RESEARCH ARTICLE

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

  • Jiqiang WU 1 ,
  • Liqin WANG 1,2 ,
  • Zhen LI 1 ,
  • Peng LIU 1 ,
  • Chuanwei ZHANG 1
Expand
  • 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

Received date: 25 Jul 2021

Accepted date: 10 Jan 2022

Published date: 15 Jun 2022

Copyright

2022 Higher Education Press

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.

Cite this article

Jiqiang WU , Liqin WANG , Zhen LI , Peng LIU , Chuanwei ZHANG . Thermal analysis of lubricated three-dimensional contact bodies considering interface roughness[J]. Frontiers of Mechanical Engineering, 2022 , 17(2) : 16 . DOI: 10.1007/s11465-022-0672-8

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).
1
Cheng H S , Sternlicht B . A numerical solution for the pressure, temperature, and film thickness between two infinitely long, lubricated rolling and sliding cylinders, under heavy loads. Journal of Basic Engineering, 1965, 87( 3): 695– 704

DOI

2
Zhu D , Wen S Z . A full numerical solution for the thermoelastohydrodynamic problem in elliptical contacts. Journal of Tribology, 1984, 106( 2): 246– 254

DOI

3
Kim K H , Sadeghi F . Three-dimensional temperature distribution in EHD lubrication: part I-circular contact. Journal of Tribology, 1992, 114( 1): 32– 41

DOI

4
Yang P , Qu S , Kaneta M , Nishikawa H . Formation of steady dimples in point TEHL contacts. Journal of Tribology, 2001, 123( 1): 42– 49

DOI

5
Guo F , Yang P R , Qu S Y . On the theory of thermal elastohydrodynamic lubrication at high slide-roll ratios-circular glass-steel contact solution at opposite sliding. Journal of Tribology, 2001, 123( 4): 816– 821

DOI

6
Kaneta M , Yang P . Formation mechanism of steady multi-dimples in thermal EHL point contacts. Journal of Tribology, 2003, 125( 2): 241– 251

DOI

7
Kim H J , Ehret P , Dowson D , Taylor C M . Thermal elastohydrodynamic analysis of circular contacts part 2: non-Newtonian model. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2001, 215( 4): 353– 362

DOI

8
Liu X L , Jiang M , Yang P R , Kaneta M . Non-Newtonian thermal analyses of point EHL contacts using the Eyring model. Journal of Tribology, 2005, 127( 1): 70– 81

DOI

9
Cui J , Yang P , Jin Z M , Dowson D . Transient elastohydrodynamic analysis of elliptical contacts. Part 3: non-Newtonian lubricant solution under isothermal and thermal conditions. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2007, 221( 1): 63– 73

DOI

10
Liu H J , Zhu C C , Gu Z L , Wang Z J , Tang J Y . Effect of thermal properties of a coated elastohydrodynamic lubrication line contact under various slide-to-roll ratios. Journal of Heat Transfer, 2017, 139( 7): 074505

DOI

11
Habchi W . On the negative influence of roller-end axial profiling on friction in thermal elastohydrodynamic lubricated finite line contacts. Journal of Tribology, 2020, 142( 11): 111601

DOI

12
He T , Wang Q J , Zhang X , Liu Y C , Li Z , Kim H J , Pack S . Modeling thermal-visco-elastohydrodynamic lubrication (TVEHL) interfaces of polymer-based materials. Tribology International, 2021, 154 : 106691

DOI

13
Zhao J X , Sadeghi F , Hoeprich M H . Analysis of EHL circular contact start up: part II—surface temperature rise model and results. Journal of Tribology, 2001, 123( 1): 75– 82

DOI

14
Zhang H B , Wang W Z , Zhang S G , Zhao Z Q . Semi-analytical solution of three-dimensional steady state thermoelastic contact problem of multilayered material under friction heating. International Journal of Thermal Sciences, 2018, 127 : 384– 399

