1. Development of RCP Vibration Monitoring System using Power Line Analysis Method
정 재 천

2. Misalignment and Shaft Crack-Related Phase Relationships for 1X and 2X Vibration Components of Rotor Responses
The most significant components of the rotating machine lateral vibration responses
The synchronous vibration (1X)
Due to rotor unbalance
The vibration with twice rotative speed frequency (2X)
Nonlinearity of the rotor/bearing stiffness characteristics
Become important when the rotor lateral deflections are high.
Asymmetry in the rotating system
The different rotor stiffnesses in two perpendicular lateral directions
“X” direction : nonrotating shaft is weaker, and deflects more under the given radial load force
“Y” direction : the shaft is stronger, and defects less under the same
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다섯째 수준

3. Phase Rule
Phase Rule
The 1X phase
The distance from the keyphasor pulse to the first positive peak of 1X time-base form
where, = phase lag
The 2X phase
The distance from the keyphasor pulse to the first positive peak of 2X time-base form

4. Orbits Versus Lassajous Figures
The Lissajous figure are particular cases of orbits
A few examples of pure Lissajous figures
The rotor horizontal motion is represented by a 1X component only
where, = 0
In the rotor vertical motion, a 2X component is the dominant.
where, = 2X component phase
The value of the resulting orbits will have different shapes
Introducing a 1X component in the “Y” wave with 90 phase different from the “X” wave.
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5. Phase Marking of Waveform

7. The orbit from X-Y wave

9. Sources of 1X and 2X components
The synchronous vibration (1X)
Due to rotor unbalance
The vibration with twice rotative speed frequency (2X)
Shaft misalignment
including gear mesh and belt drives and resulting radial preload, or radial preload generated by fluid flow
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10. Case study of Shaft Crack Failure
Comparison of the “Misalignment” and “Cracked Shaft” Related Orbits
Misalignment case
x,y responses are not matching
Cracked Shaft
Circular Orbits
For the “Misalignment” case introduce a new variable
Phase difference between 2X and 1X for the “Misalignment” case

11. The behavior of a rotor experiencing a shaft crack
A model rotor system was designed which closely duplicates the system geometry of a Reactor Coolant Pump.
“v” shaped cut to a penetration depth of 30% of the rotor diameter: 3% reduction in total stiffness of the rotor and bearing system stiffness
Resonance : 2525RPM, Normal speed of RCP : 1190RPM

12. Initial side load (acting vertically downward)
Initial side load (acting vertically downward) of 6kg

13. The side load of 8.3kg The side load of 8.3kg : Figure 3 and 4
The influence of the increased side load introduced a significant 2X vibration component.

14. 4-point FFT flow graph Bit-reversed In-place input order Computations
Butterfly -1

15. Savings due to FFT

16. Window Function
Rectangular Window:

17. Window Function (cont’d)
Hamming Window:

18. Time History Estimation Technique
Figure. Current, Power and Torque Trend
Mechanical and Electrical Failure of Machinery  Current, Voltage, Power and Torque Trend Monitoring  Correlation Method  Abnormal State Diagnosis

19. Frequency Domain Estimation Technique
Torque Frequency Monitoring
Normal State = Ws - [ Ws(1-S) + SWs] = 0
Single Stator Angular Frequency = -Ws - [ Ws(1-S) + SWs ] = -2Ws
Single Rotor Angular Frequency = Ws - [ Ws(1-S)-SWs] = 2SWs
Feature Frequency of Individual Abnormal State
Rotor Misalignment ,

20. Feature frequency of MCSA technique
Broken Rotor Bar State
Bearing Defect State

21. Feature Extraction Algorithm
Consist of;
Data reduction block
Feature data extraction block
Data filtering and reduction block

22. Feature Data Extraction by Peak -picking Method and Interval Mean Technique
Data reduction by interval mean technique
Making 10X10 matrix

23. Abnormality Detection and Diagnosis Algorithm
Calculation of sum of each row from reduced matrix
Comparison of sum of each row to the normal state data
Shaft Crack Detection
adjustment of matrix reduction

24. Conclusion
RCP VMS can be improved by adoption of power line signal analysis method
The shaft crack detection can be possible by time-frequency analysis
Matrix reduction by interval mean technique is proposed
As a further study, the following activities will be performed
Simulation by test bench
Experiments by NPP test data of coast down and startup operation