**4. Bearing fault detection methodology**

Despite major advances in bearing fault detection techniques, such as MCSA, current methodology still has limitations that make it difficult to identify incipient faults, impairing the fault prognosis. Depending on the operational environment and machine specifications, there may be a reduction in the analysis reliability as a whole.

A way to mitigate this problem consists in separation of signals coming from different sources. In general, the components in the machine vibration or current signals have specific characteristics that allow their separation and identification in order to detect changes in machinery health condition. Noise, eccentricity, gear, cavitation, rolling bearing characteristic frequencies, and broken bars are examples of components that may be present in vibration signals or electric current signals [8].

In this scenery, several techniques have been proposed to support signal separation and identification in machine fault detection. Among these techniques, it is possible to mention, for example, time synchronous averaging (TSA), which is used to remove signal components that are not synchronous with rotor speed. In this situation, a minimal disturbance could occur in the resulting signal, but it is necessary an angular sampling for each harmonic family to be separated. This technique removes harmonics, but not lateral modulation bands. Techniques related to noise cancelling, also could be used in order to mitigate noise contamination. In addition, linear prediction filtering could be used to separate the predictable deterministic signal, which must be removed from the original signal in order to highlight the signal component related to bearing fault [1]. Linear prediction was also considered for electrical signature analysis.

Another technique that was evaluated in Ref. [14] to improve the detection of fault related components was the sum of the electric currents. A common operation in three-phase circuit analysis is to obtain the current or voltage phase using information from other phases. In the case of a three-phase induction machine connected to a delta system, considering that the sum of all currents entering a node is equal to the sum of all the currents out of the node (1st Kirchhoff's Law), it is possible to assume that *I <sup>A</sup>* + *I <sup>B</sup>* + *I <sup>C</sup>* = 0, where *I <sup>A</sup>*, *I <sup>B</sup>*, and *I <sup>C</sup>* are the measured currents of the phase *A*, *B*, and *C*, respectively. In this sense, the current of any phase (*I <sup>A</sup>*, *I <sup>B</sup>*, or *I <sup>C</sup>*) can easily be defined by the other two. For example, *I <sup>C</sup>* = − (*I <sup>A</sup>* + *I B*).

This procedure is similar to the synchronous average calculation. Any mechanical effect related to the machine condition (nominal or under a fault), including periodic or random components, can be observed in any of the three phases' current, or alternatively, in the numerically obtained current, i.e. (*I <sup>C</sup>*). On the other hand, any other uncorrelated random effect will be attenuated using this procedure [14].

This way, the methodology that guided this work follows five steps:


It is also important to highlight that since faults are identified in the envelope spectrum, its amplitude can be used as severity index. Thus, a fault evolution can be analyzed as function of increases in the bearing characteristic frequency amplitude [34].

#### **4.1. Experimental issues**

A way to mitigate this problem consists in separation of signals coming from different sources. In general, the components in the machine vibration or current signals have specific characteristics that allow their separation and identification in order to detect changes in machinery health condition. Noise, eccentricity, gear, cavitation, rolling bearing characteristic frequencies, and broken bars are examples of components that may be present in vibration signals or

In this scenery, several techniques have been proposed to support signal separation and identification in machine fault detection. Among these techniques, it is possible to mention, for example, time synchronous averaging (TSA), which is used to remove signal components that are not synchronous with rotor speed. In this situation, a minimal disturbance could occur in the resulting signal, but it is necessary an angular sampling for each harmonic family to be separated. This technique removes harmonics, but not lateral modulation bands. Techniques related to noise cancelling, also could be used in order to mitigate noise contamination. In addition, linear prediction filtering could be used to separate the predictable deterministic signal, which must be removed from the original signal in order to highlight the signal component related to

bearing fault [1]. Linear prediction was also considered for electrical signature analysis.

