**Condition Monitoring and Fault Diagnosis of Roller Element Bearing**

Tian Ran Lin, Kun Yu and Jiwen Tan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67143

#### Abstract

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Rolling element bearings play a crucial role in determining the overall health condition of a rotating machine. An effective condition-monitoring program on bearing operation can improve a machine's operation efficiency, reduce the maintenance/replacement cost, and prolong the useful lifespan of a machine. This chapter presents a general overview of various condition-monitoring and fault diagnosis techniques for rolling element bearings in the current practice and discusses the pros and cons of each technique. The techniques introduced in the chapter include data acquisition techniques, major parameters used for bearing condition monitoring, signal analysis techniques, and bearing fault diagnosis techniques using either statistical features or artificial intelligent tools. Several case studies are also presented in the chapter to exemplify the application of these techniques in the data analysis as well as bearing fault diagnosis and pattern recognition.

Keywords: rolling element bearings, condition monitoring, fault diagnosis

## 1. Introduction

Rolling element bearings are the most critical but vulnerable mechanical components in a rotating machine. A bearing failure can lead to a complete machine breakdown causing unintended interruption to a production process and financial losses. It is important to have an effective bearing condition monitoring (CM) and fault diagnosis system in place so that incipient bearing faults can be detected and correctly diagnosed on time to prevent them from deteriorating further to cause damage to a machine. For instance, an early detection of incipient defect of a rolling element bearing in a high speed train or a wind turbine can lead to a timely maintenance/replacement to prevent potential disastrous consequence and human loss caused by unexpected failure of critical mechanical components.

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Many condition-monitoring and fault diagnosis techniques have been developed in the last few decades to improve the reliability of rolling element bearings. This chapter provides an overview on the most commonly employed condition-monitoring, signal analysis, and fault diagnosis techniques for rolling element bearings and discusses some of the pros and cons of these techniques.

A starting but most fundamental information in bearing condition monitoring is the characteristic bearing defect frequencies. The characteristic defect frequency components in a signal are generated by flaws or faults presented in a bearing when the bearing is operated at a specific machine rotating speed under certain loading conditions. Alternatively, defect signals can also be produced accompanying the normal wear process during a bearing's operational life.

Figure 1 shows the graphical and the cross-sectional representations of a rolling element bearing. The bearing comprises four mechanical components: an outer race, an inner race, rollers (balls), and a cage that hold the rollers (balls) in place. Correspondingly, there are four possible characteristic defect frequencies for a rolling element bearing: ball (roller) pass frequency at the outer race (BPFO), ball (roller) pass frequency at the inner race (BPFI), ball (roller) spin frequency (BSF), and fundamental train frequency (cage frequency) (FTF). The formulae for these four characteristic bearing defect frequencies are listed in Table 1.

Figure 1. (a) A graphical illustration of a roller element bearing and (b) a cross-sectional view of the roller element bearing.


Note: N is the shaft speed in revolutions per minute (RPM), n is the number of roller elements in a bearing, α is the contact angle of the bearing due to the load from the radial plane, d is the diameter of the roller, and D is the mean diameter of the bearing as shown in Figure 1.

Table 1. Formulae of the bearing defect frequencies.

A bearing defect signal can be simulated using the following equations [1]:

$$s(t,n) = \text{Qe}^{-\gamma(t-\frac{n}{\text{BDF}})} \sin\left[2\pi f\_r \left(t\text{-}\frac{n}{\text{BDF}}\right)\right] + \frac{O(t)}{r\_{\text{sn}}}, \ t < \frac{n+1}{\text{BDF}}, \ n = 0, 1, 2, \ldots \tag{1a}$$

and

Many condition-monitoring and fault diagnosis techniques have been developed in the last few decades to improve the reliability of rolling element bearings. This chapter provides an overview on the most commonly employed condition-monitoring, signal analysis, and fault diagnosis techniques for rolling element bearings and discusses some of the pros and cons of

A starting but most fundamental information in bearing condition monitoring is the characteristic bearing defect frequencies. The characteristic defect frequency components in a signal are generated by flaws or faults presented in a bearing when the bearing is operated at a specific machine rotating speed under certain loading conditions. Alternatively, defect signals can also be produced accompanying the normal wear process during a bearing's operational life.

Figure 1 shows the graphical and the cross-sectional representations of a rolling element bearing. The bearing comprises four mechanical components: an outer race, an inner race, rollers (balls), and a cage that hold the rollers (balls) in place. Correspondingly, there are four possible characteristic defect frequencies for a rolling element bearing: ball (roller) pass frequency at the outer race (BPFO), ball (roller) pass frequency at the inner race (BPFI), ball (roller) spin frequency (BSF), and fundamental train frequency (cage frequency) (FTF). The

Figure 1. (a) A graphical illustration of a roller element bearing and (b) a cross-sectional view of the roller element

Note: N is the shaft speed in revolutions per minute (RPM), n is the number of roller elements in a bearing, α is the contact angle of the bearing due to the load from the radial plane, d is the diameter of the roller, and D is the mean diameter of the

2 N <sup>60</sup> 1− <sup>d</sup> <sup>D</sup> cos <sup>α</sup> � �

2 N <sup>60</sup> <sup>1</sup> <sup>þ</sup> <sup>d</sup> <sup>D</sup> cos <sup>α</sup> � �

2 N <sup>60</sup> 1− <sup>d</sup> <sup>D</sup> cos <sup>α</sup> � �

<sup>2</sup><sup>d</sup> 1− <sup>d</sup> <sup>D</sup> cos <sup>α</sup> � �<sup>2</sup> h i

Ball-pass frequency at outer race (BPFO) BPFO <sup>¼</sup> <sup>n</sup>

Ball-pass frequency at inner race (BPFI) BPFI <sup>¼</sup> <sup>n</sup>

Ball-spin frequency (BSF) BSF <sup>¼</sup> <sup>D</sup>

Fundamental train frequency (FTF) FTF <sup>¼</sup> <sup>1</sup>

formulae for these four characteristic bearing defect frequencies are listed in Table 1.

these techniques.

40 Bearing Technology

bearing.

bearing as shown in Figure 1.

Table 1. Formulae of the bearing defect frequencies.

$$\mathbf{s}(t,n) = \mathbf{Q} \mathbf{e}^{\gamma(t-\frac{n+1}{\text{BDF}})} \sin\left[2\pi f\_r \left(t \frac{n+1}{\text{BDF}}\right)\right] + \frac{O(t)}{r\_{\text{sn}}}, \ t \ge \frac{n+1}{\text{BDF}}, \ n = 0, 1, 2, \dots \tag{1b}$$

where Q is the assumed maximum loading intensity for a bearing defect and t is the time variable, BDF represents a bearing defect frequency, fr is the assumed bearing resonance frequency and α is the energy decay constant of the bearing race. The first part in Eqs. (1a) and (1b) is the signal produced by a bearing defect, and the second part of the equations is the superimposed white Gaussian noise representing the machine background noise. n is the pulse index of the bearing defect frequency, O(t) is the white Gaussian noise and rsn is the assumed signal-to-noise ratio (SNR). A typical bearing defect signal is shown in Figure 2. The parameters used in the simulation of the signal are listed in Table 2.

Figure 2. A simulated defect signal of a roller element bearing due to a fault at the outer race: (a) pure defect signal; (b) noise-added signal.


Table 2. Parameters used in the simulation.
