energy is calculated per unit time using MATLAB, obtaining numerical values for energy as a function of the time. In the second step the trapezoid rule is applied to find total energy of the signal spectrum. To help in understanding the first and second steps [12], the process is illustrated in Figure 1.Figure 1
Schematic representation of calculation of total energy.


## 2.2. Numerical Simulation

Conventional analysis, using statistical parameters and the Fourier transform of a periodic, stationary, and deterministic signal, cannot take into account the temporal variation of the spectral characteristics of a nonstationary signal. Consider the two signals shown in Figure2. The first signal is represented in (2):
(2)f1(t)=sin(2π·25t)+sin(2π·90t)+sin(2π·150t).
This signal contains three sinusoids of equal amplitudes and frequencies 25, 90, and 150 Hz; therefore, it can be described as a stationary signal. Figure 2(a) represents a 1000 ms period of this signal, and its frequency spectrum is shown in Figure 2(b).Time- and frequency-domain representations of the two signalsf1 and f2. (a) f1 in time domain, (b) f1 in frequency domain, (c) f2 in time domain, and (d) f2 in frequency domain.
(a)
(b)
(c)
(d)A nonstationary signalf2 contains the same frequency components as f1 but in three discrete and different time intervals. A 1000 ms length of this signal is plotted in Figure 2(c), and its spectrum is plotted in Figure 2(d). The time interval from 0 to 350 ms contains a 25 Hz sinusoid, the interval from 350 to 700 ms contains a 90 Hz sinusoid, and the interval from 700 to 1000 ms contains a 150 Hz sinusoid as described in (3).Consider(3)f2(t)={sin(2π*25t),0≤t≤350,sin(2π*90t),350≤t≤700,sin(2π*150t),350≤t≤1000.
Consider the signals represented by (2) and (3) and presented in Figure 2. Both signals are composed of the same three frequency components, but while f1(t) shown in Figure 2(a) contains all three signals for the entire time interval, f2(t) shown in Figure 2(c) contains the individual components for different time intervals. The time-domain representations are completely different. However, the frequency domains shown in Figures 2(b) and 2(d) obtained using the FFT are essentially identical because the FFT does not provide information on the time when spectral components are present. In this sense the FFT is not a suitable technique for nonstationary signals.To accurately represent the frequency information contained in a nonstationary signal, a transform that presents both time and frequency information is needed to produce a signal spectrum in the time-frequency domain, preferably in a manner which plots the amplitudes against time and frequency as shown in Figure3.Time- and frequency-domain representations of the two signalsf1 and f2: (a) f1 time domain, (b) f1 time frequency-domain, (c) f2 time domain, and (d) f2 time-frequency domain.
(a)
(b)
(c)
(d)Using such a technique to analyse transient, nonstationary, and vibration signals emitted by electromechanical machinery theoretically enables every event observed in the time-frequency domain to be linked to its source. Provided that the sources can be separated in the frequency domain it should be possible to quantify the vibration energy associated with each event. This energy can then be evaluated with respect to that obtained for a healthy machine.An efficient time-frequency method should(1)
analyse the frequencies associated with each source of excitation,(2)
identify at each point of the structure the response to each source of excitation, and(3)
measure the contribution of each source of excitation in terms of its energy.


## 3. Instrumentation and Data Collection

A schematic diagram of the test rig and instrumentations is shown in Figure4. It comprised a 1.1 kW variable speed induction motor, a DC generator and a resistor bank to act as a load. The instrumentation consisted of an accelerometer B&K type 4371. The accelerometer was positioned vertically on the drive end using superglue (Figure 4). The output of the accelerometer was filtered and amplified via a charge amplifier. The measured data was then transferred to the computer using 24-bit resolution data acquisition. The sampling frequency was 50 kHz. The developed Labview-based system allowed the user to monitor and store machine variables, and subsequently a Matlab code was used for further signal processing.Figure 4
Schematic diagram of induction motor test rig.


