## 4 Diagnosis of Korea Aerospace University (KAU) Bearing Faults  
In this section, diagnosis is performed using the real vibration data made by the authors' test rig in the Korea Aerospace University (KAU). It is shown in Figure 12 which consists of DC motor, support bearings, and two roller bearings for the test. Vertical load is applied to the support bearing. The test bearing is given by NSK NJ 2306, with its geometry and dimensions in Table 1. Fault is seeded at the inner race with an artificially induced notch (0.2 mm depth, 0.3 mm width). The accelerometer is installed on top of the test bearing's housing using bolt to acquire the vibration signals. The test is performed under four different conditions as listed in Table 2.  
Figure 11: Result of envelope analysis: envelope signal in (**a**) time domain (**b**) frequency domain of faulty bearing, in (**c**) time domain and (**d**) frequency domain of normal bearing. In order to diagnose the bearing fault, the fault frequencies as stated in Equations (1)-(4) should be available. In practice, however, most of the bearing manufacturers do not provide the values of ball and pitch diameter. To solve this problem, a commercial bearing fault frequency calculator [33] is adopted in this study and the results are listed in Table 3. The bearing data are acquired through a sampling frequency of 51.2 kHz. In order to illustrate the process, the dataset for \"bearing 1\" is taken, which is operated with a rotating speed of 1200 rpm and a 0 N vertical load (note that the load by the weight of bearing housing still exists). Figure 13 shows the raw signal, of which the kurtosis is 4.9923. The four datasets listed in Table 2 can be downloaded from [[https://www.kau-sdol.com/](https://www.kau-sdol.com/)]([https://www.kau-sdol.com/](https://www.kau-sdol.com/)) and [[https://sites.google.com/view/sg-kim](https://sites.google.com/view/sg-kim)]([https://sites.google.com/view/sg-kim](https://sites.google.com/view/sg-kim)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Name** & **Value** & **Parameter Name** & **Value** \\ \hline Bearing type & NJ 2306 & Width (w) & 27 mm \\ Inner diameter (id) & 30 mm & Dynamic load rating & 51,500 N \\ Outer diameter (od) & 72 mm & Static load rating & 51,000 N \\ Number of rollers (\(n\)) & 11 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Bearing dimensions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Data Name** & **RPM** & **LOAD** \\ \hline bearing 1 & 1200 rpm & 0 N \\ bearing 2 & 1200 rpm & 200 N \\ bearing 3 & 1000 rpm & 0 N \\ bearing 4 & 1000 rpm & 200 N \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Operating conditions. Figure 12: Korea Aerospace University (KAU) bearing test rig. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency Name** & **Value** & **Frequency Name** & **Value** \\ \hline BPFO & \(4.4423\times f_{r}\) & FTF & \(0.4038\times\mathrm{f_{r}}\) \\ BPFI & \(6.5577\times f_{r}\) & BSF & \(5.0079\times\mathrm{f_{r}}\) \\ \hline \hline \end{tabular} \(f_{r}:\) shaft rotating speed [Hz].  
\end{table} 
Table 3: Bearing fault frequencies. The raw data for bearing 1 are loaded by the name bearing1. Referring to Table 2, sampRate and rpm are set at 51.2e3 and 1200, respectively. Bearing fault frequencies are assigned in bearFreq, which is [4.4423 6.5577 0.4038 5.0079] for BPFO, BPFI, FTF, and BSF, respectively, based on Table 3. The maximum order of the AR model maxP is set at 390 based on the ratio of the sampling frequency versus the highest fault frequency (51200/(6.5577*1200/60)) as mentioned before. Vector of the window lengths windLeng for STFT are given by [2^4 2^5 2^6 2^7 2^8] under the constraint of maximum length being smaller than maxP (390). As a result, the commands in the Problem definition (lines 1-7) are modified as follows:  
- Line 2: rawData = load('bearing1');  
- Line 3: sampRate = 51.2e3;  
- Line 4: rpm = 1200;  
- Line 5: bearFreq = [4.4423 6.5577 0.4038 5.0079]*rpm/60;  
- Line 6: maxP = 390;  
- Line 7: windLeng = [2^4 2^5 2^6 2^7 2^8].