**2. Bearing fault diagnosis in induction machine**

could lead to unexpected breakdowns, losses at industrial production, or have catastrophic consequences. In this context, rolling element bearings are responsible for more than 40% of induction machine faults [1]. Rolling bearings are critical mechanical components, which allow relative movement between systems, supporting radial and thrust load. Bearing faults could be associated to contamination, corrosion, inadequate lubrication, installation problems, and misalignment or overloading [2]. In general, a fault affects only one bearing component—inner race, outer race, cage, or ball; as the fault evolves, it spreads to other components; moreover, these faults could be described based on fault mechanism, location, or on a combi-

Maintenance of electrical machines is an activity of the utmost importance. Moreover, considering a scenario of cost reduction and production efficiency, the development of an effective maintenance program has been gaining more attention and several tools have been implemented to support and encourage best practices. In this sense, advanced methods for data acquisition and processing have been developed in order to allow an effective machine condition monitoring and early fault detection and identification, avoiding unexpected breakdowns and even catastrophic failures, especially for critical systems. Whenever possible, condition monitoring should be done non-invasively and without interrupting machine operation [5–7]. Over the years, the concept of maintenance became more comprehensive, reducing fault occurrence and increasing industrial system availability. Besides, requirements of reliability, safety, and criticality were associated with the system or equipment under analysis. Maintenance strategies or schemes can be classified as corrective (run-to-break), preventive (time-based) and predictive (condition-based maintenance) [8]. Corrective maintenance is only performed after an occurrence of a fault and therefore involves unexpected breakdowns, high costs, changes in the production chain, and in addition, it could lead to catastrophic events. Preventive maintenance and interventions occur based onto a scheduled maintenance plan or based on the equipment mean time between failures. Although it is more effective than corrective maintenance, by preventing most failures, unexpected failure may still occur. Additionally, the process cost is still high, especially, the costs associated with labor, inven-

tory, and even with unnecessary replacement of equipment or components [8, 9].

lished, whereby properly investigating the fault symptoms and prognosis [10].

On the other hand, predictive maintenance analyses the equipment condition so that a possible fault can still be identified at an early stage. Predictive maintenance aims to identify a machine anomaly so that it does not result in a fault. Such maintenance involves advanced technique of monitoring, processing, and signal analysis, that are generally performed noninvasively and, in many cases, in real time. In case of induction machines, these techniques can be developed based on vibration, temperature, acoustic emission, or electrical current signal monitoring [9]. It should be noted that the monitoring of such signals or parameters, in order to verify the operating condition of a machine, is called condition monitoring. In fact, condition monitoring aims to not only observe machine current operational condition, but also to predict machine future condition, keeping it under a systematic analysis during the machine's remaining life [8]. In this sense, from a systematic machine condition monitoring, a fault condition can be detected and identified, such that, a diagnosis procedure can be estab-

nation of these [3, 4].

94 Bearing Technology

Rolling bearings are one of the most important mechanical components in induction machines. Therefore, it is necessary to assess the health condition of these components, especially by means of signal processing methodologies for bearing fault diagnosis. Bearing fault diagnosis comprises a series of processes performed in order to detect, isolate, and identify the bearing condition based on the machine monitoring [10]. Although there are several techniques for monitoring of bearing condition in induction machine, i.e., vibration, acoustic emission, and ultrasound, this section describes an approach based on electrical stator current analysis or current signature analysis. This approach has been gaining attention since bearing failure causes a modulation in electrical current signal, which can be identified in a similar way, as it is done in vibration analysis [15].

This section aims to describe some of the most used methodologies for induction machine fault detection based on electrical current signature analysis. In this context, it is important to know the machine to be monitored, and often the system in which it is inserted, since practical considerations are essential to allow a proper fault diagnosis. Some of these considerations are mainly related to machine technical specifications; load variations; rotor speed variations; power supply characteristics; failure mode to be analyzed (electrical or mechanical); sensors (physical quantity to be monitored, specification, amount), among others [16, 17].

Bearing fault detection is a technique mainly based on feature extraction from acquired signal, and condition identification based on the analysis of these features [10]. In the case of a fault localized on the inner or outer race, whenever a rolling element passes through the fault surface, a series of impulses are generated. This almost periodic series of impulses present characteristics that vary with bearing geometry and fault localization; in addition, they excite resonances in the bearing and in the machine structure as a whole [8, 16].

