# Vibration Analysis of Induction Motors

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This assignment investigates the vibrations of induction motors under half, full, and no load conditions. It explores how broken rotor bars impact motor performance and vibration patterns. The focus is on using Fast Fourier Transform (FFT) analysis to detect these faults by identifying characteristic sidebands in the frequency spectrum. The document also discusses challenges faced during experimentation and proposes solutions for improving the accuracy and reliability of the method.

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Running Head: THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER

The Fast Fourier Transform Spectrum Analyzer

Name

Institutional affiliation

The Fast Fourier Transform Spectrum Analyzer

Name

Institutional affiliation

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THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER 2

FFT SPECTRUM

The Fast Fourier Transform Spectrum Analyzer uses a technique of digital signal

processing to analyze a waveform by Fourier transforms to give the analysis of signal spectra

waveform. The analyzer if FFT has the ability to provide facilities that cannot be given by the

analyzer of swept frequency, enabling first capture and styles of analysis that cannot occur with

sweep technique alone. The spectrum analyzer measures the input signal magnitude versus

frequency in the range of full frequency of the instrument (Goldman, 2012, p. 121).

Its primary use is to measure the spectrum power of both unknown and known signals.

The signal input that spectrum analyzer measures is electrical though the composition of spectral

of other signals like optical light waves and acoustic waves pressure can be taken into

consideration by the use of the appropriate transducer. Spectrum analyzer of optics also exists

which use direct optical techniques like monochromatic of filters in making measurements. This

purpose of this analysis is to perform the vibrations and identify the problems in the electrical

machinery at the plant. The curves of vibration are taken frequently for a Squirrel cage Induction

Motors from a single machine with the rating of 3 phase, 5 HP, 415V, 50Hz, 1440rpm, 28 bar

rotors, 36 stator slots (Silva, 2011, p. 111).

The vibration curves which were recorded include healthy motor FFT in the first month

for the conditions of a half, full, and no load conditions, and FFT took after 5 months during one

rotor bar failure for the conditions of a half, no, and full load. FFT took after 10 months during

two rotor bar failure conditions of full, no, and half load. The following shows the analysis and

identifications of the FFT spectrum together with their correct label:

Healthy motor no load FFT spectrum

FFT SPECTRUM

The Fast Fourier Transform Spectrum Analyzer uses a technique of digital signal

processing to analyze a waveform by Fourier transforms to give the analysis of signal spectra

waveform. The analyzer if FFT has the ability to provide facilities that cannot be given by the

analyzer of swept frequency, enabling first capture and styles of analysis that cannot occur with

sweep technique alone. The spectrum analyzer measures the input signal magnitude versus

frequency in the range of full frequency of the instrument (Goldman, 2012, p. 121).

Its primary use is to measure the spectrum power of both unknown and known signals.

The signal input that spectrum analyzer measures is electrical though the composition of spectral

of other signals like optical light waves and acoustic waves pressure can be taken into

consideration by the use of the appropriate transducer. Spectrum analyzer of optics also exists

which use direct optical techniques like monochromatic of filters in making measurements. This

purpose of this analysis is to perform the vibrations and identify the problems in the electrical

machinery at the plant. The curves of vibration are taken frequently for a Squirrel cage Induction

Motors from a single machine with the rating of 3 phase, 5 HP, 415V, 50Hz, 1440rpm, 28 bar

rotors, 36 stator slots (Silva, 2011, p. 111).

