# Bearing Fault Diagnostics Based on the Square of the Amplitude Gains Method
## 4 Experimental Results  
To better show the type and influence of the simulated bearing faults on the measured vibrations, the authors prepared an FFT analysis of all damage signals for 900 rpm. The frequencies of bearing 1207K, calculated for speed 900 rpm, are shown in Table 4:  
Figure 3: Ball bearing SKF 1207K: (**a**) undamaged; (**b**) with cut outer race; with the cut ball at the depthof: (**c**) 1 mm; (**d**) 2 mm; (**e**) 3 mm; (**f**) with cut inner race. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value [Unit]** \\ \hline Manufacturer’s model & 1207 EKTN9 \\ Outer diameter & 72 [mm] \\ Inner diameter & 35 [mm] \\ Outer ring periphery diameter & 60.9 [mm] \\ Inner ring periphery diameter & 47 [mm] \\ Width & 17 [mm] \\ Weight & 0.32 [kg] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of ball bearing SKF 1207K EXTN9 [90]. Based on the expected frequencies (Table 4) and the obtained frequency characteristics (Figures 4 and 5), the bearing faults are visible. However, the damages are not significant in the frequency characteristics, this is due to the narrow cut on the bearing elements. More significant bearing faults are visible in the amplitude change and new frequencies appearance [41]. However, the authors wanted to introduce minor damage. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value [Unit]** \\ \hline Rotational frequencies: & \\ Inner ring & 15 [Hz] \\ Outer ring & 0 [Hz] \\ Rolling element set and cage & 6.285 [Hz] \\ The rolling element about its axis & 44.581 [Hz] \\ Frequencies of over-rolling: & \\ A point on the inner ring & 130.72 [Hz] \\ A point on the outer ring & 94.28 [Hz] \\ Rolling element & 89.162 [Hz] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Frequencies of ball bearing SKF 1207K EXTN9 [90]. Figure 4: The FFT analysis of the recorded shaft displacement signal influenced by the vibration signal coming from bearing (drive side) SKF 1207K: (**a**) with cut inner race; (**b**) with cut outer race; with the cut ball at the depth of: (**c**) 1 mm; (**d**) 2 mm; (**e**) 3 mm. Upon determining the frequency characteristic, the analysis was carried out using a squared amplitude gain method. Examples of displacement signals of one shaft revolution obtained at the sampling frequency of 8192 Hz for each variant of bearing damage are shown in Figure 6.  
The recorded experimental signals included the course of shaft vibrations during rotation for 60 s after the stabilization of the set rotational speed. In addition, measurements were carried out for rotational speeds from 100 every 100 to 2000 rpm and for each damage variant. The shaft vibration signal from each sensor, containing many successive shaft revolutions, was divided into single revolutions. The analysis of the results was presented for the rotational speed of 900 rpm, and the signals were recorded for eddy current sensors located radially to the shaft in the vertical axis. For the exemplary speed of 900 rpm, 900 cycles were obtained, corresponding to the number of shaft revolutions per minute. In each analysis, the first and last cycles were discarded, assuming they could represent an incomplete shaft rotation. For each of the cycles, the procedure was performed following the description of the model (Section 2). First, the Hanning window was used, and then the signal autocorrelation was determined. Figure 5: The FFT analysis of the recorded shaft displacement signal influenced by the vibration signal coming from bearing (brake side) SKF 1207K: (**a**) with cut inner race; (**b**) with cut outer race; with the cut ball at the depth of: (**c**) 1 mm; (**d**) 2 mm; (**e**) 3 mm. The autocorrelation result was approximated by a polynomial, where the coefficient of determination R2 measured the level of the polynomial fit. Following some preliminary calculations, the order of approximating polynomials of the auto-correlation function was chosen as \(n=5\), which gives the coefficient of determination \(R^{2}>99.97\%\).