Transmission of High Frequency Vibrations in Rotating Systems. Application to Cavitation Detection in Hydraulic Turbines
Abstract
:1. Introduction
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- Detection with accelerometers in the shaft [21]: Direct path from the runner, but more complicated measurement with the possibility of having also generator excitations.
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- The transmission path from the runner to the measuring position can only be known in air (the runner could be impacted during an overhaul [17]) but not in water and under operation.
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- No correlation between existing cavitation and the measured signals can be obtained: the cavitation cannot be visualized in the prototype [25].
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- The excitation characteristics of the cavitation are an unknown.
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- It is not clear which high-frequency bands have to be used for every sensor for the analysis.
2. Experimental Investigation
2.1. Test Rig Description
2.2. Instrumentation
2.3. Tests Conducted
2.4. Signal Analysis
2.4.1. Coherence
2.4.2. Frequency Response Function (FRF)
2.4.3. Amplitude Demodulation Analysis
3. Results and Discussion
3.1. Coherence
3.2. FRF
3.3. Amplitude Demodulation Analysis
3.3.1. Without Modulating Frequencies
3.3.2. With One Modulating Frequency
3.3.3. With Two Modulating Frequencies
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
AE | Acoustic Emission |
BEP | Best Efficiency Point |
RMS | Root Mean Square |
RSI | Rotor Stator Interaction |
PS | Pseudorandom |
PZT | Piezoelectric Patch |
f | Frequency |
t | Time |
Hi | Hilbert transform |
θ | Phase shift |
ff | Rotating frequency |
f1 | Modulating frequency at 22.1 Hz |
f2 | Modulating frequency at 1.4 Hz |
FRFH1 | Frequency Response Function |
Sxx(f) | Power Spectra Density function of x(t) |
Syy(f) | Power Spectra Density function of y(t) |
Sxy(f) | Cross-spectral Density function of x(t) and y(t) |
Variable which satisfies |
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Excitation Name | Excitation Characteristics |
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Exc-1-2kHz-0 | PS1 |
Exc2-1-2kHz-1 | PS1*Envelope1 |
Exc3-1-2kHz-2 | PS1*Envelope1*Envelope2 |
Exc-10-11kHz-0 | PS2 |
Exc-10-11kHz-1 | PS2*Envelope1 |
Exc-10-11kHz-2 | PS2*Envelope1*Envelope2 |
Exc-20-21kHz-0 | PS3 |
Exc-20-21kHz-1 | PS3*Envelope1 |
Exc-20-21kHz-2 | PS3*Envelope1*Envelope2 |
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Valentín, D.; Presas, A.; Egusquiza, M.; Valero, C.; Egusquiza, E. Transmission of High Frequency Vibrations in Rotating Systems. Application to Cavitation Detection in Hydraulic Turbines. Appl. Sci. 2018, 8, 451. https://doi.org/10.3390/app8030451
Valentín D, Presas A, Egusquiza M, Valero C, Egusquiza E. Transmission of High Frequency Vibrations in Rotating Systems. Application to Cavitation Detection in Hydraulic Turbines. Applied Sciences. 2018; 8(3):451. https://doi.org/10.3390/app8030451
Chicago/Turabian StyleValentín, David, Alexandre Presas, Mònica Egusquiza, Carme Valero, and Eduard Egusquiza. 2018. "Transmission of High Frequency Vibrations in Rotating Systems. Application to Cavitation Detection in Hydraulic Turbines" Applied Sciences 8, no. 3: 451. https://doi.org/10.3390/app8030451