The vibration curves which were recorded include healthy motor FFT in the first month

for the conditions of a half, full, and no load conditions, and FFT took after 5 months during one

rotor bar failure for the conditions of a half, no, and full load. FFT took after 10 months during

two rotor bar failure conditions of full, no, and half load. The following shows the analysis and

identifications of the FFT spectrum together with their correct label:

Healthy motor no load FFT spectrum

THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER 3

Healthy motor half load FFT spectrum

Healthy motor full load FFT spectrum

When the supply of three phase of balanced applied voltage to the motor induction that is

healthy, the constant current flow in entire phases occurred. This makes a constant field of a

magnet in rotor and stator. The MMF interaction in the rotor circuit with the flux of the magnet

stator may yield a positively charged torque of motor that is steady which drives the rotor in a

Healthy motor half load FFT spectrum

Healthy motor full load FFT spectrum

When the supply of three phase of balanced applied voltage to the motor induction that is

healthy, the constant current flow in entire phases occurred. This makes a constant field of a

magnet in rotor and stator. The MMF interaction in the rotor circuit with the flux of the magnet

stator may yield a positively charged torque of motor that is steady which drives the rotor in a

THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER 4

direction of forward giving out mechanical output which is useful. An acceptable vibration radial

will be present within the stator. The evaluation of spectral signal of vibration produces a

dominate 49.81Hz of a frequency with the magnitude of 68.21dB and without harmonic band

frequencies as shown above. The frequency of 41.81 Hz is close to 50Hz components of

frequency and is a positively charged sequence that is good for a rotor driving the system in the

inward path and this element indicates a healthy motor (Goldman, 2012, p. 219).

FFT spectrum of the motor one bars of broken rotor with a condition of no load

FFT spectrum of the motor two bars of broken rotor under the condition of no load

Table 1 showing analysis of no load one broken and 2 broken rotor bars conditions

Frequency of Experimental Values Freq analytical values (Hz)

direction of forward giving out mechanical output which is useful. An acceptable vibration radial

will be present within the stator. The evaluation of spectral signal of vibration produces a

dominate 49.81Hz of a frequency with the magnitude of 68.21dB and without harmonic band

frequencies as shown above. The frequency of 41.81 Hz is close to 50Hz components of

frequency and is a positively charged sequence that is good for a rotor driving the system in the

inward path and this element indicates a healthy motor (Goldman, 2012, p. 219).

FFT spectrum of the motor one bars of broken rotor with a condition of no load

FFT spectrum of the motor two bars of broken rotor under the condition of no load

Table 1 showing analysis of no load one broken and 2 broken rotor bars conditions

Frequency of Experimental Values Freq analytical values (Hz)

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THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER 5

side band

2 Bar broken 1 Broken Bar

Amp Freq Amp Freq 2 bar broken 1 bar broken

fs(1-4s) 31.61 35.26 28.81 37.48 36 38

fs(1-2s) 37.61 42.66 38.81 43.65 43 44

Fs 61.21 49.81 64.01 49.91 50 50

fs(1+2s) 36.41 56.97 33.21 56.23 57 56

fs(1+4s) 35.61 64.12 32.81 63.39 64 62

2fsks 25.61 7.152 20.41 6.165 7 6

Due to the broken rotor bar, the quantity of current flowing in the rotor is not equal and

will make an asymmetrical field of a magnet. The interaction between the field of stator and

MMF of asymmetrical rotor gives a torque pulsating, leading to the production of the vibration in

the motor. The slip increased and the speed reduced. The spectral analysis of vibration of motor

indicates the components of a frequency of 49.81Hz with the amplitude of 64.01dB for a single

rotor broke bar and 41.81Hz with the amplitude of 61.21dB amplitude of two bar broken rotor.

The existence of left-hand fs (1-2ks) and fs (1+2ks) on the right side frequency components of

the bands are presents due to the asymmetry of rotor and fluctuation of speed. Also, the figures

above show the amplitude and the faults of frequency for two and one bar broken rotor under the

condition of half load (Silva, 2011, p. 310).