The series of generated impulses are still amplitude modulated as the fault passes by the load zone and they are influenced by the transfer function from the fault to the sensor. The impulses are generated at a rate which varies according to: the fault position (inner race, outer race, and cage), the bearing dimensions, and the machine shaft speed (*f r* ). Thus, it is possible to estimate the so called bearing characteristic frequencies, i.e., ball pass frequency of the outer race (BPFO), ball pass frequency of the inner race (BPFI), fundamental train frequency (FTF), which is related to cage speed rotation, and ball spin frequency (BSF). The following equations represent these frequencies [3]:

$$\text{BPFO} = \frac{nf\_r}{2} \left( 1 - \frac{d}{D} \cos a \right) \tag{1}$$

$$\text{BPFI} = \frac{nf\_r}{2} \left( 1 + \frac{d}{D} \cos a \right) \tag{2}$$

$$\text{FTF} = \frac{f\_i}{2} \left( 1 - \frac{d}{D} \cos a \right) \tag{3}$$

$$\text{BSF} = \frac{D}{2d} \left[ 1 - \left( \frac{d}{D} \cos \alpha \right)^2 \right] \tag{4}$$

where *n* corresponds to the number of rolling elements; *α* is the angle of the load from the radial plane; *d* is the ball diameter and *D* is the pitch diameter. When such characteristic frequencies appear (or its amplitude increase) in the analyzed signal spectrum, it is possible to identify a bearing fault and its location [10]. However, it is very difficult to extract these components, since they have low amplitude and are merged with other spectral components and background noise.

Therefore, it is possible to affirm that fault detection based on the current analysis is great a challenge, especially in industrial environments mainly due to low signal-to-noise ratio of the characteristic frequency components associated with these faults, even though several studies have shown promising results in this area [6, 18]. On the other hand, in many situations, motor current signature analysis (MCSA) becomes a useful alternative to traditional fault detection methods, e.g., vibration analysis, particularly considering the sensor installation, risks, costs associated with process, and degree of criticality of the system or machine under analysis [11].

#### **2.1. Motor current signature analysis—MCSA**

MCSA is one of the most commonly used techniques to fault detection in induction motors, since it allows identifying electrical and mechanical faults. It performs a spectral analysis of stator electrical current, which is usually monitored at one of three power supply phases. Studies related to mechanical faults effects on motor stator current mainly consider: load torque oscillations, rotating eccentricities, and air gap eccentricity [11, 15, 19].

In case of bearing faults, it is possible to consider that machines inductances can vary due to rotating eccentricities at bearing characteristic frequencies *f <sup>C</sup>*, i.e., BPFO, BPFI, etc., which produces a stator current modulation, described by [11]:

$$f\_E = f\_s \pm k \cdot f\_c \tag{5}$$

where *f <sup>E</sup>* is the frequency related to a bearing fault; *f s* is the power supply frequency; and *k* = 1, 2, 3, … is the harmonic number. Thus, *f <sup>C</sup>* appears in the current spectrum as sidebands.

In this context, it is import to observe that rotor inertia and winding inductances produce an electromechanical filtering effect in stator current, such that, this current is mainly affected by low frequency components [20, 21].

Other studies show that load torque oscillations can occur each time the rolling elements reach a localized fault on the outer or inner race, or when a fault on a rolling element reaches a race. These oscillations cause phase modulations in electrical current as described by Eq. (5) [22].

Finally, another approach considers that the effect of a localized bearing fault in stator current can be modeled as air gap eccentricity. In this case, a magnetic flux density variation affects stator current as a function of the fault location. Thus, frequencies related to the bearing faults are expressed by [19]:

$$f\_{\text{Е омататасо}} = f\_s \pm k \cdot \text{BPFGO} \tag{6}$$

$$f\_{\text{E imorraca}} = f\_s \pm f\_r \pm k \cdot \text{BIPFI} \tag{7}$$

$$f\_{E\text{ ball}} = f\_s \pm \text{FTF} \pm k \cdot \text{BSF} \tag{8}$$

where *f <sup>E</sup> outer race*, *f <sup>E</sup> inner race*, and *f <sup>E</sup> ball* are the frequencies related to a fault in outer race, inner race, and ball respectively, which correspond to an amplitude modulation of the fundamental power supply frequency (*f s* ). It is important to observe that this modulation is caused by a permeance variation on the rotor fundamental magnetomotive force [11].

