**1. Introduction**

Rotor cage faults as broken rotor bars, increased bars resistance and end-ring faults can be caused by thermal stresses, due to overload, overheating and thus mechanical stresses, magnetic stresses and dynamic stresses due to shaft torques. Environmental stresses as contamination or abrasion also contributes to the rotor cage faults. The rotor cage faults can also lead to the shaft vibration and thus bearing failures and air gap dynamic eccentricity.

Various rotor cage faults detection techniques for induction motors (IM) have been proposed during the last two decades. One of these is a widely used Motor Current Signature Analysis (MCSA) representing namely the direct spectral analysis of stator current (Thomson & Fenger, 2001; Jung et.al, 2006). MCSA can be combined with other methods as stray flux detection and a radial and axial vibration analysis. MCSA is still an open research topic, namely in the region of higher harmonics.

Strongly nonstationary working conditions as start-up current analysis require the application of methods generally called Joint Time Frequency Analysis (JTFA). These methods are Short Time Fourier Transform, Continuous Wavelet Transform (Cusido et.al, 2008; Riera-Guasp, 2008), Discrete Wavelet Transform (Kia et. al., 2009), Wigner Distribution (Blödt et al., 2008), etc. The fundamental of the wavelet analysis is the stator current decomposition into a determined number of detailed and approximation components and their pattern recognition. Wavelet analysis can be combined with other methods as a torsional vibration (Kia et. al., 2009).

The Vienna monitoring method –VMM (Kral et. al, 2008) is a rotor fault detection method based on instantaneous torque evaluation determined by voltage and current models. Other introduced methods for IM rotor fault diagnostics are multivariable monitoring (Concari et.al, 2008), artificial neural networks and neural network modeling (Su & Chong, 2007), fuzzy based approach (Zidani et. al., 2008), wavelet analysis together with hidden Markov

models (Lebaroud & Clerc, 2008), pendulous oscillation of rotor magnetic field (Mirafzal & Demerdash, 2005), vibration analysis (Dorrell et al., 1977) etc. A review of diagnostic techniques has been presented in several publications (Nandi et. al., 2005; Bellini et. al., 2008; Zhang et. al., 2011).

Rotor Cage Fault Detection in Induction Motors by Motor Current Demodulation Analysis 523

working conditions. It is mostly various IM loads which changes PM and great inertia or insufficient IM feeding which change an angle *ϕ* between AM and PM and therefore cause

The widely used rotor fault detection technique - MCSA is presented in a large number of publications. This approach analyses whole IM stator current uses the spectral low and high slip pole frequency *2sfl* sidebands *aAPL*, *aAPH* around the supply frequency *fl* for broken bars detection (Bellini et. al., 2001). According to this theory, magnetic rotor asymmetry causes a backward rotating field and formation of a current component *aAPL* at the low sideband frequency *fl-fsp*. The consequent torque and speed oscillation cause the occurrence of a new component *aAPH* at the high sideband frequency *fl+fsp.* First, the only low sideband spectral magnitude was taken as a fault indicator for broken bars. Later a new diagnostic index was

Presented theory of the spectral low *aAPL* and high *aAPH* sidebands origination and formation and broken bars detection is quite different from MCSA theory. The theory comes from general modulation principles and exactly determinates both sidebands origination

An exact detailed analysis of the stator current content at broken bars from the view of the complex air-gap rotor electromagnetic field analysis representing simultaneous stator current AM and PM, their mutual relation and changes at different load and inertia moment, and their formation to the MCS *aAPL* and *aAPH* magnitudes has been missing so far.

Introduced theory and rotor fault analysis and diagnostics come from the basic principle when periodical changes in rotor magnetomotive force (MMF) cause the periodical changes

Broken rotor bars, as an electric fault, cause the rotor asymmetry, the distortion of the rotor current distribution, rotor current pulsation and its amplitude modulation by the slip frequency *fslip*. Rotor bars current amplitude changes are transformed to stator current on slip pole frequency *fsp* and appears here as a stator current AM. This modulation can be

Rotor bars current amplitude changes cause the changes in force on coils moving in a magnetic field. The force can be obtained from the vector cross product of the current vector

the force direction. Subsequently, the total force on a current carrying rotor coils (bars), moving in a magnetic field, changes and electromagnetic torque oscillation appears. Torsion vibration also can appear. Oscillating torque causes periodical changes in the rotating phase angle and therefore the stator current PM. This modulation can be interpreted as a

*x,* where *NI* is MMF*,* 

is linked magnetic flux and *x* is

**2.1. Broken bars stator current modulation and its contribution to the MCS** 

of IM stator current amplitude and phase, and thus the stator current AM and PM.

*/*

the dependence. These rotor fault indicators dependence cannot be removed.

introduced as a sum of the two spectral sideband components *aAPL*+*aAPH.* 

including the equations for *aAPL*, *aAPH* computation.

interpreted as a primary modulation.

and the flux density vector *Fx= NI* 

**formation** 

**2. The analysis of IM current and current signature at rotor faults** 

We can see that today it is not a problem to find rotor faults. What still remains a problem is to exactly and unambiguously determine fault indicator and its fault severity with a defined measurement uncertainty under changing motor parameters - various loads and inertia. Ideally the fault indicator should be independent on IM load. The examination of the various load influence on the fault indicator changes is very important especially in the industrial applications, where the keeping the same motor loads is often difficult. It has to be known what range of parameter changes are allowed for the keeping of the fault indicator constancy. As it is not known, at repeated measurements with different fault indicators, it is not clear, if the reason is due to the varied (deteriorating) IM faults or due to IM changing parameters. What is also important is the repeatability of the measurement with the same result. The third problem is a preferably simplicity and easy implementation of the methods for practical use in industry. Introduced new demodulation methods fulfill most of these requirements.

Dynamic rotor faults of IM, namely rotor broken bars and dynamic or combined eccentricity, cause a distortion of the rotor bars current distribution, and thus they cause periodical dynamic changes related to IM rotation frequency *fr* in the rotor magnetic field and consequently torque oscillation and therefore stator current modulation. The complex stator current analysis and experiments based on simultaneous amplitude and phase demodulation techniques proved that the stator current at rotor faults consists both of amplitude modulation (AM) and phase modulation (PM). AM and PM are combined into the Joint Amplitude Phase Modulation (JAPM). Amplitude and phase modulating currents are in certain relations, both in their amplitudes and mutual phases, dependent on motor load, inertia and also on IM working conditions.

Motor Current Demodulation Analysis - MCDA comes out from the fundamental principle which arises at dynamic rotor faults - IM stator current modulation. The basic idea of MCDA is to extract only those currents from the whole stator current which are directly induced and caused by rotor faults, and to investigate only these fault currents in the time and frequency domain. At health IM these currents do not exist, practically are near zero.

The demodulation is a process, how to gain back the information about the time course of modulating signal from modulated signal. Outputs of demodulation methods are, therefore, the direct time courses of modulating i.e. fault currents. The spectrum of a fault current does not contain any sideband components, fault frequencies are determined directly and only one spectral peak represents the fault indicator. The great advantage of MCDA is its easy use in industrial diagnostics.

Most of the present diagnostic methods, both for stationary and non-stationary (Joint Time-Frequency Analysis) IM working conditions, use full IM current analysis methods for rotor fault detection. Just MCDA proved the complexity of the IM current at dynamic rotor faults and therefore the dependence of fault indicators based on full IM current on IM working conditions. It is mostly various IM loads which changes PM and great inertia or insufficient IM feeding which change an angle *ϕ* between AM and PM and therefore cause the dependence. These rotor fault indicators dependence cannot be removed.
