Abstract
Surface textures decrease friction in lubricated sliding with Newtonian fluids. Viscoelastic non-Newtonian lubricants can enhance frictional performance, but the optimal rheological material properties and their coupling to the texture design are non-obvious. In this study, we present a simultaneous design of both surface texture shape and non-Newtonian properties, which can be achieved by fluid additives that introduce viscoelasticity, shear thinning, and normal stress differences. Two models with different fidelity and computational cost are used to model laminar non-Newtonian fluid flow between a rotating flat plate and a textured disk. At lower fidelity, we use the Criminale-Ericksen-Filbey (CEF) constitutive model and a thin-film approximation for conservation of momentum (Reynolds equation). At higher fidelity, we use a fully nonlinear constitutive model typically applicable to polymer solutions (multimode Giesekus model) and the full 3-D momentum equations. Fluid additive design is parameterized by two relaxation modes each having a timescale, added viscosity, and a nonlinear anisotropic drag parameter. To manage the computational complexity and constraints between design variables, we use our previously developed multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) method. A new data-driven extension of MO-ASMO is introduced that constructs general boundaries to prevent attempts to evaluate designs that would lead to simulation failure. We demonstrate the efficiency of our MO-ASMO method and provide insights into co-designing the lubricant and textured surface. The Pareto-optimal solutions include fluid designs with both high and low viscoelastic additive loading. We rationalize this trade-off and discuss how the optimal design targets can be physically realized.
Similar content being viewed by others
References
Ashmore J, Shen A Q, Kavehpour H P, Stone H A, McKinley G H (2008) Coating flows of non-Newtonian fluids: weakly and strongly elastic limits. J Eng Math 60(1):17–41. https://doi.org/10.1007/s10665-007-9152-8
Atalık K, Keunings R (2004) On the occurrence of even harmonics in the shear stress response of viscoelastic fluids in large amplitude oscillatory shear. J Non-Newtonian Fluid Mech 122(1):107–116. https://doi.org/10.1016/j.jnnfm.2003.11.012
Batra R L, Mohan V (1978) Roller bearing lubrication with shear thinning lubricants. Wear 51(2):213–225. https://doi.org/10.1016/0043-1648(78)90261-2
Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, vol 1 Fluid Mechanics, 2nd edn. Wiley, New York. ISBN 978-0-471-80245-7
Corman R E, Rao L, Bharadwaj N A, Allison J T, Ewoldt R H (2016) Setting material function design targets for linear viscoelastic materials and structures. J Mech Des 138(5):051402. https://doi.org/10.1115/1.4032698
Criminale WO Jr, Ericksen J L, Filbey GL Jr (1957) Steady shear flow of non-Newtonian fluids. Arch Ration Mech Anal 1(1):410–417. https://doi.org/10.1007/BF00298018
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197. https://doi.org/10.1109/4235.996017
Deshmukh A P, Allison J T (2016) Multidisciplinary dynamic optimization of horizontal axis wind turbine design. Struct Multidiscip Optim 53(1):15–27. https://doi.org/10.1007/s00158-015-1308-y
Deville MO, Fischer PF, Mund EH (2002) High-order methods for incompressible fluid flow. Cambridge University Press, Cambridge. ISBN 978-0-521-45309-7
Etsion I (2004) Improving tribological performance of mechanical components by laser surface texturing. Tribol Lett 17(4):733–737. https://doi.org/10.1007/s11249-004-8081-1
Ewoldt R H (2014) Extremely soft: design with rheologically-complex fluids. Soft Robot 1(1):12–20. https://doi.org/10.1089/soro.2013.1508
