An Improved Analytical Model of a Flexible–Rigid Combined Rolling Bearing with Elastohydrodynamic Lubrication
Abstract
1. Introduction
2. FRBD with Lubrication Model
2.1. Grease Lubrication Model
- Rolling bearings operate under isothermal conditions to avoid temperature interference with the model.
- The balls of the ball bearing model are equidistant from the surface of the inner race and the surface of the outer race, and there is no interaction between them.
- The contact form between the inner/outer race and the rolling elements of the bearing is Hertz contact. The contact between the cage and the rolling elements does not generate additional force.
- The center of mass of the rolling element is always maintained at the geometric center.
- There is no relative sliding between the inner race of the rolling bearing and the shaft. The angular velocity of the inner race remains the same as the rotational speed of the shaft.
- When the rolling element comes into contact with the seat ring, elastic deformation and local contact deformation will occur, but this will not change the overall shape and size of the bearing.
2.2. Flexible–Rigid Combined Fault Dynamic Model
3. Results
3.1. Rolling Bearing SKF 6203-RS Dynamic Model
3.2. Analysis of the Influence of Flexible–Rigid Combined and Grease Lubrication on Rolling Bearing Vibration
3.3. FRBD with Lubrication Model Validation
3.4. Effect of the Rotor Speed, Defect Position, Radial Load, and Defect Size on the Time- and Frequency-Domain Vertical Vibration Accelerations of FRBD with Lubrication Model
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Defect Cases | Depth H (mm) | Length L (mm) | Circle Radius r (mm) | Inner-Race Speed | Defect Cases | Depth H (mm) | |
---|---|---|---|---|---|---|---|
Inner-race defect | 1 | 0.3 | 0.4 | 0.15 | 1397 | 50 | 6 |
2 | 0.3 | 0.4 | 0.15 | 1797 | 50 | 6 | |
3 | 0.3 | 0.4 | 0.15 | 2197 | 50 | 6 | |
4 | 0.3 | 0.4 | 0.15 | 2597 | 50 | 6 | |
5 | 0.3 | 0.4 | 0.15 | 1797 | 100 | 6 | |
6 | 0.3 | 0.4 | 0.15 | 1797 | 150 | 6 | |
7 | 0.3 | 0.4 | 0.15 | 1797 | 200 | 6 | |
8 | 0.4 | 0.6 | 0.2 | 1797 | 50 | 13 | |
9 | 0.5 | 0.8 | 0.25 | 1797 | 50 | 18 | |
Outer-race defect | 10 | 0.3 | 0.4 | 0.15 | 1397 | 50 | 6 |
11 | 0.3 | 0.4 | 0.15 | 1797 | 50 | 6 | |
12 | 0.3 | 0.4 | 0.15 | 2197 | 50 | 6 | |
13 | 0.3 | 0.4 | 0.15 | 2597 | 50 | 6 | |
14 | 0.3 | 0.4 | 0.15 | 1797 | 100 | 6 | |
15 | 0.3 | 0.4 | 0.15 | 1797 | 150 | 6 | |
16 | 0.3 | 0.4 | 0.15 | 1797 | 200 | 6 | |
17 | 0.4 | 0.6 | 0.2 | 1797 | 50 | 13 | |
18 | 0.5 | 0.8 | 0.25 | 1797 | 50 | 18 |
Parameters | Value |
---|---|
Number of balls (Z) | 8 |
Pitch diameter (dm) | 28.500 mm |
Ball diameter (db) | 6.746 mm |
Inner race diameter (di) | 17 mm |
Outer race diameter (do) | 40 mm |
Width (B) | 12 mm |
) | ) | ) |
---|---|---|
29.950 Hz | 91.445 Hz | 11.430 Hz |
Numerical Comparison Between Simulation Results and Experimental Results of Outer-Race Defect Bearing | |||
---|---|---|---|
Frequency | Simulation (HZ) | Experiment (HZ) | Error |
27.94 | 30 | 6.87% | |
91.58 | 91.8 | 0.24% | |
181.6 | 183.4 | 0.99% | |
274.7 | 275.2 | 0.18% | |
364.8 | 366.8 | 0.32% | |
Numerical Comparison Between Simulation Results and Experimental Results of Inner-Race Defect Bearing | |||
Frequency | Simulation (HZ) | Experiment (HZ) | Error |
28.99 | 30 | 3.48% | |
152.6 | 147.6 | 3.28% | |
296 | 299.2 | 1.08% | |
447.1 | 448.8 | 0.38% |
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Wang, Q.; Liu, Z.; Ma, X.; Wang, Z.; Yu, J. An Improved Analytical Model of a Flexible–Rigid Combined Rolling Bearing with Elastohydrodynamic Lubrication. Machines 2025, 13, 499. https://doi.org/10.3390/machines13060499
Wang Q, Liu Z, Ma X, Wang Z, Yu J. An Improved Analytical Model of a Flexible–Rigid Combined Rolling Bearing with Elastohydrodynamic Lubrication. Machines. 2025; 13(6):499. https://doi.org/10.3390/machines13060499
Chicago/Turabian StyleWang, Qinchao, Zhilong Liu, Xinguang Ma, Zhengquan Wang, and Junqin Yu. 2025. "An Improved Analytical Model of a Flexible–Rigid Combined Rolling Bearing with Elastohydrodynamic Lubrication" Machines 13, no. 6: 499. https://doi.org/10.3390/machines13060499
APA StyleWang, Q., Liu, Z., Ma, X., Wang, Z., & Yu, J. (2025). An Improved Analytical Model of a Flexible–Rigid Combined Rolling Bearing with Elastohydrodynamic Lubrication. Machines, 13(6), 499. https://doi.org/10.3390/machines13060499