*<sup>A</sup>* + *I <sup>B</sup>* + *I*

This way, the methodology that guided this work follows five steps:

of increases in the bearing characteristic frequency amplitude [34].

of the phase *A*, *B*, and *C*, respectively. In this sense, the current of any phase (*I*

**5.** Bearing fault identification based on bearing characteristic frequency detection.

It is also important to highlight that since faults are identified in the envelope spectrum, its amplitude can be used as severity index. Thus, a fault evolution can be analyzed as function

Another technique that was evaluated in Ref. [14] to improve the detection of fault related components was the sum of the electric currents. A common operation in three-phase circuit analysis is to obtain the current or voltage phase using information from other phases. In the case of a three-phase induction machine connected to a delta system, considering that the sum of all currents entering a node is equal to the sum of all the currents out of the node (1st Kirchhoff's

*<sup>C</sup>* = 0, where *I*

This procedure is similar to the synchronous average calculation. Any mechanical effect related to the machine condition (nominal or under a fault), including periodic or random components, can be observed in any of the three phases' current, or alternatively, in the

*<sup>C</sup>* = − (*I*

*<sup>A</sup>*, *I*

*<sup>A</sup>* + *I B*).

*<sup>B</sup>*, and *I*

*<sup>C</sup>*). On the other hand, any other uncorrelated random

*<sup>C</sup>* are the measured currents

*<sup>A</sup>*, *I <sup>B</sup>*, or *I*

*<sup>C</sup>*) can

electric current signals [8].

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Law), it is possible to assume that *I*

numerically obtained current, i.e. (*I*

**3.** Spectral kurtosis based algorithm.

**1.** Sum of the electric currents.

**4.** Squared envelope spectrum.

easily be defined by the other two. For example, *I*

effect will be attenuated using this procedure [14].

**2.** Prewhitening (linear prediction filtering).

In this section, damaged rolling bearings (model 6203-ZZ) are installed on a three-phase induction motor; for each bearing, stator current signals are acquired and squared envelope spectrum was analyzed in order to detect outer race faults by means of ball pass frequency outer race (BPFO) identification. Rolling bearings were artificially damaged, such that, through holes of 1.0 mm, 2.0 mm, and 3.0 mm diameter were drilled on the outer race to simulate localized faults with different levels of severity. Experiments were performed using 6203-ZZ shielded metric radial bearings, also described as deep groove ball bearing, single row, double shielded, pressed steel cage, normal clearance, prelubricated with grease, with inner (bore) diameter: 17mm; outside diameter: 40mm; and overall width: 12mm.

Experimental test rig (**Figure 1**) consists of a three-phase squirrel cage induction motor with 0.37 kW power, four poles, and 60 Hz supply frequency, coupled to an electric machine working as a power generator (constant mechanical load), without any speed or torque control. A 24-bit/4-channel data acquisition board (National Instruments NI 9239) and current probes were used to acquire electric current signals at 50 kHz sample rate. Prior to any processing, data was filtered using a low pass filter of 25 kHz.

Two of the three stator currents (*I <sup>A</sup>* and *I <sup>B</sup>*) were measured, and the third one (*I C*) was numerically obtained, such that *I <sup>C</sup>* = − (*I <sup>A</sup>* + *I <sup>B</sup>*), and used in the fault detection process. **Figure 2** shows the damaged bearings used in the experiments. Rotational speed was estimated to be 28.80 Hz (1728 rpm), and the characteristic frequency for a fault on the bearing outer race was estimated in (BPFO = 87.93 Hz ± 2%).

The methodology was applied to calculate electric stator current. Following, prewhitening was performed, such that the AR model order was chosen by using the kurtosis maximization criterion of the residual signal. In this work, it is proposed as a simplified methodology, where the healthy

**Figure 1.** Experimental test rig.

bearing is initially tested and the resulting AR model order is also used for the faulty bearings analysis. Therefore, an AR model order (*p* = 32) is used for all experiments. Following, fast kurtogram algorithm was applied at five levels of decomposition. It is important to notice that this process, including sampling, signal processing, and feature extraction, lasts about 2 minutes on a modern computer. Although the wavelet kurtogram algorithm has been analyzed, only the results obtained with the fast kurtogram are presented, mainly due to its performance in this application, as explained in Refs. [14, 34]. The signal processing is performed offline using Matlab®.

**Figure 2.** Damaged bearings used in the experimental tests. From left to right holes of 1.0 mm, 2.0 mm, and 3.0 mm.

Thus, the described methodology was applied for all damaged bearing cases. The fast kurtogram color map was similar to that in **Figure 3**; then, only the resulting squared envelope spectrum was shown for the other experiments. The bandpass filter with center frequency *f <sup>C</sup>* = 6250 Hz and bandwidth *Bw* = 4167 Hz, at decomposition level (*k* = 2.6), indicated by black circle in **Figure 3**, was used in all squared envelope calculations, which was very useful for comparisons. In the Figures, an arrow indicates the amplitude of the bearing outer race characteristic frequency (BPFO).