Fornberg B (2009) A practical guide to pseudospectral methods. Cambridge University Press, Cambridge. ISBN 978-0-511-62635-7. https://doi.org/10.1017/CBO9780511626357
Freund J B, Ewoldt R H (2015) Quantitative rheological model selection: good fits versus credible models using Bayesian inference. J Rheol 59(3):667–701. https://doi.org/10.1122/1.4915299
Gropper D, Wang L, Harvey T J (2016) Hydrodynamic lubrication of textured surfaces: a review of modeling techniques and key findings. Tribol Int 94:509–529. https://doi.org/10.1016/j.triboint.2015.10.009
Hamilton D B, Walowit J A, AC M (1966) A theory of lubrication by microirregularities. J Basic Eng 88(1):177–185. https://doi.org/10.1115/1.3645799
Heath MT (2002) Scientific computing: an introductory survey, 2nd edn. McGraw-Hill, New York. ISBN 978-0-07-239910-3
Herber D R, Allison J T (2019) Nested and simultaneous solution strategies for general combined plant and control design problems. J Mech Des 141(1):011402. https://doi.org/10.1115/1.4040705
Hirani H, Athre K, Biswas S (2008) Lubricant shear thinning analysis of engine journal bearings. Tribol Trans 44(1):125–131. https://doi.org/10.1080/10402000108982435
Huggins M L (1942) The viscosity of dilute solutions of long-chain molecules. IV. Dependence on concentration. J Am Chem Soc 64(11):2716–2718. https://doi.org/10.1021/ja01263a056
Johnston M T, King W P, Ewoldt R H (2015) Shear stress characteristics of microtextured surfaces in gap-controlled hydrodynamic lubrication. Tribol Int 82:123–132. https://doi.org/10.1016/j.triboint.2014.10.005
Keunings R (2000) A survey of computational rheology. In: Proceedings of the XIIIth international congress on rheology, pp 7–14
Kopriva DA (2009) Implementing spectral methods for partial differential equations. Springer, Netherlands, ISBN 978-90-481-2260-8. https://doi.org/10.1007/978-90-481-2261-5
Lee YH, Corman RE, Ewoldt RH, Allison JT (2017a) A multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) framework using efficient sampling strategies. In: Proceedings of the ASME 2017 IDETC/CIE conference. https://doi.org/10.1115/DETC2017-67541, vol 2B. 43rd Design Automation Conference, DETC2017-67541, Cleveland, p V02BT03A023
Lee YH, Schuh JK, Ewoldt RH, Allison JT (2017b) Enhancing full-film lubrication performance via arbitrary surface texture design. J Mech Des 139 (5):053401–1–13. https://doi.org/10.1115/1.4036133
Lin C, Lee YH, Schuh JK, Ewoldt RH, Allison JT (2018) Efficient optimal surface texture design using linearization. In: Schumacher A, Vietor T, Fiebig S, Bletzinger KU, Maute K (eds) Advances in structural and multidisciplinary optimization: Proceedings of the 12th world congress of structural and multidisciplinary optimization (WCSMO12). https://doi.org/10.1007/978-3-319-67988-4_48. Springer, Cham, pp 632–647
Macosko CW (1994) Rheology: principles, measurements, and applications. Wiley, New York. ISBN 978-0-471-18575-8
Malak RJ Jr, Paredis C J J (2010) Using support vector machines to formalize the valid input domain of predictive models in systems design problems. J Mech Des 132(10):101001. https://doi.org/10.1115/1.4002151
Nelson A Z, Ewoldt R H (2017) Design of yield-stress fluids: a rheology-to-structure inverse problem. Soft Matter 13(41):7578–7594. https://doi.org/10.1039/C7SM00758B
Oldroyd J G (1950) On the formulation of rheological equations of state. Proc R Soc A: Math Phys Eng Sci 200(1063):523–541. https://doi.org/10.1098/rspa.1950.0035
Owens RG, Phillips TN (2002) Computational rheology. Imperial College Press, London. ISBN 978-1-86094-186-3
Pettersson U, Jacobson S (2003) Influence of surface texture on boundary lubricated sliding contacts. Tribol Int 36(11):857–864. https://doi.org/10.1016/S0301-679X(03)00104-X
Reynolds O (1886) 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. https://doi.org/10.1098/rspl.1886.0021
