Dynamics-Based Calculation of the Friction Power Consumption of a Solid Lubricated Bearing in an Ultra-Low Temperature Environment
Abstract
:1. Introduction
2. Calculation of Traction Coefficient of Solid Lubricant
3. Bearing Dynamics Modeling
3.1. Differential Formula of Ball
3.2. Differential Formula of Cage
3.3. Differential Formula of Inner Ring
4. Source and Theoretical Calculation of Friction Power Consumption
4.1. Friction Power Consumption Caused by Elastic Lag between Ball and Raceway
4.2. Friction Power Consumption Caused by Differential Sliding between Ball and Raceway
4.3. Friction Power Consumption Caused by Ball Spin Sliding
4.4. Friction Power Consumption Caused by Sliding between Cage and Guide Surface
4.5. Friction Power Consumption Caused by Contact between Ball and Cage
4.6. Total Friction Power Consumption of Ball Bearings
5. Influencing Factors of Friction Power Consumption
5.1. Influence of the Bearing Speed on Friction Power Consumption
5.2. Influence of Load on Friction Power Consumption
5.3. Influence of Radial Clearance on Friction Power Consumption
6. Experimental Comparison of Friction Power Consumption of Solid Lubricated Ball Bearings
6.1. Main Parameters of Test Bearing
6.2. Test Equipment and Experimental Principle
6.3. Analysis of Test Results
7. Conclusions
- The traction coefficient of MoS2 solid lubricating material first increases and then slightly decreases with an increase in sliding speed. The traction coefficient decreases with an increase in load.
- As the bearing speed increases, total friction power consumption also increases. A slight upward trend is observed in total friction power consumption with an increase in radial load and radial clearance, while an increase in axial load results in a more obvious upward trend in total friction power consumption.
- The simulation value of friction torque, based on the bearing dynamic model proposed in this study, shows good consistency with the experimental results.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Rolling Speed (m/s) | Load (N) | A | B | C | D | Residual Error | Correlation Coefficient |
---|---|---|---|---|---|---|---|
10 | 85 | −0.0320 | 0.154 | 4.445 | 0.0320 | 0.0009 | 0.998 |
10 | 167 | −0.0270 | 0.158 | 5.280 | 0.0270 | 0.0014 | 0.9933 |
10 | 288 | −0.022 | 0.0797 | 5.714 | 0.022 | 0.0008 | 0.9959 |
10 | 458 | −0.0199 | 73,932 | 133,607 | 0.0199 | 0.0026 | 0.9532 |
Ai | Bi | Ci | Di | ||
---|---|---|---|---|---|
i | 0 | −1.05 × 10−3 | −4.14 × 10−5 | 42.64 | 1.05 × 10−3 |
1 | −0.32 | −0.54 | 0.18 | −0.32 | |
Correlation coefficient | 0.99 | 0.956 | 0.987 | 0.956 |
Parameters | Symbol | Value |
---|---|---|
Outside diameter | D | 47 mm |
Bore diameter | d | 20 mm |
Width | B | 14 mm |
Ball diameter | DW | 7.938 mm |
Initial radial clearance | u0 | 0.091 mm |
Number of balls | Z | 10 |
Contact angle | α | 25° |
Axial loading | Fa | 2000 N |
Bearing speed | n | 20,000 rpm |
Material | Modulus of Elasticity (GPa) | Poisson’s Ratio | Density (g/cm3) | Coefficient of Linear Expansion (10−6 °C−1) | Thermal Conductivity (W/(m·°C)) |
---|---|---|---|---|---|
G95Cr18 | 200 | 0.28 | 7.8 | 11.5 | 29.3 |
Nylon 66 | 2.83 | 0.4 | 1.15 | 1.2 | 0.25 |
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Su, B.; Mao, S.; Zhang, G.; Li, H.; Cui, Y. Dynamics-Based Calculation of the Friction Power Consumption of a Solid Lubricated Bearing in an Ultra-Low Temperature Environment. Lubricants 2023, 11, 372. https://doi.org/10.3390/lubricants11090372
Su B, Mao S, Zhang G, Li H, Cui Y. Dynamics-Based Calculation of the Friction Power Consumption of a Solid Lubricated Bearing in an Ultra-Low Temperature Environment. Lubricants. 2023; 11(9):372. https://doi.org/10.3390/lubricants11090372
Chicago/Turabian StyleSu, Bing, Shuanglong Mao, Guangtao Zhang, Han Li, and Yongcun Cui. 2023. "Dynamics-Based Calculation of the Friction Power Consumption of a Solid Lubricated Bearing in an Ultra-Low Temperature Environment" Lubricants 11, no. 9: 372. https://doi.org/10.3390/lubricants11090372
APA StyleSu, B., Mao, S., Zhang, G., Li, H., & Cui, Y. (2023). Dynamics-Based Calculation of the Friction Power Consumption of a Solid Lubricated Bearing in an Ultra-Low Temperature Environment. Lubricants, 11(9), 372. https://doi.org/10.3390/lubricants11090372