# Rolling Bearing Incipient Fault Detection Based on a Multi-Resolution Singular Value Decomposition
## 5 Experiment Studies  
In order to verify the effectiveness of the MRSVD method in practical application, vibration signals of the outer race fault rolling bearing were collected from the experimental setup shown in Figure 8. The signal from the sensor (ICP\({}^{\text{R}}\) accelerometer, model 623C01) is fed to an NI data acquisition module (NI USB-6212 BNC) and is recorded by the computer with the LABVIEW software. The sampling frequency is 20 kHz and acquired data length is 40 k. The fault characteristics of incipient failure are not obvious; the periodic shock vibration associated with faults is often drowned in the background noise and the harmonic interference. Therefore, a more challenging condition is created at the experiment; the sensor signal conditioner is removed. Hence, the raw signal from sensor is not altered and not amplified. Obviously, the signal collected in this way is less clean and is considered more realistic. In the raw data, the interference, such as the power line frequency around 60 Hz, cannot be ignored. The background noise will be more obvious. For example, the noise caused by casualization error of the NI data acquisition module is inevitable and becomes relatively stronger when the raw signal voltage of the accelerometer output is very low. The ER16K ball bearings, manufactured by Rexnord Industries, are used throughout the experiments. The bearing parameters are shown in Table 3. The outer race fault is in the top position, see Figure 9. In Table 3, the Ball Pass Frequency Outer Race (BPFO) and \(f_{\text{r}}\) terms represent the characteristic frequency of outer race failure and the rotation frequency of the rotating shaft, respectively. To be specific, the frequency of the rotary shaft rotation frequency \(f_{\text{r}}\) is the resonance harmonic signal caused by the imbalance of the rotary table. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Roll diameter** & **Pitch diameter** & **Number of rolls** & **BPFO** \\ \hline ER16K & 7.94 mm & 38.52 mm & 9 & 3.572 \(f_{r}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The related parameters of the outer fault bearing. Ball Pass Frequency Outer Race (BPFO). Figure 8: The test rig. Figure 9: The fault bearing used in the experiment. The ER16K ball bearings, manufactured by Rexnord Industries, are used throughout the experiments. The bearing parameters are shown in Table 3. The outer race fault is in the top position, see Figure 9. In Table 3, the BPFO and \(f_{\tau}\) terms represent the characteristic frequency of outer race failure and the rotation frequency of the rotating shaft, respectively. To be specific, the frequency of the rotary shaft rotation frequency \(f_{\tau}\) is the resonance harmonic signal caused by the imbalance of the rotary table. The rotation speed of the rotation axis was 1440 rpm, so \(f_{\tau}\) = 12 Hz and BPFO = 85.728 Hz. The time domain waveform and the Hilbert envelope demodulation spectrum of the collected vibration signal with the noise and the resonance interference are shown in Figure 10a,b. For Figure 10b, the display interval of the coordinate axis is reduced, and a detailed graph is obtained in order to see the details shown in Figure 11. The resonant frequency of 24 Hz and the power line frequency of 60 Hz can be clearly seen in Figure 11. However, the failure characteristic frequency of the bearing outer race cannot be seen. The measured signal shown in Figure 10a is decomposed by MRSVD. The time domain waveform and the Hilbert envelope demodulation spectrum of the detail signal with the maximum kurtosis value are displayed in Figure 12a,b. The periodic shock oscillations with single-sided attenuations which were caused by the bearing failure can be seen in Figure 12a. The characteristic frequency of the outer race failure (BPFO) and its double are highlighted in Figure 12b. The five detail signals with maximum kurtosis values obtained using MRSVD decomposition are plotted in Figure 13d1-d5.