Tribology Letters

, 65:35 | Cite as

Design-Driven Modeling of Surface-Textured Full-Film Lubricated Sliding: Validation and Rationale of Nonstandard Thrust Observations

  • Jonathon K. Schuh
  • Yong Hoon Lee
  • James T. Allison
  • Randy H. EwoldtEmail author
Original Paper


Our recent experimental work showed that asymmetry is needed for surface textures to decrease friction in full-film lubricated sliding (e.g., thrust bearings) with Newtonian fluids; textures reduce the shear load and produce a separating normal force (Schuh and Ewoldt in Tribol Int 97:490–498, 2016). However, standard slider bearing theory cannot explain the sign of the observed normal thrust, and any effort to optimize surface textures would be premature if modeling and simulations are not validated with experiments. Here we model the flow with the Reynolds equation in cylindrical coordinates, numerically implemented with a pseudo-spectral method. The model predictions match experiments, rationalize the sign of the normal force, and allow for design of surface texture geometry. To minimize sliding friction with angled cylindrical textures, an optimal angle of asymmetry β exists. The optimal angle depends on the film thickness but not the sliding velocity within the applicable range of the model. Outside the scope of this paper, the model is being used to optimize generalized surface texture topography (Lee et al. in J Mech Design, to appear).


Surface textures Reynolds equation Pseudo-spectral method Optimization 



The authors would like to thank Paul Fischer, who taught the basics of the pseudo-spectral method that this work is based on. This work was supported by the National Science Foundation under Grant No. CMMI-1463203 and also by the Engineering Research Center for Compact and Efficient Fluid Power (CCEFP), supported by the National Science Foundation under Grant No. EEC-0540834.

Supplementary material

11249_2017_818_MOESM1_ESM.pdf (1.6 mb)
Supplementary material 1 (DOCX 1617 kb)


