3.Corrosion

When the rolling bearing is working, the surface and internal metal and the substances in the environment, such as acid and alkali, or the consumption phenomenon caused by chemical reaction into water, that is corrosion.

### 4.Wear and tear

The relative movement of the two contact metal surfaces is inevitable. In relative motion, friction, metal consumption, deformation, change the size of the rolling bearing, and then cause a change in performance. This phenomenon is wearing.

*Perspective Chapter: On Rolling Bearing Fault Feature Extraction Based on Entropy Feature DOI: http://dx.doi.org/10.5772/intechopen.105095*

#### 5.Wriggle

Rolling bearing in the work, affected by the load, the inner ring and axis in rotation, in the circular direction, relative movement, on the metal surface of friction, wear and other abnormal damage, this phenomenon is peristalsis.

### 6. Scaling loss

In the process of use of the rolling bearing, due to the excessive bad lubrication load and other factors, itself is affected by high temperature, and not timely cooling will make the element surface burn, serious, the probability of the rolling bearing stuck, this phenomenon is burning loss.

#### *2.1.3 Category of rolling bearings*

The most used part in the machinery industry is bearings, and because bearings are often needed in all walks of life, the categories of bearings are also very diverse. The bearing can be divided into multiple categories according to the rolling body shape, column number, and outer diameter size of the bearing [11].

According to the shape of the rolling body, it can be divided into the ball bearing and the ball bearing, the ball bearing is well understood, that is, the rolling body is the ball bearing, and the rolling body in the roller bearing is generally other types of rolling body such as the cylindrical roller.

If the rolling bearings are classified according to the bearing load direction, they can be divided into thrust bearings, centripetal bearing, and centripetal thrust bearing. The load direction of the thrust bearing is from the axial direction, while the center bearing mainly bears the radial load. And the centripetal thrust bearing is more powerful, can bear the load formed by the axial and radial combination, but because of this reason, the life of the centripetal thrust bearings is often shorter than other bearings.

At the same time, it can also be classified according to the number of rolling body columns, there are single column bearings, double column bearings, and multiple column bearings, the literal meaning can be understood, and it will not repeat.

Finally, it can also be classified by the size of the bearing outer diameter, from micro bearings less than 26 mm in diameter to a major class bearing greater than 2000 mm in diameter, divided into bearings of various specifications.

#### **2.2 Vibration mechanism**

#### 1.Vibration caused by the structural characteristics

Inherent vibration of the collar, vibration caused by the elastic characteristics of the bearing, vibration when the rolling body passes through the bearing area.

As a mechanical element, vibration is inevitable, mainly reflected in the outer circle, and is determined by its own structural characteristics. When the rolling bearing is affected by the external force, the external circle vibration inevitably occurs.

Rolling bearing in work, it is impossible to idling, must bear the load. Usually, the load is not small, which requires the rolling body to be very rigid. But large rigidity means that in special cases, the rolling experience produces a spring-like effect, producing vibration.

The different number of rolling bodies serving as supports when passing through the carrying area also causes the inner circle ring to vibrate back and forth in the front and rear directions.

2.Vibration caused by the rolling bearing processing process

In the processing process of the bearing production, due to the equipment accuracy and other problems, there will inevitably be an inner ring, and the outer ring will have a slight fluctuation. Only in the high-speed rotation, the effects of these fluctuations are also magnified, causing vibration.

On the other hand, the uneven size of the rolling body is also one of the causes of the vibration, which will greatly reduce the service life of the bearing.

3.Vibration caused by component failure

When the failure of the outer ring or the rolling body in the outer ring of the inner circle occurs, the vibration situation is also different. Different data can be obtained.

#### **2.3 Feature frequency**

To quantify the processing, the bearing fault characteristic frequency is given below. The rotation frequency of the ordering axis is *fr*, the number of rolls is z, d is the diameter of ball, D is the diameter of rolling frame, and contact angle θ. When the outer ring of the rolling bearing is fixed, the theoretical calculation formula of the fault characteristic frequency of each element is as follows [12].

Inner ring fault frequency:

$$f\_i = \frac{Zf\_r}{2} \left( \mathbf{1} - \frac{d}{D} \cos \theta \right) \tag{1}$$

Outer ring fault frequency:

$$f\_o = \frac{Zf\_r}{2} \left( 1 + \frac{d}{D} \cos \theta \right) \tag{2}$$

Ball failure frequency:

$$f\_{BS} = \frac{Df\_r}{2d} \left( 1 - \left(\frac{d}{D}\right)^2 \cos^2\Theta \right) \tag{3}$$

#### **2.4 Diagnosis test of rolling bearing**

#### *2.4.1 Test device*

**Figure 2** shows the equipment used in the bearing data center of the rolling bearing data, with a 1kw motor on the left as the power provider, while in the center is the torque sensor, on the right is the power measuring motor, and the electronic control device.

