## 3 Numerical Simulation  
The type of the FCBB in the simulation is selected as 6304, and the parameter table is shown in Table 1. The radial load is \(F_{\mathrm{r}}\) = 50 N. The crack length-outer ring thickness \(e\) is set as \(e\) = 0-0.8 mm, and the step is 0.2. The spindle speed is set to 1800 r/min. The fourth-order Runge-Kutta algorithm is used to solve the differential equation, and the vibration displacement responses of the outer ring with different crack sizes are analyzed. According to Equations (1) and (2), the change of stiffness weakening coefficient is obtained. In order to quantify the subsurface mesoscale cracks more easily, the crack length-outer ring thickness \(e\) = \(d/a\) is selected as an indicator. To quantify the change in the stiffness weakening factor more intuitively, the absolute value of the change rate \(\left\lvert\,h\,\right\rvert=\left\lvert\,\Delta\mu/\Delta e\,\right\rvert\) is shown in Figure 7.  
As shown in Figure 7, the bearing outer ring stiffness weakening coefficient first shows a slow decline, then has a sharp decline, and finally comes to stabilization. At the stage of \(e\) = 0-0.18, the mesoscale cracks start to appear on the outer ring, the stiffness of the outer ring starts to be weakened by the appearance of mesoscale cracks, and the stiffness weakening curve decreases slowly. With the increase of the crack depth, the stiffness \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Numerical Value** \\ \hline Outer diameter of bearing outer ring (mm) & 52 \\ Inner diameter of bearing outer ring (mm) & 46 \\ Inner diameter of bearing inner race (mm) & 20 \\ Outer diameter of bearing inner ring (mm) & 26 \\ Bearing radial clearance (\(\mu\)m) & 2 \\ Bearing width (mm) & 15 \\ Contact angle (\({}^{\circ}\)) & 0 \\ Number of rolling elements & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters of FCBB. Figure 6: Calculation flow chart. The contact stiffness of the outer ring becomes smaller due to the existence of subsurface mesoscale cracks. The contact force between the rolling element and the inner raceway of the bearing outer ring fluctuates, so an additional displacement appears in the fault area. In the process of crack depth change, three representative depths with \(e\) = 0.2, 0.4, and 0.8 are selected to observe the effect of mesoscale cracks on the FCBB dynamic response. The time-domain signals with healthy outer ring and with outer ring cracks are obtained by numerical simulation. In the time-domain signal, a signal peak appears near the small value between the maximum value and the minimum value, which presents a periodic impact phenomenon, as shown in Figures  
It is seen from the results that when there is no fault in the bearing, the dynamic response is close to sinusoidal, and the contact force between the rolling element and the inner raceway of the outer ring of the bearing is periodic and fluctuates with equal amplitude. When the mesoscale crack starts to make impact, there are obvious periodic impacts with small peaks, and the contact force between the rolling element and the inner raceway of the outer ring of the bearing is periodic and fluctuates with unequal amplitude. The amplitudes of the overall vibration and the small wave peak rise with the increase of crack depth, which indicates that the crack length has a significant effect on the motion of the outer ring of the FCBB. As a result, the presence of small wave peak in the time-domain signal can be used as the evaluation criterion of subsurface mesoscale crack faults in the FCBB outer ring. However, the small wave peaks in the time domain are not obvious enough, and are likely to be covered by strong noise in actual measurement. In order to make a more accurate quantitative analysis of the crack in the outer ring of FCBB, the fast Fourier transform (FFT) and the empirical modal decomposition (EMD) method is carried out in the processing of the time-domain signal.