A Numerical Investigation of the Effects of Groove Texture on the Dynamics of a Water-Lubricated Bearing–Rotor System
Abstract
:1. Introduction
2. Mathematical Models
2.1. Governing Equations
2.2. Dynamic Characteristics
2.3. Bearing–Rotor Dynamic Model
2.3.1. Stability Analysis
2.3.2. Unbalance Response Analysis
2.4. Calculation Process
3. Validation of the Calculation Process
4. Results and Discussion
4.1. Dynamic Characteristics of Groove-Textured WLHB
4.1.1. Effects of Rotary Speed
4.1.2. Effects of Eccentricity Ratio
4.1.3. Effects of Groove Depth
4.1.4. Effects of Groove Width
4.1.5. Effect of Groove Length Ratio
4.2. Stability of Groove-Textured, Water-Lubricated Bearing–Rotor System
4.2.1. Effects of Rotary Speed
4.2.2. Effects of Eccentricity Ratio
4.2.3. Effects of Groove Depth
4.2.4. Effect of Groove Width
4.2.5. Effect of Groove Length
4.3. Unbalance Response of Groove-Textured, Water-Lubricated Bearing–Rotor System
4.3.1. Effect of Rotary Speed
4.3.2. Effect of Eccentricity Ratio
4.3.3. Effect of Groove Depth
4.3.4. Effect of Groove Width
4.3.5. Effect of Groove Length Ratio
5. Conclusions
- (1)
- The groove texture can enhance the direct stiffness along the load direction and weaken the stiffness in the orthogonal direction , especially at greater rotational speed, smaller eccentricity ratio, and a shallower and longer groove. When a bearing with a groove depth of 10 μm, a groove length of 1 and width of 1.1 degrees is working at 20,000 rpm and a 0.1 eccentricity ratio, the stiffness can be improved by 98.4%. With the increased width of the groove, the dynamic coefficients show an increase–decrease–increase trend or decrease–increase–decrease trend; with increased eccentricity ratio and rotary speed, the groove texture has little effect on the direct damping coefficients but improves the coupled damping coefficients; for most of the cases, the damping coefficients can be improved with increased groove depth; with the increased width of the groove, the damping coefficients increase slightly. These complex variations may be attributed to the combination of cavitation and flow vortex.
- (2)
- The groove texture can play a more obvious positive effect on the stability of a rotor supported by WLHBs with shallow and longer grooves at a greater rotary speed and smaller eccentricity ratio; there exists an optimum groove width to achieve the largest critical mass. When the length ratio is 1, the stability is improved by about 20.5% with groove widths of 0.1 degrees and 1.1 degrees at a rotary speed of 20,000 rpm. The main reason for this phenomenon is due to the improvement of direct stiffness and direct damping coefficient in the direction of the applied load, as well as the weakening of whirling motion due to the existence of a groove texture with proper parameter settings.
- (3)
- As for the unbalance response, the groove texture is beneficial for the dynamics of the rotor at a small eccentricity ratio and great rotary speed. A shallower and longer groove can decrease the unbalance response more apparently; there exists an optimal groove width to decrease the amplitude of the unbalance response. The most significant decrease in groove texture on unbalance response exists at a rotary speed of 20,000 rpm, groove depth of 10 μm, groove length ratio of 1, groove width of 0.1 degree and 1.1 degrees. However, it should be noted that the improvement of the groove texture on the unbalance response of the bearing–rotor system is not as significant as that on the dynamic characteristics of the bearing. As a result, in actual application, considering the manufacturing cost of texture, the effects of texture should be comprehensively considered.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
WLHB | Water-lubricated hydrodynamic bearing | ||
UDF | User Defined Function | ||
DLC | Difference of the load capacity method | ||
Nomenclature | |||
k | Turbulent kinetic energy | Cxx, Cyy, Cxy, Cyx. | Damping coefficients |
Radial clearance | External body force | ||
Critical mass | Evaporation coefficient | ||
Density | Kxx and Kyy; Kxy and Kyx | Stiffness | |
ε | Turbulent dissipation rate | Length of the bearing | |
Mst | Non-dimension critical mass | ||
λl | Groove length ratio | P | Static pressure |
Viscosity | Pv | Vaporization pressure | |
Stress tensor | RB, | bubble radius | |
Nucleation site volume fraction | Re and Rc | mass transfer source terms | |
Velocity vector | Rotary speed | ||
Gravitational body force |
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Item | Value |
---|---|
Radial clearance h0 (um) | 50 |
Diameter D (mm) | 50 |
Length L (mm) | 50 |
Groove width (°) | 0.1 |
Groove depth (μm) | 10 |
Groove length (mm) | 50 |
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Feng, H.; Gao, Z.; Van Ostayen, R.A.J.; Zhang, X. A Numerical Investigation of the Effects of Groove Texture on the Dynamics of a Water-Lubricated Bearing–Rotor System. Lubricants 2023, 11, 242. https://doi.org/10.3390/lubricants11060242
Feng H, Gao Z, Van Ostayen RAJ, Zhang X. A Numerical Investigation of the Effects of Groove Texture on the Dynamics of a Water-Lubricated Bearing–Rotor System. Lubricants. 2023; 11(6):242. https://doi.org/10.3390/lubricants11060242
Chicago/Turabian StyleFeng, Huihui, Zhiwei Gao, Ron. A. J. Van Ostayen, and Xiaofeng Zhang. 2023. "A Numerical Investigation of the Effects of Groove Texture on the Dynamics of a Water-Lubricated Bearing–Rotor System" Lubricants 11, no. 6: 242. https://doi.org/10.3390/lubricants11060242