## 3 Validation
### Hybrid Ceramic Bearing Run-to-Failure Test Setup  
The hybrid ceramic bearing run-to-failure tests were performed using a bearing test rig in the laboratory as shown in Figure 5. The bearing test rig consisted of the following main components: (1) 3-HP AC motor with a maximum speed up to 3600 rpm and variable speed controller; (2) Hydraulic dynamic loading system with a maximum radial load up to 4400 lbs or 19.64 kN; (3) Integrated loading and bearing housing. The rig can be used for testing both ball and tapered roller bearings. An automatic data acquisition system was constructed using a National Instrument CI 4462 board (NI, Austin, TX, USA) and NI LabVIEW software (LabView 2012, NI, Austin, TX, USA). The automatic data acquisition system is characterized with the following key features: (1) Maximum sampling rate up to 102.4 kHz; (2) 4 Input simultaneous anti-aliasing filters; (3) Software-configurable AC/DC coupling and IPEE conditioning; (4) Vibration analysis functions such as envelope analysis, cepstrum analysis, and so on for computing necessary condition indicators. The tested hybrid ceramic ball bearing was a SMR6205C-ZZ/C3 #3 L55/MG2 type bearing by Boca Bearing Company (Boca Bearings, Boynton Beach, FL, USA). It consisted of stainless steel inner outer races, and ceramic balls. The bearing was mounted on the test rig. Two accelerometers were stunt mounted on the bearing housing in the direction perpendicular to the shaft. During the tests, the rig was run at a speed of 1800 rpm (30 Hz) and was subjected to a radial load of 600 psi. Vibration data were collected with a sampling rate of 102.4 kHz for two seconds at each sampling point. There was a 5 min gap between any two sampling points. At the end of the test, the test bearing was disassembled, checked, and photographed. The bearing data contained a total of 849 data files with a length of approximately 71 hours. Table 1 describes the run-to-failure test setting. Table 2 provides the specifications of the tested bearing. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test Bearing Name** & **Type of Bearing** & **Load (psi)** & **Input Shaft Speed** \\  & & & **(hz)** \\ \hline B2 & Hybrid ceramic bearing & 600 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The settings of the run-to-failure test. Figure 5: The bearing run-to-failure test rig. The root mean square (RMS) of the vibration signals was computed to represent the degradation of the bearing over time during the run to failure tests. The RMS at each time interval (denoted as \(RMS_{t}\)) can be calculated as follows:  
\[RMS_{t}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}f_{ti}^{2}} \tag{30}\]  
where \(f_{ti}\) represents the \(i\)th raw vibration data point at time interval \(t\) and \(n\) is the length of the signal at time interval \(t\). The RMS for the bearing data can be seen in Figure 6.  
For the bearing data, the \(RUL_{t}\) (remaining useful life at time \(t\)) was calculated simply by taking the time index of the maximum recorded RMS value as the point of failure denoted as \(RMS_{t_{end}}\) and subtracting it from each time step:  
\[RUL_{t}=RMS_{T_{end}}-t \tag{31}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Specification** \\ \hline Bearing material & Stainless steel 440c \\ Ball material & Ceramic SI3N4 \\ Inner diameter (d) & 25 mm \\ Outer diameter (D) & 52 mm \\ Width & 15 mm \\ Enclosure & Two shields \\ Enclosure material & Stainless steel \\ Enclosure type & Removable (S) \\ Retainer material & Stainless steel \\ ABEC/ISO rating & ABEC \#3/ISOP6 \\ Radial play & C3 \\ Lube & Klubber L55 grease \\ RPM grease (\(\times\)1000 rpm) & 19 \\ RPM oil (\(\times\)1000): & 22 \\ Dynamic load (kgf) & 1429 \\ Basic load (kgf) & 804 \\ Working temperature (\({}^{\circ}\)C) & 121 \\ Weight (g) & 110.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of the test bearing. Figure 6: The bearing RMS values.