Rapid Freeze Prototyping (RFP) builds three-dimensional ice parts according to CAD models by depositing and freezing water droplets in a layer-by-layer manner. This paper studies the layer thickness and surface roughness of ice parts built by the RFP process. The equations governing the water line formed by a sequence of water droplets are developed, and then a model of the water line is proposed by simplifying these equations based on our experimental condition. The analysis using this model shows that the cross-section of an ice line is circular, which is verified by experimental observations. Based on the analysis, equations for predicting layer thickness as a function of nozzle scanning speed, water feed rate, and water-ice contact angle in building vertical and slant walls by the RFP are derived and the predictions from these equations are shown to agree well with experimental measurements. The surface roughness of ice parts built by the RFP process is also studied.

1.
Jacobs, P. F., 1992, Rapid Prototyping & Manufacturing: Fundamentals of Stereolithography, SME publication, Dearborn, MI.
2.
Comb, J. W., Priedemsn, W. R., and Turley, P. W., 1994, “FDM Technology Process Improvements,” Proceedings of Solid Freeform Fabrication Symposium, Austin, TX, pp. 42–49.
3.
Beaman, J. J., Barlow, J. W., Bourell, D. L., Crawford, R. H., Marcus, H. L., and McAlea, K. P., 1997, Solid Freeform Fabrication: A New Direction in Manufacturing, Kluwer Academic Publishers, Norwell, MA, pp. 25–49.
4.
Feygin, M., and Hsieh, B., 1991, “Laminated Object Manufacturing (LOM): A Simpler Process,” Proceedings of Solid Freeform Fabrication Symposium, Austin, TX, pp. 123–130.
5.
Michaels, S., Sachs E. M., and Cima, M. J., 1992, “Metal Parts Generation by Three-Dimensional Printing,” Proceedings of Solid Freeform Fabrication Symposium, Austin, TX, pp. 244–250.
6.
Sachs, E., Allen, S., Guo, H. L., Banos, J., Cima, M., Serdy, J., and Brancazio, D., 1997, “Progress on Tooling by 3D Printing: Conformal Cooling, Dimensional Control, Surface Finish and Hardness,” Proceedings of Solid Freeform Fabrication Symposium, Austin, TX, pp. 115–123.
7.
Mazumder
,
J.
,
Schifferer
,
A.
, and
Choi
,
J.
,
1999
, “
Direct Materials Deposition: Designed Macro and Microstructure
,”
Mater. Res. Innovations
,
3
, pp.
118
131
.
8.
Leu, M. C., and Zhang, W., 1998, “Research and Development in Rapid Prototyping and Tooling in the United States,” Proceedings of the First International Conference in RP&M’ 98, Tsinghua University, Beijing, China, pp. 707–718.
9.
Kruth
,
J. P.
,
Leu
,
M. C.
, and
Nakagawa
,
T.
,
1998
, “
Progress in Additive Manufacturing and Rapid Prototyping
,”
CIRP Ann.
,
47
(
2
), pp.
525
540
.
10.
Zhang
,
W.
,
Leu
,
M. C.
,
Ji
,
Z.
, and
Yan
,
Y.
,
1999
, “
Rapid Freezing Prototyping with Water
,”
Mater. Des.
,
20
, pp.
139
145
.
11.
Kattethota, G., and Henderson, M., 1998, “A Visual Tool to Improve Layered Manufacturing Part Quality,” Proceedings of Solid Freeform Fabrication Symposium, Austin, TX, pp. 327–334.
12.
Reeves, P. E., and Cobb, R. C., 1998, “Reducing the Surface Deviation of Stereolithography Using an Alternative Building Strategy,” Proceedings of Solid Freeform Fabrication Symposium, Austin, TX, pp. 193–203.
13.
Fukai
,
J.
,
Zhao
,
Z.
,
Poulikakos
,
D.
,
Megaridis
,
C.
, and
Miyatake
,
O.
,
1993
, “
Modeling of the Deformation of a Liquid Droplet Impinging Upon a Flat Surface
,”
Phys. Fluids A
,
5
, pp.
2588
2599
.
14.
Hatta
,
N.
,
Fujimoto
,
H.
, and
Takuta
,
H.
,
1995
, “
Deformation Process of a Water Droplet Impinging on Solid Surface
,”
ASME J. Fluids Eng.
,
117
, pp.
394
401
.
15.
Chandra
,
S.
,
1991
, “
On the Collision of a Droplet with a Solid Surface
,”
Proc. R. Soc. London, Ser. A
,
432
, pp.
13
41
.
16.
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
,
122
, pp.
544
556
.
17.
Zhao
,
Z.
,
Poulikakos
,
D.
, and
Fukai
,
J.
,
1996
, “
Heat Transfer and Fluid Dynamics during the Collision of a Liquid Droplet on a Substrate—II. Experiments
,”
Int. J. Heat Mass Transf.
,
39
(
13
), pp.
2791
2802
.
18.
Healy
,
W. M.
,
Hartley
,
J. G.
, and
Abdel-Khalik
,
S. I.
,
2001
, “
Surface Wetting Effects on the Spreading of Liquid Droplets Impacting a Solid Surface at Low Weber Numbers
,”
Int. J. Heat Mass Transf.
,
44
, pp.
235
240
.
19.
Liu
,
W.
,
Wang
,
G. X.
, and
Matthys
,
E. F.
,
1995
, “
Thermal Analysis and Measurements for a Molten Metal Drop Impacting on a Substrate: Cooling, Solidification and Heat Trasfer Coefficient
,”
Int. J. Heat Mass Transf.
,
38
(
8
),
1387
1395
.
20.
Schiaffino
,
S.
, and
Sonin
,
A. A.
,
1997
, “
Molten Droplet Deposition and Solidification at Low Weber Nembers
,”
Phys. Fluids
,
9
, pp.
3172
3187
.
21.
Anderson
,
D. M.
,
Worster
,
M. G.
, and
Davis
,
S. H.
,
1996
, “
The Case for a Dynamic Contact Angle in Containerless Solidification
,”
J. Cryst. Growth
,
163
, pp.
329
338
.
22.
Clanet
,
C.
, and
Lasheras
,
J. C.
,
1999
, “
Transition from Dripping to Jetting
,”
J. Fluid Mech.
,
383
, pp.
307
326
.
23.
Behroozi
,
F.
,
Macomber
,
H.
,
Dostal
,
J.
,
Behroozi
,
C.
, and
Lambert
,
B.
,
1996
, “
The Profile of a Dew Drop
,”
Am. J. Phys.
,
64
, pp.
1120
1125
.
24.
Adam, N. K., 1941, The Physics and Chemistry of Surfaces, Oxford University Press, London, pp. 8–9.
25.
Dorsey, N. E., 1940, Properties of Ordinary Water-Substance in All Its Phases: Vapor, Water, and All the Ices, Reinhold, New York.
26.
Neumann, A. W., and Spelt, J. K., 1996, Applied Surface Thermodynamics, M. Dekker, New York.
27.
ANSI/ASME Standard B46.1, 1993, Surface Roughness, Waviness, and Lay.
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