**5.1. The results of MCDA fault indicators for broken bars at different IM load**

The complex stator current analysis using simultaneous amplitude and phase demodulation of the two-pole IM is depicted in Fig. 6 – individual windows from above: stator current autospectrum i.e. MCS, AM fault current extracted from the stator current by the amplitude demodulation (9), PM fault current extracted from the stator current by the phase demodulation (10). Corresponding spectra are depicted in the 4th and 5th windows. The time courses of AM and also PM clearly show fault currents with 2 dominating frequencies *fsp* and *fr* which are better seen in the corresponding spectra. It is clearly seen that the phases of AM and PM at *fsp* are exactly opposite, compare 2nd window to 3rd window from the top.

MCDA fault indicators are depicted in 4th window from the top.

**Figure 6.** Complex demodulation analysis of IM current, 2-poles 1.1.kW motor, 75% of full load

Demodulation methods suppress large *Il* and therefore the relatively accurate linear scale for spectrum can be used, but for the observation of higher harmonics of *fsp* a logarithmic scale also can be used.

Equation (5) which pays only under steady conditions and low inertia, was verified. The full agreement with the theory of *aAPL* and *aAPH* equality was found in the range of possible *aAPL, aAPH* variations, which can be in the range of ± 2.5dB.

There are two reasons for the *aAPL* and *aAPH* variation:

534 Induction Motors – Modelling and Control

Spectrum averaging, which lowers stator current non-stationary errors, should be always used for the error minimization. FFT computation time is substantially shorter than the acquisition time, so the start of a new acquisition and a new averaging can start earlier than the end of the previous acquisition time. This process is called overlapping. It is expressed in percent of the acquisition time in the range of 0% - no overlapping- to max, when the new acquisition starts immediately at the end of previous FFT. The overlapping implementation

Spectrum of demodulated current does not contain any sidebands components, it is transparent and easy readable and only one simple spectral peak is the fault indicator.

The fault indicator *Ispa* [A] for broken bars is the amplitude of the amplitude modulating current on fault frequency *fsp* so the spectral magnitude of amplitude demodulated IM current on *fsp*, see Fig.6, 4rd window from the top. The fault indicator *Ira* [A] for dynamic eccentricity is the amplitude of the amplitude modulating current on fault frequency *fr* so the

Fault indicators clearly show the rotor faults but do not show the real fault severity. *Ispa* and

Fault severity dimensionless coefficients *ksp, kr* [%] are fault indicators normalized by a

/ *r ra nom kII* (14)

In order to keep the independence of fault severity coefficients of the different load, the normalizing value must be a constant. Therefore the coefficients *ksp, kr* as the basic evaluating

Five various experiments, presented in paragraphs 5.1 to 5.5, covering different IM states,

**5.1. The results of MCDA fault indicators for broken bars at different IM load** 

The complex stator current analysis using simultaneous amplitude and phase demodulation of the two-pole IM is depicted in Fig. 6 – individual windows from above: stator current autospectrum i.e. MCS, AM fault current extracted from the stator current by the amplitude demodulation (9), PM fault current extracted from the stator current by the phase demodulation (10). Corresponding spectra are depicted in the 4th and 5th windows. The time courses of AM and also PM clearly show fault currents with 2 dominating frequencies *fsp* and *fr* which are better seen in the corresponding spectra. It is clearly seen that the phases of AM and PM at *fsp* are exactly opposite, compare 2nd window to 3rd window from the top.

tool for the assessment of fault severity and for the state of rotor bars was suggested.

time varying load and IM energized from inverters were performed.

MCDA fault indicators are depicted in 4th window from the top.

/ *sp spa nom kII* (13)

spectral magnitude of amplitude demodulated IM current on *fr*, Fig.6, 4rd window.

(programming) is easy. Overlapping more than 50% is recommended.

*Ira* amplitudes considerably differ with the IM power.

where fault indicators *Ispa*,*Ira* are expressed in RMS.

constant value - motor rated current *Inom*


The shortened experimental results are briefly summarized in Table 2 (suffix*<sup>H</sup>* for the demodulation using Hilbert transform, suffix*<sup>P</sup>* for the demodulation using space transform) for 2-pole motors and Table 3 for 4-pole motors.


Rotor Cage Fault Detection in Induction Motors by Motor Current Demodulation Analysis 537

At no load and at low load below 20 % of full load *Ispa* decreases- see Table 5. Therefore for the industrial diagnostics the recommended load range is from 20% of load to the full load. For more accurate diagnostics, the range from 25% of load to the full load is recommended.

