Thermal Analysis of Herringbone Gears Based on Thermal Elastohydrodynamic Lubrication Considering Surface Roughness
Abstract
:1. Introduction
2. Mathematical Methods
2.1. Meshing Parameter Analysis
2.2. Governing Equations
2.2.1. Reynolds Equation
2.2.2. Film Thickness Equation
2.2.3. Lubricant Viscosity–Pressure and Density–Pressure Equations
2.2.4. Load Balance Equation
2.2.5. Energy Equation
2.3. Measurement of Real Tooth Surface Topography
2.4. Method of the Temperature Field Solution
3. Numerical Solution
3.1. Validation of the Numerical Model
3.2. Meshing Parameters Solution
3.3. Analysis of Heat Generation and Heat Dissipation
3.3.1. Calculation Method of Friction Coefficient
3.3.2. Frictional Heat Flux
3.4. Effect of Different Parameters on Frictional Heat Flux
3.4.1. Influence of Roughness
3.4.2. Influence of Torque
3.4.3. Influence of Rotating Speed
3.5. Evaluation for the Convection Heat Transfer Coefficient
3.5.1. End Surface
3.5.2. Meshing Surface
3.5.3. Other Surfaces
3.6. Analysis of Herringbone Gears Temperature Field
3.6.1. Simulation of the Steady Temperature Field
3.6.2. Simulation of the Transient Temperature Field
4. Test Verification
5. Conclusions
- (1)
- The TEHL effect of herringbone gears with a rough face was studied. The TEHL model of herringbone gears was established, and the lubrication state of meshing point was obtained by iterative calculation. The comparison of the film thickness numerical results between the calculated value and Dowson–Higginson empirical formula value demonstrated that the correctness of the TEHL model was verified.
- (2)
- The influence of different parameters on the distribution of frictional heat flux was analyzed. The results show that under the conditions of mixed TEHL and smoother tooth surface, lower speed and torque, the frictional heat flux significantly changes with the meshing point, which favors the reduction in the frictional heat flux.
- (3)
- The temperature distribution was obtained and it approximately presents an elliptical distribution along the tooth width. In addition, the highest temperature of the gear tooth occurred near the inner-end surface.
- (4)
- The simulation and the experimental results demonstrated good agreement which verified the feasibility of the present numerical method.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
pitch diameter (i = 1 for the driving pinion, i = 2 for the driven gear), mm | |
pressure angle, deg | |
curvature radius (i = 1 for the driving pinion, i = 2 for the driven gear), mm | |
equivalent curvature radius, mm | |
tangential velocity (i = 1 for the driving pinion, i = 2 for the driven gear), m/s | |
entrainment velocity, m/s | |
sliding velocity, m/s | |
sliding–rolling ratio | |
rotating speed (i = 1 for the driving pinion, i = 2 for the driven gear), r/min | |
specific heat capacity (i = f for the lubricant, i = 1 for the driving pinion, i = 2 for the driven gear), | |
normal modulus, mm | |
viscosity–pressure coefficient | |
density of gears (i = 1 for the driving pinion, i = 2 for the driven gear), | |
Reynolds number of the fluid | |
periods of gears (j = 1 for the driving pinion, j = 2 for the driven gear), s | |
oil film pressure, Pa | |
oil film thickness, | |
viscosity of lubricant, Pa/s | |
density of lubricant, | |
rigid central film thickness, | |
ambient viscosity of lubricant, Pa/s | |
ambient density of lubricant, | |
comprehensive Young’s modulus, Pa | |
torque (i = in for the input torque, i = out for the output torque), n/m | |
thermal conductivity, (i = f for the lubricant, i = 1 for the driving pinion, i = 2 for the driven gear), W | |
average contact pressure, Pa | |
kinematic viscosity of the fluid, | |
Prandtl number of the fluid | |
Hertz contact half-width, mm | |
angular velocity of the gear, rad/s |
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Item | Parameter | Item | Parameter |
---|---|---|---|
Number of teeth | Normal pressure angle | ||
Normal module | mm | Density of gears | |
Face width | Specific heat capacity of gears | ||
Poisson’s ratio | Thermal conductivity of gears | ||
Input rotating speed | Ambient viscosity of lubricant | ||
Input torque | Ambient density of lubricant | ||
Young’s modulus | Thermal conductivity of lubricant |
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Hu, X.; Chen, J.; Wu, M.; Wang, J. Thermal Analysis of Herringbone Gears Based on Thermal Elastohydrodynamic Lubrication Considering Surface Roughness. Energies 2021, 14, 8564. https://doi.org/10.3390/en14248564
Hu X, Chen J, Wu M, Wang J. Thermal Analysis of Herringbone Gears Based on Thermal Elastohydrodynamic Lubrication Considering Surface Roughness. Energies. 2021; 14(24):8564. https://doi.org/10.3390/en14248564
Chicago/Turabian StyleHu, Xiaozhou, Jie Chen, Minggui Wu, and Jianing Wang. 2021. "Thermal Analysis of Herringbone Gears Based on Thermal Elastohydrodynamic Lubrication Considering Surface Roughness" Energies 14, no. 24: 8564. https://doi.org/10.3390/en14248564