### 3.1. Experimental Results

The 1.1 kW motor was tested at 1500 rpm and 100% load in a healthy condition and then under four different phase imbalance voltages of 5, 10, 15, 20, and 25 V; these represented 2%, 4%, 6%, 8%, and 10%, respectively, of the main nominal voltage level. 1 mm and  2 mm motor offset misalignment as shown in Figure5. The 3 kW motor was tested at 100% load in a healthy condition then under two different phase imbalance voltages of 20 and 40 V and with one rotor bar broken.Figure 5
Motor offset misalignment [13].A number of statistical parameters (RMS, CF, and kurtosis) were extracted from the measured vibration signal, see Figure6. No discernible trend or statistically significant differences could be found between the different conditions even in the case of 10% voltage imbalance.Statistical parameters from the time domain of the vibration signal.
(a)
(b)
(c)Where fault 1 and fault 2 are 8% and 10%, respectively, of the main nominal voltage level. And fault 3 is 2 mm motor load misalignment.The measured signals were transformed into the frequency-domain, where the frequencies of their main components were identified, see Figure7. Three major frequency components were determined within the vibration signal: the first component was at 25 Hz, rotor rotation speed, the second was at 50 Hz, power supply or second harmonic of rotor speed, and the third was at 100 Hz, second harmonic of power supply frequency or fourth harmonic of the rotor frequency. There appears to be a slight increase in the amplitudes of these components between healthy and faults cases, but it was not statistically significant.Measured frequency domain of vibration signal with voltage imbalance in one phase of the supply, at 100% load.
(a)
(b)
(c)
(d)
(e)
(f)Spectral analysis of the measured vibration signal does not provide sufficient information about the motor condition and the severity of the phase imbalance to detect and identify a fault definitively.In an effort to extract fault severity information the total energy method was applied to the measured vibration signals. Figure8 presents the STFT analysis of the vibration signal when the 1.1 kW motor was running at 1500 rpm, with various phase imbalances. Figure 9 presents the STFT analysis of the vibration signals when the 1.1 kW motor was running at 1500 rpm with misalignments of 1 mm and 2 mm. Figures 10 and 11 present the STFT analysis of the vibration signals when 3 kW motor running with various voltage imbalances in one phase of the supply and with one rotor broken, respectively.STFT of vibration signals from 1.1 kW motor with various voltage imbalances in one phase of the supply, 1500 rpm and 100% load.
(a)
(b)
(c)
(d)
(e)
(f)STFT of vibration signals from 1.1 kW motor with 1 mm and 2 mm misalignment faults, 1500 rpm and 100% load.
(a)
(b)
(c)STFT of vibration signal from 3 kW motor with various voltages imbalances in one phase of the supply, 1500 rpm and 75% load.
(a)
(b)
(c)STFT vibration signal from 3 kW motor with broken rotor bar, 1500 rpm 100% load.
(a)
(b)For the 1.1 kW motor operating at both 1300 and 1500 rpm the total energy levels were determined for a rotation speed frequency band from 15 to 30 Hz, supply frequency band from 40 to 60 Hz, and twice the power supply frequency band from 80 to 120 Hz. Figures12, 13, 14, 15, 16 and 17 show the measured total energy for all the cases.Figure 12
Total energy levels in the frequency band 15–30 Hz, for motor speeds of 1300 and 1500 rpm, for voltage imbalance in one phase of the supply, for 1.1 kW motor at 100% load.Figure 13
Total energy levels in the frequency band 40–60 Hz, for motor speeds of 1300 and 1500 rpm, for voltage imbalance in one phase of the supply, for 1.1 kW motor at 100% load.Figure 14
Total energy levels in the frequency band 80–120 Hz, for motor speeds of 1300 and 1500 rpm, for voltage imbalance in one phase of the supply, for 1.1 kW motor at 100% load.Figure 15
Total energy levels in the frequency band 15–30 Hz, for motor speeds of 1300 and 1500 rpm, for 1 mm and 2 mm misalignment, for 1.1 kW motor at 100% load.Figure 16
Energy levels in 80 to 120 Hz frequency band for 3 kW motor, for voltage imbalance in one phase of the supply speed 1500 rpm at 100% load.Figure 17
Energy levels in 20–30 Hz frequency band for healthy 3 kW motor and motor with one and two broken rotor bars, speed 1500 rpm at 100% load.In Figure12 it can be seen that there is a direct relationship between the fault severity and the total energy levels at both speeds for the 1.1 kW motor. The increase in total energy is particularly apparent at 1300 rpm once the phase imbalance reached 2%. The rate of increase of the total energy at 1500 rpm is much less marked. The same general pattern for voltage phase imbalance can be seen for the frequency bands from 40 to 60 Hz (Figure 13) and from 80 to 120 Hz (Figure 14).Figure15 shows the total energy under the 15–30 Hz frequency band for 1 mm and 2 mm misalignments. It can be seen that for the 1.1 kW motor a misalignment of 1 mm gives a very significant change in the total energy level. Once again, however, the response when running at 1500 rpm is nowhere near so marked.Figures16 and 17 show the results for phase imbalance and damaged rotor bar, respectively, for the 3 kW motor running at 1500 rpm and 100% load.