*Perspective Chapter: On Rolling Bearing Fault Feature Extraction Based on Entropy Feature DOI: http://dx.doi.org/10.5772/intechopen.105095*

**Figure 2.** *Experimental Equipment of Western Reserve University.*

#### *2.4.2 Basic parameters of rolling bearing fault*

In this experiment, 6205-2RSJEMSKF bearing was used. The fault setting of the bearing was a single fault, and four damage degree faults were set on the inner ring, outer ring, and rolling body, respectively, namely 0.1778 mm, 0.3556 mm, 0.5334 mm, and 0.7112 mm. The rotational speed of the motor is 1797 r/min, 1772 r/min, 1750 r/ min, and 1730 r/min, respectively.

This paper uses the SKF6205 bearing at a 12K sampling frequency, a fault diameter of 0.1778mm, a motor speed of 1750 r/min, and the vibration signal from the drive end bearing fault data of the acceleration sensor at the 6 o'clock position.

#### **2.5 Influence and relationship between rolling bearing motion and chaos**

### *2.5.1 Chaos phenomenon*

With the advent of Lorentz nonlinear dynamical system, chaos has attracted more and more attention. As the representatives of nonlinear dynamical systems, Lorentz equation, and Lorentz-like equation have attracted the general attention of many scholars at home and abroad, and they have been deeply studied.

Lorentz system is a pioneer of chaos research. Chaos research based on Lorentz system can be divided into two independent methods, one is the study of the properties of equation solutions, numerical simulation by computer [13–15], and the other is chaotic water wheel physics experiment.

In Lorentz nonlinear dynamical system, the degree of randomness is generally determined by entropy. At present, in Lorentz nonlinear dynamical system, the determined entropy has no name, so we can call it Lorentz entropy for the time being.

The overall chaotic level of the system can be measured by the maximum Lyapunov exponent, which quantitatively describes the divergence rate of the phase volume exponent of the adjacent orbits of the system in the phase space. Although chaos is an irregular phenomenon, it comes from the deterministic system, so it is possible to predict it in a short term.

For Lorentz nonlinear dynamical systems, there is a relationship between Lorentz entropy and Lyapunov exponent. In chaotic one-dimensional mapping, a single Lyapunov exponent is consistent with Lorentz entropy.

An important quantitative method to judge whether the system is chaotic is whether there is a positive Lyapunov exponent. Lyapunov exponent is an important quantitative index reflecting the characteristics of dynamic system, which indicates the long-term average exponent of convergence or divergence between adjacent orbits of the system in phase space. For a time-delay dynamic system, its initial condition is a continuous function, so its Lyapunov exponent is related to the continuous function as the initial condition. The continuous function defined in the initial time period is uncountable, and so is the number of Lyapunov exponents of the system. Calculating Lyapunov exponents of time-delay dynamical systems is a complicated task. In the process of calculation, there may be some strange situations that make the results inaccurate. Therefore, judging whether the system is chaotic, as long as the maximum Lyapunov exponent is greater than zero, it can be used as a reliable basis for the existence of chaos.

The following diagram shows the transformation of the maximum Lyapunov exponent with parameters in the chaotic waterwheel experiment of Lorenz typical system. It can be seen that when the parameter reaches 15, the maximum Lyapunov exponent is positive, resulting in chaos.

#### *2.5.2 Brief introduction of chaotic waterwheel device*

As shown in **Figure 3**, the chaotic waterwheel device is similar to the ancient waterwheel, with a constant water flow at the top of the waterwheel injected into the water cup hanging on the edge of the wheel. There is a small hole at the bottom of each cup that can constantly discharge water. If the water flow speed on the top is very slow, the water in the top cup is small, so the friction force of the axle cannot be overcome, and the water wheel will not rotate; If the water flow speeds up, with the increase of water in the top cup, the water wheel will start to rotate at a constant speed; As the water flow continues to increase, the rotation will be chaotic, and the direction and speed of rotation will have complex motion characteristics due to the inherent nonlinearity of the system (**Figure 4**).

**Figure 3.** *Maximum Lyapnov exponential.*

*Perspective Chapter: On Rolling Bearing Fault Feature Extraction Based on Entropy Feature DOI: http://dx.doi.org/10.5772/intechopen.105095*

**Figure 4.** *Schematic diagram of chaotic water wheel experimental device.*
