# Bearing Severity Fault Evaluation Using Contour Maps--Case Study
## 2 Method  
The main objective of this method is to build health maps for bearings, which allow for the efficient and accurate assessment of the severity of a fault. For this purpose, the variation of vibration amplitudes is characterised (by means of envelope analysis) for each characteristic frequency of a bearing (i.e., fundamental frequencies) and harmonics. In other words, in this study, bearing health maps are constructed, considering the effect caused by each type of failure (fundamental frequencies) on the power content of the signal. For this, the use of Contour Maps is proposed, which allows us to compact the information and better understand the footprint generated in fault evolution. The main phases of this method are presented below:  
1. The sensing of the equipment under analysis and acquisition of vibration records for different fault levels (\(F0\), \(F1\),..., \(Fn\)), marking the life history of the bearing. We obtained a record for each fault level in the time domain, \(R_{F0}(t),\ldots,\ R_{Fn}(t)\). This study presents the creation of the life history of a bearing located on a test bench [16], considering four failure levels (\(n=4\)) and the normal state, as described in Section 2.2. The extraction of representative samples of records that were taken in Phase 1 (Section 2.3). 1. The determination of the sample time length, \(l(s)=\frac{number\ of\ turns}{w(\ trips)}\). 2. The division of the signal into intervals by means of a sliding window, with the sample length calculated in (2.a). 3. The identification of intervals with constant angular velocity for each fault level. 4. The selection, among the time intervals identified in (2.c), of the intervals with both constant angular velocity and fault frequency (BPFO, BPFI, BSF, FTF). The first interval that accomplishes these conditions is the selected one. This procedure will allow for consideration of the possible slippage between the contact of rolling elements and the inner and outer races. 3. A pre-processing stage, which will be applied to each fault level's selected time interval, (Section 2.4). 1. Frequency band selection in the presence of transient events associated with bearing fault modes. 2. Signal filtering using the selected frequency band, obtaining a time-domain filtered signal (2.a). 3. Signal envelope extraction (time domain), from the signal of (3.b). 4. Envelope Spectrum (frequency domain), from the signal (3.c). 4. The processing and construction of the Contour map of the Envelope Spectrum, representing the fault level, frequency and amplitude (associated to 3d). 1. Consideration of the threshold value calculated with the spectrum to be diagnosed 5.a, \(E(NR)\), as described in Section 2.5.1. 2. The identification of the upper limit associated with the highest amplitude frequency of the envelope spectrum used in the construction of the contour map, \(E(R_{F0})\), \(E(R_{F1})\),..., \(E(R_{Fn})\), as described in Section 2.5.2. 3. Contour interval estimation (Section 2.5.3). 4. The calculation of the values of the isolines (Section 2.5.4). 5. The treatment of the new record, \(NR(t)\), or record to be diagnosed (the new record will also be subjected to the criteria stipulated in Phases 2 and 3). 1. The determination of the threshold value or isoline of the lowest value (Section 2.5.1). 2. The identification of the analysis points or points of intersection between the amplitudes of the spectrum to be diagnosed and the isoline values (Section 2.6). 6. Diagnosis of the failure level of the new record (\(NR\)), using the contour map created in Phase 4 of the proposed method. The abbreviations indicated in the description of the method and variables used in the construction of the contour maps and the bearing diagnosis are expressed in the form of nomenclature in Table 1.  
The method described above, based on six main phases, is detailed in Figure 1.