Bearing faults are the most frequent faults of induction motors. The current spectrum analysis is an easy and popular method for the monitoring and detection of bearing faults. After a presentation of the existing fault models, this paper illustrates an analytical approach to evaluate the effects of the slot harmonics on the stator current in an induction motor with bearing fault. Simple and clear theoretical analysis results in some new current characteristic frequencies. Experimental tests with artificial bearing outer raceway fault are carried out by measuring stator current signals. The experimental results by spectral analysis of the stator current agree well with the theoretical inference.
Induction motors (IMs) play a critical role in agricultural, industrial, and commercial sectors. Such popularity is increasing mainly because of their simple organizational structure, easy maintenance, premium power efficiency, and high reliability. Even if induction motors are reliable, unexpected failures may still occur under environmental stresses which could lead to production shutdown and extra maintenance cost. Thus, the online monitoring and fault diagnosis of induction motors have been extensively studied and many techniques have been published about this issue, as described in [
Depending on the type of the measured variables, methods that are used for diagnosing IM bearing faults can be categorized as acoustic emission, temperature measurements, vibration monitoring, motor current signal analysis (MCSA), and so forth. Among them, vibration signals have been widely applied in IM bearing faults detection [
The relationship between bearing vibration characteristics and current spectrum effects was first proposed by Schoen et al. based on the generation of a rotating eccentricity, but the author did not give a detailed theoretical derivation [
In view of the advantages of the aforementioned models, together with the effects of rotor and stator slotting, a more comprehensive mathematical model is proposed in this paper based on rotating wave approach where airgap flux density is determined by the product of permeance and magnetomotive force waves. At last, the theoretical analysis is verified by bearing outer raceway fault detection and the experimental results are well in agreement with the theoretical investigation.
The rest of the paper is constructed as follows. Section
The typical geometric structure of a rollingelement bearing is shown in Figure
Typical structure of a rollingelement bearing with main parameters.
Localized faults can be usually divided into four categories depending on the affected element, namely, outer raceway fault, inner raceway fault, ball fault, and cage fault. The vibration characteristic frequencies of these faults, when the outer raceway is stationary, are expressed as follows [
If the bearings are with a number of rolling elements between 6 and 12, the outer and inner raceway fault frequencies can be computed as follows [
In rollingelement bearing, the stationary ring (outer raceway in this case) fault happens first due to the stationary ring material in load area receiving more dynamic load cycles than other bearing components (e.g., the rotating ring and rolling elements) [
In a typical induction motor, the dominant components of stator current are the fundamental supply frequency, the eccentricity harmonics, the slot harmonics, and other components including environmental noise [
The airgap permeance, accounting for stator and rotor slotting, can be approximated, expressed as follows [
In the following text, after the explicit mathematical derivation process of the airgap permeance and the airgap flux density, some new characteristic frequencies which can be used for bearing outer raceway fault detection around the rotor slot harmonics are obtained.
Under ideal condition, the airgap length in a machine is constant. However, due to unsuitable assembling and manufacturing process, an inherent level of static and dynamic eccentricity tends to coexist. In the case of static eccentricity, by assuming a smooth stator and rotor surface, the length of the airgap can be expressed as follows [
In the case of dynamic eccentricity, the length of the airgap can be expressed as follows [
If Fourier series are developed, then,
The airgap length of an ideal motor with bearing outer raceway fault can be described as follows [
When the Dirac function is expressed as a complex Fourier series, (
In order to simplify the airgap permeance coefficient, the fraction
The airgap length for the induction motor with bearing outer raceway fault and mixed eccentricity can thus be represented as follows [
A good approximation for the airgap permeance which takes into account the mixed eccentric motor with bearing outer raceway fault is given by
Then taking into account the interaction of stator and rotor slot harmonics, airgap eccentricity harmonics, and bearing outer raceway fault harmonics, the permeance of the airgap could be written as follows:
Only the stator magnetomotive force (MMF) is taken into account and, neglecting skew, it can be represented by
Then the airgap flux density, deduced from the product of the permeance (
Then, the change in the flux density distribution results in the current having harmonics as follows:
The models for bearing fault detection proposed by Blödt et al. show that bearing outer raceway characteristic frequencies
To assess the effectiveness of the proposed techniques for IM bearing fault detection, a series of comparisons have been conducted between the spectrum of the stator current in healthy and faulty cases. In a rollingelement bearing, artificially produced defect is introduced by simply drilling a hole in the outer raceway to simulate a localized fault, which is similar to other literatures [
This section is divided into two parts: first, an overview of the experiment test rig is presented, and then the proposed techniques are verified offline using stator current signals for bearing outer race fault detection.
Schematic diagram of the experiment setup used in this paper is shown in Figure
Test induction motor rated parameters.
Nominal power  3 kW 
Nominal rated voltage  380 V 
Nominal rated current  6.8 A 
Frequency  50 Hz 
Pole pairs  2 
Stator slots  36 
Rotor slots  32 
Stator winding connection  Y 
Schematic diagram of the experiment setup.
Photograph of the experimental setup used for bearing fault detection.
The induction machine has two CU6206RZ type bearings (single row and deep groove ball bearings) with a width of
Tested bearings: (a) healthy, (b) outer raceway fault.
In the experiments, two induction motors have been considered: a healthy motor and a faulty one affected by bearing outer raceway fault. Firstly, tests have been performed with faulty motor under several different loads by randomly adjusting the field voltage of the DC machine. Then, supplementary test is performed with the healthy motor for the sake of spectra contrastive analysis. All the tests are done in steadystate conditions. The motors under study are fed by a 50 Hz power supply. The stator current and speed signals are sampled at 50 kHz with a recording length of 25 s.
Linear plots of the current spectrum when the motor runs at the shaft speed of 1431 r/min (23.85 Hz) are given in Figures
Comparison of stator current spectrums with 50 Hz supply frequency around fundamental frequency region between healthy IM and IM with outer raceway defect: (a) healthy IM and (b) IM with a bearing outer raceway defect.
Comparison of stator current spectrums with 50 Hz supply frequency around PSHs region between healthy IM and IM with outer raceway defect: (a) healthy IM and (b) IM with a bearing outer raceway defect.
A comparison of the stator current spectrums from a healthy case and a faulty bearing around the PSHs region is shown in Figure
In order to further prove the effectiveness of the proposed model for bearing fault detection, the current signals under several different load conditions have been processed using MATLAB. The offline experimental results are summarized in Tables
The experimental results of healthy and faulty motors under several different load conditions.
State 