Fault severity coefficient *ksp* for 2 broken bars at 4-poles motor are little smaller in

Healthy motor shows some residual modulation, due to irregularities in rotor bars layout,

The acceptable limits for *ksp,* should be experimentally stated for various motor types because they can differ. Namely the sizes of *ksp* for large IM can have different acceptable

The values of fault severity coefficient *kr* for dynamic eccentricity slightly decrease with increasing load. Over the 85% of full load the decrease is slightly greater. The values of *Ira* at a factory balanced rotor are still sufficient for a sensorless rotor electromagnetic field speed and speed irregularities measurement (Jaksch & Zalud, 2010). PM for rotor eccentricity

Two introduced demodulation methods for dynamic rotor fault detection - Hilbert and space transforms - give the same results and both can be used for rotor fault diagnostic. Both measurement systems - Bruel&Kjaer PULSE and NI 4472B give the same fault indicators.

The second experiment examined the spectral magnitudes of amplitude and phase demodulated IM current on *fsp* at different loads, together with the comparison of the MCSA low sideband *aAPL* on *fl-fsp*. The results are depicted in Fig.7 -9 and summarized in Table 4.

AM - MCDA fault indicator *Ispa* [mA] 70 77 78 78

The experiment proved the theory that PM substantially increases with increasing load

PM increases 2.2 times within the interval between 25 - 85%. The increase of PM spectral magnitude *aP* is caused both by *Il* increase at increasing load and also by *Ispp* increase, (3). It is the real cause of MCS fault indicators *aAPL* and *aAPH* increasing with increasing load, Fig.3

**Table 4.** AM and PM, 2 broken bars, at different IM load in comparison to low sideband *aAPL*

(2nd row in Table 4 and peaks in circles on *fsp* in lower window in Fig.7 to Fig.9).

25% load

PM [mrad] 24 33 44 49

Low sideband *aAPL* [mA] 36 44 46 48

50% load 75% load

85% load

comparison with 2-poles motor owing to a greater number of rotor bars *nrb* - 26 on 23.

but *ksp* were not at all measurements greater than 0.3 %.

slightly decreases with increasing load unlike PM for broken bars.

**5.2. The comparison of AM and PM at different loads** 

2-poles IM, 1.1 kW 2 broken bars

limits.

and (5).

**Table 2.** Fault Indicators and fault severity coefficients for broken bars and dynamic eccentricity, Hilbert and Space Transforms, 2- poles IM


**Table 3.** Fault Indicators and fault severity coefficients for broken bars and dynamic eccentricity, Hilbert and Space Transforms, 4- poles IM

## *5.1.1. The experimental results discussion*

The experiments proved the correctness of JAPM theory and the correctness of the used demodulation techniques.

The experiments show that broken bar AM is almost insensitive to the motor load. The *Ispa* changes are in the range of 11% within the interval between 25 – 85% and in the range of 7 % in the interval 50 – 85%. The same holds for the fault severity coefficient *ksp* because the denominator in (13) is a constant value. The values of fault indicator for 2 continuous rotor bars are almost twice greater then indicators for 1 broken bar.

At no load and at low load below 20 % of full load *Ispa* decreases- see Table 5. Therefore for the industrial diagnostics the recommended load range is from 20% of load to the full load. For more accurate diagnostics, the range from 25% of load to the full load is recommended.

Fault severity coefficient *ksp* for 2 broken bars at 4-poles motor are little smaller in comparison with 2-poles motor owing to a greater number of rotor bars *nrb* - 26 on 23.

Healthy motor shows some residual modulation, due to irregularities in rotor bars layout, but *ksp* were not at all measurements greater than 0.3 %.

The acceptable limits for *ksp,* should be experimentally stated for various motor types because they can differ. Namely the sizes of *ksp* for large IM can have different acceptable limits.

The values of fault severity coefficient *kr* for dynamic eccentricity slightly decrease with increasing load. Over the 85% of full load the decrease is slightly greater. The values of *Ira* at a factory balanced rotor are still sufficient for a sensorless rotor electromagnetic field speed and speed irregularities measurement (Jaksch & Zalud, 2010). PM for rotor eccentricity slightly decreases with increasing load unlike PM for broken bars.

Two introduced demodulation methods for dynamic rotor fault detection - Hilbert and space transforms - give the same results and both can be used for rotor fault diagnostic. Both measurement systems - Bruel&Kjaer PULSE and NI 4472B give the same fault indicators.

## **5.2. The comparison of AM and PM at different loads**

536 Induction Motors – Modelling and Control

Hilbert and Space Transforms, 2- poles IM

Hilbert and Space Transforms, 4- poles IM

demodulation techniques.

*5.1.1. The experimental results discussion* 

bars are almost twice greater then indicators for 1 broken bar.

