## 4 Sample Preparation  
### Experiment Test  
Coupled with the increasing attention on vibration-based diagnosis and prognostics of rolling bearing, providing an open access databases is of more importance than ever before. There are so far several available datasets such as the Case Western Reserve University datasets (CWRU) [41] and University of Cincinnati datasets [42] that can be used to validate or improve the condition assessment and diagnostic techniques. In this paper, the vibration datasets from the CWRU data center are adopted. Vibration data was collected using accelerometers, which were attached to the housing with magnetic bases. Accelerometers were placed at the 12 o'clock position at both the drive end and fan end of the motor housing. Vibration signals were collected using a 16-channel DAT recorder. Speed and horsepower data were collected using the torque transducer/encoder and were recorded by hand.  
Figure 4a shows the test stand used for the CWRU datasets.  
The motor bearings are seeded with faults of 0.1778 mm, 0.3556 mm, 0.5334 mm, and 0.7112 mm in diameter introduced at the inner ring (IR), rolling element (RE), and outer ring (OR), separately. The data used in this paper are acceleration signals in the vertical directions on the bearing housing of drive end (DE) recorded by 12,000 samples per second at four rotation speeds: 1797, 1772, 1750,  
Figure 4: The test stand and structure of tested rolling element bearing of the Case Western Reserve University (CWRU) datasets: (**a**) The test stand of CWRU datasets; (**b**) Structure of the tested bearing in drive end.  
and 1730 RPM. Figure 4b illustrates the structure of the bearing in drive end with parameters in Table 1, where d, D, D\({}_{\text{B}}\), B, and D\({}_{\text{P}}\) denote inside diameter, outside diameter, ball diameter, thickness, and pitch diameter, respectively.  
Based on kinematic relationships assuming no slip, the bearing fault frequencies of IR, OR, and RE are as follows [6; 41],  
\[\text{IR}=\frac{nf_{r}}{2}(1+\frac{d}{D}\cos\phi), \tag{14}\]  
\[\text{OR}=\frac{nf_{r}}{2}(1-\frac{d}{D}\cos\phi) \tag{15}\]  
\[\text{RE}=\frac{Df_{r}}{2d}(1-[\frac{d}{D}\cos\phi]^{2}) \tag{16}\]  
where \(f_{r}\) is the shaft speed, \(n\) is the number of rolling elements, and \(\Phi\) is the angle of the load from the radial plane. Table 2 lists the bearing details and fault frequencies at the drive end as the multiple of shaft speed. Taking the raw signals collected at 1797 rpm as an example, we give the envelope signals and corresponding envelope spectrum with respect to IR fault, OR fault, and RE fault as Figure 5. The results show the fault frequencies as well as harmonics are in accord with theoretical analysis.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **d** & **D** & **D\({}_{\text{B}}\)** & **B** & **D\({}_{\text{P}}\)** \\ \hline Value (mm) & 25 & 52 & 7.94 & 15 & 39.04 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Bearing size at the drive end (unit: mm) [43].  
Figure 5: Envelope signal and corresponding envelope spectrum of raw signals at 1797 rpm with respect to (**a**) IR fault, (**b**) OR fault, and (**c**) RE fault.