Analytical Determination of Stick–Slip Whirling Vibrations and Bifurcations in Rotating Machinery
Abstract
:1. Introduction
2. Friction-Induced Nonlinear System
3. Friction-Induced Vibration
3.1. Friction-Induced Bifurcations
3.2. Sliding Vibrations
3.3. Cross-Coupling Stiffness Effects
4. Existence of Backward Whirling
5. Discussion and Conclusions
5.1. Discussion
5.2. Conclusions
- (1)
- In such a rotor/stator-coupled nonlinear system, pure rolling vibration (), continuous crossing vibration (), and grazing–sliding-bifurcation-induced vibration can occur;
- (2)
- If the coefficient () of the dry friction is very large or the cross-coupling stiffness () is very small, the pure rolling vibration may occur;
- (3)
- If the angular velocity () is very low, the backward whirling oscillation induced by dry friction can be produced in the rotor/stator system, and the pure rolling vibration may also happen. Meanwhile, if he cross-coupling stiffness is in the low range, pure rolling exists for larger ranges;
- (4)
- When increases, the pure rolling vibration at the sliding time length () happens for the larger friction coefficient;
- (5)
- The stick–slip vibrations that happen are associated with grazing–sliding bifurcations for the range in which the coefficients of the dry friction are smaller than and larger than ;
- (6)
- As the cross-coupling stiffness coefficient () increases from 0 to 0.12, the limit friction coefficient of the existence conditions of backward whirling oscillation induced by dry friction in the rotor/stator system is increased from 0.11 to 0.23.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Damping of shaft, N·s/m | |
e | Rotor mass eccentricity, m |
Contact stiffness | |
Stiffness of shaft, N/m | |
Mass of disk, kg | |
Cross-coupling stiffness of shaft, N/m | |
Clearance between disk and stator, m | |
Nondimensional clearance | |
r | Displacement of disk geometric center, m |
R | Nondimensional deflection of the shaft |
Radius of disk at contact point, m | |
Nondimensional radius of the rotor | |
t | Time, s |
Relative velocity of the disk, m/s | |
Normalized relative velocity of the disk | |
Normalized contact stiffness ratio = | |
Normalized cross-coupling stiffness of rotor | |
Whirling angle at contact point, rad | |
Friction coefficient | |
Nondimensional time | |
Relative sliding duration in one period of oscillation | |
Rotating speed of the disk, rad/s | |
Normalized rotating speed of rotor = | |
Critical rotating speed of the rotor for backward whirl induced by dry friction | |
Natural frequency of the rotor with zero clearance, rad/s | |
Damping ratio of the shaft |
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Lu, D.; Wang, M.; Xu, Y.; Wang, X.; Wang, S. Analytical Determination of Stick–Slip Whirling Vibrations and Bifurcations in Rotating Machinery. Appl. Sci. 2024, 14, 7338. https://doi.org/10.3390/app14167338
Lu D, Wang M, Xu Y, Wang X, Wang S. Analytical Determination of Stick–Slip Whirling Vibrations and Bifurcations in Rotating Machinery. Applied Sciences. 2024; 14(16):7338. https://doi.org/10.3390/app14167338
Chicago/Turabian StyleLu, Duhui, Mukai Wang, Yeyin Xu, Xinya Wang, and Shunzeng Wang. 2024. "Analytical Determination of Stick–Slip Whirling Vibrations and Bifurcations in Rotating Machinery" Applied Sciences 14, no. 16: 7338. https://doi.org/10.3390/app14167338