Georgia Institute of Technology | Marquette University | Milwaukee School of Engineering | North Carolina A&T State University | Purdue University | University of California, Merced | University of Illinois, Urbana-Champaign | University of

Minnesota | Vanderbilt University

Fluid Power Innovation & Research Conference

Minneapolis, MN | October 10 - 12, 2016

General surface texture shape reduces friction

and increases load capacity simultaneously in

sliding contact with full-film lubrication

Yong Hoon Lee, Graduate Student, Presenting authorJonathon K. Schuh, Randy H. Ewoldt, James T. Allison

University of Illinois at Urbana-ChampaignAdvisor: James T. Allison, Randy H. Ewoldt

Photo

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Project overview

• Surface texturing improves friction properties:

– Micro-dimpled surface reduces friction [1,2]

– Asymmetric texture generates a normal force [3-5]

• Previous design studies on surface texturing:

– Restricted to simple predefined shapes [1-3,6-8]

• Design exploration of free form texture shapes.

[1] Wakuda et al., Wear, 254(3-4), 2003, pp. 356-363.

[2] Ramesh et al., Tribology International, 57, 2013, pp. 170-176.

[3] Johnston et al., Tribology International, 82, 2015, pp. 123-132.

[4] Rao et al., ASME 2015 IDETC/CIE, DETC2015-46832, 2015.

[5] Schuh et al., Tribology International, 97, 2016, pp. 490-498.

[6] Hsu et al., Journal of Physics D: Applied Physics, 47(33), 2014.

[7] Kango et al., Meccanica, 47(2), 2011, pp. 469-482.

[8] Fesanghary et al., Tribology International, 67, 2013, pp. 254-262.

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Research goal

• Design a shape of surface texture

1. to reduce shear friction and

2. to increase normal force

beyond what is possible for limitedtypical textures.

• Utilize

1. design-specific model and

2. efficient design explorationtechnique

to extract qualitative design knowledge from the resultant data.

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Problem description

• Design problem adapted from previous experimental study [5]

– Tribo-rheometer measures torque M and normal force FN.

– Fixed textured bottom disk.

– Rotating top flat disk drives shear flow.

– Revealed asymmetric dimpled surface textures decrease frictional loss.

[5] Schuh et al., Tribology International, 97, 2016, pp. 490-498.

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Design objectives

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1. Minimize normalized apparent viscosity ηa/η0

(=Normalized torque, ηa/η0 = M/M0)

2. Maximize normal force FN

Resultant shear viscosity and normal forcewill show a trade-off relation.

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Flow simulation method [9]

[9] Schuh et al., FPIRC16, 2016.

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Flow simulation method

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A sector designrepresentation

A full disk designrepresentation with

top view

A full disk designrepresentation with

iso-angle view

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Optimization in two approaches

• Direct optimization [10]

– Utilize full simulation of fluid flow throughout the optimization process (computationally intensive).

• Optimization using surrogate model [4]

– Construct a surrogate model using a small number of data set from full simulation.

– Accuracy of surrogate model can be refined by “adaptive sampling” sequences.

[4] Rao et al., ASME 2015 IDETC/CIE, DETC2015-46832, 2015.

[10] Lee et al., ASME 2016 IDETC/CIE, DETC2016-60168, 2016.

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Compare parameterizations

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[5] Schuh et al., Tribology International, 97, 2016, pp. 490-498.[5]

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Symmetric cylindrical dimples

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Asymmetric cylindrical dimples

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Inclined plane (1 parameter)

• Slow expansion followed by rapid contraction with inclination of 3.6° or higher produces a Pareto-optimal designs.

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Arbitrary continuous textures

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30 design variables60 linear constraints

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Optimization strategy #1

• Direct Optimization (Nonlinear Programming)

– Computationally expensive

– But, we have a efficient simulation model: Reynolds equation

• Multiobjective optimization method

– Scalarization: epsilon-constraint method

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Symmetric texture

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Asymmetric textures

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Asymmetric textures• The geometric result converged to

shape that is similar to a spiral blades

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Pareto set (to see trade-offs)

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Optimization strategy #2

• Multiobjective Adaptive Surrogate Model-Based Optimization (MO-ASMO)

– Computationally cheaper (less function call)

– We can eventually have more complex and accurate simulations, e.g. Stokes flow solver, etc., using reasonable amount of computation resource

– MOGA (Multiobjective genetic algorithm) explores the optimal solutions on the surrogate model

– Accuracy can be enhanced by sequential refinement of surrogate model

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MO-ASMO1. Training points with full simulation

2. Construct a surrogate model

3. Explore optimal solution on the surrogate model using MOGA

4. Validate the Pareto set (optimal solutions)

5. Create new sample points as additional training points

6. Repeat to 2 until the solution converges

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Update

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Pareto set convergence (Iter 1)

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ηa/η0

-FN

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Pareto set convergence (Iter 2)

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ηa/η0

-FN

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Pareto set convergence (Iter 4)

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ηa/η0

-FN

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Pareto set convergence (Iter 8)

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ηa/η0

-FN

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Pareto set convergence (Iter 12)

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ηa/η0

-FN

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Computation time reduction

The design problem contains:2 objectives, 30 design variables,and 60 linear constraints

• Direct optimization: 40,000+ computation on Reynolds equation

• MO-ASMO: 285 computation for total 12 iterations

+ 5min of MOGA procedure per each iteration

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Pareto set comparison

DirectOptimization

MO-ASMO

CylindricalDimples

InclinedPlane

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Height contour comparison

FN = 0.618N FN = 0.883N FN = 1.197N FN = 1.577N FN = 1.851N FN = 2.284N FN = 2.619N

Solution of Direct Optimization

MO-ASMO Solution

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Height contour comparison

Direct Optimization MO-ASMO

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Conclusions• Study aims to improve two objectives simultaneously

– Minimize friction (shear viscosity)

– Maximize load capacity (normal force)

• Predefined texture shapes could not improve performance as much as more general surface texture designs

• Resulting optimal designs resemble spiral blades– Direct flow to the center to create positive net pressure

• MO-ASMO reduces computation time drastically, but converged to a set of suboptimal designs

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Future work• More comprehensive and computationally expensive

simulations will be performed with MO-ASMO framework.

• Use of design abstraction methods (e.g., GDA) will be tested for surface representation.

• On-going work is addressing novel large-scale optimization formulation for convex programming to manage high resolution direct design representation.

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