## 3 Materials and Methods
### Possible Mechanical Faults to Be Detected in PdM  
Mechanical faults that have the potential to cause a breakdown can be listed in two major categories according to their occurrence in the observable frequency range [2; 72; 73]:  
* Low frequency: Considering industrial machinery rotating in a speed range of 10-4000 rpm, mechanical faults that are directly associated with rotation frequency and its harmonics are considered here. These can be given as unbalance in the shaft or fan rotor, turbulence in rotating parts such as fan blades or pump vanes, imbalance of the motor stator/rotor, misalignment in the coupling of bearing races or pulleys, a soft foot, mechanical looseness, a bent shaft, eccentricity, and finally loose belts. Within the collected set of parameters, rotation speed (rpm or Hz) and overall velocity (mm/s) are used to classify these faults [74].
* Rest of the frequency range:
* Mid- and High-Frequency Range: Applying the same considerations on the machinery given at point 1, that is, bearing race defects such as cracks or pits producing periodic impulses exciting the entire frequency range and gear faults, bearing/gear wear and fatigue damage give rise to vibrations in the mid- and high-frequency range. Within the collected set of parameters, peak, peak acceleration, RMS acceleration, as well as Kurtosis are used to classify the faults listed hereby.
* Ultra-High-Frequency Range: Metal-metal contact due to a lack of lubrication, pressurized vapor, or fluid leak, as well as cavitation and subsurface cracks in bearings and gears, produces sound waves above the audible frequency range (>20 kHz). Within the collected set of parameters, the ultrasound RMS level (dB) is used to classify the faults in this category.  
The mechanical faults given in Table 2[3; 4; 6; 10; 69] were categorized according to the definitions given above. In any industrial machinery and its common rotating parts--such as bearings and gears--subsurface defects that might start to occur due to the low-frequency failures in point 1 will manifest themselves within the ultrasonic range, as high-frequency shock waves will be generated due to metal-metal contact. Detecting these faults in their early stages would provide a lead time for maintenance personnel. Categorization then proceeds with developed bearing or gear defects and finally ends with low-frequency defects related to shaft rotation.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Fault Category** & **Symptoms** & **Possible Root Causes** \\ \hline
0—Ultrasonic Level & Ultrasonic level rises. & Lack of Lubrication. \\ \hline
1—Ultrasonic Impulses & ULI and ultrasonic impulses. & Early stage of bearing or gear damage. \\ \hline
2—Wideband Vibration Impulses & ULI, UP, vibration frequency level increases, and vibration impulses in a wide frequency range. & Later stage of bearing or gear damage, wear, or cracks. \\ \hline
3—Vibration Impulses & Vibration frequency level increases, vibration impulses in a wide frequency range. & Later stage of rolling element bearing wear and gear wear. \\ \hline
4—High-Frequency Vibrations & Vibration signals occurring at a high-frequency band. & Gear damage and electrical motor problems such as loose rotor bars. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Fault category with symptoms and possible root causes.