Analysis of Friction Torque Characteristics of a Novel Ball–Roller Composite Turntable Bearing
Abstract
1. Introduction
2. Relevant Fundamental Theories
2.1. Kinematic Characteristics of Rolling Elements
2.2. Contact Load and Distribution Characteristics
2.3. Fundamental Principles of the Slice Method
3. Static Model of the Novel Ball–Roller Composite Turntable Bearing
3.1. Bearing Structure
3.2. Static Modeling and Reasonable Assumptions
3.3. Force Analysis
3.3.1. Contact Load Analysis Between Axial Cylindrical Rollers and Raceways
3.3.2. Contact Load Analysis Between Axial Steel Balls and Raceways
3.3.3. Contact Load Analysis Between Radial Cylindrical Rollers and Raceways
3.4. Mechanical Equilibrium Equations of the Bearing Inner Ring and Numerical Solution
3.5. Kinematic Analysis
4. Calculation of Bearing Friction Torque
4.1. Friction Torque Caused by Elastic Hysteresis of Cylindrical Rollers and Steel Balls
- (1)
- Friction torque generated by elastic hysteresis of cylindrical rollers.
- (2)
- Friction torque caused by elastic hysteresis of steel balls [5].
4.2. Friction Torque Caused by Differential Sliding of Cylindrical Rollers
4.3. Friction Torque Caused by Viscous Friction of Rollers and Steel Balls
- (1)
- The friction torque of the roller due to the viscosity of the lubricant.
- (2)
- The friction torque generated by the viscosity of the lubricating grease on the axial steel balls.
4.4. Friction Torque Due to Spinning and Sliding of Axial Steel Balls
4.5. Friction Torque Due to Sliding Friction Between Retainer and Guide Surface
4.6. Total Friction Torque of the Bearing
5. Experimental Verification of Bearing Friction Torque
5.1. Friction Torque Testing
5.2. Test Bearing-Related Parameters
5.3. Analysis of Test Results
5.3.1. Comparative Analysis of Experimental Results Between the Novel and Conventional Bearings
5.3.2. Experimental Results Analysis of the Novel Ball–Roller Composite Turntable Bearing
- (1)
- Test results of bearing friction torque under different rotational speeds.
- (2)
- Test results of bearing friction torque under different axial loads.
- (3)
- Test results of bearing friction torque under different overturning moments.
6. Analysis of Friction Torque Characteristics for Novel Ball–Roller Composite Turntable Bearings
6.1. Single-Factor Influence Analysis
6.1.1. Influence of Axial Clearance on Bearing Friction Torque
6.1.2. Influence of Axial Steel Ball Groove Curvature Radius Coefficient on Bearing Friction Torque
6.1.3. Influence of Axial Load Application Position on Bearing Friction Torque
6.1.4. Influence of the Numerical Ratio of Axial Steel Balls to Rollers on Bearing Friction Torque
6.1.5. Influence of Roller Crowning Methods on Bearing Friction Torque
6.2. Analysis of Multi-Factor Coupling Effects
- (1)
- (2)
- Evaluation of the influence degree of each factor on the friction torque.
7. Conclusions
- (1)
- The friction torque of the novel ball–roller composite turntable bearing is primarily generated by the rollers. The negative axial roller clearance has a significant impact on the friction torque. By appropriately adjusting the clearance parameters—specifically, setting the axial roller clearance to -1 μm and the axial steel ball clearance to −5 μm—it is possible to achieve a more balanced load distribution between the axial rollers and the steel balls, thereby reducing the overall friction torque;
- (2)
- By comparing the friction torque and contact stress at various ratios of steel balls to rollers, it is observed that a 1:1 ratio of axial steel balls to rollers yields optimal friction and load-carrying performance, demonstrating excellent overall operational characteristics;
- (3)
- The curvature radius coefficient of the axial steel ball raceway significantly influences the friction torque; as this coefficient increases, the friction torque also increases markedly. Considering the challenges associated with processing and structural adaptability, the recommended range for the curvature radius coefficient is between 0.515 and 0.53;
- (4)
- The eccentric distance of the axial load significantly influences the friction torque. As the eccentric distance increases, the friction torque also rises. Therefore, in engineering design and application, it is essential to minimize load eccentricity to enhance the operational stability and service life of the bearing;
- (5)
- Different cylindrical roller crowning methods significantly influence the friction characteristics and contact stress distribution of bearings. Notably, the cylindrical roller structure featuring logarithmic crowning demonstrates superior performance in reducing friction torque and alleviating contact stress.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
Inner diameter/mm | 120 |
Outer diameter/mm | 210 |
Pitch circle diameter of axial upper and lower row rollers/mm | 167 |
Pitch circle diameter of axial upper and lower row steel balls/mm | 177.8 |
Pitch circle diameter of radial rollers/mm | 155.25 |
Number of axial row rollers/pcs | 31 × 2 |
Number of axial row steel balls/pcs | 31 × 2 |
Number of radial row rollers/pcs | 97 |
Axial roller diameter/mm | 4 |
Axial roller effective length/mm | 4.8 |
Axial steel ball diameter/mm | 6 |
Radial roller diameter/mm | 5 |
Radial roller effective length/mm | 8 |
Factor Number | Name | Level 1 | Level 2 | Level 3 |
---|---|---|---|---|
A | Axial roller clearance/um | 0 | −1 | −2 |
B | Axial ball clearance/um | −4 | −5 | −6 |
C | Groove curvature radius coefficient | 0.51 | 0.52 | 0.53 |
D | Axial load eccentricity/m | 0.2 | 0.3 | 0.4 |
Test No | A (Axial Roller Clearance/um) | B (Axial Ball Clearance/um) | C (Groove Curvature Radius Coefficient) | D (Axial Load Eccentricity/m) | Friction Torque/N·mm |
---|---|---|---|---|---|
1 | 0 | 4 | 0.51 | 0.2 | 2871.7 |
2 | 0 | 5 | 0.52 | 0.3 | 4045.4 |
3 | 0 | 6 | 0.53 | 0.4 | 5379.6 |
4 | −1 | 4 | 0.52 | 0.4 | 5692.0 |
5 | −1 | 5 | 0.53 | 0.2 | 3208.1 |
6 | −1 | 6 | 0.51 | 0.3 | 4092.0 |
7 | −2 | 4 | 0.53 | 0.3 | 4767.5 |
8 | −2 | 5 | 0.51 | 0.4 | 5774.0 |
9 | −2 | 6 | 0.52 | 0.2 | 3772.4 |
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Tian, H.; Li, W.; Shao, X.; Zhang, Z.; Zhang, W. Analysis of Friction Torque Characteristics of a Novel Ball–Roller Composite Turntable Bearing. Machines 2025, 13, 588. https://doi.org/10.3390/machines13070588
Tian H, Li W, Shao X, Zhang Z, Zhang W. Analysis of Friction Torque Characteristics of a Novel Ball–Roller Composite Turntable Bearing. Machines. 2025; 13(7):588. https://doi.org/10.3390/machines13070588
Chicago/Turabian StyleTian, Heng, Weiwang Li, Xiuhua Shao, Zhanli Zhang, and Wenhu Zhang. 2025. "Analysis of Friction Torque Characteristics of a Novel Ball–Roller Composite Turntable Bearing" Machines 13, no. 7: 588. https://doi.org/10.3390/machines13070588
APA StyleTian, H., Li, W., Shao, X., Zhang, Z., & Zhang, W. (2025). Analysis of Friction Torque Characteristics of a Novel Ball–Roller Composite Turntable Bearing. Machines, 13(7), 588. https://doi.org/10.3390/machines13070588