Efficient Optimal Surface Texture Design Using Linearization

  • Chendi LinEmail author
  • Yong Hoon Lee
  • Jonathon K. Schuh
  • Randy H. Ewoldt
  • James T. Allison
Conference paper


Surface textures reduce friction in lubricated sliding contact. This behavior can be modeled using the Reynolds equation, a single partial differential equation (PDE) that relates the hydrodynamic pressure to the gap height. In a previous study, a free-form texture design optimization problem was solved based on this model and two competing design objectives. A pseudo-spectral method was used for PDE solution, which was treated as a black box in the optimization problem. This optimization implementation did not exploit model structure to improve numerical efficiency, so design representation fidelity was limited. Here a new strategy is introduced where design representation resolution and computational efficiency are improved simultaneously. This is achieved by introducing a new optimization variable involving both pressure gradient and the cube of gap height at each mesh node location, and simultaneously solving the flow and texture design problems. This transformation supports linearization of the governing equations and design objectives. Sequential Linear Programming (SLP) is used with the epsilon-constraint method to generate Pareto-optimal texture designs with high resolution and low computational expense. An adaptive trust region is used, based on solution improvement, to manage linearization error. Comparing to the non-linear programming implementation, the solution converged to a set of slightly suboptimal points (maximum 25% objective function degradation when normalized apparent viscosity is 0.5, and moderately better when normalized apparent viscosity is 0.2), but results in significant improvement in computational speed (8.4 times faster).


Multi-objective optimization Linearization Shape optimization Reynolds equation 



This work was supported by National Science Foundation under Grant NO. CMMI-1463203.


  1. 1.
    Etsion, I.: Improving tribological performance of mechanical components by laser surface texturing. Tribol. Lett. 17(4), 733–737 (2004)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. Des. (2017, in press)Google Scholar
  3. 3.
    Dong, C., Yuan, C., Wang, L., Liu, W., Bai, X., Yan, X.: Tribological properties of water-lubricated rubber materials after modification by mos2 nanoparticles. Sci. Rep. 6, 35023 (2016). (12 pp)CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    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(2), 123–130 (2010)CrossRefGoogle Scholar
  6. 6.
    Shen, C., Khonsari, M.M.: Effect of dimples internal structure on hydrodynamic lubrication. Tribol. Lett. 52(3), 415–430 (2013)CrossRefGoogle Scholar
  7. 7.
    Fesanghary, M., Khonsari, M.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
  8. 8.
    Hsu, S.M., Jing, Y., Hua, D., Zhang, H.: Friction reduction using discrete surface textures: principle and design. J. Phys. D Appl. Phys. 47(33), 335307 (2014). (12 pp)CrossRefGoogle Scholar
  9. 9.
    Schuh, J.K., Ewoldt, R.H.: Asymmetric surface textures decrease friction with Newtonian fluids in full film lubricated sliding contact. Tribol. Int. 97, 490–498 (2016)CrossRefGoogle Scholar
  10. 10.
    Lee, Y.H., Schuh, J.K., Ewoldt, R.H., Allison, J.T.: Shape parameterization comparison for full-film lubrication texture design. In: ASME 2016 IDETC/CIE, Volume 2B: 42nd Design Automation Conference, Boston, MA, p. V02BT03A037 (11 pp), ASME, August 2016Google Scholar
  11. 11.
    Ronen, A., Etsion, I., Kligerman, Y.: Friction-reducing surface texturing in reciprocating automotive componenets. Tribol. Trans. 44, 359–366 (2001)CrossRefGoogle Scholar
  12. 12.
    Siripuram, R., Stephens, L.: Effect of deterministic asperity geometry on hydrodynamic lubrication. J. Tribol. 126, 527–534 (2004)CrossRefGoogle Scholar
  13. 13.
    Qiu, Y., Khonsari, M.M.: On the prediction of cavitation in dimples using a mass-conservative algorithm. J. Tribol. 131, 041702-1–041702-11 (2009)CrossRefGoogle Scholar
  14. 14.
    Schuh, J.K., Lee, Y.H., Allison, J.T., Ewoldt, R.H.: Design-driven modeling of surface-textured full-film lubricated sliding: validation and rationale of nonstandard thrust observations. Tribol. Lett. 65(2), 35 (2017). (17 pp)CrossRefGoogle Scholar
  15. 15.
    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. Proc. R. Soc. Lond. 40(242–245), 191–203 (1886)CrossRefzbMATHGoogle Scholar
  16. 16.
    Cramer, E.J., Dennis, J.J.E., Frank, P.D., Lewis, R.M., Shubin, G.R.: Problem formulation for multidisciplinary optimization. SIAM J. Optim. 4(4), 754–776 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Reddy, M.J., Kumar, D.N.: Elitist-Mutated multi-objective particle swarm optimization for engineering design. In: Khosrow-Pour, M. (ed.) Encyclopedia of Information Science and Technology, 3rd edn, pp. 3534–3545. IGI Global, Hershey (2015)CrossRefGoogle Scholar
  18. 18.
    Haimes, Y.V., Lasdon, L.S., Wismer, D.A.: On a bicriterion formation of the problems of integrated system identification and system optimization. IEEE Trans. Syst. Man Cybern. SMC–1, 296–297 (1971). 7zbMATHGoogle Scholar
  19. 19.
    Papalambros, P., Wilde, D.: Principles of Optimal Design: Modeling and Computation. Cambridge University Press, Cambridge (2000)CrossRefzbMATHGoogle Scholar
  20. 20.
    John, K.V., Ramakrishnan, C.V., Sharma, K.G.: Minimum weight design of trusses using improved move limit method of sequential linear programming. Comput. Struct. 27(5), 583–591 (1987)CrossRefzbMATHGoogle Scholar
  21. 21.
    Lin, C., Schuh, K.J., Lee, Y.H.: Efficient optimal surface texture design using linearization (2017).

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

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

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