Skip to main content
SpringerLink
Log in

Numerical Prediction of Wear Process of an Initial Line Contact in Mixed Lubrication Conditions

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

In mixed lubrication, wear is inevitable under the sliding condition due to the existence of the asperity contacts that bear partial normal load. This study proposes a numerical approach to predict the wear process of a cylinder sliding over a ring disk in mixed lubrication. Elastohydrodynamic lubrication of the rough contact, which is a line contact at the beginning of the sliding and gradually becomes a flatten cylinder/disk contact with the wear progress, is simulated with the three-dimensional finite element method. The elastic–plastic asperity contact model is adopted to calculate the asperity contact pressure. Based on the asperity contact load, the cylinder wear is computed with the Archard’s wear law. The wear process is simulated step by step, starting from an initial line contact configuration. In each calculation step, the cylinder geometry profile is updated, and the balance of the externally applied load with the elastohydrodynamic and the asperity contact loads is achieved. Variations of the cylinder geometry profile, the lubricant film thickness, and the friction coefficient are obtained for the whole rubbing process. Reasonable agreements on the changes of the wear scar width and the friction coefficient during the rubbing process between the simulation and the experiment results are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

Abbreviations

b :

Semi-width of Hertz contact (m)

b c :

Semi-width of the contact of a cylinder against a rough surface (m)

b w :

Semi-width of cylinder wear scar (m)

C :

Heat capacity (J kg−1 K−1)

E 1,2 :

Young’s modulus (Pa)

E′:

Effective modulus of elasticity (Pa)

f :

Mixed lubrication friction coefficient

f c :

Boundary condition friction coefficient

H :

Material hardness (Pa)

H T :

Total enthalpy (J Kg−1)

h :

Nominal film thickness (m)

h static :

Static enthalpy (J Kg−1)

Δh :

Mesh motion (m)

K :

Wear coefficient

K m :

Maximum contact pressure factor

k :

Turbulent kinetic energy (J)

k T :

Thermal conductivity (W m−1 K−1)

L :

Length of the cylinder wear scar (m)

P k :

Production rate of turbulence

p :

Hydrodynamic pressure (Pa)

p c :

Asperity contact pressure (Pa)

R :

Cylinder radius (m)

R s :

Asperity radius (m)

s :

Sliding distance (m)

Δs :

Sliding distance increment (m)

T :

Temperature (K)

T 0 :

Ambient temperature (K)

t :

Time (s)

u :

Vector of velocity (m/s)

u + :

Near-wall velocity (m/s)

V :

Total wear volume (m3)

ΔV :

Wear volume increment (m3)

W :

Normal load (N)

W c :

Asperity contact load (N)

W f :

Hydrodynamic load (N)

x, y, z :

Coordinate (m)

y s :

Distance between the mean line of asperities and the mean line of surface heights (m)

α :

Pressure viscosity index (m2 N−1)

β :

Thermoviscosity index (oC−1)

\(\dot{\gamma }\) :

Shear rate (s−1)

η :

Dynamic viscosity of fluid (Pa.s)

η 0 :

Fluid viscosity in the ambient conditions (Pa.s)

η s :

Asperity density (m−2)

η t :

Turbulence viscosity (Pa.s)

ν 1,2 :

Poisson’s ratios

ρ :

Fluid density (kg/m3)

ρ 0 :

Fluid density in the ambient conditions (kg/m3)

σ :

Equivalent surface roughness (m)

σ 1,2 :

Standard deviation of surface heights (m)

σ s :

Standard deviation of the asperity heights (m)

τ :

Stress tensor (Pa)

τ 0 :

Eyring stress (Pa)

ϕ :

Distribution function of asperity heights

ω :

Turbulent frequency (s−1)

ω c :

Asperity contact interference (m)

ω cr :

Critical interference (m)

References

  1. Meng, H.C., Ludema, K.C.: Wear models and predictive equations: their form and content. Wear 181, 443–457 (1995). doi:10.1016/0043-1648(95)90158-2

    Article  Google Scholar 

  2. Archard, J.F.: Contact and rubbing of flat surfaces. J. Appl. Phys. 24(8), 981–988 (1953). doi:10.1063/1.1721448

    Article  Google Scholar 

  3. Põdra, P., Andersson, S.: Simulating sliding wear with finite element method. Tribol. Int. 32(2), 71–81 (1999). doi:10.1016/S0301-679X(99)00012-2

    Article  Google Scholar 

  4. Põdra, P., Andersson, S.: Wear simulation with the Winkler surface model. Wear 207(1–2), 79–85 (1997). doi:10.1016/S0043-1648(96)07468-6

    Article  Google Scholar 

  5. Olofsson, U., Andersson, S., Björklund, S.: Simulation of mild wear in boundary lubricated spherical roller thrust bearings. Wear 241(2), 180–185 (2000). doi:10.1016/S0043-1648(00)00373-2