Schuh JK (2015a) Surface textures and non-Newtonian fluids for decreased friction in full film lubrication. Master’s thesis, University of Illinois at Urbana-Champaign. http://hdl.handle.net/2142/78561
Schuh J K, Lee Y H, Allison J T, Ewoldt RH (2015b) Surface textures and non-Newtonian fluids for decreasing friction in lubricated sliding contact. In: 2015 fluid power innovation and research conference. Minneapolis, MN
Schuh JK, Lee YH, Allison JT, Ewoldt RH (2017) Design-driven modeling of surface-textured full-film lubricated sliding: validation and rationale of nonstandard thrust observations. Tribol Lett 65(2):35–1–17. https://doi.org/10.1007/s11249-017-0818-8
Schuh JK (2018) Co-design of surface textures and non-Newtonian fluids for decreased friction. PhD thesis, University of Illinois at Urbana-Champaign, http://hdl.handle.net/2142/100988
Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464. https://doi.org/10.1214/aos/1176344136
Shan S, Wang G G (2004) An efficient Pareto set identification approach for multiobjective optimization on black-box functions. J Mech Des 127(5):866–874. https://doi.org/10.1115/1.1904639
Steponaviĉè I, Shirazi-Manesh M, Hyndman RJ, Smith-Miles K, Villanova L (2016) On sampling methods for costly multiobjective black-box optimization. In: Advances in Stochastic and deterministic global optimization. Springer, Cham. ISBN 978-3-319-29975-4, pp 273–296. https://doi.org/10.1007/978-3-319-29975-4_15
Suh N P, Mosleh M, Howard P S (1994) Control of friction. Wear 175(1-2):151–158. https://doi.org/10.1016/0043-1648(94)90178-3
Tax D M, Duin R P (1999) Support vector domain description. Pattern Recogn Lett 20(11-13):1191–1199. https://doi.org/10.1016/S0167-8655(99)00087-2
Varenberg M, Halperin G, Etsion I (2002) Different aspects of the role of wear debris in fretting wear. Wear 252(11-12):902–910. https://doi.org/10.1016/S0043-1648(02)00044-3
Wakuda M, Yamauchi Y, Kanzaki S, Yasuda Y (2003) Effect of surface texturing on friction reduction between ceramic and steel materials under lubricated sliding contact. Wear 254(3–4):356–363. https://doi.org/10.1016/S0043-1648(03)00004-8
Wang G G, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Des 129(4):370–380. https://doi.org/10.1115/1.2429697
Wilson B, Cappelleri D, Simpson TW, Frecker M (2001) Efficient Pareto frontier exploration using surrogate approximations. Optim Eng 2(1):31–50. https://doi.org/10.1023/A:1011818803494
Xiaodi L, Haosheng C, Darong C, Jiadao W (2009) Normal stress effects in journal bearing lubrication with maxwell fluid. In: Luo J, Meng Y, Shao T, Zhao Q (eds) Advanced tribology. Springer, Berlin, pp 231–234. https://doi.org/10.1007/978-3-642-03653-8_73
Yu H, Wang X, Zhou F (2010) Geometric shape effects of surface texture on the generation of hydrodynamic pressure between conformal contacting surfaces. Tribol Lett 37(2):123–130. https://doi.org/10.1007/s11249-009-9497-4
Funding
This work was supported by the National Science Foundation under Grant No. CMMI-1463203. The authors also gratefully acknowledge support from the Procter & Gamble Company.
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible Editor: Felipe A. C. Viana
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work was presented in part at the AIAA SciTech Forum 2018, Kissimmee, FL, January 8-12, 2018. Y. H. Lee and J. K. Schuh contributed equally to this work.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Lee, Y.H., Schuh, J.K., Ewoldt, R.H. et al. Simultaneous design of non-Newtonian lubricant and surface texture using surrogate-based multiobjective optimization. Struct Multidisc Optim 60, 99–116 (2019). https://doi.org/10.1007/s00158-019-02201-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-019-02201-1