## 4 Analysis of the Rolling-Bearing on an Experimental Bench  
Generally, the rolling-bearing is an important part of machinery. In the actual operation, the inner ring, the outer ring and rolling element parts are related to each other. Hence, there is a strong correlation between the different vibration sources. Limited by the testing experiment, one channel observation signal is monitored in normal conditions. In order to verify the validity of the proposed method in the experiment, this signal was used to detect the coupling faults of the inner and outer rings of a rolling-bearing. The experimental apparatus was provided by the experimental center of institute of mechanical automation in Wuhan University of Science and Technology, which is customized by the American SQi company. This apparatus was composed of a motor drive, encoder, and fault simulation of the two-level reduction gear box and load device. The specific device is shown in Figure 10.  
In this paper, the deep-groove ball bearing ER-16k (FAFNIR, Springfield, MA, USA) with faults on the outer and inner rings was simulated. According to the bearing parameters and the coefficient of the gear transmission ratio, the frequency of the inner ring and the outer ring of the bearing fault were calculated, which are listed in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline
**Rotating** & **Transmission** & **Output Frequency** & **Inner Ring Fault** & **Outer Ring Fault** \\
**Frequency** & **Frequency** & **Frequency** & **Frequency** \\ \hline \(f\) & 0.29\(f\) & 0.11\(f\) & 5.43\(f\) & 3.572\(f\) \\ \hline \end{tabular}
\end{table} 
Table 3: Main characteristic frequencies of the SQi simulation test table. Figure 10: Fault simulation experimental table for the rolling-bearing of a gear box. (**a**) The physical map of the test rig; (**b**) The structure diagram of the test rig: 1-motor, 2-encoder, 3-gearbox, 4-measured point and 5-load device. It is noted that \(f\) is the actual motor rotational frequency, which corresponds to the input shaft frequency. Motor rotating frequency was set to be 30 Hz. As the speed of the three-phase asynchronous motor will fluctuate, the measured rotating frequency is \(f=29\) Hz in reality. Hence, the characteristic frequencies of the inner and outer rings of the bearing can be calculated as \(f_{i}=157.47\) Hz and \(f_{o}=103.59\) Hz, which are shown in Table 4. The original time-domain waveform and frequency spectrum of the measured single-channel are shown in Figure 11.  
In order to perform the blind source separation of a single-channel composite signal in the experiment station, the RPSEMD was first employed to decompose the composite signal, with the mode components then being obtained. Subsequently, the original signal and the decomposed mode components were decomposed by SVD to obtain characteristic values, before the number of source \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rotating Frequency \(f\)/Hz** & **Inner Ring Fault Frequency \(f_{i}\)/Hz** & **Outer Ring Fault Frequency \(f_{o}\)/Hz** \\ \hline
29 & 157.47 & 130.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Characteristic frequencies of FAFNIR deep groove ball bearing. Figure 11: Time domain and frequency spectrum of a single channel composite signal. **(a)** The time response of a measured single channel vibration signal; **(b)** The frequency domain of measured single channel vibration signal. signals was determined by the method of BIC. Following this, the new observation signal was processed by the proposed blind source separation and the analyzed result is drawn in Figure 12.  
Figure 12a,b present the frequency spectrum of the estimated signal by the proposed method. From Figure 12a, the rotating frequency \(f_{r}\) and its double frequency \(2f_{r}\) can be inspected. In addition, the inner ring fault frequency \(f_{i}\), its double frequency \(2f_{i}\) and its third harmonic frequency \(3f_{i}\) can also be identified.