Calculation Method and Experimental Study on Circumferential Total Clearance of Cageless Bearings
Abstract
:1. Introduction
2. Cageless Logarithmic Spiral Bearings
2.1. Logarithmic Spirals
2.2. Logarithmic Spiral Bearings
2.3. Contact Angles of Bearings
3. Calculation and Influence Analysis of Total Circumferential Clearance of Cageless Bearing
3.1. Circumferential Clearance
3.2. Calculation Method of Total Circumferential Clearance
- (1)
- The bearing is in a stable state.
- (2)
- The rolling elements do not slip, tilt, or migrate.
- (3)
- There is no sliding at the contact points between the rolling elements and the raceways of the inner and outer rings.
3.2.1. Orbital Speed of Rolling Elements
3.2.2. Calculation of Circumferential Clearance
3.3. Influence of Bearing Parameters on Total Circumferential Clearance
4. Optimization of the Number of Rolling Elements in Cageless Bearings
5. Circumferential Clearance Test of Bearings
5.1. Sample
5.2. Experimental Method
6. Results and Discussion
6.1. Surface Abrasion Morphology
6.2. Temperature
7. Conclusions
- (1)
- As the diameter of the rolling elements, the contact angle, and the number of rolling elements increase, the minimum total circumferential clearance needed to prevent collisions also increases. Conversely, as the pitch diameter of the bearing increases, the minimum total circumferential clearance decreases.
- (2)
- To minimize collisions between rolling elements, the number of rolling elements in cage-less bearings was optimized. The optimization results indicated that with 21 rolling elements, the actual total circumferential clearance of the bearing ranges from 14.63 mm to 17.47 mm, exceeding the minimum required clearance of 9.967 mm to prevent collisions. Furthermore, this moderate total circumferential clearance helps reduce bearing stress, lower the risk of rolling element deflection, and extend the bearing’s service life.
- (3)
- Both experimental group (EG) and control group (CG) tests were conducted to validate the accuracy of the total circumferential clearance calculation. The results indicate that the control group experienced more pronounced wear marks and significant spalling than the experimental group. The average temperature and temperature rise in the control group were higher, with average temperatures exceeding those of the experimental group by 0.2 to 5.1 °C, and the average temperature rose by 21.8 to 26.7 °C. The comparison of wear marks, average temperature, and temperature rise demonstrates that the proposed calculation method effectively reduces collisions and wear between the rolling elements.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Title | Traditional Method | Xu’s Method | New Method |
---|---|---|---|
Number of rollers | 22 | 20 | 21 |
Calculated total circumferential clearance/mm | 9.967 | 9.0659 | 9.967 |
Actual total circumferential clearance/mm | 0–2.78 | 29.26–32.1 | 14.63–17.47 |
Parameters | Quantity | Parameters | Quantity |
---|---|---|---|
Outer diameter/mm | 130 | Bearing width/mm | 31 |
Inner diameter/mm | 75 | Roller diameter/mm | 14.63 |
Number of rollers | 22 | Pitch diameter/mm | 103.7 |
Total circumferential clearance/mm | 0.78 | Contact angle/° | 15 |
Parameters | Quantity | Parameters | Quantity |
---|---|---|---|
Outer diameter/mm | 130 | Bearing width/mm | 31 |
Inner diameter/mm | 75 | Roller diameter/mm | 14.63 |
Number of rollers | 21 | Pitch diameter/mm | 103.7 |
Total circumferential clearance/mm | 15.2 | Contact angle/° | 15 |
Test Procedure | Speed (r/min) | Axial Load (kN) | Time (min) | Lubricant Flow Ranges (L/min) |
---|---|---|---|---|
1 | 1500 | 10 | 35 | 3.848~4.340 |
2 | 2000 | 20 | 90 | |
3 | 2500 | 30 | 120 | |
4 | 2500 | 40 | 90 | |
5 | 2500 | 50 | 90 | |
6 | 2500 | 60 | 90 | |
7 | 2500 | 70 | 90 | |
8 | 2500 | 80 | 90 | |
9 | 2500 | 95 | 140 |
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Zhao, X.; Xu, S.; Xu, T.; Xu, Q.; Huang, K. Calculation Method and Experimental Study on Circumferential Total Clearance of Cageless Bearings. Lubricants 2024, 12, 238. https://doi.org/10.3390/lubricants12070238
Zhao X, Xu S, Xu T, Xu Q, Huang K. Calculation Method and Experimental Study on Circumferential Total Clearance of Cageless Bearings. Lubricants. 2024; 12(7):238. https://doi.org/10.3390/lubricants12070238
Chicago/Turabian StyleZhao, Xiaofeng, Shuidian Xu, Tao Xu, Qianqian Xu, and Kai Huang. 2024. "Calculation Method and Experimental Study on Circumferential Total Clearance of Cageless Bearings" Lubricants 12, no. 7: 238. https://doi.org/10.3390/lubricants12070238
APA StyleZhao, X., Xu, S., Xu, T., Xu, Q., & Huang, K. (2024). Calculation Method and Experimental Study on Circumferential Total Clearance of Cageless Bearings. Lubricants, 12(7), 238. https://doi.org/10.3390/lubricants12070238