Research Papers

Design for Additive Manufacturing: Optimization of Piping Network in Compact System With Enhanced Path-Finding Approach

[+] Author and Article Information
Pei Cao

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269

Zhaoyan Fan

Department of Mechanical,
Industrial and Manufacturing Engineering,
Oregon State University,
Corvallis, OR 97331

Robert X. Gao

Cady Staley Professor of Engineering,
Department of Mechanical and
Aerospace Engineering,
Case Western Reserve University,
Cleveland, OH 44106

J. Tang

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: jiong.tang@uconn.edu

1Corresponding author.

Manuscript received November 20, 2017; final manuscript received May 11, 2018; published online June 4, 2018. Assoc. Editor: Sam Anand.

J. Manuf. Sci. Eng 140(8), 081013 (Jun 04, 2018) (15 pages) Paper No: MANU-17-1724; doi: 10.1115/1.4040320 History: Received November 20, 2017; Revised May 11, 2018

This research aims at unleashing the potential of additive manufacturing technology in industrial design that can produce structures/devices with irregular component geometries to reduce sizes/weights. We explore, by means of path-finding, the length minimization of freeform hydraulic piping network in compact space under given constraints. Previous studies on path-finding have mainly focused on enhancing computational efficiency due to the need to produce rapid results in such as navigation and video-game applications. In this research, we develop a new Focal Any-Angle A* approach that combines the merits of grid-based method and visibility graph-based method. Specifically, we formulate pruned visibility graphs preserving only the useful portion of the vertices and then find the optimal path based on the candidate vertices using A*. The reduced visibility graphs enable us to outperform approximations and maintain the optimality of exact algorithms in a more efficient manner. The algorithm proposed is compared to the traditional A* on Grids, Theta* and A* on visibility graphs in terms of path length, number of nodes evaluated, as well as computational time. As demonstrated and validated through case studies, the proposed method is capable of finding the shortest path with tractable computational cost, which provides a viable design tool for the additive manufacturing of piping network systems.

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Fig. 1

Piping design for traditional manufacturing versus piping design for additive manufacturing: (a) a piping design blueprint for traditional manufacturing; (b) a piping design prototype for traditional manufacturing; (c) a piping design prototype for additive manufacturing (implemented by the proposed approach)

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Fig. 2

(a) The shortest graph path and (b) the shortest continuous path

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Fig. 3

Path found by Theta* versus true shortest path

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Fig. 4

Visibility graph of two nodes and two obstacles and the shortest path

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Fig. 5

Diagonal move between obstacles

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Fig. 6

An example of finding candidate vertices: (a) vertices in V1, (b) blocking cluster and V2 (inside the box), (c) vertex corresponding to the largest angle, (d) vertices in V3, and (e) candidate vertices (marked with dotted circles)

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Fig. 7

Flowchart of finding the candidate vertices as part of path-finding

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Fig. 8

The obstacles in between starting node and target node

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Fig. 9

Visibility check example

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Fig. 10

Node evaluations comparison between A* on grids and FA-A*

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Fig. 11

Random 50*50 maps with different proportion of obstacles

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Fig. 12

Runtime versus path length: (a) 50*50: 5%, (b) 100*100: 5%, (c) 50*50: 10%, (d) 100*100: 10%, (e) 50*50: 20%, (f) 100*100: 20%, (g) 50*50: 30%, (h) 100*100: 30%, (i) 50*50: 50%, and (j) 100*100: 50%

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Fig. 13

Random 100*100 maps with different proportion of obstacles

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Fig. 14

Paths found and nodes evaluated by each algorithm (100*100, 50%): (a) A* on G, (b) Theta*, (c) A* on V, and (d) FA-A*

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Fig. 15

Paths comparison of FA-A* with and without post smoothing (100*100, 50%)

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Fig. 16

Random 300*300 maps with different proportion of obstacles

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Fig. 17

Paths found and nodes evaluated by each algorithm (300*300, 5%): (a) A* on G, (b) Theta*, (c) A* on V, and (d) FA-A*

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Fig. 18

Performance comparison (50*50)

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Fig. 19

Paths found and nodes evaluated by each algorithm (300*300, 35 clusters): (a) A* on G, (b) Theta*, (c) A* on V, and (d) FA-A*

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Fig. 20

Path found for 511*511 maze routing: (a) A* on G, (b) Theta*, (c) A* on V, and (d) FA-A*

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Fig. 21

Number of evaluations comparison: (a) 50*50, (b) 100*100, (c) 300*300, and (d) 50*50 with different number of clusters

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Fig. 22

Piping design example: (a) CAD model of prespecified components, (b) geometry model, (c) gridding, and (d) optimal paths

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Fig. 23

Piping design comparison: (a) A* on G and (b) FA-A*

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Fig. 24

Optimal piping design. Inlet and outlet locations of the system are prespecified at the top-right and bottom-right in the figure.

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Fig. 25

Path refinement through perturbation

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Fig. 26

Stereolithography prototype of a freeform piping network designed by FA-A*




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