## 3 Results
### The Detection of PCRRf Patterns
#### 3.2.1 The Extraction of the PCRRf1 Patterns  
The variation of the VIAEPf1 over time during the first experiment at 750 rpm is shown in Figure 15 (2,000,000-h samples, with \(\Delta t=10\) us). A zoomed-in region, A, suggests that there is a dominant component within the VIAEPf1 that is expected to have the period of \(T_{p1}\), which is expected to be reflected in the PCRRf1a pattern. Figure 14: The variation of the IV frequency over time during the same stationary regime at the theoretical synchronous speed of 750 rpm. This PCRRf1a pattern is extracted by FASS, based on Equation (3), with \(T_{p}\), \(m\) and \(n\) particularized as \(T_{p1a}=0.080086727921266\) s, \(m_{1a}=245\) and \(n_{1a}=\left[T_{p1a}/\Delta t\right]=8009\) samples. Figure 16 shows two periods of this PCRRf1a pattern (curve 1, in blue). This PCRRf1a pattern (with a peak-to-peak amplitude of approximately 9 W) is plotted relative to the position of the angular marker placed on the rotor (2, Figure 3); more precisely, it starts (\(t=0\)) at the time when this marker passes through the angular origin. This moment is marked by a minimum value on the PCSL1a pattern. This PCSL1a pattern (shown in Geneva green colour, with curve 2 in Figure 16, also with two periods) is obtained by FASS treatment of the variable part of the signal \(u_{SL}(\cdot\Delta t)\) with exactly the same values \(T_{p1}\), \(m_{1}\) and \(n_{1}\) used previously to extract the PCRRf1a pattern. The \(x\)-axis of Figure 16 also shows the phase angle of the patterns with respect to the origin. However, this phase angle must be seen in the light of the fact that there is a gap (phase difference) between the variable mechanical phenomena and their reflection in the VIAEPf due to the dynamics of the rotor (its inertia, the rigidity of the rotating magnetic field, dry and viscous friction, rotation frequency, etc.). Figure 16: A representation of two periods from PCRRf1a pattern (1), PCSL1a pattern (2) and PCRRf1b pattern (3). Figure 15: The variation of VIAEPf1 over time during a first experiment with the motor running with no load (at 750 rpm theoretical synchronous speed), which was used to extract the PCRRf1a pattern by FASS. The fact that this PCRRf1a pattern can be used to synthetically characterise this motor, running at first speed under no load, is confirmed by its repeatability. A new VIAEPf signal (identical in time and number of samples but acquired the next day) was processed with an identical FASS, resulting in a new pattern as PCRRf1b, represented by the red curve 3 in Figure 16. The PCSL1b pattern is identical to PCSL1a. Despite slightly different conditions (\(T_{p1b}=0.080057415179776\) s, \(n_{1b}=8006\) samples, \(f_{IV1b}=50.0017\) Hz, s\({}_{1b}=0.07511\%\)), the similarities with the PCRRf1a pattern are quite obvious. The difference between these two patterns is partly explained by the variation of the instantaneous speed of rotation and consequently of the instantaneous periods \(T_{pi1}\) and \(T_{pi1a}\) and probably by some minor, normal changes in the condition of the motor. To be very rigorous, we must also point out a fact that proves that the accuracy of the PCRRf1a and PCRRf1b patterns is not perfect because, according to detail A, shown enlarged in Figure 17, there is a very small abnormal step discontinuity between the two periods. Conversely, this discontinuity is not observed in PCSL1a and PCSL1b. According to Figure 3, a permanent magnet 5 (weighing about 10 g), as a dynamically unbalanced mass (DUM), was placed (at a distance of 35 mm from the axis) on the jaw coupling hub 4 mounted on the rotor in three different angular positions relative to the angular marker 2. For each position, the PCRRf1 pattern was recorded under the experimental conditions already described.