Effect of Surface Roughness on the Friction Moment in a Lubricated Deep Groove Ball Bearing
Abstract
1. Introduction
2. Theoretical Model
- The model is designed for open bearings, so the friction moments from seals and dust covers are not considered;
- The frictional moments from lubricant drag losses, churning, and splashing are ignored;
- The contact patch at the point of contact is assumed to have a Hertzian elliptical shape and the bodies are assumed to deform elastically at a local level.
2.1. Ball and Race Contact Friction Model
2.2. Ball and Cage Contact Friction Model
2.3. Mixed Elastohydrodynamic Lubrication Model
2.3.1. Asperity Contact Model
2.3.2. Lubrication Model
3. Methodology
4. Results and Discussion
4.1. Effect of Surface Roughness on the Total Friction Torque
4.2. Effect of Surface Roughness and Speed on Friction Coefficient at Ball–Race and Ball–Cage Contacts
4.3. Effect of Surface Roughness and Speed on Friction Torque at Ball–Race and Ball–Cage Contacts
- (a)
- Ball–Race Friction Torque ():
- At Sq = 1 μm, the torque remained almost constant at around 17 N·mm across all the speeds from 100 RPM to 500 RPM;
- For Sq = 0.5 μm, the torque was lower, starting at around 9.5 N·mm at 100 RPM and remaining constant at approximately the same value as the speed increased to 500 RPM;
- At Sq = 0.1 μm, the lowest roughness, the torque started at about 8 N·mm and slowly decreased over the speed range to 7 N·mm;
- The torque values remained relatively constant across the speed range for each roughness level.
- (b)
- Ball–Cage Friction Torque ():
- At Sq = 1 μm, the torque started at around 0.6 N·mm at 100 RPM but rapidly increased to approximately 8.2 N·mm at 500 RPM;
- For Sq = 0.5 μm, the initial torque at 100 RPM was close to 0.6 N·mm, but it increased more slowly compared to the rougher surface, reaching around 8 N·mm at 500 RPM;
- At Sq = 0.1 μm, the torque at 100 RPM was about 0.5 N·mm and increased to 6 N·mm at 500 RPM;
- The rougher surfaces produced higher torque values at all the speeds.
4.4. Effect of Surface Roughness on Different Factors Contributing to the Ball–Race Friction Torque
4.5. Effect of Surface Roughness on the Ball–Cage Contact Force
4.6. Validation
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Semi minor axis of elliptical contact (m) | |
Semi major axis of elliptical contact (m) | |
Pitch circle diameter (m) | |
Diameter of the ball (m) | |
Equivalent Young’s Modulus (Pa) | |
Hertzian contact stiffness | |
Spin moment (N·m) | |
Rolling moment due to conformity (N·m) | |
Rolling moment due to hysteresis (N·m) | |
Normal load at point of contact (N) | |
Tangential load at point of contact (N) | |
Radius of the ball (m) | |
Distance of inner and outer contacts from the bearing axis (m) | |
Radius of curvature at contact point (m) | |
Friction moment at ball–race contact (N·m) | |
Friction moment at ball–cage contact (N·m) | |
Total friction moment (N·m) | |
Number of balls | |
Contact angle of bearing (rad) | |
Hysteresis loss factor | |
Angular position of the ball (rad) | |
Complete elliptic integral of second kind | |
Spin-to-roll ratio | |
Ratio of major and minor axis length | |
Half width of the cage pocket (m) | |
Friction coefficient at ball–race and ball–cage contact | |
Angular velocity of inner race and outer race (rad/s) | |
Total load at contact (N) | |
Load carried by asperity (N) | |
Load carried by lubricant film (N) | |
Friction force at contact (N) | |
Friction force due to asperity (N) | |
Friction force due to lubricant film (N) | |
Lubricant film separation (m) | |
Gap between mean plane of equivalent rough surface and asperity (m) | |
Total actual contact area of asperity (m2) | |
Boundary friction coefficient | |
Dimensionless central film thickness | |
Central film thickness (m) | |
Reduced radius of curvature in x direction ( (m) | |
Radius of curvature of surface 1 and surface 2 in contact in x direction (m) | |
Reduced radius of curvature in y direction ( (m) | |
Radius of curvature of surface 1 and surface 2 in contact in y direction (m) | |
Sum of the velocity of surface 1 and surface 2 at the contact (m/s) | |
Dynamic viscosity of oil at ambient pressure and temperature (Pa·s) | |
Equivalent Young’s Modulus () (Pa) | |
Young’s Modulus of surface 1 and surface 2 in contact (Pa) | |
Poisson’s ratio of surface 1 and surface 2 in contact |
Appendix A
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Parameters | Value |
---|---|
9 | |
(gm) | 2.04 |
(gm) | 6.58 |
(mm) | 7.94 |
Mass of inner race (gm) | 38.63 |
Mass of outer race (gm) | 54.21 |
Radius of inner race (mm) | 15.53 |
Radius of outer race (mm) | 23.48 |
Groove radius of inner race (mm) | 4.13 |
Groove radius of outer race (mm) | 4.21 |
Pocket diameter (mm) | 13.9 |
Pocket depth (mm) | 6.81 |
Parameters | Value |
---|---|
Young’s modulus (GPa) | 230 |
Poisson’s ratio | 0.3 |
Hysteresis loss factor (%) | 0.5 |
(rad) | 0.18 |
Boundary friction coefficient | 0.13 |
Axial load (N) | 1000, 3000 |
Speed (RPM) | 100, 200, 300, 400, 500 |
Parameters | Value |
---|---|
Viscosity at 40 °C (mPa·s) | 20 |
Pressure viscosity index | 0.65 |
Eyring Shear Stress | 2.5 |
Pressure viscosity coefficient (Pa−1) | 2.0 × 10−8 |
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Kumar, H.; Gupta, V.; Bharath, V.; Tiwari, M.; Paul, S.K.; Agrawal, L.; Singh, A.P.; Jain, A. Effect of Surface Roughness on the Friction Moment in a Lubricated Deep Groove Ball Bearing. Lubricants 2024, 12, 443. https://doi.org/10.3390/lubricants12120443
Kumar H, Gupta V, Bharath V, Tiwari M, Paul SK, Agrawal L, Singh AP, Jain A. Effect of Surface Roughness on the Friction Moment in a Lubricated Deep Groove Ball Bearing. Lubricants. 2024; 12(12):443. https://doi.org/10.3390/lubricants12120443
Chicago/Turabian StyleKumar, Harsh, Vaibhav Gupta, Velamala Bharath, Mayank Tiwari, Surajit Kumar Paul, Lokesh Agrawal, Arendra Pal Singh, and Ayush Jain. 2024. "Effect of Surface Roughness on the Friction Moment in a Lubricated Deep Groove Ball Bearing" Lubricants 12, no. 12: 443. https://doi.org/10.3390/lubricants12120443
APA StyleKumar, H., Gupta, V., Bharath, V., Tiwari, M., Paul, S. K., Agrawal, L., Singh, A. P., & Jain, A. (2024). Effect of Surface Roughness on the Friction Moment in a Lubricated Deep Groove Ball Bearing. Lubricants, 12(12), 443. https://doi.org/10.3390/lubricants12120443