Modelling Transitions in Regimes of Lubrication for Rough Surface Contact
Abstract
:1. Introduction
2. Mathematical Approach
2.1. Hydrodynamic Pressure
2.2. Interacting Asperity Pressure
2.3. Frictional Conjunction
2.4. Numerical Method
3. Experimental Approach
3.1. Friction Testing
3.2. Lubricant Viscosity-Pressure Correlation
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
A | Apparent contact area (m2) |
a | Hertzian contact radius in the x-direction (m) |
b | Hertzian contact radius in the y-direction (m) |
D | Influence coefficient (m) |
E | Modulus of elasticity (m) |
Effective modulus of elasticity (m) | |
Boundary friction force (N) | |
Rough surface model statistical function, and (−) | |
Viscous friction force (N) | |
Total friction force (N) | |
Non-dimensional material parameter (−) | |
Non-dimensional elasticity parameter (−) | |
Non-dimensional viscosity parameter (−) | |
H | Non-dimensional elastic lubricant film profile (−) |
h | Elastic lubricant film profile (m) |
Minimum clearance (m) | |
Local gap along conjunction (m) | |
m | Pressure coefficient of boundary shear strength (−) |
Slope of the logarithmic linear relationship between the lubricant (−) | |
Dynamic viscosity and temperature (−) | |
Interception of the logarithmic linear relationship between | |
The lubricant dynamic viscosity and temperature (−) | |
P | Non-dimensional hydrodynamic pressure (−) |
Asperity interacting pressure (Pa) | |
Hydrodynamic pressure (Pa) | |
Maximum Hertzian pressure (Pa) | |
R | Pin curvature radius (m) |
T | Temperature (°C) |
t | Time (s) |
U | Non-dimensional average contact surface sliding speed in the x-direction (m/s) |
Non-dimensional sliding speed parameter (−) | |
u | Contact surface sliding speed in the x-direction (m/s) |
Average contact surface sliding speed in the x-direction (m/s) | |
V | Non-dimensional average contact surface sliding speed in the y-direction (m/s) |
v | Contact surface sliding speed in the y-direction (m/s) |
Average contact surface sliding speed in the y-direction (m/s) | |
W | Contact load (N) |
Reference contact load (N) | |
Non-dimensional load parameter (−) | |
X | Non-dimensional coordinate along the x-direction (−) |
Coordinate along the x-direction (m) | |
Y | Non-dimensional coordinate along the y-direction (−) |
Coordinate along the y-direction (m) | |
Lubricant viscosity-pressure coefficient (Pa−1) | |
Curvature radius at the asperity peak (m) | |
Slope of the limiting shear stress-pressure relation (−) | |
Contact elastic deformation (m) | |
Surface density of asperity peaks (−) | |
Lubricant dynamic viscosity (Pa.s) | |
Bulk lubricant dynamic viscosity at (Pa.s) | |
Non-dimensional lubricant dynamic viscosity (−) | |
Separation parameter (−) | |
Poisson’s ratio (−) | |
Lubricant density (kg/m3) | |
Bulk lubricant density at (kg/m3) | |
Non-dimensional lubricant density (−) | |
Composite surface roughness (m) | |
Boundary shear (Pa) | |
Eyring shear stress (Pa) | |
Viscous shear (Pa) | |
Relaxation factor for pressure convergence loop (−) | |
Relaxation factor for load balance loop (−) |
Appendix A
Parameters | Non-Dimensional | Relation |
---|---|---|
x | X | |
y | Y | |
h | H | |
p | P | |
U | ||
V |
Appendix B. Finite Difference Scheme
Appendix C
Parameter | Value | Unit |
---|---|---|
Pin curvature radius, R | 5 | mm |
Wear track radius | 20 | mm |
Young’s modulus (disk) | 210.0 | GPa |
Young’s modulus (pin) | 110.0 | GPa |
Poisson’s ratio (disk) | 0.27 | - |
Poisson’s ratio (pin) | 0.21 | - |
Eyring shear stress | 2 | MPa |
Appendix D
Lubricant Type | Tsupply (°C) | (-) | m (-) |
---|---|---|---|
SAE5W40 | 35 | 0.048 | 0.107 |
SAE10W40 | 30 | 0.043 | 0.106 |
SAE15W40 | 23 | 0.051 | 0.115 |
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Parameter | Value | Unit |
---|---|---|
Composite surface roughness, | 0.105 | μm |
0.4 | - | |
0.055 | - |
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Chong, W.W.F.; Hamdan, S.H.; Wong, K.J.; Yusup, S. Modelling Transitions in Regimes of Lubrication for Rough Surface Contact. Lubricants 2019, 7, 77. https://doi.org/10.3390/lubricants7090077
Chong WWF, Hamdan SH, Wong KJ, Yusup S. Modelling Transitions in Regimes of Lubrication for Rough Surface Contact. Lubricants. 2019; 7(9):77. https://doi.org/10.3390/lubricants7090077
Chicago/Turabian StyleChong, William Woei Fong, Siti Hartini Hamdan, King Jye Wong, and Suzana Yusup. 2019. "Modelling Transitions in Regimes of Lubrication for Rough Surface Contact" Lubricants 7, no. 9: 77. https://doi.org/10.3390/lubricants7090077
APA StyleChong, W. W. F., Hamdan, S. H., Wong, K. J., & Yusup, S. (2019). Modelling Transitions in Regimes of Lubrication for Rough Surface Contact. Lubricants, 7(9), 77. https://doi.org/10.3390/lubricants7090077