FFT spectrum of the motor one bars broken rotor under condition of half load

side band

2 Bar broken 1 Broken Bar

Amp Freq Amp Freq 2 bar broken 1 bar broken

fs(1-4s) 31.61 35.26 28.81 37.48 36 38

fs(1-2s) 37.61 42.66 38.81 43.65 43 44

Fs 61.21 49.81 64.01 49.91 50 50

fs(1+2s) 36.41 56.97 33.21 56.23 57 56

fs(1+4s) 35.61 64.12 32.81 63.39 64 62

2fsks 25.61 7.152 20.41 6.165 7 6

Due to the broken rotor bar, the quantity of current flowing in the rotor is not equal and

will make an asymmetrical field of a magnet. The interaction between the field of stator and

MMF of asymmetrical rotor gives a torque pulsating, leading to the production of the vibration in

the motor. The slip increased and the speed reduced. The spectral analysis of vibration of motor

indicates the components of a frequency of 49.81Hz with the amplitude of 64.01dB for a single

rotor broke bar and 41.81Hz with the amplitude of 61.21dB amplitude of two bar broken rotor.

The existence of left-hand fs (1-2ks) and fs (1+2ks) on the right side frequency components of

the bands are presents due to the asymmetry of rotor and fluctuation of speed. Also, the figures

above show the amplitude and the faults of frequency for two and one bar broken rotor under the

condition of half load (Silva, 2011, p. 310).

FFT spectrum of the motor one bars broken rotor under condition of half load

THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER 6

FFT spectrum of the motor two bars broken rotor under condition of half load

Table 2 showing analysis of one and two bars broken rotor under the condition of half load

Freq of side band Values from Experiment Values of analytical frequency

2 bar broken 1 bar broken

Amp Freq Amp Freq 2 bar broken 1 bar broken

fs(1-4s) 28.01 33.79 26.01 25.15 34.16 25.4

fs(1-2s) 37.61 41.92 33.61 37.48 42.08 37.7

Fs 60.41 49.81 63.61 49.81 50 50

fs(1+2s) 35.21 57.71 39.21 62.14 57.92 62.3

fs(1+4s) 38.41 65.6 26.81 74.48 65.84 74.6

2fsks 25.61 7.89 21.61 12.82 7.92 12.3

When the load of the motor verified improved to 50 percent of the value evaluated, there

will be the increase in current and slip but a decrease in speed. The magnetic field effect

asymmetrical will be higher related to the condition of no load. Therefore, oscillations of speed

and the torque pulsating in rotor setup will produce vibration and noise buzzing in the motor.

The evaluation of spectrum of vibration of signal illustrates that the side band's modular of

frequency fb = (1+ or - 2ks) fs increases compared to the condition of no-load which is shown in

the figures above where frequency and magnitude of the side harmonic band components of

frequency for two and one bar broken through half load conditions (Goldman, 2012, p. 66).

FFT spectrum of the motor one bars broken rotor under condition of full load

FFT spectrum of the motor two bars broken rotor under condition of half load

Table 2 showing analysis of one and two bars broken rotor under the condition of half load

Freq of side band Values from Experiment Values of analytical frequency

2 bar broken 1 bar broken

Amp Freq Amp Freq 2 bar broken 1 bar broken

fs(1-4s) 28.01 33.79 26.01 25.15 34.16 25.4

fs(1-2s) 37.61 41.92 33.61 37.48 42.08 37.7

Fs 60.41 49.81 63.61 49.81 50 50

fs(1+2s) 35.21 57.71 39.21 62.14 57.92 62.3

fs(1+4s) 38.41 65.6 26.81 74.48 65.84 74.6

2fsks 25.61 7.89 21.61 12.82 7.92 12.3

When the load of the motor verified improved to 50 percent of the value evaluated, there

will be the increase in current and slip but a decrease in speed. The magnetic field effect

asymmetrical will be higher related to the condition of no load. Therefore, oscillations of speed

and the torque pulsating in rotor setup will produce vibration and noise buzzing in the motor.

