Abstract
Surface roughness and thermal action are of remarkable importance in the lubrication performance of mechanical components, especially in extreme conditions. However, available studies mainly focus on the full-film lubrication conditions without considering temperature rise and real 3D surface roughness due to the complexity of surface topography and temperature characteristics. Moreover, studies on the interfacial thermal behaviors of 3D rough surface lubricated contact in an extended range of working conditions remain limited. In this paper, a deterministic mixed thermal elastohydrodynamic lubrication model considering real 3D surface roughness and thermal effects is proposed. In this model, pressure and temperature are coupled with each other, the computation of elastic deformation is accelerated through the discrete convolution and fast Fourier transform method, the temperature field is calculated with the column sweeping technique, and the semi-system method is introduced to improve convergence and numerical stability under severe conditions. The model is validated by comparing its results with available published numerical and experimental results. The thermal behaviors of the contact interface are studied in a wide range of working conditions. The influences of surface roughness and thermal effect on lubrication performance are revealed. The results show that the proposed model can be used as a powerful analysis tool for lubrication performance and temperature prediction in various heavy-load, high-speed lubricated components over a wide range of lubrication conditions.
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Abbreviations
- a, b :
-
Semi axis Hertzian contact ellipse in the x and y directions, respectively
- c 1, c 2 :
-
Specific heats of solids 1 and 2, respectively
- c f :
-
Specific heat of lubricant
- d :
-
Thickness of the temperature calculation domain of solids
- E′ :
-
Effectively elastic modulus
- f b :
-
Boundary lubrication friction coefficient
- h :
-
Film thickness
- h 0(t):
-
Rigid body central distance
- h a :
-
Average film thickness
- h b :
-
Boundary film thickness
- h cen :
-
Central film thickness
- h min :
-
Minimum film thickness
- k :
-
Hertzian contact ellipticity
- k 1, k 2 :
-
Thermal conductivities of solids 1 and 2, respectively
- k f :
-
Thermal conductivity of lubricant
- p :
-
Pressure
- p h :
-
Maximum Hertzian pressure
- q :
-
Lubricant velocity in the z direction
- R x, R y :
-
Equivalent radius of contact surfaces in the x and y directions, respectively
- s 0 :
-
Coefficient for Roelands equation
- s 1(x, y), s 2(x, y):
-
Discretized roughness height data matrix of surfaces 1 and 2, respectively
- SRR :
-
Slide—roll ratio
- t :
-
Time
- Δt :
-
Dimensionless time step length
- T :
-
Temperature
- T 0 :
-
Ambient temperature
- T g :
-
Temperature on the surface of glass
- T m :
-
Mean temperature of oil film
- T mid :
-
Central film temperature
- T s :
-
Temperature on the surface of steel
- T xoz :
-
Temperature in the x-o-z cross section
- u :
-
Lubricant velocity in the x direction
- u 1, u 2 :
-
Velocities of surfaces 1 and 2, respectively
- u e :
-
Entrainment velocity
- v :
-
Lubricant velocity in the y direction
- V e(x, y, t):
-
Elastic deformation
- w :
-
Applied load
- W c :
-
Contact load ratio
- x :
-
Coordinate in entrainment direction
- x in xout :
-
Inlet and outlet edges in the x direction, respectively
- ΔX :
-
Dimensionless mesh size in the x direction
- y :
-
Coordinate perpendicular to entrainment direction
- y in, y out :
-
Inlet and outlet edges in the y direction, respectively
- z :
-
Vertical coordinate across oil film
- z 0 :
-
Coefficient for Roelands equation
- z 1, z 2 :
-
Vertical coordinates for solids 1 and 2, respectively
- α :
-
Viscosity-pressure coefficient
- β :
-
Thermal expansion coefficient of lubricant
- γ :
-
Viscosity-temperature coefficient
- δ 1(x, y, t):
-
Roughness heights of surfaces 1 and 2, respectively δ1(x, y, t)
- ε p, δ w, δ t :
-
Convergence factors of pressure, load, and temperature, respectively
- η :
-
Lubricant viscosity
- η 0 :
-
Ambient viscosity of lubricant
- η* :
-
Lubricant effective viscosity
- ξ :
-
x coordinate of pressure when calculating deformation
- ρ :
-
Lubricant density
- ρ 0 :
-
Ambient density of lubricant
- ρ 1, ρ 2 :
-
Densities of solids 1 and 2, respectively
- ϛ :
-
y coordinate of pressure when calculating deformation
- τ :
-
Shear stress
- τ 0 :
-
Characteristic shear stress
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Acknowledgements
This work was supported by the National Key R&D Program of China (Grant No. 2018YFB0703804).
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Wu, J., Wang, L., Li, Z. et al. Thermal analysis of lubricated three-dimensional contact bodies considering interface roughness. Front. Mech. Eng. 17, 16 (2022). https://doi.org/10.1007/s11465-022-0672-8
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DOI: https://doi.org/10.1007/s11465-022-0672-8