Research Papers

Representation of Graded Materials and Structures to Support Tolerance Specification for Additive Manufacturing Application

[+] Author and Article Information
G. Ameta

Dakota Consulting Inc.,
Silver Spring, MD 20910
e-mail: gaurav.ameta@nist.gov

P. Witherell

National Institute of Standards and
Gaithersburg, MD 20899
e-mail: paul.witherell@nist.gov

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received April 19, 2018; final manuscript received December 11, 2018; published online February 22, 2019. Assoc. Editor: Yong Chen.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Comput. Inf. Sci. Eng 19(2), 021008 (Feb 22, 2019) (9 pages) Paper No: JCISE-18-1097; doi: 10.1115/1.4042327 History: Received April 19, 2018; Revised December 11, 2018

Additive manufacturing (AM) has enabled control over heterogeneous materials and structures in ways that were not previously possible, including functionally graded materials and structures. This paper presents a novel method for representing and communicating heterogeneous materials and structures that include tolerancing of geometry and material together. The aim of this paper is to propose a means to specify nominal materials, nominal structures and allowable material variations in parts, including (a) explicit material and structural transitions (implying abrupt changes) and (b) functional transitions to support single and multiple material and structural behaviors (implying designed function-based gradients). The transition region combines bounded regions (volumes and surfaces) and material distribution and structural variation equations. Tolerancing is defined at two levels, that of the geometry including bounded regions and that of the materials. Material tolerances are defined as allowable material variations from nominal material fractions within a unit volume at a given location computed using material distribution equations. The method is described thorough several case studies of abrupt transitions, lattice-based transitions, and multimaterial and structural transitions.

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Fig. 1

Bounded volume shown with local note VR and profile tolerance

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Fig. 2

Part with the material transition region (heterogeneous material indicator) and specification of tolerance

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Fig. 3

Nominal, limit, and acceptable material fractions along the z-axis for VR2, based on the equations embedded in the part model (The unit of z is inches)

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Fig. 4

Implication of material tolerances. Given material fractions of MAT2, the acceptable material fractions of MAT1 marked as a gray area. Any value of MAT1 below the upper line marked with black triangles will lead to acceptable void fractions (The unit of z is inches).

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Fig. 5

Implication of material tolerances. Given material fractions of MAT1, the acceptable material fractions of MAT2 marked as a gray area. Any value of MAT2 below the upper line marked with gray circles will lead to acceptable void fractions (The unit of z is inches).

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Fig. 6

Material fractions for MAT1 and MAT2 (The unit of x and z is inches): (a) MAT1 fractions along x and z axes and (b) MAT2 fractions along x and z axes

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Fig. 7

A part with four volume regions with three material specifications

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Fig. 8

Nominal material distributions as computed from Eqs. (5)(7). Cross section of the part from Fig. 7 showing the material composition encoded as shades.

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Fig. 9

Impact of material distribution based on the allowable material variations from Fig. 7

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Fig. 10

Example of material transition specification with tolerance between bounded lattice regions

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Fig. 11

Four cases of functionally defined graded structures: (a) simple lattice, (b) thickness graded lattice, (c) conformal lattice with the graded thickness, and (d) conformal lattice with the graded thickness and material

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Fig. 12

Three cases of desired porosity in a part: (a) uniformly distributed, (b) normally distributed, and (c) following a function

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Fig. 13

Cylindrical lattice composed of two materials as a function of x, y, and z

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Fig. 14

(a) Geometrical profile tolerance on VR1 with its tolerance zone and (b) geometrical profile tolerance with nominal material and material tolerance for VR2. Shade and boundary variations indicate interactions of two tolerance zones.



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