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.

1.
Liu
,
Q.
,
Sui
,
G.
, and
Leu
,
M. C.
, 2002, “
Experimental Study on the Ice Pattern Fabrication for the Investment Casting by Rapid Freeze Prototyping (RFP)
,”
J. Comput. Ind.
,
48
(
3
), pp.
181
197
.
2.
Liu
,
Q.
,
Leu
,
M. C.
,
Richards
,
V.
, and
Schmitt
,
S. M.
, 2004, “
Dimensional Accuracy and Surface Roughness of Rapid Freeze Prototyping Ice Patterns and Investment Casting Metal Parts
,”
Int. J. Adv. Manuf. Technol.
0268-3768,
24
(
7-8
), pp.
485
495
.
3.
Leu
,
M. C.
,
Liu
,
Q.
, and
Bryant
,
F. D.
, 2003, “
Study of Part Geometric Features and Support Materials in Rapid Freeze Prototyping
,”
CIRP Ann.
0007-8506,
52
(
1
), pp.
185
188
.
4.
Sui
,
G.
, and
Leu
,
M. C.
, 2003, “
Investigation of Layer Thickness and Surface Roughness in Rapid Freeze Prototyping
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
125
(
3
), pp.
556
563
.
5.
Liu
,
Q.
,
Fu
,
Z.
,
Yang
,
H.
, and
Wu
,
S.
, 1997, “
Coupled Thermo-Mechanical Analysis of High Speed Hot-Forging Processes
,”
J. Mater. Process. Technol.
0924-0136,
69
, pp.
190
197
.
6.
Liu
,
Q.
,
Wu
,
S.
, and
Sun
,
S.
, 1998, “
Preform Design in Axisymmetric Forging by a New FEM-UBET Method
,”
J. Mater. Process. Technol.
0924-0136,
74
, pp.
218
222
.
7.
Shiomi
,
M.
,
Yoshidome
,
A.
,
Abe
,
F.
, and
Osakada
,
K.
, 1999, “
Finite Element Analysis of Melting and Solidifying Processes in Laser Rapid Prototyping of Metallic Powders
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
39
, pp.
237
252
.
8.
Weissman
,
E. M.
, and
Hsu
,
M. B.
, 1991, “
A Finite Element Model of Multi-Layered Laser Sintered Parts
,”
Proc. of 2nd Solid Freeform Fabrication Symposium
, Austin, Aug. 12–14,
University of Texas
,
Austin, TX
, pp.
86
94
.
9.
Matsumoto
,
M.
,
Shiomi
,
M.
,
Osakada
,
K.
, and
Abe
,
F.
, 2002, “
Finite Element Analysis of Single Layer Forming on Metallic Powder Bed in Rapid Prototyping by Selective Laser Processing
,”
Int. J. Mach. Tools Manuf.
0890-6955,
42
, pp.
61
67
.
10.
Bugeda
,
G.
,
Cervera
,
M.
, and
Lombera
,
G.
, 1999, “
Numerical Prediction of Temperature and Density Distributions in Selective Laser Sintering Processes
,”
Rapid Prototyping J.
1355-2546,
5
(
1
), pp.
21
26
.
11.
Sun
,
M. M.
, and
Beaman
,
J. J.
, 1991, “
A Three Dimensional Model for Selective Laser Sintering
,”
Proc. of 2nd Solid Freeform Fabrication Symposium
, Austin, Aug. 12–14,
University of Texas
,
Austin, TX
, pp.
102
109
.
12.
Jiang
,
W.
,
Dalgarno
,
K. W.
, and
Childs
,
T. H. C.
, 2002, “
Finite Element Analysis of Residual Stresses and Deformation in Direct Metal SLS Process
,”
Proc. of 13th Solid Freeform Fabrication Symposium
, Austin, Aug. 5–7,
University of Texas
,
Austin, TX
, pp.
340
348
.
13.
Yardimci
,
M. A.
,
Guceri
,
S. I.
, and
Danforth
,
S. C.
, 1995, “
A Phenomenological Numerical Model for Fused Deposition Processing of Particle Filled Parts
,”
Proc. of 6th Solid Freeform Fabrication Symposium
, Austin, Aug. 7–9,
University of Texas
,
Austin, TX
, pp.
189
195
.
14.
Dai
,
K.
,
Crocker
,
J.
,
Shaw
,
L.
