## 4 Simulation and Experiment Validation  
### Experimental Procedure  
To validate the effectiveness of the fault dynamics model studied in this article, the vibration signal acquisition experiment of rolling bearing inner ring spalling fault was carried out on the bearing vibration signal acquisition test bench, as shown in Figure 11. The experimental equipment includes a shaft with a shaft diameter of 1/2 inch, which is connected to a load motor through a flexible coupling to avoid the influence of motor vibration on the experimental results, a bearing pedestal for fixing the bearing, and a vibration signal collection sensor. The outer ring is fixed in the bearing seat; the inner ring is in an interference fit on the shaft and rotates with the shaft. The coupling connects the motor to the shaft, and the sensor is fixed at the top of the bearing seat. The sampling frequency is 102.4 kHz and processed utilizing MATLAB (R2022b) software. The experimental results are shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vibration** & **Axial Position** & \multirow{2}{*}{**Axial Position \(\tau\) = 15\({}^{\circ}\)**} & **Year-on-Year** \\
**Direction** & \(\tau\) = 0\({}^{\circ}\) & & **Growth** \\ \hline x & 0.2590 & 0.1997 & \(-\)22.9\% \\ y & 0.1113 & 0.1113 & 0\% \\ z & 0 & 0.615 & ++ \\ \hline \hline \end{tabular}
\end{table}
Table 2: Root mean square comparison of simulated vibration signals.  
Figure 10: Simulation results of fault axial position 15\({}^{\circ}\).  
In order to avoid randomness in the experiment, several bearingss with the same type of fault were selected, and these bearingss came from the same factory batch. Conduct multiple experiments and select the optimal experimental results for comparison with simulation results. The type of deep groove ball bearing used in the experiment is 6205, and the specific parameters are shown in Table 1. Processing is carried out at the center position of the inner raceway by drilling, and the peeling axial position is \(\tau=0^{\circ}\) as shown in Figure 11(a). Processing is carried out at the non-center position of the inner raceway by drilling, and the peeling axial position is \(\tau=15^{\circ}\), as shown in Figure 11(b). \(\tau\) is the position angle of the peeling path relative to the center of the rolling body. Both spalling fault size parameters are the same, with a diameter of 2 mm and a depth of 0.5 mm. The experimental results were shown in Figure 13.  
Figure 13 shows the time domain of the measured vibration signal in x, y, and z at \(\tau=0^{\circ}\) and \(\tau=15^{\circ}\) at the experimental stage. From the figure, it can be seen that the amplitude fluctuations of the measured signal exhibit periodicity similar to the simulated signal. When the peeling fault occurs in the center area of the raceway, the axial impact generated is relatively small. While the axial impact generated in the non-center area of the raceway increases, the vibration signal strength in the x-direction decreases, and the vibration signal in the y-direction is not affected.  
Figure 11: Bearing vibration signal acquisition experimental platform.  
Figure 12: Physical picture of bearing with inner ring peeling off.