The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts
Abstract
:1. Introduction
2. Materials and Methods
2.1. Average Reynolds Equation
2.2. Lubricant Properties
2.3. Lubricant Film Thickness
2.4. Asperity Contact Pressure
2.4.1. Probability Density Function for the Non-Gaussian Surface
2.5. The Method of Solution
2.6. Numerical Generation of Artificially Rough Surfaces
3. Results and Discussion
3.1. The Influence of the Shape Parameter (kw)
3.2. The Influence of Correlation Length (1/λ)
3.3. The Influence of the Wavelength Ratio (Δl/Δs)
3.4. The Influence of the Hurst Coefficient (Hf)
3.5. Validation of the Model
4. Conclusions
- For the specified operating conditions (W = 1 × 10−6, U = 1 × 10−11, G = 4972, V = 0.03, and σ* = 1 × 10−5), it is found that the film parameter (Λ) varies between one and three for each artificial rough surface, which ensures the manifestation of the mixed lubrication regime. It is also shown that the present ML model excellently simulates the mixed and full-film lubrication regimes.
- It is revealed that the shape parameter (kw) leads to a significant change in the asperity height distribution. A change in the asperity height distribution profoundly affects the asperity and hydrodynamic pressures. It is found that the asperity load ratio increases from 4% to 38% as the shape parameter increases from 1.5 (non-Gaussian) to 3.602 (Gaussian). A slight increase in the film parameter is observed as the asperity height distribution changes from non-Gaussian to Gaussian.
- It is concluded that a higher wavelength ratio increases the hydrodynamic lift significantly. The asperity load ratio decreases with an increase in wavelength ratio. The film parameter slightly decreases at higher wavelength ratios.
- It is observed that the Hurst coefficient (Hf) slightly improves the hydrodynamic action. At the middle of the contact zone, a small increase in the hydrodynamic lift is observed for a large value of the Hurst coefficient (Hf > 0.1). A trivial effect of the Hurst coefficient is found on the film thickness or film parameter. It is also found that the hydrodynamic lift increases with a decrease in the correlation length (1/λ) due to a significant drop in the asperity load ratio (La).
- The present ML model is validated from Ref. [20], and a good match is found by comparing the asperity load ratio (La) for different dimensionless surface roughness levels (σ*).
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
1/λ | Correlation length, m |
Ah | EHL domain area, m2 |
β | Mean summit radius, m |
Δl | Shortest cut-off wavelength |
Δs | Longest cut-off wavelength |
η | Summit density, m−2 |
G | Dimensionless material parameter |
γ | Anisotropy factor |
h | Film thickness, m |
Hc | Dimensionless central film thickness |
hd | Rigid body approach, m |
Hf | Hurst coefficient |
hmin | Minimum film thickness, m |
Hmin | Dimensionless minimum film thickness |
hT | Average gap height, m |
La | Asperity load ratio, % |
ML | Mixed lubrication |
pa | Dimensional hydrodynamic pressure, Pa |
Pa | Dimensionless asperity pressure |
ph | Dimensional hydrodynamic pressure, Pa |
Ph | Dimensionless hydrodynamic pressure |
R(r) | Autocorrelation function for isotropic surface |
Rx | Reduced radius of curvature, mm |
σ | Composite root-mean-square (RMS) roughness, m |
SRR | Slide-to-roll ratio, ur/um |
Ssk | Skewness |
Sku | Kurtosis |
ur | Sliding speed, (u2−u1), m/s |
um | Mean rolling speed, (u1 + u2/2), m/s |
U | Dimensionless speed parameter |
W | Dimensionless load parameter |
x | Dimensional X-axis, m |
X | Dimensionless X-axis |
y | Dimensional Y-axis, m |
Y | Dimensionless Y-axis |
Appendix A. Expression of Residuals
Appendix B. A Brief Description of Weibull Height Distribution and PSD
Appendix B.1. Probability Density Function for Weibull Distribution of Asperity Heights
Appendix B.2. Power Spectral Density (PSD)
Appendix C. Hertzian Point Contact
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Parameter | Value |
---|---|
Hurst coefficient, Hf | 0.2, 0.5, and 1.0 |
Shortest wavelength, Δs | 0.001 |
Wavelength ratio, Δl/Δs | 100 and 500 |
Weibull shape parameter, kw | 1.5, 2, and 3.602 |
Correlation length, 1/λ | 0.1 and 0.0067 |
Anisotropy ratio, γ | 1 |
Parameter | Factor | Dimensionless Form |
---|---|---|
ph | 1/pmax | Ph |
pa | 1/pmax | Pa |
FN | 1/Eeq·R2 | |
x | 1/ac | X |
y | 1/ac | Y |
h | 1/Rx | H |
um | U | |
Hd | 1/Eeq | V |
σ | 1/Rx | σ* |
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Prajapati, D.K.; Björling, M. The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts. Lubricants 2024, 12, 71. https://doi.org/10.3390/lubricants12030071
Prajapati DK, Björling M. The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts. Lubricants. 2024; 12(3):71. https://doi.org/10.3390/lubricants12030071
Chicago/Turabian StylePrajapati, Deepak K., and Marcus Björling. 2024. "The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts" Lubricants 12, no. 3: 71. https://doi.org/10.3390/lubricants12030071
APA StylePrajapati, D. K., & Björling, M. (2024). The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts. Lubricants, 12(3), 71. https://doi.org/10.3390/lubricants12030071