DOI

15
Yang W Y , Zhou Q H , Huang Y Y , Wang J X , Jin X Q , Keer L M . A thermoelastic contact model between a sliding ball and a stationary half space distributed with spherical inhomogeneities. Tribology International, 2019, 131 : 33– 44

DOI

16
Zhang Y G , Wang W Z , Liang H , Zhao Z Q . Layered oil slip model for investigation of film thickness behaviours at high speed conditions. Tribology International, 2019, 131 : 137– 147

DOI

17
Johnson K L , Greenwood J A , Poon S Y . A simple theory of asperity contact in elastohydro-dynamic lubrication. Wear, 1972, 19( 1): 91– 108

DOI

18
Patir N , Cheng H S . An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication. Journal of Lubrication Technology, 1978, 100( 1): 12– 17

DOI

19
Zhu D , Cheng H S . Effect of surface roughness on the point contact EHL. Journal of Tribology, 1988, 110( 1): 32– 37

DOI

20
Venner C H , ten Napel W E . Surface roughness effects in an EHL line contact. Journal of Tribology, 1992, 114( 3): 616– 622

DOI

21
Chang L , Cusano C , Conry T F . Effects of lubricant rheology and kinematic conditions on micro-elastohydrodynamic lubrication. Journal of Tribology, 1989, 111( 2): 344– 351

DOI

22
Kweh C C , Patching M J , Evans H P , Snidle R W . Simulation of elastohydrodynamic contacts between rough surfaces. Journal of Tribology, 1992, 114( 3): 412– 419

DOI

23
Ai X . Numerical analyses of elastohydrodynamically lubricated line and point contacts with rough surfaces by using semi-system and multigrid methods. Dissertation for the Doctoral Degree. Evanston: Northwestern University, 1993, 56– 82

24
Hu Y Z , Zhu D . A full numerical solution to the mixed lubrication in point contacts. Journal of Tribology, 2000, 122( 1): 1– 9

DOI

25
He T , Ren N , Zhu D , Wang J X . Plasto-elastohydrodynamic lubrication in point contacts for surfaces with three-dimensional sinusoidal waviness and real machined roughness. Journal of Tribology, 2014, 136( 3): 031504

DOI

26
He T , Zhu D , Yu C J , Wang Q J . Mixed elastohydrodynamic lubrication model for finite roller-coated half space interfaces. Tribology International, 2019, 134 : 178– 189

DOI

27
He T , Wang Z J , Wu J Q . Effect of imperfect coating on the elastohydrodynamic lubrication: dislocation-like and force-like coating-substrate interfaces. Tribology International, 2020, 143 : 106098

DOI

28
He T , Wang Q J , Zhang X , Liu Y C , Li Z , Kim H J , Pack S . Visco-elastohydrodynamic lubrication of layered materials with imperfect layer-substrate interfaces. International Journal of Mechanical Sciences, 2021, 189 : 105993

DOI

29
Pu W , Wang J X , Yang R S , Zhu D . Mixed elastohydrodynamic lubrication with three-dimensional machined roughness in spiral bevel and hypoid gears. Journal of Tribology, 2015, 137( 4): 041503

DOI

30
Wang Z Z , Pu W , Zhang Y , Cao W . Transient behaviors of friction, temperature and fatigue in different contact trajectories for spiral bevel gears. Tribology International, 2020, 141 : 105965

DOI

31
Gan L , Xiao K , Wang J X , Pu W , Cao W . A numerical method to investigate the temperature behavior of spiral bevel gears under mixed lubrication condition. Applied Thermal Engineering, 2019, 147 : 866– 875

DOI

32
Chen S , Yin N , Cai X J , Zhang Z N . Iteration framework for solving mixed lubrication computation problems. Frontiers of Mechanical Engineering, 2021, 16( 3): 635– 648

