**5. Experimental results**

The main aim of the experiments was to verify the introduced theory of JAPM, to verify the both fault indicators *Ispa*, *Ira* changes at different IM load and to verify the influence of the time varying load.

Two sorts of IM were used for the experiments.

The first IM was SIEMENS type 1LA7083-2AA10, 1.1 kW, two-pole, rated revolutions 2850 min-1, *Inom*=2.4A, *nrb* =23, air gap dimension=0.25 mm, health motor, 1 interrupted rotor bar and 2 contiguous interrupted rotor bars, both 3 rotors were balanced with factory set-up dynamic eccentricity (setting the exact value of dynamic eccentricity is at so small air gap very difficult). The 2nd IM was SIEMENS type 1LA 7083-4AA10, 0.75 kW, four-pole motor, *Inom* = 1.8A, *nrb* =26, balanced rotor and rotor with 2 contiguous interrupted rotor bars.

532 Induction Motors – Modelling and Control

Input data for the simulation result from (12). Simulation values of *Il*, *Ispa*, *Ispp*, *Ira*, *Irp*, *ϕ* start from the measurement, but various values can also be used. Other data processing is the same as in experiments. Hilbert transform, (9), (10) was used for the IM current amplitude and phase demodulation. The values for *aAPL, aAPH* (2nd window in Fig.5) were compared to

The simulation was also used for the case where angle *ϕ* is positive and *aAPL< aAPH*. But this

Simulation results are depicted in Fig.5. Note that the time course of amplitude demodulated current follows the envelope of IM current – compare the window 3 to the window 1. Time course of amplitude and phase demodulation (windows 3, 4) shows small ripple at the beginning - t=0, given by nonsequenced modulating current in time window.

> *fl-fr fl+fr aAPL* > *aAPH*

**Figure 5.** The demodulation analysis of stator current, 4-poles motor 0.75 kW, 2 broken bars, great

*MCDA fault indicators*

*fr* 

The main aim of the experiments was to verify the introduced theory of JAPM, to verify the both fault indicators *Ispa*, *Ira* changes at different IM load and to verify the influence of the

inertia - *ϕ* <0, low dynamic eccentricity. Simulation results.

*2fsp* 

*fsp* 

Two sorts of IM were used for the experiments.

**5. Experimental results** 

time varying load.

the values computed from (3),(6). Full identity with the theory was found.

IM state is not stable and can come only in IM dynamic regime.

Various motors and fault rotors used in experiments were manufactured directly at Siemens Electromotor. Motors were tested at 25%, 50%, 75% and 85% of the full load according to the motor load record from Siemens. The changes in the broken bar fault indicator *Ispa* was also tested in the low load range from no load to 20% of full load.

The experiments were based on Bruel&Kjaer PULSE 20 bits dynamic signal analyzer (DSA) based on the frequency filtration and decimation principle. All channels are sampled simultaneously. FFT analyzer was set on the base band mode, frequency span 100Hz, 400 frequency lines, *Δf* =0.25Hz, Hanning window, continuous RMS exponential averaging with 75% overlapping. For the experiment of *Ispa* changes at very low load the measuring time T= 32s, *Δf* =0.03125Hz was used.

To find out the possible differences in both introduced demodulation methods, both Hilbert and space transform were simultaneously evaluated in the real time.

The experiments results were verified by 16 channels PC measurement system based on two 8 channels, 24-bit DSA NI 4472B from National Instruments setting in the lowest possible frequency range 1kHz.

To obtain the maximal measurement accuracy the possible errors in Digital Signal Processing (DSP) should be avoided. Sampling theorem with full agreement between the sampling frequency and surveyed analog frequency band should be strictly kept. At the violation of sampling theorem, signal frequencies higher than Nyquist frequency *fN* are tilted - masked to the basic frequency region from *0-fN* and they can create there aliasing frequencies or interfere with regular frequencies, changing their amplitudes. Masking can come through many higher bands of the sampling frequency. Unlike dynamic signal analyzers, simple PC cards and scopes are usually not equipped with anti aliasing filters.

The measurement acquisition time *T* should be optimally set. Spectral frequency resolution *f* is a reciprocal value of the acquisition window *T, f =1/T*.

A great DSP error, both in frequency and magnitude, occurs if the analog frequency of the examined signal is exactly in the centre of *f*. In the case of a rectangular window, the spectral magnitude decline is *sinc*(*/2)=2/=0.636=-3.92 dB*, representing 36% fault in magnitude! In the case of Hanning window the decline is *(3/ -1/(3))=0.848=-1.43 dB.* If the low analog sideband frequency *fl-fsp* is nearer to the discrete spectral frequency than the high sideband frequency *fl+fsp*, the *aAPL* can be higher than *aAPH* and vice versa. The optimal acquisition time should be longer than 1sec. e.g. 4sec. with *f* = 0.25Hz. In the case of very low load, the minimal acquisition time 8 sec with *f* = 0.125Hz can be used for the accurate *fsp* detection and for the decrease of DSP errors probability.

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

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

Fault indicators clearly show the rotor faults but do not show the real fault severity. *Ispa* and *Ira* amplitudes considerably differ with the IM power.

Fault severity dimensionless coefficients *ksp, kr* [%] are fault indicators normalized by a constant value - motor rated current *Inom*

$$k\_{sp} = I\_{spa} \; / I\_{nom} \tag{13}$$

Rotor Cage Fault Detection in Induction Motors by Motor Current Demodulation Analysis 535

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

*aAPL, aAPH* variations, which can be in the range of ± 2.5dB.

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

2. DSP errors. DSP errors come owing to the finite

for 2-pole motors and Table 3 for 4-pole motors.

previous part of this section 5.

also can be used.

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

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

1. The non-stationarity of IM current. The rotor analog current is not a fully stationary signal and therefore the phase shift *ϕ* between AM and PM may not be exactly zero and due to small dynamic changes it can oscillate around zero and therefore causes changes in *aAPL* and *aAPH* according to (6). Linear or exponential spectrum averaging lowers this error.

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)

*f* which was described in detail in the

$$k\_r = \mathbf{I}\_{ru} / \mathbf{I}\_{num} \tag{14}$$

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

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

Five various experiments, presented in paragraphs 5.1 to 5.5, covering different IM states, time varying load and IM energized from inverters were performed.