, and
Marcus
,
H.
, 2000, “
Finite Element Analysis of the SALDVI Process
,”
Proc. of 11th Solid Freeform Fabrication Symposium
, Austin, Aug. 8–10,
University of Texas
,
Austin, TX
, pp.
393
398
.
15.
Niebling
,
F.
,
Otto
,
A.
, and
Geiger
,
M.
, 2002, “
Analyzing the DMLS-Process by a Macroscopic FE-Model
,”
Proc. of 13th Solid Freeform Fabrication Symposium
, Austin, Aug. 5–7,
University of Texas
,
Austin, TX
, pp.
384
391
.
16.
Kovacevic
,
R.
, and
Beardsley
,
H.
, 1998, “
Process Control of 3D Welding as a Droplet-Based Rapid Prototyping Technique
,”
Proc. of 9th Solid Freeform Fabrication Symposium
, Austin, Aug. 10–12,
University of Texas
,
Austin, TX
, pp.
57
64
.
17.
Jandric
,
Z.
,
Ouyang
,
J. H.
, and
Kovacevic
,
R.
, 2002, “
Effect of Volume of Heat Sink on Process and Physical Properties of Parts Built by Welding Based SFF
,”
Proc. of 13th Solid Freeform Fabrication Symposium
, Austin, Aug. 5–7,
University of Texas
,
Austin, TX
, pp.
331
339
.
18.
Chin
,
R. K.
,
Beuth
,
J. L.
, and
Amon
,
C. H.
, 2001, “
Successive Deposition of Metals in Solid Freeform Fabrication Processes, Part 1: Thermomechanical Models of Layers and Droplet Columns
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
123
, pp.
623
631
.
19.
Chin
,
R. K.
,
Beuth
,
J. L.
, and
Amon
,
C. H.
, 2001, “
Successive Deposition of Metals in Solid Freeform Fabrication Processes—Part 2: Thermomechanical Models of Adjacent Droplets
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
23
, pp.
632
638
.
20.
ANSYS, 1996,
ANSYS Theory Manual
, Release 5.3,
ANSYS Inc.
21.
Tszeng
,
T. C.
,
Im
,
Y. T.
, and
Kobayashi
,
S.
, 1989, “
Thermal Analysis of Solidification by the Temperature Recovery Method
,”
Int. J. Mach. Tools Manuf.
0890-6955,
29
(
1
), pp.
107
120
.
22.
Tamma
,
K. K.
, and
Namburu
,
R. R.
, 1990, “
Recent Advances, Trends and New Perspectives via Enthalpy-Based Finite Element Formulations for Applications to Solidification Problems
,”
Int. J. Numer. Methods Eng.
0029-5981,
30
, pp.
803
820
.
23.
Schiaffino
,
S.
, and
Sonin
,
A. A.
, 1997, “
Molten Droplet Deposition and Solidification at Low Weber Numbers
,”
Phys. Fluids
1070-6631,
9
, pp.
3172
3187
.
24.
Attinger
,
D.
,
Zhao
,
Z.
, and
Poulikakos
,
D.
, 2000, “
An Experimental Study of Molten Microdroplet Surface Deposition and Solidification: Transient Behavior and Wetting Angle Dynamics
,”
ASME J. Heat Transfer
0022-1481,
122
, pp.
544
556
.
25.
Ozisik
,
M. N.
, 1993,
Heat Conduction
,
Willey
New York, p.
29
.
26.
Amon
,
C. H.
,
Schmaltz
,
K. S.
,
Merz
,
R.
, and
Prinz
,
F. B.
, 1996, “
Numerical and Experimental Investigation of Interface Bonding via Substrate Remelting of an Impinging Molten Metal Droplet
,”
ASME J. Heat Transfer
0022-1481,
118
, pp.
164
172
.
27.
Schmaltz
,
K. S.
,
Zarzalejo
,
L. J.
, and
Amon
,
C. H.
, 1999, “
Molten Droplet Solidification and Substrate Remelting in Microcasting—Part II: Parametric Study and Effect of Dissimilar Materials
,”
Int. J. Heat Mass Transfer
0017-9310,
35
, pp.
17
23
.
28.
Mills
,
A. F.
, 1999,
Heat Transfer
, 2nd edition,
Prentice-Hall
, Englewood Cliffs, NJ, pp.
168
182
.
You do not currently have access to this content.