DOI

33
Wang W Z , Liu Y C , Wang H , Hu Y Z . A computer thermal model of mixed lubrication in point contacts. Journal of Tribology, 2004, 126( 1): 162– 170

DOI

34
Wang W Z , Hu Y Z , Liu Y C , Wang H . Deterministic solutions and thermal analysis for mixed lubrication in point contacts. Tribology International, 2007, 40( 4): 687– 693

DOI

35
Yan X L , Zhang Y Y , Xie G X , Qin F , Zhang X W . Effects of spinning on the mixed thermal elastohydrodynamic lubrication and fatigue life in point contacts. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2019, 233( 12): 1820– 1832

DOI

36
Wang X P , Liu Y C , Zhu D . Numerical solution of mixed thermal elastohydrodynamic lubrication in point contacts with three-dimensional surface roughness. Journal of Tribology, 2017, 139( 1): 011501

DOI

37
Zhu D . On some aspects of numerical solutions of thin-film and mixed elastohydrodynamic lubrication. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2007, 221( 5): 561– 579

DOI

38
Kim H J , Ehret P , Dowson D , Taylor C M . Thermal elastohydrodynamic analysis of circular contacts part 1: Newtonian model. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2001, 215( 4): 339– 352

DOI

39
Roelands C J A , Vlugter J C , Waterman H I . The viscosity-temperature-pressure relationship of lubricating oils and its correlation with chemical constitution. Journal of Basic Engineering, 1963, 85( 4): 601– 607

DOI

40
Dowson D Higginson G R. Elasto-hydrodynamic lubrication: the fundamentals of roller and gear lubrication. Oxford: Pergamon Press, 1966

41
Cui J L , Yang P R . Transient thermo-EHL theory of point contact—the process of a bump on the fast surface passing a bump on the slower surface. Tribology Series, 2003, 43 : 253– 261

DOI

42
Shi X J , Wu J Q , Zhao B , Ma X , Lu X Q . Mixed thermal elastohydrodynamic lubrication analysis with dynamic performance of aero ball bearing during start-up and shut-down. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2020, 234( 6): 873– 886

DOI

43
Liu S B , Wang Q . Studying contact stress fields caused by surface tractions with a discrete convolution and fast Fourier transform algorithm. Journal of Tribology, 2002, 124( 1): 36– 45

DOI

44
Liu S B , Wang Q , Liu G . A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses. Wear, 2000, 243( 1−2): 101– 111

DOI

45
Guo F , Yang P , Wong P L . On the thermal elastohydrodynamic lubrication in opposite sliding circular contacts. Tribology International, 2001, 34( 7): 443– 452

DOI

46
Kaneta M , Yang P , Hooke C J . Effects of the thermal conductivity of contact materials on elastohydrodynamic lubrication characteristics. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2010, 224( 12): 2577– 2587

DOI

47
Liang H , Guo D , Reddyhoff T , Spikes H , Luo J B . Influence of thermal effects on elastohydrodynamic (EHD) lubrication behavior at high speeds. Science China Technological Sciences, 2015, 58( 3): 551– 558

DOI

48
He T , Zhu D , Wang J X , Wang Q J . Experimental and numerical investigations of the stribeck curves for lubricated counterformal contacts. Journal of Tribology, 2017, 139( 2): 021505

DOI

49
Sun H Y Yang P R Chen X Y. Study on abnormal temperature field of slide/roll contact under elastohydrodynamic lubrication. Tribology, 2004, 24(1): 66− 69 (in Chinese)

50
Zhu D , Liu Y C , Wang Q . On the numerical accuracy of rough surface EHL solution. Tribology Transactions, 2014, 57( 4): 570– 580

DOI

51
Zhang Y G , Wang W Z , Zhang S G , Zhao Z Q . Experimental study of EHL film thickness behaviour at high speed in ball-on-ring contacts. Tribology International, 2017, 113 : 216– 223

DOI

Outlines

/