# Early Warning Signals for Bearing Failure Using Detrended Fluctuation Analysis
## 2 Experimental Platform and Vibration Data Sets
### Vibration Data Sets  
In this work, accelerated degradation tests were conducted on 17 ball bearings running in the experimental platform PRNOOSTIA. There are several conditions that may cause a failure in a bearing, including high running speed and excessive dynamic loading. In these tests, several loads greater than or equal to the maximum dynamic load (4000 N) were applied to different bearings. All the operating conditions of the bearings are shown in Table 2. Since the experimental data are extracted from the laboratory tests instead of the real-life field, the need for different considerations (de-noising, time synchronous averaging, and order tracking) is minimal.  
\begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{2}{c}{**Characteristics**} & **Value** \\ \hline Bearing type & NSK 6804 DD \\ Basic dynamic load rating (N) & 4000 \\ Basic static load rating (N) & 2470 \\ Limiting speed (rpm) & 13,000 \\ Sealant & rubber sealed (DD) \\ Inner/outer ring material & steel \\ Lubricant & grease \\ \hline \hline \end{tabular}
\end{table}
Table 1: Technical data of the ball bearings.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multicolumn{3}{c}{**Operating Conditions**} \\ \cline{2-4}  & **Condition 1** & **Condition 2** & **Condition 3** \\ \hline Synchronous motor rated power (W) & 250 & 250 & 250 \\ Running speed of synchronous motor (rpm) & 2830 & 2830 & 2830 \\ Applied torque (primary shaft) (N.m.) & 0.843 & 0.843 & 0.843 \\ Running speed of secondary shaft (rpm) & 1800 & 1650 & 1500 \\ Transferred torque (secondary shaft) (N.m.) & 1.326 & 1.447 & 1.591 \\ Bearing running speed (rpm) & 1800 & 1650 & 1500 \\ Radial load (N) & 4000 & 4200 & 5000 \\ \hline \hline \end{tabular}
\begin{tabular}{l c c c} \hline \hline  & Bearing 1\_1 & Bearing 2\_1 & Bearing 3\_1 \\  & Bearing 1\_2 & Bearing 2\_2 & Bearing 3\_2 \\  & Bearing 1\_3 & Bearing 2\_3 & Bearing 3\_3 \\ Data sets & Bearing 1\_4 & Bearing 2\_4 & \\  & Bearing 1\_5 & Bearing 2\_5 & \\  & Bearing 1\_6 & Bearing 2\_6 & \\  & Bearing 1\_7 & Bearing 2\_7 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Operating conditions of the different data sets.  
Figure 2: Detailed labeling of the experimental platform and the ball bearing dimensions.  
All the bearings were running under a radial load greater than or equal to the maximum dynamic load (4000 N) to accelerate the degradation process. Even though several other factors (lubricant degradation, wear debris, high temperature, etc.) may play a role in bearing degradation, especially at the final stage before the failure, the dynamic overloading of the bearing is the dominant factor in the degradation. During these tests, the vibration data of the bearing were only monitored via the horizontal and vertical accelerometers. In the future, it would be interesting to monitor other factors, such as subsurface stresses and lubricant condition [20; 21; 22], and study their effect on the vibration data.  
The vibration data of a rolling bearing can be measured via displacement, velocity, or acceleration sensors. In this paper, the vibration data sets were measured using an accelerometer (DYTRAN 3035B). The sampling rate of the accelerometer was 25.6 kHz and the data were measured for 0.1 s duration every 10 s. The accelerometer is a device capable of measuring bearing vibration using acceleration. The main advantages of the accelerometer are its lightweight and compact design, and wide-range frequency response. However, it is known to have higher sensitivity at high frequencies compared to low frequencies. On the other hand, the underometer measures bearing vibration using a velocity sensor [23]. It can overcome the accelerometer's disadvantages by working at low signal magnification and measuring at low frequencies up to 30 Hz [24].