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

doi:10.1007/s11465-022-0672-8

Front. Mech. Eng.

2022, Vol. 17

Issue (2) : 16 https://doi.org/10.1007/s11465-022-0672-8

RESEARCH ARTICLE

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

Jiqiang WU¹, Liqin WANG^1,², Zhen LI¹, Peng LIU¹, Chuanwei ZHANG¹

¹. MIIT Key Laboratory of Aerospace Bearing Technology and Equipment, Harbin Institute of Technology, Harbin 150001, China
². State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150080, China

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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.

Keywords thermal elastohydrodynamic lubrication surface roughness effect thermal effect temperature characteristics severe conditions

Corresponding Author(s): Liqin WANG

About author:

Tongcan Cui and Yizhe Hou contributed equally to this work.

Just Accepted Date: 31 March 2022 Issue Date: 16 June 2022

Cite this article:

Jiqiang WU,Liqin WANG,Zhen LI, et al. Thermal analysis of lubricated three-dimensional contact bodies considering interface roughness[J]. Front. Mech. Eng., 2022, 17(2): 16.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-022-0672-8
https://academic.hep.com.cn/fme/EN/Y2022/V17/I2/16

Fig.1 Geometry and computational domain of mixed TEHL in an elliptical contact.

Fig.2 Numerical calculation flowchart for solving the mixed TEHL problem.

Tab.1 Contacting bodies and lubricant properties parameter for the validation case

Fig.3 Present simulations compared with the numerical results from Ref. [46]: (a) centerline pressure and film thickness distributions, (b) centerline temperature distributions.

Fig.4 Comparison of central film thickness between simulations and experimental data in Ref. [47] at different entrainment velocities.

Tab.2 Parameters of Hertzian contact at different applied loads

Tab.3 Properties of contacting bodies and lubricant

Fig.5 Effect of SRR on film thickness and pressure under different load levels when u_e = 20 m/s: (a) central film thickness, (b) minimum film thickness, (c) maximum pressure, and (d) centerline film thickness and pressure distributions for p_h = 2 GPa.

Fig.6 Effect of SRR on temperature when u_e = 20 m/s and p_h = 2 GPa: (a) central film temperature distributions in the rolling direction at y = 0, (b) maximum temperature, and (c) temperature distributions in the x-o-z cross section at y = 0.

Fig.7 Effect of load on temperature when u_e = 20 m/s and SRR = 0.02: (a) central film temperature distributions in the rolling direction at y = 0, (b) maximum temperature, and (c) temperature distributions in the x-o-z cross section at y = 0.

Fig.8 3D roughness profiles of (a) surface 1 and (b) surface 2. (c) Sketch of mesh discretization in the model.

Fig.9 Comparison of centerline pressure, film thickness, and central film temperature distribution between rough TEHL and smooth TEHL at different SRRs when u_e = 20 m/s and p_h = 2 GPa.

Fig.10 Comparison of the results between rough TEHL and smooth TEHL at different loads when u_e = 20 m/s and SRR = 0.02: (a) maximum pressure and (b) minimum film thickness.

Fig.11 Variations of film thickness, pressure, and temperature distributions at different entrainment velocities when SRR = 0.02 and p_h = 2 GPa.

Fig.12 Effect of entrainment velocity on lubrication performance when SRR = 0.02 and p_h = 2 GPa: (a) central film temperature distributions in the rolling direction at y = 0 and (b) maximum temperature.

Fig.13 Comparison of the results between thermal and isothermal models at different entrainment velocities: (a) average film thickness and (b) maximum pressure.

Fig.14 Comparison of pressure and film thickness profiles at y = 0 between thermal and isothermal models with different entrainment velocities when SRR = 0.02 and p_h = 2 GPa.

a, b	Semi axis Hertzian contact ellipse in the x and y directions, respectively
c₁, c₂	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
h₀(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
k₁, k₂	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
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
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
u₁, u₂	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, x_out	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
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
ε_p, ε_w, ε_T	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
?	y coordinate of pressure when calculating deformation
τ	Shear stress
τ₀	Characteristic shear stress

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