**2. Rolling element bearings**

314 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

diagnostic and prognostic software, communication protocols, maintenance software

The concept of condition monitoring consists of a selection of measurable parameters which correlate with the health or condition of a machine, and an interpretation of the collected data to determine the machinery fault existence and identify specific components (e.g. gear set, bearings) in the machine that are degrading, *Detection mode*. Moreover, the condition monitoring activities may include: specify the component failure causes, *Diagnostic mode*, and estimate the remaining life of the monitored component, *Prognostic mod*e. For example, the particles content in the lubricant oil is an indicator of the machine's wearing condition. By setting warning limits for the particles content of the lubricant a preventive action can be taken before the catastrophic failure occurs. With more detailed analysis of the measurement the nature of the problem can be identified, and lead to the diagnosis of the problem. The level of automation in assessing the machine condition can vary from human visual inspection to fully automated systems with sensors, data manipulation, condition

Various parameters e.g. vibration, temperature, lubricant oil analysis, thermography, electric current, acoustic emission, etc, and different data analysis techniques have been

*Time domain methods*: using different statistical indicators such as, Root Mean Square (RMS),

*Frequency domain methods*: such as Fourier Transform (FT) spectrum (Reeves, 1994), envelope

*Time-Frequency methods*: which include Short Time Fourier Transform (STFT) (Thanagasundram and Schlindwein, 2006), Wavelet Analysis (WA) (Peng and Chu, 2004)

*Adaptive noise cancellation methods*: such as Adaptive Noise Canceling (ANC), and Adaptive

Bearing failures represent a high percentage of the breakdowns in the rotating machinery and result in serious problems, mainly in places where machines are rotating at constant and high speeds, not only because of the large quantity of them installed in rotating

This chapter presents the application of wavelet analysis combined with artificial neural networks as an automatic rolling bearing fault detection and diagnosis, with applied to both

The chapter has been divided into two parts, in the first part the application of the wavelet analysis as a bearing fault detection/diagnosis technique is presented. The wavelet fault detection techniques are based on the use of the autocorrelation of the wavelet de-noised vibration signal and the wavelet envelope power spectrums for the identification of bearing

The second part includes the application of wavelet analysis as a feature extraction method combined with the neural network classifier for automatic detection and diagnosis of the

applied and developed to provide significant data analysis for CM, which include:

(Wang and Gao , 2003), (Junsheng *et al.* , 2007 ) and (Kahaei et al. , 2006), etc.

Peak value, Kurtosis, etc. (Orhan et al. .2006) and (Tandon , 1994).

Line Enhancer (ALE), etc. (Khemili and Chouchane, 2005)

machinery, but also due to their role in relation to product quality.

simulated (modeling) and real (measured) bearing vibration signals.

applications and computer networking technologies.

monitoring, diagnosis, and prognosis.

detection (Weller, 2004), Cepstrum, etc.

fault frequencies.

rolling bearing fault.

Bearings permit a smooth low friction motion between two surfaces (usually a shaft and housing) loaded against each other. The terms rolling-contact bearing, antifriction bearing, and rolling bearing are all used to describe that class of bearing in which the main load is transferred through elements in rolling contact rather than in sliding contact (sliding bearings).

The basic concept of the rolling element bearing is simple. If loads are to be transmitted between surfaces in relative motion in a machine, the action can be achieved in the most effective way if the rolling elements are interposed between the sliding members. The frictional resistance encountered in sliding is then largely replaced by much smaller resistance associated with rolling, although this arrangement is accompanied with high stresses in the contact regions of effective load transmission.

The standard configuration of a rolling element bearing is an assembly of the outer and inner rings which enclose the rolling elements such as balls (ball bearings), Figure 1a, and cylindrical rollers (roller bearings), Figure 1b, and the cage or separator which assures annular equidistance between the rolling elements and prevents undesired contacts and rubbing friction among them. Some bearings also have seals as integrated components.

Fig. 1. Rolling element bearing (a) deep groove ball bearing, (b) roller bearing (c) angular contact ball bearing, and (d) thrust bearing (Harris, 2001).

Wavelet Analysis and Neural Networks for Bearing Fault Diagnosis 317

The Wavelet Transform (WT) coefficients are analyzed in both the time and frequency domains. In the time domain the autocorrelation of the wavelet de-noised signal is applied to evaluate the period of the fault pulses using the impulse wavelet as a wavelet base function. However, in the frequency domain the wavelet envelope power spectrum has been used to identify the fault frequencies with the single sided complex Laplace wavelet as the

The WT is the inner product of a time domain signal with the translated and dilated waveletbase function. The resulting coefficients reflect the correlation between the signal and the selected wavelet-base function. Therefore, to increase the amplitude of the generated wavelet coefficients related to the fault impulses, and to enhance the fault detection process, the selected wavelet-base function should be similar in characters to the bearing impulse response generated by the presence of a bearing incipient fault. Based on that, the investigated wavelet-

<sup>2</sup> <sup>1</sup> ( ) sin( )

*<sup>c</sup> t Ae t* 

Where *β* is the damping factor that controls the decay rate of the exponential envelope in time and hence regulates the resolution of the wavelet, simultaneously it corresponds to the frequency bandwidth of the wavelet in the frequency domain, *ωc* determining the number of significant oscillations of the wavelet in the time domain and correspond to the wavelet centre frequency in frequency domain, and *A* is an arbitrary scaling factor. Figure 3 shows

(a) (b)

0.2

0.4

0.6

**Power Spectrum**

0.8

1

1.2 x 10-3

Fig. 3. (a) the impulse wavelet time waveform, (b) its FFT-spectrum.

*c t*

(1)

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>45</sup> <sup>0</sup>

**Frequency (Hz)**

50

base function is denoted as the impulse-response wavelet and given by,

the proposed wavelet and its power spectrum.


**Time (s)**


**Amplitude**

**3. Bearing fault diagnosis using wavelet analysis** 

mother wavelet function.

**3.1 Wavelet de-noising method 3.1.1 Impulse wavelet function** 

The rolling surfaces on the rings are referred to as raceways. The number of balls is defined as *Nb*, their diameter as *Db*. The pitch diameter or the diameter of the cage is designated *Dp*. The point of contact between a ball and the raceways is characterized by the contact angle α, Figure 2.

Fig. 2. Rolling element bearing basic geometry and velocities.

The rolling bearings that support loads perpendicular to their axis of rotation are called radial bearing. However, the bearings which support loads parallel to the axis of rotation are termed thrust bearings (the contact angle exceeding 45o), Figure 1d. Angular contact bearings have one ring shoulder removed; this may be from the inner or outer ring, Figure 1c. This allows a larger ball complement than found in comparable deep groove bearings, giving a greater load capacity. Speed capacity of angular contact bearings is also greater than deep groove ball bearing. The normal angular contact bearings have a contact angle which does not exceed 40o. Angular contact bearings support a combination of radial and thrust loads or heavy thrust loads depending on the contact angle. A single angular contact bearing can be loaded in one thrust direction only.

Because roller bearings have a greater rolling surface area in contact with inner and outer races, they generally support a greater load than comparably sized ball bearings. The small contact area (point contact) in the ball bearing compared with the roller bearing (line contact) leads to more stress concentration and is more affected by the fatigue failure during the bearing rotation. Moreover, the angular contact ball bearing can easily separate its components (separable) to introduce the artificial faults. Based on that the angular contact ball bearings have been used in this research for fault detection.
