## 4 Design of Faulty Bearing Experiment Platform  
The bearing fault monitoring experiment platform is built with UG software. It mainly includes a drive motor, a coupling, a bearing 1, a bearing 2, a fiber Bragg grating resonant sensor, a fiber Bragg grating demodulator, and a computer, as shown in Figure 6.  
The fiber Bragg grating resonant sensor is fixed on bearing 1 and is used to detect shock vibration signals. Bearing 1 is a test bearing, and bearing 2 is a symmetrical support bearing. The diameter of the rotating shaft at the output end of the drive motor is 20 mm. The shaft diameter is 35 mm. The coupling is used to connect the drive motor and the shaft to transmit power and buffer the excessive instantaneous speed difference. When the sensor detects the bearing vibration, the fiber Bragg grating is deformed by force. When a bearing component has a fault and a small shock occurs, the sensor absorbs the shock energy to generate a generalized resonance wave, and releases energy at the natural frequency of the sensor. The vibration signal is collected by fiber Bragg grating, and then the change of  
Figure 4: Bearing fault detection process.  
Figure 5: Bearing fault identification process.  
central wavelength is read by the demodulator. Finally, the collected data is analyzed by computer to diagnose whether the bearing is faulty.  
Based on fiber Bragg grating resonant sensor, signal coupling caused by electromagnetic interference can be effectively avoided, and micro shock monitoring can be realized. The sensor has the advantages of high sensitivity, good stability, small volume, convenient installation, etc.  
The sampling rate of the fiber Bragg grating resonant sensor is 200 KHz and the natural frequency is 6325 Hz. This frequency belongs to the high-frequency, which can effectively avoid the influence of low-frequency interference during the bearing rotation process [30].  
The bearing model selected in the experiment is Harbin bearing 7307. The number of rolling elements is 8, and the contact angle is 0\({}^{\circ}\). The outer ring diameter and the inner ring diameter of the bearing are 80 mm and 35 mm. The diameter of the rolling element is 14.5 mm. The pitch diameter of the bearing is 57.5 mm. The motor rotates at a constant speed and the speed is 300 rpm (5 Hz).  
Substituting the bearing parameters into the formula in Table 1, the fault characteristic frequencies of four parts can be obtained.  
Table 1: Z is the number of rolling elements, \(\propto\) is the angle between the force direction of the rolling element and the vertical line of the inner and outer raceways, \(f_{\text{s}}\) is the rotation frequency of the bearing, \(d\) is the average diameter of the rolling elements, and D is the pitch diameter of the bearing and the spherical center distance of the two rolling elements on the same line.  
In order to simulate the fault of the bearing in actual operation, a small incision with a width of 0.5 mm is produced in the inner ring of the bearing, as shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Fault Type** & **Formula** & **Fault Characteristic Frequency** \\ \hline Inner Ring & BPFI/BPFO = \(\frac{1}{2}\)Z\(\left(1\pm\frac{d}{D}\cos\alpha\right)\)\(f_{\text{s}}\) & 25 Hz \\ \hline Outer Ring & BPFO = \(\frac{1}{2}\)Z\(\left(1-\frac{d}{D}\cos\alpha\right)\)\(f_{\text{s}}\) & 15 Hz \\ \hline Rolling Element & BSF = \(\frac{D}{d}\left(1-\left(\frac{d}{D}\right)^{2}\cos^{2}\alpha\right)\)\(f_{\text{s}}\) & 18.57 Hz \\ \hline Cage & FTF = \(\frac{1}{2}\)\(\left(1-\frac{d}{D}\cos\alpha\right)\)\(f_{\text{s}}\) & 1.87 Hz \\ \hline \hline \end{tabular}
\end{table}
Table 1: The calculation formula of bearing fault characteristic frequency.