A Method for Mathematical Modeling of Hydrodynamic Friction of Plunger Pairs with Consideration of Microgeometry
Abstract
:1. Introduction
2. Idea: Simple Discrete Model
3. Generalization of the Model
4. The Equation of Motion for a Plunger Pair
5. Results of Modeling
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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Diameter of Plunger, mm | Mass of Plunger, grams | Length of Working Part of Plunger, mm | Eccentricity, mm | Rotational Speed of Shaft, RPM | Average Velocity of Plunger, m/s |
---|---|---|---|---|---|
11.0 | 56.0 | 55.60 | 3.5 | 3300 | 0.77 |
Density, kg/m3 | Thermal Capacity, joule/K·kg | Coefficient of Thermal Conduction, W/m·K | Coefficient of Dynamic Viscosity, Pa·s |
---|---|---|---|
730 | 2090 | 0.149 | 0.0024 |
№ | Varied Parameters | Quality Criteria (Hydrodynamic Characteristics) | |||||||
---|---|---|---|---|---|---|---|---|---|
X1, m | X2, m | d, m | ry, m | D, % | , μm | , MPa | N*, W | Q*, cm3/s | |
1 | 0.1533 × 10−1 | 0.4378 × 10−1 | 1.19 × 10−5 | 4.76 × 10−6 | 37.5599 | 3.01 × 10−2 | 102.651 | 113.384 | 2.20 × 10−4 |
2 | 0.1583 × 10−1 | 0.4444 × 10−1 | 1.22 × 10−5 | 4.89 × 10−6 | 38.8817 | 2.98 × 10−2 | 105.045 | 112.774 | 2.21 × 10−4 |
3 | 0.1375 × 10−1 | 0.4166 × 10−1 | 1.08 × 10−5 | 4.33 × 10−6 | 33.3326 | 3.08 × 10−2 | 96.340 | 114.463 | 2.19 × 10−4 |
4 | 0.1535 × 10−1 | 0.4380 × 10−1 | 1.19 × 10−5 | 4.76 × 10−6 | 37.6066 | 3.01 × 10−2 | 102.724 | 113.369 | 2.20 × 10−4 |
5 | 0.1370 × 10−1 | 0.4161 × 10−1 | 1.08 × 10−5 | 4.32 × 10−6 | 33.2203 | 3.09 × 10−2 | 96.306 | 115.307 | 2.18 × 10−4 |
6 | 0.1361 × 10−1 | 0.4148 × 10−1 | 1.07 × 10−5 | 4.30 × 10−6 | 32.9657 | 3.09 × 10−2 | 95.989 | 115.406 | 2.18 × 10−4 |
7 | Plunger pair without microgeometry | 3.31 × 10−2 | 85.603 | 121.908 | 2.17 × 10−4 |
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Gavrilov, K.; Rozhdestvenskii, Y.; Umurzakov, I. A Method for Mathematical Modeling of Hydrodynamic Friction of Plunger Pairs with Consideration of Microgeometry. Mathematics 2023, 11, 2637. https://doi.org/10.3390/math11122637
Gavrilov K, Rozhdestvenskii Y, Umurzakov I. A Method for Mathematical Modeling of Hydrodynamic Friction of Plunger Pairs with Consideration of Microgeometry. Mathematics. 2023; 11(12):2637. https://doi.org/10.3390/math11122637
Chicago/Turabian StyleGavrilov, Konstantin, Yuriy Rozhdestvenskii, and Ildar Umurzakov. 2023. "A Method for Mathematical Modeling of Hydrodynamic Friction of Plunger Pairs with Consideration of Microgeometry" Mathematics 11, no. 12: 2637. https://doi.org/10.3390/math11122637
APA StyleGavrilov, K., Rozhdestvenskii, Y., & Umurzakov, I. (2023). A Method for Mathematical Modeling of Hydrodynamic Friction of Plunger Pairs with Consideration of Microgeometry. Mathematics, 11(12), 2637. https://doi.org/10.3390/math11122637