  1. 1.
    Schuh, J., Ewoldt, R.: Asymmetric surface textures decrease friction with Newtonian fluids in full film lubricated sliding contact. Tribol. Int. 97, 490–498 (2016)CrossRefGoogle Scholar
  2. 2.
    Lee, Y.H., Schuh, J.K., Ewoldt, R.H., Allison, J.T.: Enhancing full-film lubrication performance via arbitrary surface texture design. J. Mech. Design. (to appear)Google Scholar
  3. 3.
    Schuh, J.: Surface textures and non-Newtonian fluids for decreased friction in full film lubrication. Masters Thesis, Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign (2015)Google Scholar
  4. 4.
    Shen, C., Khonsari, M.: Effect of dimple’s internal structure on hydrodynamic lubrication. Tribol. Lett. 52, 415–430 (2013)CrossRefGoogle Scholar
  5. 5.
    Nanbu, T., Ren, N., Yasuda, Y., Zhu, D., Wang, Q.: Micro-textures in concentrated conformal-contact lubrication: effects of texture bottom shape and surface relative motion. Tribol. Lett. 29, 241–252 (2008)CrossRefGoogle Scholar
  6. 6.
    Han, J., Fang, L., Sun, J., Wang, Y., Ge, S., Zhu, H.: Hydrodynamic lubrication of surfaces with asymmetric microdimple. Tribol. Trans. 54, 607–614 (2011)CrossRefGoogle Scholar
  7. 7.
    Stachowiak, G., Bachelor, A.: Engineering Tribology. Elsevier, Amsterdam (2014)Google Scholar
  8. 8.
    Ronen, A., Etsion, I., Kligerman, Y.: Friction-reducing surface-texturing in reciprocating automotive components. Tribol. Trans. 44(3), 359–366 (2001)CrossRefGoogle Scholar
  9. 9.
    Siripuram, R., Stephens, L.: Effect of deterministic asperity geometry on hydrodynamic lubrication. J. Tribol. 126, 527–534 (2004)CrossRefGoogle Scholar
  10. 10.
    Qiu, Y., Khonsari, M.: On the prediction of cavitation in dimples using a mass-conservative algorithm. J. Tribol. 131, 041702-1-11 (2009)CrossRefGoogle Scholar
  11. 11.
    Qiu, M., Raeymaekers, B.: The load-carrying capacity and friction coefficient of incompressible textured parallel slider bearings with surface roughness inside the texture features. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol 229(547–556), 1–10 (2015)Google Scholar
  12. 12.
    Zhang, J., Su, L., Talke, F.E.: Effect of surface texture on the flying characteristics of pico sliders. IEEE Trans. Magn. 41, 3022–3024 (2005)CrossRefGoogle Scholar
  13. 13.
    Kango, S., Singh, D., Sharma, R.: Numerical investigation on the influence of surface texture on the performance of hydrodynamic journal bearing. Meccanica 47, 469–482 (2012)CrossRefGoogle Scholar
  14. 14.
    Tala-Ighil, N., Maspeyrot, P., Fillon, M., Bountif, A.: Effects of surface texture on journal-bearing characteristics under steady-state operating conditions. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol 221, 623–633 (2007)CrossRefGoogle Scholar
  15. 15.
    Wang, L., Wang, W., Wang, H., Ma, T., Hu, Y.: Numerical analysis on the factors affecting the hydrodynamic performance for the parallel surfaces with microtextures. J. Tribol. 136, 021702-1-8 (2014)Google Scholar
  16. 16.
    Yu, H., Wang, X., Zhou, F.: Geometric shape effects of surface texture on the generation of hydrodynamic pressure between conformal contacting surfaces. Tribol. Lett. 37, 123–130 (2010)CrossRefGoogle Scholar
  17. 17.
    Dobrica, M., Fillon, M., Pascovici, M., Cicone, T.: Optimizing surface texture for hydrodynamic lubricated contacts using a mass-conserving numerical approach. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol 224, 737–750 (2010)CrossRefGoogle Scholar
  18. 18.
    Shen, C., Khonsari, M.: Numerical optimization of texture shape for parallel surface under unidirectional and bidirectional sliding. Tribol. Int. 82, 1–11 (2015)CrossRefGoogle Scholar
  19. 19.
    Wakuda, M., Yamauchi, Y., Kanzaki, S., Yasuda, Y.: Effect of surface texturing on friction reduction between ceramic and steel materials under lubricated sliding contact. Wear 254(3–4), 356–363 (2003)CrossRefGoogle Scholar
  20. 20.
    Feldman, Y., Kligerman, Y., Etsion, I., Haber, S.: The validity of the Reynolds equation in modeling hydrostatic effects in gas lubricated textured parallel surfaces. J. Tribol. 128, 345–350 (2006)CrossRefGoogle Scholar
  21. 21.
    Qiu, M., Bailey, B., Stoll, R., Raeymaekers, B.: The accuracy of the compressible Reynolds equation for predicting the local pressure in gas-lubricated textured parallel slider bearings. Tribol. Int. 72, 83–89 (2014)CrossRefGoogle Scholar
  22. 22.
    Woloszynski, T., Podsiadlo, P., Stachowiak, G.: Evaluation of discretization and integration methods for the analysis of hydrodynamic bearings with and without surface texturing. Tribol. Lett. 51, 25–47 (2013)CrossRefGoogle Scholar
  23. 23.
    Dobrica, M., Fillon, M.: About the validity of Reynolds equation and inertia effects in textured sliders of infinite width. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol 223, 69–78 (2009)CrossRefGoogle Scholar
  24. 24.
    Jang, G., Lee, S., Kim, H.: Finite element analysis of the coupled journal and thrust bearing in a computer hard disk drive. J. Tribol. 128, 335–340 (2006)CrossRefGoogle Scholar
  25. 25.
    Wahl, M.E., Talke, F.E.: Numerical simulation of the steady state flying characteristics of a 50% slider with surface texture. IEEE Trans. Magn. 30, 4122–4124 (1994)CrossRefGoogle Scholar
  26. 26.
    Schumack, M.: Application of the pseudospectral method to thermohydrodynamic lubrication. Int. J. Numer. Methods Fluids 23, 1145–1161 (1996)CrossRefGoogle Scholar
  27. 27.
    Gantasala, S., Krishna, I.R.P., Sekhar, A.S.: Dynamic analysis of rotors supported on journal bearings by solving Reynolds equation using pseudospectral method. In: Proceedings of the 9th IFToMM International Conference on Rotor Dynamics (2015)Google Scholar
  28. 28.
    Hussaini, M., Zang, T.: Spectral methods in fluid dynamics. Annu. Rev. Fluid Mech. 19, 339–367 (1987)CrossRefGoogle Scholar
  29. 29.
    Fornberg, B., Sloan, D.: A review of pseudo spectral methods for solving partial differential equations. Acta Numer. 3, 203–267 (1994)CrossRefGoogle Scholar
  30. 30.
    Shen, J.: Efficient spectral-Galerkin method I. Direct solvers of second- and fourth-order equations using Legendre polynomials. SIAM J. Sci. Comput. 15, 1489–1505 (1994)CrossRefGoogle Scholar
  31. 31.
    Heath, M.: Scientific Computing: An Introductory Survey, 2nd edn. McGraw-Hill, New York (2002)Google Scholar
  32. 32.
    Beschorner, K.E., Higgs III, C.F., Lovell, M.R.: Derivation of Reynolds equation in cylindrical coordinates applicable to pin-on-disk and CMP. In: Proceedings of the STLE/ASME International Joint Tribology Conference, Miami, FL, USA (2008)Google Scholar
  33. 33.
    Lewis, H., Bellan, P.: Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates. J. Math. Phys. 31(11), 2592–2596 (1990)CrossRefGoogle Scholar
  34. 34.
    Karniadakis, G., Sherwin, S.: Spectral/hp Element Methods for Computational Fluid Dynamics. Oxford University Press, Oxford (2005)CrossRefGoogle Scholar
  35. 35.
    Kopriva, D.: Implementing Spectral Methods for Partial Differential Equations. Springer, Berlin (2009)CrossRefGoogle Scholar
  36. 36.
    Fesanghary, M., Khonsari, M.: On the optimum groove shapes for load-carrying capacity enhancement in parallel flat surface bearings: theory and experiment. Tribol. Int. 67, 254–262 (2013)CrossRefGoogle Scholar
  37. 37.
    Macosko, Rheology: Principles, Measurements, and Applications. Wiley-VCH, Weinheim (1994)Google Scholar
  38. 38.
    Reynolds, O.: On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments including an experimental determination of the viscosity of olive oil. Philos. Trans. R. Soc. Lond. 177, 157–234 (1886)CrossRefGoogle Scholar
  39. 39.
    Rayleigh, L.: Notes on the theory of lubrication. Lond. Edinb. Dublin Philos. Mag. J. Sci. 35, 1–12 (1918)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Jonathon K. Schuh
    • 1
  • Yong Hoon Lee
    • 1
  • James T. Allison
    • 2
  • Randy H. Ewoldt
    • 1
    Email author
  1. 1.Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of Industrial Enterprise and Systems EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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