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TECHNICAL PAPERS

Finite Element Analysis of Solidification in Rapid Freeze Prototyping

[+] Author and Article Information
Qingbin Liu

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, MO 65409qbliu@umr.edu

Ming C. Leu

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, MO 65409mleu@umr.edu

J. Manuf. Sci. Eng 129(4), 810-820 (Feb 03, 2007) (11 pages) doi:10.1115/1.2738095 History: Received March 30, 2005; Revised February 03, 2007

Rapid freeze prototyping (RFP) can generate three-dimensional ice patterns from computer-aided design (CAD) models by depositing and solidifying water droplets layer by layer. One important issue of the RFP process is how to fabricate the ice pattern to desired accuracy in an acceptable short time. The waiting time between two successive layers is a critical factor. A waiting time that is too short will lead to unacceptable part accuracy, while a waiting time that is too long will lead to an excessive build time. Finite element analysis is employed in this study to predict the solidification time of a newly deposited water layer and to develop a better understanding of heat transfer during the RFP process. ANSYS Parametric Development Language (APDL) is utilized to develop software for the prediction of solidification time. The result is used to investigate the effect of various process parameters on the solidification time of an ice column and a vertical ice wall. These parameters include environment temperature, heat convection coefficient, initial water droplet temperature, layer thickness, and waiting time between two successive layers. Experiments are conducted and the measured results are shown to agree well with simulation results.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Principle of rapid freeze prototyping

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Figure 2

Schematic of successive deposition of water droplets on top of one another to build an ice column

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Figure 3

Mesh and boundary conditions for the 2D axisymmetric model of water droplets deposited on top of one another to build an ice column

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Figure 4

Schematic of successive deposition of water droplets to build a vertical ice wall

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Figure 5

Mesh and boundary conditions for the 2D model of building a vertical ice wall

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Figure 6

Solidification time versus column height for different environment temperatures in building an ice column

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Figure 7

Solidification time versus column height for different heat convection coefficients (in watts per meters squared per degrees Kelvin) in building an ice column

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Figure 8

Solidification time versus layer thickness in building an ice column

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Figure 9

Solidification time versus initial temperature of water droplets in building an ice column

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Figure 10

Time history of temperature for the top center point of each new layer and the ice column on which it is being deposited. The heat convection coefficient is 250W∕(m2K).

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Figure 11

Time history of temperature for the top center point of each new layer and previously deposited ice column. The original column height is 5.00mm. Waiting time: (a)4s, (b)10s, and (c)35s.

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Figure 14

Time history of temperature for the top left, top middle, and top right points on each new layer in building an ice wall starting from the top of an aluminum substrate. The waiting time is 2s. The numbers in the legend area refer to the x and y coordinates of each point, whose unit is millimeters.

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Figure 15

Time history of temperature for the top left, top middle, and top right points on each new layer. The unit of the coordinates in the legend areas is millimeters. The original ice wall height is 5mm. The waiting times are (a)2s, (b)10s, and (c)30s.

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Figure 16

Built vertical walls with different waiting times: (a)2s, (b)10s, and (c)30s

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Figure 17

Ice wall with a microprobe imbedded

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Figure 18

Comparison between experimental and simulation results; waiting times are (a)2s, (b)10s, and (c)30s

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Figure 13

Time history of temperature for the top center points of each new layer and the previously deposited ice column. The convection coefficient is 250W∕(m2K), the original column height is 5.00mm, and the waiting time is 10s.

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Figure 12

Time history of temperature for the top center points of each new layer and the previously deposited ice column, the environment temperature is −40°C. The original column height is 5.00mm, and the waiting time is 25s.

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