## 3.1. Experimental Results

The 1.1 kW motor was tested at 1500 rpm and 100% load in a healthy condition and then under four different phase imbalance voltages of 5, 10, 15, 20, and 25 V; these represented 2%, 4%, 6%, 8%, and 10%, respectively, of the main nominal voltage level. 1 mm and  2 mm motor offset misalignment as shown in Figure5. The 3 kW motor was tested at 100% load in a healthy condition then under two different phase imbalance voltages of 20 and 40 V and with one rotor bar broken.Figure 5
Motor offset misalignment [13].A number of statistical parameters (RMS, CF, and kurtosis) were extracted from the measured vibration signal, see Figure6. No discernible trend or statistically significant differences could be found between the different conditions even in the case of 10% voltage imbalance.Statistical parameters from the time domain of the vibration signal.
(a)
(b)
(c)Where fault 1 and fault 2 are 8% and 10%, respectively, of the main nominal voltage level. And fault 3 is 2 mm motor load misalignment.The measured signals were transformed into the frequency-domain, where the frequencies of their main components were identified, see Figure7. Three major frequency components were determined within the vibration signal: the first component was at 25 Hz, rotor rotation speed, the second was at 50 Hz, power supply or second harmonic of rotor speed, and the third was at 100 Hz, second harmonic of power supply frequency or fourth harmonic of the rotor frequency. There appears to be a slight increase in the amplitudes of these components between healthy and faults cases, but it was not statistically significant.Measured frequency domain of vibration signal with voltage imbalance in one phase of the supply, at 100% load.
(a)
(b)
(c)
(d)
(e)
(f)Spectral analysis of the measured vibration signal does not provide sufficient information about the motor condition and the severity of the phase imbalance to detect and identify a fault definitively.In an effort to extract fault severity information the total energy method was applied to the measured vibration signals. Figure8 presents the STFT analysis of the vibration signal when the 1.1 kW motor was running at 1500 rpm, with various phase imbalances. Figure 9 presents the STFT analysis of the vibration signals when the 1.1 kW motor was running at 1500 rpm with misalignments of 1 mm and 2 mm. Figures 10 and 11 present the STFT analysis of the vibration signals when 3 kW motor running with various voltage imbalances in one phase of the supply and with one rotor broken, respectively.STFT of vibration signals from 1.1 kW motor with various voltage imbalances in one phase of the supply, 1500 rpm and 100% load.
(a)
(b)
(c)
(d)
(e)
(f)STFT of vibration signals from 1.1 kW motor with 1 mm and 2 mm misalignment faults, 1500 rpm and 100% load.
(a)
(b)
(c)STFT of vibration signal from 3 kW motor with various voltages imbalances in one phase of the supply, 1500 rpm and 75% load.
(a)
(b)
(c)STFT vibration signal from 3 kW motor with broken rotor bar, 1500 rpm 100% load.
(a)
(b)For the 1.1 kW motor operating at both 1300 and 1500 rpm the total energy levels were determined for a rotation speed frequency band from 15 to 30 Hz, supply frequency band from 40 to 60 Hz, and twice the power supply frequency band from 80 to 120 Hz. Figures12, 13, 14, 15, 16 and 17 show the measured total energy for all the cases.Figure 12
Total energy levels in the frequency band 15–30 Hz, for motor speeds of 1300 and 1500 rpm, for voltage imbalance in one phase of the supply, for 1.1 kW motor at 100% load.Figure 13
Total energy levels in the frequency band 40–60 Hz, for motor speeds of 1300 and 1500 rpm, for voltage imbalance in one phase of the supply, for 1.1 kW motor at 100% load.Figure 14
Total energy levels in the frequency band 80–120 Hz, for motor speeds of 1300 and 1500 rpm, for voltage imbalance in one phase of the supply, for 1.1 kW motor at 100% load.Figure 15
Total energy levels in the frequency band 15–30 Hz, for motor speeds of 1300 and 1500 rpm, for 1 mm and 2 mm misalignment, for 1.1 kW motor at 100% load.Figure 16
Energy levels in 80 to 120 Hz frequency band for 3 kW motor, for voltage imbalance in one phase of the supply speed 1500 rpm at 100% load.Figure 17
Energy levels in 20–30 Hz frequency band for healthy 3 kW motor and motor with one and two broken rotor bars, speed 1500 rpm at 100% load.In Figure12 it can be seen that there is a direct relationship between the fault severity and the total energy levels at both speeds for the 1.1 kW motor. The increase in total energy is particularly apparent at 1300 rpm once the phase imbalance reached 2%. The rate of increase of the total energy at 1500 rpm is much less marked. The same general pattern for voltage phase imbalance can be seen for the frequency bands from 40 to 60 Hz (Figure 13) and from 80 to 120 Hz (Figure 14).Figure15 shows the total energy under the 15–30 Hz frequency band for 1 mm and 2 mm misalignments. It can be seen that for the 1.1 kW motor a misalignment of 1 mm gives a very significant change in the total energy level. Once again, however, the response when running at 1500 rpm is nowhere near so marked.Figures16 and 17 show the results for phase imbalance and damaged rotor bar, respectively, for the 3 kW motor running at 1500 rpm and 100% load.


## 4. Conclusion

A condition-monitoring scheme based on vibration signals measurements and STFT analysis has been successfully applied to a three phase induction motor. The adopted technique of total energy level offers a tool with which to evaluate any abnormality or deviation in the motor processes.The signal processing procedures developed in this work and their application to measure induction motor vibration signals show promising results in the early detection and diagnosis of faults. The following few conclusions could be highlighted.(a)
Time-domain analysis provided a rough assessment but was not sufficient for fault classification and ranking. Frequency-domain analysis can provide sufficiently detailed spectral information to reveal some hidden features of short duration.(b)
The use of joint time-frequency-domain representation using STFT can extract information about the time domains of different bands of frequencies.(c)
The approach developed here proved to be very good detecting small changes in phase imbalance which make it good condition-monitoring tool for weak signatures.It is concluded that there can be big advantages in using STFT and total energy level calculations as a fault severity evaluators.



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*Source: 230314-2012-10-18.xml*