**Figure 3.** Fast kurtogram color map.

**Figure 4** shows the squared envelope spectrum of the electric current for the damaged bearing with the 1.0 mm hole. In this case, the envelope spectrum clearly shows the fault signature around the estimated BPFO, with amplitude *A* = 2.9 × 10− 9.

bearing is initially tested and the resulting AR model order is also used for the faulty bearings analysis. Therefore, an AR model order (*p* = 32) is used for all experiments. Following, fast kurtogram algorithm was applied at five levels of decomposition. It is important to notice that this process, including sampling, signal processing, and feature extraction, lasts about 2 minutes on a modern computer. Although the wavelet kurtogram algorithm has been analyzed, only the results obtained with the fast kurtogram are presented, mainly due to its performance in this application,

Thus, the described methodology was applied for all damaged bearing cases. The fast kurtogram color map was similar to that in **Figure 3**; then, only the resulting squared envelope spectrum was shown for the other experiments. The bandpass filter with center frequency

**Figure 2.** Damaged bearings used in the experimental tests. From left to right holes of 1.0 mm, 2.0 mm, and 3.0 mm.

*<sup>C</sup>* = 6250 Hz and bandwidth *Bw* = 4167 Hz, at decomposition level (*k* = 2.6), indicated by black circle in **Figure 3**, was used in all squared envelope calculations, which was very useful for comparisons. In the Figures, an arrow indicates the amplitude of the bearing outer

*f*

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race characteristic frequency (BPFO).

**Figure 3.** Fast kurtogram color map.

as explained in Refs. [14, 34]. The signal processing is performed offline using Matlab®.

**Figure 4.** Squared envelope spectrum of the electric current for the damaged bearing with the 1.0 mm hole.

The same procedure was applied to the damaged bearing with 2.0 mm hole, as presented in **Figure 5**. Here, a significant increase in the bearing characteristic fault frequency amplitude (*A* = 7.9 × 10− 9) was observed, confirming the fault effect in the stator current envelope spectrum amplitude.

**Figure 5.** Squared envelope spectrum of the electric current for the damaged bearing with the 2.0 mm hole.

The last experiment assessed the damaged bearing with 3.0 mm hole. In this case, it is important to observe a change in the envelope spectrum graphic scale (**Figure 6**), due to the increase in amplitude (*A* = 11.3 × 10− 9) in the observed fault frequency.

**Figure 6.** Squared envelope spectrum of the electric current for the damaged bearing with the 3.0 mm hole.

The obtained results validate the methodology, and therefore, the involved theoretical concepts. A BFPO frequency (at 88.1 Hz) was detected for each damaged bearing experiment, strongly indicating a bearing outer race fault. Besides, the characteristic frequency amplitude increases with the fault severity, which could be used as a prognosis indication. In the envelope spectra, it was also observed that as the amplitude of BPFO increased, the amplitude of another frequency component decreased. Thus, as in Ref. [11], it is possible to conclude that, although the stator current analysis is more complex than the vibration analysis, it is an important alternative to bearing fault detection in induction motors, mainly due to its advantages related to cost, availability and applications.

#### **5. Conclusions and comments**

This work describes a methodology to enhance MCSA for bearing fault detection and identification in induction machines by combining electrical currents sum, prewhitening based on linear prediction filtering, spectral kurtosis, and squared envelope analysis. This methodology is based on successful methodologies and algorithms, initially proposed to be applied to vibration signals. An experimental test of such methodology was depicted using a test rig where artificially damaged bearings were created in order to simulate faults at different severity levels. Results show that the methodology improves MCSA in comparison with traditional spectrum analysis. Besides, the methodology provides an indication of fault severity based on bearing characteristic frequency (e.g. BPFO) amplitude in squared envelope, which can be used for prognosis purposes. For real industrial applications, the authors believe that this methodology could be easily carried by a professional predictive maintenance team, given adequate equipment and analysis software.