    Article  Google Scholar 

  6. Öqvist, M.: Numerical simulation of mild wear using updated geometry with different step size approaches. Wear 249(1–2), 6–11 (2001). doi:10.1016/S0043-1648(00)00548-2

    Article  Google Scholar 

  7. Flodin, A., Andersson, S.: Simulation of mild wear in spur gears. Wear 207(1–2), 16–23 (1997). doi:10.1016/S0043-1648(96)07467-4

    Article  Google Scholar 

  8. Flodin, A., Andersson, S.: A simplified model for wear prediction in helical gears. Wear 249(3–4), 285–292 (2001). doi:10.1016/S0043-1648(01)00556-7

    Article  Google Scholar 

  9. Brauer, J., Andersson, S.: Simulation of wear in gears with flank interference: a mixed FE and analytical approach. Wear 254(11), 1216–1232 (2003). doi:10.1016/S0043-1648(03)00338-7

    Article  Google Scholar 

  10. Põdra, P., Andersson, S.: Finite element analysis wear simulation of a conical spinning contact considering surface topography. Wear 224(1), 13–21 (1999). doi:10.1016/S0043-1648(98)00318-4

    Article  Google Scholar 

  11. Hugnell, A.B.J., Bjorklund, S., Andersson, S.: Simulation of the mild wear in a cam-follower contact with follower rotation. Wear 199(2), 202–210 (1996). doi:10.1016/0043-1648(96)06920-7

    Article  Google Scholar 

  12. Sawyer, W.G.: Wear predictions for a simple-cam including the coupled evolution of wear and load. Lubr. Eng. 57(9), 31–36 (2001)

    Google Scholar 

  13. Mukras, S., Kim, N.H., Sawyer, W.G., Jackson, D.B., Bergquist, L.W.: Numerical integration schemes and parallel computation for wear prediction using finite element method. Wear 266(7–8), 822–831 (2009). doi:10.1016/j.wear.2008.12.016

    Article  Google Scholar 

  14. McColl, I.R., Ding, J., Leen, S.B.: Finite element simulation and experimental validation of fretting wear. Wear 256(11–12), 1114–1127 (2004). doi:10.1016/j.wear.2003.07.001

    Article  Google Scholar 

  15. Hegadekatte, V., Huber, N., Kraft, O.: Finite element based simulation of dry sliding wear. Model. Simul. Mater. Sci. Eng. 13(1), 57–75 (2005). doi:10.1088/0965-0393/13/1/005

    Article  Google Scholar 

  16. Benabdallah, H., Olender, D.: Finite element simulation of the wear of polyoxymethylene in pin-on-disc configuration. Wear 261(11–12), 1213–1224 (2006). doi:10.1016/j.wear.2006.03.040

    Article  Google Scholar 

  17. Telliskivi, T.: Simulation of wear in a rolling-sliding contact by a semi-Winkler model and the Archard’s wear law. Wear 256(7–8), 817–831 (2004). doi:10.1016/S0043-1648(03)00524-6

    Article  Google Scholar 

  18. Sfantos, G.K., Aliabadi, M.H.: Wear simulation using an incremental sliding boundary element method. Wear 260(9–10), 1119–1128 (2006). doi:10.1016/j.wear.2005.07.020

    Article  Google Scholar 

  19. Zhu, D., Martini, A., Wang, W., Hu, Y., Lisowsky, B., Wang, Q.J.: Simulation of sliding wear in mixed lubrication. Tribol. Trans. 129(3), 544–552 (2007). doi:10.1115/1.2736439

    Article  Google Scholar 

  20. Bowden, F.P., Leben, L.: The friction of lubricated metals. Philos. Trans. R. Soc. Lond. A 239(799), 1–27 (1940). doi:10.1098/rsta.1940.0007

    Article  Google Scholar 

  21. Adamson, A.W.: Physical chemistry of surfaces. Interscience, New York (1976)

    Google Scholar 

  22. Greenwood, J.A., Williamson, J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. Lond. Ser. A. 295(1442), 300–319 (1966). doi:10.1098/rspa.1966.0242

    Article  Google Scholar 

  23. Chang, W.R., Etsion, I., Bogy, D.B.: An elastic-plastic model for the contact of rough surfaces. J. Tribol. 109(2), 257–263 (1987). doi:10.1115/1.3261348

    Article  Google Scholar 

  24. Cohen, D., Kligerman, Y., Etsion, I.: A model for contact and static friction of nominally flat rough surfaces under full stick contact condition. J. Tribol. 130(3), 031401-1-9 (2008). doi:10.1115/1.2908925

    Article  Google Scholar 

  25. Tabor, D.: The hardness of metals. Oxford University Press, Oxford (1951)

    Google Scholar 

  26. Zhu, D., Cheng, H.S.: Effect of surface roughness on the point contact EHL. J. Tribol. 110(1), 32–37 (1988). doi:10.1115/1.3261571