The evaluation of spectrum of vibration of signal illustrates that the side band's modular of

frequency fb = (1+ or - 2ks) fs increases compared to the condition of no-load which is shown in

the figures above where frequency and magnitude of the side harmonic band components of

frequency for two and one bar broken through half load conditions (Goldman, 2012, p. 66).

FFT spectrum of the motor one bars broken rotor under condition of full load

THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER 7

FFT spectrum of the motor two bars broken rotor under condition of full load

Table 3 below shows the analysis of the one and two bars broken under condition of full load

Freq of side band Values of Experiment Values of Analytical

Frequency2 bar broken 1 bar broken

Amp Freq Amp Freq 2 bar broken 1 bar broken

fs(1-4s) 29.21 31.32 22.81 18.74 31.6 18.33

fs(1-2s) 42.41 40.44 32.41 34.03 40.8 34.07

fs 57.61 49.57 59.21 49.81 50 50

fs(1+2s) 32.42 58.69 36.41 65.1 59.2 65.54

fs(1+4s) 36.41 67.82 26.81 80.89 68.4 81.28

2fsks 22.81 9.124 16.41 11.84 6.6 15.73

When the load on the fault motor increases to the peak value of the load, the speed and

terminal voltage reduces while the slip increases. The asymmetry of the magnet in the oscillation

speed and rotor escalates, resulting in extra vibration in the setup motor (Goldman, 2012, p. 97).

The side band of harmonic magnitude components fb = (1+ or – 2ksfs) increase when compared

FFT spectrum of the motor two bars broken rotor under condition of full load

Table 3 below shows the analysis of the one and two bars broken under condition of full load

Freq of side band Values of Experiment Values of Analytical

Frequency2 bar broken 1 bar broken

Amp Freq Amp Freq 2 bar broken 1 bar broken

fs(1-4s) 29.21 31.32 22.81 18.74 31.6 18.33

fs(1-2s) 42.41 40.44 32.41 34.03 40.8 34.07

fs 57.61 49.57 59.21 49.81 50 50

fs(1+2s) 32.42 58.69 36.41 65.1 59.2 65.54

fs(1+4s) 36.41 67.82 26.81 80.89 68.4 81.28

2fsks 22.81 9.124 16.41 11.84 6.6 15.73

When the load on the fault motor increases to the peak value of the load, the speed and

terminal voltage reduces while the slip increases. The asymmetry of the magnet in the oscillation

speed and rotor escalates, resulting in extra vibration in the setup motor (Goldman, 2012, p. 97).

The side band of harmonic magnitude components fb = (1+ or – 2ksfs) increase when compared

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THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER 8

to the condition of half and no load. This is shown in the figures above where magnitudes and

frequencies (1+ or – 2ks) fs harmonic side band components under a condition of the full load. In

every situation, the results of the experiment are analyzed and validated using equations and the

final results gotten are matching closely.

Problems Faced During the Experiment of Vibration Analysis

Analysis and experimental results of the broken bar detection grouped on the motor

operation vibration under half, full and no load condition by the use of the presented

accelerometer. The outcome of the experiment shows that the presence of two frequency slip

(2sfs) because of torque pulsation in the range of low frequency and the side band of harmonic

frequency component fs (1+ or – 2ks) nearby the essential components of frequency may show

clearly that the rotor fault bar was damaged (Goldman, 2012, p. 248).

The more the number bars that have been broken, the greater harmonic side bands fs (1+

or – 2ks) monitored by extra buzzing noise vibration and this, in turn, reduce the torque of the

motor (Silva, 2011, p. 134). Also as there is variation between load and broken motor bar, the

side band of harmonic amplitude (1+ or – 2ks) fs increases. This severity of fault becomes high

causing the premature failure.

