# Bearing Severity Fault Evaluation Using Contour Maps--Case Study
## 2 Method
### Angular Speed Influence  
During this investigation, we observed that the turning speed is also an important parameter to consider in the representation of contour maps. [PERSON] et al. [53] emphasised the importance of keeping the rotational speed constant when capturing logs. Thus, by analysing vibrations at a constant angular velocity, repetitive impacts can be identified through the characteristic frequencies of the bearing. This criterion was applied in the analysis by means of contour maps, to eliminate frequency lags and variations in the impact force, as shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Study Factor**} & \multicolumn{5}{c}{**Levels**} & \multirow{2}{*}{**Units**} \\ \cline{3-6}  & & **F0** & **F1** & **F2** & **F3** & **F4** \\ \hline \multirow{2}{*}{RE} & Area & 0 & 11.05 & 11.57 & 11.7 & 13 & mm\({}^{2}\) \\  & Depth & 0 & 0.006 & 0.014 & 0.019 & 0.027 & mm \\  & Area & 0 & 25.874 & 28.928 & 31.983 & 33.241 & mm\({}^{2}\) \\  & Depth & 0 & 0.007 & 0.013 & 0.02 & 0.028 & mm \\ \hline \multirow{2}{*}{**Control Factor**} & \multicolumn{5}{c}{**Levels**} & \multirow{2}{*}{**Units**} \\ \cline{3-6}  & & **R1** & **R2** & **R3** & \\ \hline Regime & & 200 & 350 & 500 & rpm \\ \hline \hline \end{tabular}
\end{table}
Table 5: Factors and levels considered in the design of the experiment.  
Figure 6 represents the segment of the contour map associated with a fault, built with the records used in Figure 5. In this case, the entire length of the record (45 s) was used. Obviously, the registers have a variable speed of rotation in each second. Thus, the frequency represented in the contour map will be associated with the predominant turning speed which, as observed, was not equivalent between fault levels. Added to this was the large number of points used to construct the contour map, causing a loss of information between fault levels.  
Figure 5: Contour map of the evolution of a fault frequency, with variable speed of rotation.  
Figure 6: Contour map of the evolution of a fault frequency, with 45 s records and variable speed of rotation.  
For the identification of the segments at a constant speed, we carried out a scan of the signal of each record (time domain), which forms the contour map and the record to be analysed. Subsequently, the rotation frequency was identified in the envelope spectrum. Given that different rotation speeds are handled in this work, drawbacks were observed in establishing the same analysis section for all rotation regimes. For this reason, we proposed to determine the sweep section of the signal, based on the number of turns of the shaft. Observing that, regardless of the turning speed, for a number of 17.5 turns, the same turning frequency can be properly identified in each register. Table 6 presents the section of the register used in each rotation regime.  
Despite identifying register sections at a constant speed, it was necessary to consider the slip at the contact between the rolling elements and the races, which occurs during the operation of a bearing. This creates uncertainty in the identification of fault frequencies. [PERSON] and [PERSON] [54] considered a variation of the calculation of the frequencies between 1% or 2%, from which the following hypothesis can be established:  
_The maximum amplitude-frequency close to the theoretical fault frequency, in a range of \(\pm\) 1% of the theoretical frequency, corresponds to the actual fault frequency._  
From this, once the constant velocity sections have been identified--and considering the previously described hypothesis--the sections of each record were identified, where the actual failure frequencies coincided.