## 3 Experimental Setup
The bearing used for the simulations of the two types of fault were different. Their main characteristics are reported in Table 2.  
The single-point defect on the outer ring of the bearing gives rise to characteristic harmonics on the vibration spectra expressed by:  
\[f_{o}=BPFO=N/2\cdot f_{r}(1-d/D\cdot cos\alpha) \tag{7}\]  
where \(BPFO\) stands for Ball Pass Frequency Outer, referring to a fault in the outer ring; \(N\) is the number of bearing balls; \(f_{r}\) is the motor rotational frequency in hertz, \(d\) and \(D\) are the ball and pitch diameters, respectively; and \(\alpha\) is the ball contact angle. In the electromagnetic signals, the characteristic harmonics are visible as sidebands of the supply frequency:  
\[f_{p}=|f_{s}\pm kf_{o}| \tag{8}\]  
where \(k\) is a positive integer and \(f_{o}\) is calculated from (7). Regarding the generalized roughness, it does not manifest harmonics at specific frequencies, but the spectra of vibration and stator current of the machine change in an unpredictable way, often giving rise to broadband harmonic excitation [56]. For the tests with generalized roughness, two fault severity levels were used in addition to the healthy measurements, considered as the baseline; Step 1 and Step 2 faults were generated through the use of acid corrosion wear as described below. Step 1 represents an early stage; the bearing was disassembled and all balls were degreased and immersed for 30 min in a solution composed of 5 mL of concentrated sulfuric acid (96%) dissolved in 50 mL of water. Step 2 represents an advanced stage; all balls were immersed for 70 min in \begin{table}
\begin{tabular}{c c} \hline
**Features** & **Values** \\ \hline Bandwidth & 0–50 MHz \\  & 25 A DC \\ Current-carrying capacities & 17.7 A rms \\  & 50 A peak \\ Typical precision & 1\% of the measured value \\ Sensibility & 5 mA \\ \hline \end{tabular}
\end{table} 
Table 1: Features of the Tektronix TCP (Transmission Control Protocol) 305 current sensor. \begin{table}
\begin{tabular}{c c c c} \hline
**Bearing Model** & **Fault Simulated** & **Number of Balls** & **Ball Diameters** \\ \hline NSK 6205Z & Single-point defect & 9 (single row) & d \(\cong\) 7.9 mm \\ SKF 1205 ETN9 & Generalized roughness & 26 (double row) & d = 7.45 mm \\ \hline \end{tabular}
\end{table} 
Table 2: Main characteristics of the bearings used. a solution identical to that of Step 1. A representation of the balls worn by the acid solution and the localized fault is reported in Figure 3.  
The single-point defects consisted of a localized crack in the outer ring of the bearing in four different angular positions; the angular position of the defect was marked as an hourly index, as shown in Figure 4. The analyzed fault locations were at hours 12, 3, 4.5, and 6, and in the following, they will be denoted by H12, H3, H45, and H6, respectively. The acquisition parameters for each case are shown in Table 3. Each case analyzed was composed of several acquisitions to obtain measurements distributed over a longer time period for the purpose of thermal stability and for calculating the mean of the spectra to reduce noise as in previous works, such as in [52; 54]. The exact number of the acquisitions could change from 40 to 80 for each class depending on the particular test carried out. The number of images are presented in the following section, in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{N}^{\circ}\) of Sample for Each Acquisition & **Acquisition** & **Achievable FFT** & **Number of Acquisition** & **Time of the Whole Set** \\ \hline \(2^{20}=1\),048,576 & 120 kHz & 0.115 Hz & 40 & 40 \(\times\) 8.73 = 349 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Characteristics of each set of acquisitions. Figure 4: The different hour locations of the single-point defect analyzed. The crack positions considered are circled in light blue. Figure 3: Representation of the wear for the fault of generalized roughness: (**a**) baseline, (**b**) step 1, (**c**) step 2.