    Article  Google Scholar 

  27. Jiang, X., Cheng, H.S., Hua, D.Y.: A theoretical analysis of mixed lubrication by macro micro approach: part I—results in a gear surface contact. Tribol. Trans. 43(4), 689–699 (2000). doi:10.1080/10402000008982398

    Article  Google Scholar 

  28. Lo, C.C.: Elastic contact of rough cylinders. Int. J. Mech. Sci. 11(1), 105–115 (1969). doi:10.1016/0020-7403(69)90083-6

    Article  Google Scholar 

  29. CFX 13.0. Users Guide. ANSYS Inc. (2013)

  30. Roelands, C. J. A.: Correlational aspects of the viscosity–temperature–pressure relationship of lubricating oils. Ph.D. thesis, Delft University of Technology, Netherlands (1966)

  31. Dowson, D., Higginson, G.R.: Elasto-hydrodynamic lubrication. Pergamon Press, Oxford (1977)

    Google Scholar 

  32. Wen, S.Z., Huang, P.: Principles of tribology. Tsinghua University Press, Beijing (2008)

    Google Scholar 

  33. Kim, N.H., Won, D., Burris, D., Holtkamp, B., Gessel, G.R., Swanson, P., Sawyer, W.G.: Finite element analysis and experiments of metal/metal wear in oscillatory contacts. Wear 258(11–12), 1787–1793 (2005). doi:10.1016/j.wear.2004.12.014

    Article  Google Scholar 

  34. Jackson, R.L., Green, I.: The behavior of thrust washer bearings considering mixed lubrication and asperity contact. Tribol. Trans. 49(2), 233–247 (2006). doi:10.1080/05698190600614841

    Article  Google Scholar 

  35. Ruan, B., Salant, R.F., Green, I.: A mixed lubrication model of liquid/gas mechanical face seals. Tribol. Trans. 40(4), 647–657 (1997). doi:10.1080/10402009708983705

    Article  Google Scholar 

  36. Hu, Y.Z., Li, N., Tønder, K.: A dynamic system model for lubricated sliding wear and running-in. J. Tribol. 113(3), 499–505 (1991). doi:10.1115/1.2920651

    Article  Google Scholar 

  37. Wang, W., Wong, P.L., Guo, F.: Application of partial elastohydrodynamic lubrication analysis in dynamic wear study for running-in. Wear 257(7), 823–832 (2004). doi:10.1016/j.wear.2004.05.003

    Article  Google Scholar 

  38. Akbarzadeh, S., Khonsari, M.M.: On the prediction of running-in behavior in mixed -lubrication line contact. J. Tribol. 132(3), 032102-1-11 (2010). doi:10.1115/1.4001622

    Article  Google Scholar 

  39. Qiu, Y., Khonsari, M.M.: Investigation of tribological behaviors of annular rings with spiral groove. Tribol. Int. 44(12), 1610–1619 (2011). doi:10.1016/j.triboint.2011.05.008

    Article  Google Scholar 

  40. Larsson, R.: Modelling the effect of surface roughness on lubrication in all regimes. Tribol. Int. 42(4), 512–516 (2009). doi:10.1016/j.triboint.2008.07.007

    Article  Google Scholar 

  41. Wang, W., Wong, P.L., Zhang, Z.: Experimental study of the real time change in surface roughness during running-in for PEHL contacts. Wear 244(1), 140–146 (2000). doi:10.1016/S0043-1648(00)00448-8

    Google Scholar 

  42. Johnson, K., Greenwood, J.A., Poon, S.Y.: Simple theory of asperity contact in elastohydrodynamic lubrication. Wear 19(1), 91–108 (1972). doi:10.1016/0043-1648(72)90445-0

    Article  Google Scholar 

  43. Gelinck, E.R.M., Schipper, D.J.: Deformation of rough line contacts. J. Tribol. 121(3), 449–454 (1999). doi:10.1115/1.2834088

    Article  Google Scholar 

  44. Masjedi, M., Khonsari, M.M.: Film thickness and asperity load formulas for line-contact elastohydrodynamic lubrication with provision for surface roughness. J. Tribol. 134(1), 011503-1-10 (2012). doi:10.1115/1.4005514

    Article  Google Scholar 

  45. Kovalchenko, A., Ajayi, O., Erdemir, A., Fenske, G.: Friction and wear behavior of laser textured surface under lubricated initial point contact. Wear 271(9–10), 1719–1725 (2011). doi:10.1016/j.wear.2010.12.049

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Tribology, Tsinghua University, Beijing, 100084, China

    Lichun Hao & Yonggang Meng

Authors
  1. Lichun Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yonggang Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yonggang Meng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hao, L., Meng, Y. Numerical Prediction of Wear Process of an Initial Line Contact in Mixed Lubrication Conditions. Tribol Lett 60, 31 (2015). https://doi.org/10.1007/s11249-015-0609-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11249-015-0609-z

Keywords

Search

Navigation