Vertical Transient Response Analysis of a Cracked Jeffcott Rotor Based on Improved Empirical Mode Decomposition
Abstract
:1. Introduction
2. Jeffcott Rotor and Crack Modeling
2.1. Crack Modeling
2.2. Method of Solution
3. Time–Frequency Analysis
Empirical Mode Decomposition (EMD)
4. Results and Discussion
5. Conclusions and Future Work
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
a | crack depth |
C | external damping coefficient |
Intrinsic Mode Function, IMF | |
D | shaft diameter |
E | shaft modulus of elasticity |
crack breathing function | |
shaft compliance matrix in the rotating system | |
g | acceleration due to gravity |
compliance elements of the cracked shaft cross-section | |
in the rotating coordinates | |
Hilbert transform operation | |
I | shaft area moment of inertia about x-axis |
instantaneous frequency of the IMF | |
strain energy density function due to the crack | |
stress intensity factors | |
shaft stiffness matrix in the rotating system | |
stiffness elements of the cracked shaft cross-section | |
in the rotating coordinates | |
lower envelope of the original signal | |
disc location on the shaft | |
shaft length | |
M | disc mass |
instantaneous mean of the original signal | |
, | forces acting on the shaft cracked cross-area |
R | shaft radius |
upper envelope of the original signal | |
additional strain energy due to the crack | |
lateral (vertical and horizontal) response of the shaft, original signal | |
additional deflections due to the crack () | |
residual signal | |
shaft rotational speed | |
whirling speed of the shaft | |
shaft acceleration rate | |
unbalance disc eccentricity | |
shaft rotational angle | |
short-time Fourier transform parameter | |
normalized crack depth |
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Description | Value |
---|---|
Modulus of elasticity (Pa) | 69 × 109 |
Modulus of rigidity (Pa) | 34 × 109 |
Shaft diameter (m) | 0.01905 |
Shaft length (m) | 1.27 |
Shaft density (kg/m3) | 2700 |
Disc density (kg/m3) | 2700 |
Disc diameter (m) | 0.1524 |
Disc thickness (m) | 0.0254 |
Normalized disc location | 0.5 |
Unbalance mass (kg) | 0.01 |
Unbalance eccentricity (m) | 0.0508 |
Normalized Crack Depth | Computational Cost (s) | Transient Responses Similarity | |
---|---|---|---|
Proposed Breathing Function | Darpe et al. [4] Breathing Model | ||
1 | 12.866 | 446.942 | 0.9296 |
0.5 | 12.319 | 408.907 | 0.9943 |
0.2 | 12.673 | 369.702 | 0.9995 |
0.1 | 12.364 | 341.060 | 0.9999 |
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Khorrami, H.; Sedaghati, R.; Rakheja, S. Vertical Transient Response Analysis of a Cracked Jeffcott Rotor Based on Improved Empirical Mode Decomposition. Vibration 2022, 5, 408-428. https://doi.org/10.3390/vibration5030023
Khorrami H, Sedaghati R, Rakheja S. Vertical Transient Response Analysis of a Cracked Jeffcott Rotor Based on Improved Empirical Mode Decomposition. Vibration. 2022; 5(3):408-428. https://doi.org/10.3390/vibration5030023
Chicago/Turabian StyleKhorrami, Hamid, Ramin Sedaghati, and Subhash Rakheja. 2022. "Vertical Transient Response Analysis of a Cracked Jeffcott Rotor Based on Improved Empirical Mode Decomposition" Vibration 5, no. 3: 408-428. https://doi.org/10.3390/vibration5030023