Fault  23.8500  85.8600  Calculated/Hz  135.9279  159.7779  627.2721  727.4079  775.1421  875.2779 
Estimated/Hz  135.9463  159.6451  626.4210  727.1767  774.5743  874.6624  
Amplitude/dB  −66.9323  −69.9651  −72.6639  −74.7578  −77.3310  −73.2667  


Health  23.8500  —  Amplitude/dB  −76.2459  −77.6033  −81.5884  −82.4756  −82.0215  −82.0451 


Fault  23.9655  86.2758  Calculated/Hz  136.3437  160.3092  630.5523  730.6881  779.1384  879.2742 
Estimated/Hz  136.3277  160.1696  629.2343  730.6576  777.1015  878.1433  
Amplitude/dB  −67.8734  −75.5752  −77.3139  −78.9183  −81.8125  −77.7823  


Health  23.9655  —  Amplitude/dB  −79.1248  −84.4931  −85.4721  −85.9430  −85.1713  −85.4535 


Fault  24.0907  86.7265  Calculated/Hz  136.7944  160.8851  634.1080  734.2438  783.4703  883.6061 
Estimated/Hz  136.7569  160.6941  633.7643  733.6617  783.1097  882.5779  
Amplitude/dB  −66.9565  −80.2746  −77.7492  −78.7337  −81.7378  −77.8168  


Health  24.0907  —  Amplitude/dB  −84.4098  −85.5045  −85.3693  −85.1180  −85.2143  −85.2862 


Fault  24.1980  87.1128  Calculated/Hz  137.1807  161.3787  637.1553  737.2911  787.1829  887.3187 
Estimated/Hz  137.1384  161.2186  637.2929  736.4750  788.3072  888.9675  
Amplitude/dB  −70.0095  −77.2724  −77.8660  −79.1447  −81.7262  −78.4580  


Health  24.1980  —  Amplitude/dB  −78.0160  −82.9799  −85.0438  −85.4245  −85.2521  −85.6223 
The average and standard deviation values of fault frequency components under three different load conditions (/Hz).
State 










Fault  23.8500  85.8600  Calculated  135.9279  159.7779  627.2721  727.4079  775.1421  875.2779 
Average value  135.9384  159.6292  627.1203  727.4466  774.6935  875.4969  
Standard deviation  0.0359  0.0718  0.4097  0.7135  0.3501  0.9974  


Fault  23.9655  86.2758  Calculated  136.3437  160.3092  630.5523  730.6881  779.1384  879.2742 
Average value  136.3744  160.2650  630.0769  729.7913  779.9864  880.0586  
Standard deviation  0.1626  0.3358  0.5213  0.5148  0.6060  0.8409  


Fault  24.0907  86.7265  Calculated  136.7944  160.8851  634.1080  734.2438  783.4703  883.6061 
Average value  136.7648  160.7179  634.2332  734.4882  782.8474  883.2693  
Standard deviation  0.0925  0.0261  0.7259  0.4272  0.7084  0.4389 
This paper has studied the effects of the slot harmonics on the stator current signals in an induction motor with bearing fault. Based on the airgap flux density calculation by the product of the permeance and the MMF, a more comprehensive mathematical model has been obtained when considering not only inherent eccentricity but also the slot harmonics in an induction motor with bearing fault. Some experimental investigations in this paper have proved that some new characteristic fault frequencies can be found around the rotor slot harmonics in the stator current spectrum. These experimental results agree well with the theoretical inference and the new characteristic frequencies expression can be used as effective assessment indicator for bearing fault detection.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research was supported by the Science and Technology Project of Liaoning Province, no. 2015020140, and the subproject of Shandong Independent Innovation and Achievements Transfer Project, no. 2014CGZH0601.