Influence of Cavitation and Shaft Deformation in the Analysis of Lubrication of the Stern Bearing
Abstract
:1. Introduction
2. Governing Equations of Lubrication Model
2.1. Force Balance Model of Shaft
2.2. Coefficient of Friction
2.3. Mixed Lubrication Model Considering Surface Roughness
2.4. Contact Force of Micro-Convex Body
3. General Equation Considering Cavitation Effect
3.1. Boundary Conditions of Oil Film Rupture
3.2. Boundary Conditions of Oil Film Reformation
3.3. Control Equation of Cavitation Zone
4. Oil Film Thickness Equation Considering Shaft Deflection
- (1)
- The basic parameters of the bearing are input, such as bearing diameter, bearing radius clearance, bearing width, external load, lubricating oil viscosity, etc. The surface roughness of the bearing and the shaft and the pressure of the cavitation zone are input. The initial value of the eccentricity and the deviation angle are given, and the switching function (g) is set to 1;
- (2)
- The general Reynolds Equation (37) is solved to obtain the distribution of and update the value of g. The finite difference method and the successive over-relaxation algorithm are applied for the calculation. The contact force of the asperity is solved. Then, the oil film force and the contact force of the asperity are substituted into the following formula to determine if the calculation is convergent:
- (3)
5. Results and Analysis
5.1. The Influence of Cavitation
5.2. The Mixed Lubrication State
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Radius (mm) | Radius Clearance (mm) | Length–Diameter Ratio | Cavitation Pressure (kPa, Gage) |
---|---|---|---|
50 | 0.1455 | 1.333 | −72 |
Angular Velocity (rad/s) | Dynamic Viscosity (Pa·s) | Ambient Pressure (kPa, Gage) | Density (kg/m) |
48.1 | 0.0127 | 0 | 950 |
Inner radius of bearing (mm) | 100 | Outer radius of bearing (mm) | 160 |
Radius clearance (mm) | 0.3 | Width of Bearing(mm) | 240 |
Rotational speed (rpm) | 20–60 | Lubricating oil viscosity (Pa·s) | 0.082 |
Roughness of bushing ( m) | 8 | Roughness of journal ( m) | 2 |
Elastic modulus of bushing (GPa) | 100 | Elastic modulus of journal (GPa) | 210 |
Poisson ratio of bushing | 0.29 | Poisson ratio of journal | 0.3 |
Load of bearing (N) | 38,000 | Initial Bearing-journal contact friction coefficient | 0.1 |
Speed (rpm) | Eccentricity | Film Load (N) | Contact Load (N) | Friction Force (N) | Friction Coefficient |
---|---|---|---|---|---|
20 | 0.95360 | 19,066.50 | 18,943.96 | 1970.07 | 0.05183 |
30 | 0.94960 | 26,172.52 | 11,639.29 | 1261.44 | 0.03336 |
40 | 0.94480 | 31,588.07 | 6231.27 | 729.33 | 0.01928 |
50 | 0.93930 | 35,510.86 | 2815.49 | 388.55 | 0.01014 |
60 | 0.93175 | 37,494.50 | 831.29 | 188.50 | 0.00492 |
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He, T.; Zhou, Y.; Liu, Y.; Xia, Y. Influence of Cavitation and Shaft Deformation in the Analysis of Lubrication of the Stern Bearing. Appl. Sci. 2023, 13, 9033. https://doi.org/10.3390/app13159033
He T, Zhou Y, Liu Y, Xia Y. Influence of Cavitation and Shaft Deformation in the Analysis of Lubrication of the Stern Bearing. Applied Sciences. 2023; 13(15):9033. https://doi.org/10.3390/app13159033
Chicago/Turabian StyleHe, Tao, Yingzhi Zhou, Yong Liu, and Yang Xia. 2023. "Influence of Cavitation and Shaft Deformation in the Analysis of Lubrication of the Stern Bearing" Applied Sciences 13, no. 15: 9033. https://doi.org/10.3390/app13159033
APA StyleHe, T., Zhou, Y., Liu, Y., & Xia, Y. (2023). Influence of Cavitation and Shaft Deformation in the Analysis of Lubrication of the Stern Bearing. Applied Sciences, 13(15), 9033. https://doi.org/10.3390/app13159033