## 3 Results and Discussion
### Amplitude Demodulation Analysis
#### 3.3.2 With One Modulating Frequency  
The results presented in this section are the ones obtained with the excitations called \"Exc-1-2 kHz-1\", \"Exc-10-11 kHz-1\", and \"Exc-20-21 kHz-1\" in Table 1. With the modulating frequency of \(f_{1}\) = 22.1 Hz and the pseudorandom excitation, after an amplitude demodulation analysis, the frequencies expected to be found are the rotating frequency (\(f_{t}\)) for those cases under rotation, as in the previous case commented in Section 3.3.1, and the modulating frequency \(f_{1}\) = 22.1 Hz.  
Figure 9 shows the results for the rotating sensors as well for the PZT. The results for the PZT give the information of the excitation for the different excitation patterns. The amplitude of the modulating frequency \(f_{1}\) is higher for the lower frequency band tested. This fact is due to the PZT characteristics, which behave differently at different frequency bands. Comparing the AE sensor in the shaft (ESH) with the excitation (PZT), the results are almost the same, which confirms that the EA sensor in the shaft represents very well the excitation in the disk. The cases where the rotating frequency was not found have been zoomed around the \(f_{1}\) in Figure 9. The accelerometers in the disk (ADISK) and in the shaft (ASH) give the same information than without any modulating frequency for the rotating frequency (\(f_{t}\)), but adding the modulating frequency \(f_{1}\). In the case of the accelerometer of the disk (ADISK), this frequency (\(f_{1}\)) is better seen in the frequency band of 10-11 kHz, whereas in the shaft it  
Figure 8: Amplitude demodulation for the sensors on the stationary frame and the excitation without any modulating frequencies. Rotating case (\(f_{t}\) = 4.1 Hz).  
is better seen in the frequency band of 20-22 kHz. This is related to the frequency resonance of every accelerometer, which is different for this both cases.  
The results for some stationary sensors are shown in Figure 10. In this figure the most relevant sensors for the detection of the \(f_{1}\) modulating frequency are shown. It is observed that the accelerometer located in the bearing (ABEAR) presents similar results than the one located in the shaft (ASH in Figure 9). This observation was also pointed out in the analysis without any modulating frequency (Section 3.3.1). Again, the high-frequency band is better able to detect the modulating frequency \(f_{1}\). The accelerometer installed in the upper cover (ATT) does not detect the modulating frequency in air, since the transmission of the disk vibration without water is very poor for this sensor (this was also confirmed in the coherence Section 3.1). However, it is clearly detected in the configuration with water, and the results obtained are very similar to those obtained with the accelerometer installed in the disk (ADISK in Figure 9). For this kind of accelerometer, the band 10-11 kHz is the best to detect the modulating frequency \(f_{1}\). Moreover, the microphone does not detect the modulating frequency \(f_{1}\) since it is mainly receiving the information of the motor rotating speed, as it was commented in Section 3.3.1. Again, the AE sensor located in the head cover presents the same results than the microphone, since it is detecting the acoustic waves transmitted by the motor more than the ones transmitted by the PZT.  
Figure 9: Amplitude demodulation for the sensors on the rotating frame and the excitation with one modulating frequency. Rotating case (\(f_{\rm f}\) = 4.1 Hz).