Motor state 25% load 50% load 75% load 85% load 2-poles *fr* [Hz] 48.95 48.6 48.1 47.6 1.1.kW *fsp* [Hz] 1.99 2.8 3.8 4.62 Health *IspaP* [mA] 9.4 9.5 9.3 8.5 motor *IspaH* [mA] 9.5 9.6 9.6 8.2

1 *IspaP* [mA] 35 40 39 39 interrupted *IspaH* [mA] 36 41 40 39 rotor bar *ksp*[%] 1.11 1.28 1.26 1.25 2 contin. *IspaP* [mA] 69 78 79 77 interrupted *IspaH* [mA] 67 75 77 76 rotor bars *ksp*[%] 1.93 1.98 1.95 2.01 Dynamic ecc. *IraP*[mA] 3.9 3.9 3.9 3.5 Balanced *IraH*[mA] 3.8 3.9 4.1 3.3 rotor *kr*[%] 0.15 0.15 0.16 0.13

**Table 2.** Fault Indicators and fault severity coefficients for broken bars and dynamic eccentricity,

Motor state 25% load 50% load 75% load 85% load 4- poles *fr* [Hz] 24.56 24.41 24.21 24.12 0.75 kW *fsp* [Hz] 1.73 2.3 3.1 3.45 Health *IspaP* [mA] 3.3 3.4 3.4 3.3 motor *IspaH* [mA] 3.4 3.3 3.4 3.2

2 contin. *IspaP* [mA] 37 41 43 42 interrupted *IspaH* [mA] 38 42 43 41 Rotor bars *ksp*[%] 1.46 1.68 1.70 1.68 Balanced *IraP*[mA] 5.1 5.4 5.3 4.9 rotor *IraH*[mA] 5.2 5.5 5.4 4.9

**Table 3.** Fault Indicators and fault severity coefficients for broken bars and dynamic eccentricity,

The experiments proved the correctness of JAPM theory and the correctness of the used

The experiments show that broken bar AM is almost insensitive to the motor load. The *Ispa* changes are in the range of 11% within the interval between 25 – 85% and in the range of 7 % in the interval 50 – 85%. The same holds for the fault severity coefficient *ksp* because the denominator in (13) is a constant value. The values of fault indicator for 2 continuous rotor

*ksp* [%] 0.28 0.29 0.28 0.25

*ksp* [%] 0.18 0.18 0.18 0.17

*kr*[%] 0.28 0.28 0.27 0.26

The second experiment examined the spectral magnitudes of amplitude and phase demodulated IM current on *fsp* at different loads, together with the comparison of the MCSA low sideband *aAPL* on *fl-fsp*. The results are depicted in Fig.7 -9 and summarized in Table 4.


**Table 4.** AM and PM, 2 broken bars, at different IM load in comparison to low sideband *aAPL*

The experiment proved the theory that PM substantially increases with increasing load (2nd row in Table 4 and peaks in circles on *fsp* in lower window in Fig.7 to Fig.9).

PM increases 2.2 times within the interval between 25 - 85%. The increase of PM spectral magnitude *aP* is caused both by *Il* increase at increasing load and also by *Ispp* increase, (3). It is the real cause of MCS fault indicators *aAPL* and *aAPH* increasing with increasing load, Fig.3 and (5).

Rotor Cage Fault Detection in Induction Motors by Motor Current Demodulation Analysis 539

**5.3. The analysis of indicator** *Ispa* **at very low load from no load to 20 % of full load** 

The 3rd experiment analyses the changes of *Ispa* in the range of no load to 20 % of full load. Table 5 shows the MCDA broken bars fault indicator *Ispa* decline under 20% of full load. For very low load at *s*=0.44%, *fsp*=0.44 Hz the *Ispa* for 2 broken bars decreases to *Ispa*=31mA, which is approximately the half of its nominal value and it corresponds to *Ispa* for 1 broken bar

> s[%] 0.21 0.37 0.44 0.69 0.94 1.16 1.37 fsp [Hz] 0.21 0.37 0.44 0.69 0.94 1.16 1.37 IspaH [mA] 19 25 31 37 47 56 69

The decrease of *Ispp* representing PM, and therefore the decrease of MCSA fault indicators *aAPL, aAPH* under 20% are substantially faster than the decrease of MCDA fault indicator *Ispa*

The aim of 4th experiment was to verify presented theory of the time varying load and its influence on MCDA fault indicator *Ispa*. The time varying load frequency *fload* = 4 Hz was

*aAPL aAPH* 

*fl-fload* 

*fl+fload* 

*fr* 

**Figure 10.** Windows from above: MCS, time course of amplitude demodulated current, and its MCDA

(Table 2), so great confusion in broken bar diagnostics may come.

**Table 5.** *Ispa* changes from no load to 20% of full load, 2 broken bars, 1.1.kW IM

chosen very near to the broken bars fault indicator frequency *fsp* =1.9 Hz.

**5.4. IM rotor fault diagnostics at time varying load** 

(Fig.7–Fig.9, PM in circles).

spectrum, 25% of full load.

*Iload*

*Ispa* 

*fsp fload* 

**Figure 7.** IM spectrum, spectrum of amplitude and phase demodulated current, 25% of full load

**Figure 8.** IM spectrum, spectrum of amplitude and phase demodulated current, 50% of full load

**Figure 9.** IM spectrum, spectrum of amplitude and phase demodulated current, 85% of full load
