## 5 Diagnosis of CWRU Bearing Faults  
Vibration data provided by the Case Western Reserve University (CWRU) Bearing Data Center are employed [36; 37] to demonstrate another application of the diagnosis code. In this case, artificial faults ranging in diameter from 0.007 to 0.028 inches were seeded with the electro-discharge machining (EDM) on drive-end (SKF 6205-2 RS JEM) and fan-end (SKF 6203-2 RS JEM) bearings. During the tests, data were collected at 12 and 48 kHz sampling rates for several datasets. Test bearings were driven with different rotation speeds ranging from 1797 to 1720 rpm. Accelerometers were installed on three  
Figure 16: Frequency domain of envelope analysis. Figure 15: Demodulation band selection for data of bearing 1: (**a**) spectral kurtosis, and (**b**) vibration signal after band-pass filtering. different locations: on the drive-end bearing (DE), the fan-end bearing housing (FE), and the motor supporting base plate (BA). Among others, this paper considers the bearing with inner race fault on the fan end. Geometry information and fault frequencies of the bearings are listed in Table 4 (the number of rolling elements and contact angles are not provided directly, and they are calculated by using the suggested fault frequencies), and the sampling rate and rotation speed are 12 kHz and 1796 rpm, respectively. The data are also available with the name \"bearing 270\" (the original data was rescued with two variables: vib for vibration data, and t for measuring time in rawData) at [[https://www.kau-sdol.com/](https://www.kau-sdol.com/)]([https://www.kau-sdol.com/](https://www.kau-sdol.com/)). Further details regarding the data and test rig can be found in references [36; 37]. Based on the information provided by the literature, the code to test the bearings is changed as follows:  
- Line 2: rawData = load ('bearing270');  
- Line 3: samRate = 12e3;  
- Line 4: rpm = 1796;  
- Line 5: bearFreq = [3.053 4.947 0.382 1.994]*rpm/60;  
- Line 6: maxP = 82;  
- Line 7: windLeng = [2^4 2^5 2^6]. In line 6, since the highest fault frequency is BPFI with 148.0802 Hz (4.947*1796/60), the maximum order of the AR model should be 82 (12000/148.0802), which is the number of data within a fault interval. In line 7, window lengths are set based on the criteria mentioned in Section 3.3. The results are shown in Figure 17. Based on the visual inspection of spectral kurtosis in Figure 17a, [5.3e3 5.9e3] Hz is selected in the command window for the demodulation band selection. After band-pass filtering by this interval, the results of the envelope analysis are shown in Figure 17b, which shows a dominant peak at BPFI (148.08 Hz) and sidebands with harmonics at the interval of shaft frequency (29.93 Hz), convincing that the bearing has inner race fault. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Name** & **Value** & **Parameter Name** & **Value** \\ \hline Pitch diameter (D) & 1.122 inch & BPFO & 3.0530\(f_{r}\) \\ Ball diameter (d) & 0.2656 inch & BPFI & 4.9469\(f_{r}\) \\ Number of rolling element (n) & 13 & FTF & 0.3817\(f_{r}\) \\ Contact angle (\(\alpha\)) & 0 & BSF & 1.994\(f_{r}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Bearing information. Figure 17: Results obtained from the code: CWRU bearing data (bearing280.mat) (**a**) Spectral kurtosis for bearing 270, and (**b**) Envelope spectrum after SK filtering. As a supplementary explanation, the effects of each step in the signal preprocessing are also demonstrated in Figure 18, in which the envelope analysis are carried out to the raw signal (a) and to the residual signal that went through the AR filtering (b), respectively. In Figure 18a, the peak at BPFI in the spectrum is apparent but is smaller than the others, which is doubtful of the fault. Another peak appeared at BSF (59.69 Hz) also does not give us the confidence because it coincides with the harmonic of shaft frequency, which are the multiples of 29.93 Hz.