#### **2.2. Power spectral density**

fault localized on the inner or outer race, whenever a rolling element passes through the fault surface, a series of impulses are generated. This almost periodic series of impulses present characteristics that vary with bearing geometry and fault localization; in addition, they excite

The series of generated impulses are still amplitude modulated as the fault passes by the load zone and they are influenced by the transfer function from the fault to the sensor. The impulses are generated at a rate which varies according to: the fault position (inner race, outer

to estimate the so called bearing characteristic frequencies, i.e., ball pass frequency of the outer race (BPFO), ball pass frequency of the inner race (BPFI), fundamental train frequency (FTF), which is related to cage speed rotation, and ball spin frequency (BSF). The following

<sup>2</sup> (<sup>1</sup> <sup>−</sup> \_\_*<sup>d</sup>*

<sup>2</sup> (<sup>1</sup> <sup>+</sup> \_\_*<sup>d</sup>*

\_\_*d <sup>D</sup>* cosα)

2

\_\_*r* <sup>2</sup>(<sup>1</sup> <sup>−</sup> \_\_*<sup>d</sup>*

<sup>2</sup>*d*[<sup>1</sup> <sup>−</sup> (

where *n* corresponds to the number of rolling elements; *α* is the angle of the load from the radial plane; *d* is the ball diameter and *D* is the pitch diameter. When such characteristic frequencies appear (or its amplitude increase) in the analyzed signal spectrum, it is possible to identify a bearing fault and its location [10]. However, it is very difficult to extract these components, since they have low amplitude and are merged with other spectral components

Therefore, it is possible to affirm that fault detection based on the current analysis is great a challenge, especially in industrial environments mainly due to low signal-to-noise ratio of the characteristic frequency components associated with these faults, even though several studies have shown promising results in this area [6, 18]. On the other hand, in many situations, motor current signature analysis (MCSA) becomes a useful alternative to traditional fault detection methods, e.g., vibration analysis, particularly considering the sensor installation, risks, costs associated with process, and degree of criticality of the system or machine under

MCSA is one of the most commonly used techniques to fault detection in induction motors, since it allows identifying electrical and mechanical faults. It performs a spectral analysis of stator electrical current, which is usually monitored at one of three power supply phases. Studies related to mechanical faults effects on motor stator current mainly consider: load

torque oscillations, rotating eccentricities, and air gap eccentricity [11, 15, 19].

BSF = \_\_\_ *<sup>D</sup>*

*r*

*<sup>D</sup>* cosα) (1)

*<sup>D</sup>* cosα) (2)

*<sup>D</sup>* cosα) (3)

] (4)

). Thus, it is possible

resonances in the bearing and in the machine structure as a whole [8, 16].

race, and cage), the bearing dimensions, and the machine shaft speed (*f*

equations represent these frequencies [3]:

BPFO <sup>=</sup> *<sup>n</sup> <sup>f</sup>* \_\_\_*<sup>r</sup>*

BPFI <sup>=</sup> *<sup>n</sup> <sup>f</sup>* \_\_\_*<sup>r</sup>*

FTF <sup>=</sup> *<sup>f</sup>*

**2.1. Motor current signature analysis—MCSA**

and background noise.

96 Bearing Technology

analysis [11].

Generally, the MCSA is carried out using classical or nonparametric spectral estimation methods. Nonparametric methods require little information regarding the signal to be analyzed and its computational complexity is low, especially compared to modern spectral estimation methods [16, 23].

Among the most common nonparametric techniques are the periodogram and its refined variations, i.e., Bartlett, Welch, and Daniell methods [22]. Periodogram can be obtained by [23]:

$$\dot{\Phi}\_p(\omega) = \frac{1}{N} \left| \sum\_{\nu=0}^{N-1} y(t) \, e^{-|\omega t|} \right|^2 \tag{9}$$

where *y*(*t*) is signal under analysis and its samples could be represented by [*y*(*t*)]*<sup>t</sup>*=1 *N* .

Mean squared error, represented by the sum of the bias squared and the variance, is a parameter commonly used to evaluate the performance of an estimator. In this sense, bias reduction is obtained by applying a window. In order to reduce periodogram variance, Bartlett method uses an average of several periodograms obtained from different segments of the signal. In this case, the original signal [*y*(*t*)]*<sup>t</sup>*=1 *<sup>N</sup>* with *N* samples is split into *K* segments, such that, an average of *L* = *N*/*K* periodograms is computed. Welch method can be seen as evolution of Bartlett method; since the estimation is performed considering that the signal segments are overlapped and windowed. Thus, variance is reduced, but also the resolution [23].
