## 2 Analysis Model and Experimental Verification
### Validation Experiment  
The accuracy of the model should be verified before analyzing the model. The analysis results of the vibration model of the ring block friction pair established in the previous section are shown in Figure 5. Figure 5a shows the low-speed operating condition vibration time-domain diagram extracted from the finite element software, and Figure 5b shows the startup process vibration time-domain diagram extracted from the finite element software.  
The validation experiment for loading is conducted using the UMT-TriboLab friction and wear testing machine (Figure 2a), and the Donghua 5922D dynamic signal testing and analysis system is used for data collection. The block is fixed onto the testing machine through a fixture, and the acceleration sensor obtains the acceleration signal during vibration by adsorbing it onto the fixture (Figure 2b).  
The validation experiment is also divided into two parts, which verify the accuracy of the low-speed operating condition and the startup process model. The first step is to validate the finite element model under low-speed operating condition. The machine applies a radial load of 50 N to the block, followed by a rotational speed of 50 rpm to the ring. The vibration data in the experiment are obtained through an acceleration sensor. Figure 6a shows the background noise signal, in which noisy signals already  
Figure 4: COF curve and speed loading curve of startup process.  
Figure 5: Vibration time-domain diagram: (**a**) low-speed operating condition; (**b**) startup process.  
appear. These signals are caused by internal vibration during operation of the testing machine after loading. Figure 6b shows the vibration noise signal. Compared with the background noise signal and the vibration noise signal, only new vibration noise signals appeared between 1500-2000 Hz (in the blue shading shown in Figure 6a,b), while the remaining signals can be considered as amplified signals of the background signal after loading the speed. By performing bandpass filtering on the vibration noise signal, the frequency domain diagram in Figure 6c is obtained. From Figure 6c, it can be seen that the peak frequency is 1785.2 Hz, which is considered as a frictional vibration signal of the interaction between the ring and block. Similarly, the frequency domain map extracted by finite element software is used for bandpass filtering to obtain the frequency domain map shown in Figure 6d. Through verification, the error of the low-speed operating condition finite element model is only 0.16%.  
The second step is to validate the finite element model of the startup process. The machine applies a radial load of 50 N to the block, followed by a rotational speed of 216 rpm applied to the ring. The verification process is similar to that previously described (Figure 7). Through verification, the error of the finite element model is only 3.16%.  
After verification, the error of the finite element model analysis results for low-speed operating condition and startup process is 0.16% and 3.16%, respectively. So it is believed that the model is accurate and reliable, and it is used to conduct subsequent factor impact analysis.  
Figure 6: Verification results of low-speed operating condition: (**a**) background noise signal; (**b**) vibration noise signal; (**c**) experimental vibration noise signal after bandpass filtering; (**d**) analyzed vibration noise signal after bandpass filtering.