How to Rectify the Problem

In ensuring the consistency, repeatability and effectiveness of the proposed method of

getting % factor of severity as in another comparison, it should be useful to simulation results

plus experiments with different ratings of the motor induction under conditions of different

loading (Goldman, 2012, p. 82). The person performing the experiment should also be in a

position to detect the abnormalities in the induction motor to avoid the damages mentioned

to the condition of half and no load. This is shown in the figures above where magnitudes and

frequencies (1+ or – 2ks) fs harmonic side band components under a condition of the full load. In

every situation, the results of the experiment are analyzed and validated using equations and the

final results gotten are matching closely.

Problems Faced During the Experiment of Vibration Analysis

Analysis and experimental results of the broken bar detection grouped on the motor

operation vibration under half, full and no load condition by the use of the presented

accelerometer. The outcome of the experiment shows that the presence of two frequency slip

(2sfs) because of torque pulsation in the range of low frequency and the side band of harmonic

frequency component fs (1+ or – 2ks) nearby the essential components of frequency may show

clearly that the rotor fault bar was damaged (Goldman, 2012, p. 248).

The more the number bars that have been broken, the greater harmonic side bands fs (1+

or – 2ks) monitored by extra buzzing noise vibration and this, in turn, reduce the torque of the

motor (Silva, 2011, p. 134). Also as there is variation between load and broken motor bar, the

side band of harmonic amplitude (1+ or – 2ks) fs increases. This severity of fault becomes high

causing the premature failure.

How to Rectify the Problem

In ensuring the consistency, repeatability and effectiveness of the proposed method of

getting % factor of severity as in another comparison, it should be useful to simulation results

plus experiments with different ratings of the motor induction under conditions of different

loading (Goldman, 2012, p. 82). The person performing the experiment should also be in a

position to detect the abnormalities in the induction motor to avoid the damages mentioned

THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER 9

above. The fault of premature failure during the FFT spectrum experiment can be mitigated

through reducing the number of broken bars which will enable the reduction of harmonic side

bands fs (1+ or – 2ks) monitored by extra buzzing noise vibration. This step will prevent the

reduction in the torque of the motor hence preventing the fault of premature failure.

Conclusion

This experiment presents the method of rotor bar detection. The use of FFT allows for the

classical detection of the bar which has been broken based on the transform of Fourier

applications to the current stator of the motor induction running in a stable state. The discovery

of faults is attained by evaluating the components of two side band that occur around the

frequency components of supply. This approach has its important advantages like being simple

in the acquisition of data system and software required, and also toughness and provides results

of satisfaction. Even though in some situations, induction motors that are unloaded, the

sidebands usually overlap the frequency of supply and the slip is normally low. This makes the

detection of their presence difficult and also their use.

above. The fault of premature failure during the FFT spectrum experiment can be mitigated

through reducing the number of broken bars which will enable the reduction of harmonic side

bands fs (1+ or – 2ks) monitored by extra buzzing noise vibration. This step will prevent the

reduction in the torque of the motor hence preventing the fault of premature failure.

Conclusion

This experiment presents the method of rotor bar detection. The use of FFT allows for the

classical detection of the bar which has been broken based on the transform of Fourier

applications to the current stator of the motor induction running in a stable state. The discovery

of faults is attained by evaluating the components of two side band that occur around the

frequency components of supply. This approach has its important advantages like being simple

in the acquisition of data system and software required, and also toughness and provides results

of satisfaction. Even though in some situations, induction motors that are unloaded, the

sidebands usually overlap the frequency of supply and the slip is normally low. This makes the

detection of their presence difficult and also their use.

THE FAST FOURIER TRANSFORM SPECTRUM ANALYZER 10

References

Goldman, S. (2012). Vibration Spectrum Analysis: A Practical Approach. London: Industrial Press Inc.

Silva, C. W. (2011). Vibration: Fundamentals and Practice, Second Edition. Michigan: CRC Press.

References

Goldman, S. (2012). Vibration Spectrum Analysis: A Practical Approach. London: Industrial Press Inc.

Silva, C. W. (2011). Vibration: Fundamentals and Practice, Second Edition. Michigan: CRC Press.

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