# Bearing Fault Diagnostics Based on the Square of the Amplitude Gains Method
## 4 Experimental Results
Adoption of the lower orders of polynomials leads to lower values of the coefficients of determination (i.e., less accurate approximations). Higher orders do not noticeably improve the approximation accuracy (because it is already close to 1), but they significantly extend the calculation time and the number of coefficients to analyze. Examples of auto-correlation functions and their fifth-order polynomial approximations in two observation zones of the selected cycle of the rotor displacement signal (from Figure 1) are shown in Figure 7.  
The damage map of the bearing technical condition consists of the 30 cycles, randomly selected (which is a statistical sample) from all (for a speed of 900 rpm, 900 cycles) recorded cycles, for a given speed. It is expected that the damage maps obtained for each draw will  
Figure 6: The recorded shaft displacement signal influenced by the vibration signal coming from the bearing: (**a**) from the brake side; (**b**) from the drive side. Figure 7: Auto-correlation signal for the rotor supported on the SKF 1207K bearing (with the ball cut on a depth of 1 mm) with the matching curve: (**a**) during the observation period \(T_{01}\); (**b**) during the observation period \(T_{12}\). give the same picture of the technical condition of the bearing (which will confirm the method's effectiveness). First, a damage map was created for the undamaged bearing. The diagnostic thresholds set for it were the reference thresholds used for damaged bearings. The damage map contains 30 rows marked with numbers of randomly selected cycles and 12 columns, which consist of coefficients of 5 th-order polynomials (six coefficients each) for the numerator and denominator of the model. Comparing the model results for different damage variants is possible, using only the same degree of the matching polynomial. The numbers of the damaged bearings cycles were the same as for the previously randomly selected cycles of the undamaged bearing. The technical condition of the bearing is represented by 12 coefficients: six in the first observation period (\(T_{01}\)) and six in the second observation period (\(T_{12}\)). These zones are visible as the left and right parts of the technical condition damage maps (Figures 8a-f and 9a-f), separated by a thick black line. Figure 8: The damage map of bearing (drive side) SKF 1207K: (**a**) undamaged; (**b**) with a damaged outer race; with the cut ball at the depth of: (**c**) 1 mm; (**d**) 2 mm; (**e**) 3 mm; (**f**) with cut inner race. Based on Figures 8 and 9, it can be seen that the technical condition of each bearing is clearly and unambiguously indicated on the damage maps obtained. Dominant _red_ and _black_ fields are characteristic of severely damaged bearings. Moreover, the undamaged bearing is dominated by _blue_ and _green_. Since damage thresholds are based on statistics, slight variations between the colors of a given damage map are possible. Therefore, it is important to analyze the map globally for a reasonable number of rotation cycles (map rows). Damage maps can present the technical condition of all analyzed bearings in a concise, graphical form. Based on the generated maps (Figures 8 and 9), it is possible to present a quantitative form of the technical condition. Collective graphs of quantitative analysis (Figure 10) will facilitate the comparison of damage maps in terms of the increase in the number of _black_ and _red_ fields and the decrease in _green_ in relation to the increasing damage. Figure 9: The damage map of bearing (brake side) SKF 1207K: (**a**) undamaged; (**b**) with a damaged outer race; with the cut ball at the depth of: (**c**) 1 mm; (**d**) 2 mm; (**e**) 3 mm; (**f**) with cut inner race. Figure 10 presents a quantitative summary of all tested bearing variants at the rotor speed of 900 rpm (Figure 10a-bearing closer to the brake, 10b-bearing closer to the drive).