Thermal analysis of lubricated three-dimensional contact bodies considering interface roughness

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.

Key words： thermal elastohydrodynamic lubrication; surface roughness effect; thermal effect; temperature characteristics; severe conditions

Nomenclature

a, b	Semi axis Hertzian contact ellipse in the x and y directions, respectively
c1, c2	Specific heats of solids 1 and 2, respectively
cf	Specific heat of lubricant
d	Thickness of the temperature calculation domain of solids
Eʹ	Effectively elastic modulus
fb	Boundary lubrication friction coefficient
h	Film thickness
h0(t)	Rigid body central distance
ha	Average film thickness
hb	Boundary film thickness
hcen	Central film thickness
hmin	Minimum film thickness
k	Hertzian contact ellipticity
k1, k2	Thermal conductivities of solids 1 and 2, respectively
kf	Thermal conductivity of lubricant
p	Pressure
ph	Maximum Hertzian pressure
q	Lubricant velocity in the z direction
Rx, Ry	Equivalent radius of contact surfaces in the x and y directions, respectively
s0	Coefficient for Roelands equation
s1(x, y), s2(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
T0	Ambient temperature
Tg	Temperature on the surface of glass
Tm	Mean temperature of oil film
Tmid	Central film temperature
Ts	Temperature on the surface of steel
Txoz	Temperature in the x-o-z cross section
u	Lubricant velocity in the x direction
u1, u2	Velocities of surfaces 1 and 2, respectively
ue	Entrainment velocity
v	Lubricant velocity in the y direction
Ve(x, y, t)	Elastic deformation
w	Applied load
Wc	Contact load ratio
x	Coordinate in entrainment direction
xin, xout	Inlet and outlet edges in the x direction, respectively
ΔX	Dimensionless mesh size in the x direction
y	Coordinate perpendicular to entrainment direction
yin, yout	Inlet and outlet edges in the y direction, respectively
z	Vertical coordinate across oil film
z0	Coefficient for Roelands equation
z1, z2	Vertical coordinates for solids 1 and 2, respectively
α	Viscosity–pressure coefficient
β	Thermal expansion coefficient of lubricant
γ	Viscosity–temperature coefficient
δ1(x, y, t), δ2(x, y, t)	Roughness heights of surfaces 1 and 2, respectively
εp, εw, εT	Convergence factors of pressure, load, and temperature, respectively
η	Lubricant viscosity
η0	Ambient viscosity of lubricant
η*	Lubricant effective viscosity
ξ	x coordinate of pressure when calculating deformation
ρ	Lubricant density
ρ0	Ambient density of lubricant
ρ1, ρ2	Densities of solids 1 and 2, respectively
ς	y coordinate of pressure when calculating deformation
τ	Shear stress
τ0	Characteristic shear stress

Acknowledgements

This work was supported by the National Key R&D Program of China (Grant No. 2018YFB0703804).

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