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.
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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.
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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.
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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
- Simultaneous co-design
- Non-Newtonian lubricant
- Nonlinear viscoelasticity
- Surrogate-based optimization