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Research Papers: Design Automation

Systematic Design Optimization of the Metamaterial Shear Beam of a Nonpneumatic Wheel for Low Rolling Resistance

[+] Author and Article Information
Christopher Czech

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634-0921
e-mail: christopher.d.czech@gmail.com

Paolo Guarneri

Technical University of Cluj-Napoca,
Cluj-Napoca, Cluj 400489, Romania
e-mail: paolo.guarneri@emd.utcluj.ro

Niranjan Thyagaraja, Georges Fadel

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634-0921

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 13, 2014; final manuscript received December 15, 2014; published online February 16, 2015. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 137(4), 041404 (Apr 01, 2015) (9 pages) Paper No: MD-14-1351; doi: 10.1115/1.4029518 History: Received June 13, 2014; Revised December 15, 2014; Online February 16, 2015

Systematic engineering of components that employ metamaterials has expanded the mechanical design field in recent years. Yet, topology optimization remains a burdensome tool to utilize within a systematic engineering paradigm. In this work, the design of a metamaterial shear beam for a nonpneumatic wheel using a systematic, two-level design approach is discussed. A top-level design process is used to determine the geometric and effective material properties of the shear beam, and linking functions are established and validated for the design of a shear layer mesoscale structure. At the metamaterial design level, innovative homogenization and topology optimization methods are employed to determine a set of locally optimal geometric designs for the shear layer. One geometry, the auxetic honeycomb, is shown to be an optimum to the minimum volume topology optimization problem for materials subjected to pure shear boundary conditions. As such, this geometry is identified as a candidate for the shear layer.

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Figures

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Fig. 1

Components of the nonpneumatic wheel

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Fig. 2

Material selection chart depicting loss coefficient as a function of elastic modulus (Adapted from Ref. [9].)

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Fig. 3

Illustration of the nonpneumatic wheel model. Inside the area of interest surrounding the contact patch, a fine mesh is used. Outside the area of interest, a coarser mesh is used.

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Fig. 4

Effect sizes of changing the design variables on the objective and constraint functions

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Fig. 6

(Top) Illustration of the FEA of an optimal design solution for the nonpneumatic wheel. (Bottom) Plot of CPs across the nodes in the contact patch.

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Fig. 5

Set of optimal solutions from system optimization to be targeted for the design of the metamaterial shear beam

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Fig. 7

(Left) Simply (standard) connected lattice. (Right) Nonsimply connected (layer-staggered) lattice.

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Fig. 8

(Top) Honeycomb (solid) constructed using a nonsimply connected lattice of rectangular unit cells (dotted). (Bottom) Honeycomb constructed using a simply connected lattice of parallelogram unit cells.

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Fig. 12

Feasible design results from the topology optimization studies. The dashed line indicates the optimal results, Eq. (2), from the system-level optimization of the wheel. The letters on the plot indicate the initial solutions from Fig. 9 were used to generate a feasible design at that point. The asterisks indicate solutions found using a nonsimply connected unit cell domain.

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Fig. 9

Initial unit cell solutions used for topology optimization

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Fig. 10

Simple connectivity optimization results

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Fig. 11

Nonsimple connectivity optimization results

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