## 4 Experiment  
### Experimental Setting  
In this section, an experiment was designed on a mechanical simulator to testify the proposed method. The used simulator was produced by Spectra Quest, Inc. (Richmond, VA, USA). and is illustrated in Figure 2. This simulator is driven by a 1 Hp AC motor, and its speed can range from 0 to 6000 rpm through the control of the matched converter. The power of the motor is transmitted to the shaft through a flexible coupling, and then the bearings and well-balanced rotor disc are driven. To realize the function of increasing the rotor weight and simulating an unbalanced fault, several tapped holes are symmetrically arranged in the edge of the rotor. The above mechanical parts include several accessories, both those that function normally and those with different faults. According to the literature [45], one of the key factors affecting mechanical running states is bearing detection. Therefore, only faulty bearings were installed in this test bench to simulate the different bearing working conditions to verify the proposed method. From Figure 2, we can also see that there are two housings: the one near the AC motor is defined as inboard bearing housing and the one far from the AC motor is named outboard bearing housing. The extreme case of simultaneous failure of both bearings was not considered in this paper, so only this bearing in outboard bearing housing was defined as the test bearing, and the other one was defined as normal bearing. Some key technical characteristics are shown in Table 1. Moreover, the test bench also includes a loading system; however, all of our simulations were performed under a no loading condition. For a bearing, its faults are usually appear in inner race, outer race, and rolling elements. Considering this, four bearing working states were set: normal (S1), inter-race fault (S2), ball fault (S3), and outer-race fault (S4). These above faults were artificially processed and are shown in Figure 3. To make the simulated faults as real as possible, the diameter and depths of these faults were 2 and 0.5 mm, respectively. When the vibration signal passed to the sensor, each intermediate transmission unit caused information loss. That is to say, the more the intermediate transmission units existed, the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Items** & **Type** & **Number of Rolling Elements** & **Pitch Diameter** & **Rolling Elements Diameter** \\ \hline Components & ER-12k & 8 & 1.318 inches & 0.3125 inches \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Some key technical characteristics of used bearings. Figure 2: Multi-function mechanical fault simulator: (1) AC motor, (2) sensor, (3) shaft, (4) rotor disc, (5) test bearing, (6) outboard bearing housing, (7) normal bearing, (8) inboard bearing housing, (9) flexible coupling, (10) converter. more the loss of information would be. Based on this issue, three ICP acceleration sensors (AC 240-1D), bought from the Connection Technology Center, Inc. (New York, NY, USA), were placed on each bearing housing, and they are shown in Figure 4. For each housing, two sensors, installed on the sides, were all in the \(X\) axis; the other one, installed on the top of housing, was in the \(Y\) axis. Therefore, a total of six identical sensors were considered in this work. In addition, data acquisition equipment, produced by Donghua Testing Technology Co., Ltd. (Jingjiang, China), was also used to collected vibration signals. This device has 16 channel data recorders and can collect signals from 16 sensors at the same time. Even though the max sampling frequency of each recorder is up to 256 kHz, the real used sampling frequency is only 2 kHz by considering that the rotational speed is 1800 rpm and main fault character frequencies are less than 1 kHz. Figures 5-8 illustrate the vibration signals of the six sensors installed on the above simulator.