A novel method is presented for modeling the abrasive waterjet machining process. Particle motion on the cross section of particle-laden jetflow is simulated in order to quantify the erosion contributions of millions of particles having different kinematic behaviors. The simulation is performed using fractal point sets with chaotic behavior for the cases of circular and noncircular (elliptical, triangular) jets. The jetflow constructed can be endowed with any desired velocity profile and/or particle flowrate. In association with a classical constitutive equation for estimating the penetration ability of a particle, the drilling and cutting operations are simulated and verified by experiment for titanium, glass, and other materials. Roughness and waviness of the cutting surfaces are also simulated and there is good consistency between theory and experiment. Triangular and elliptical jetflows are utilized to explore potential applications of noncircular abrasive waterjets.

1.
Alajbegovic
A.
, et al.,
1994
, “
Phase Distribution and Turbulence Structure for Solid/Fluid Upflow in a Pipe
,”
Int. J. Multiphase Flow
, Vol.
20
, pp.
453
479
.
2.
Bitter
J. G. A.
,
1963
, “
A Study of Erosion Phenomena—Part I
,”
Wear
, Vol.
16
, pp.
5
21
.
3.
Bitter
J. G. A.
,
1963
, “
A Study of Erosion Phenomena—Part II
,”
Wear
, Vol.
16
, pp.
169
190
.
4.
Currie, I. G., 1992, Fundamental Mechanics of Fluid, McGraw-Hill, New York.
5.
Finnie, I., 1958, “The Mechanisms of Erosion of Ductile Metals,” Proceedings of the Third National Congress of Applied Mechanics, ASME, pp. 527–532.
6.
Finnie
I.
,
1960
, “
Erosion of Surfaces by Solid Particles
,”
Wear
, Vol.
3
, pp.
87
103
.
7.
Gulden, M. E., 1979, “Solid Particle Erosion of High Technology Ceramics,” ASTM STP664, W. F. Afler, ed., pp. 101–122.
8.
Hashish
M.
,
1984
, “
A Modeling Study of Metal Cutting with Abrasive-Waterjets
,”
ASME Journal of Engineering Materials and Technology
, Vol.
106
, pp.
88
100
.
9.
Hashish
M.
,
1992
, “
Three Dimensional Machining with Abrasive Waterjet
,”
Jet Cutting Technology
, Vol.
13
, pp.
605
620
.
10.
Hashish
M.
,
1994
, “
Controlled-Depth Milling Techniques Using Abrasive Waterjet
,”
Jet Cutting Technology
, Vol.
13
, pp.
449
461
.
11.
Hongawa
H.
, et al.,
1992
, “
Annular Jet and Its Applications
,”
Journal of Jet Technology Society of Japan
, Vol.
9
, pp.
1
11
(in Japanese).
12.
Hutchings, I. M., 1979, “Mechanisms of the Erosion of Metals by Solid Particles,” ASTM STP 664, Erosion: Prevention and Useful Applications, pp. 59–76.
13.
Kovacevic
R.
,
1992
, “
Monitoring of Depth of Abrasive Waterjet Penetration
,”
Int. J. Mach. Tools Manufact.
, Vol.
1
, pp.
55
72
.
14.
Lee
S. L.
, and
Durst
F.
,
1982
, “
On the Motion of Particle in Turbulent Duct Flow
,”
Int. J. Multiphase Flow
, Vol.
8
, pp.
125
146
.
15.
Neilson
J. H.
, and
Gilchrist
,
1968
, “
Erosion by a Stream of Solid Particles
,”
Wear
, Vol.
11
, pp.
111
122
.
16.
Rankin, G. J. and Wu, S. S., 1995, “Abrasive Waterjet Cutting with a Shapejet,” Proceeding of 7th American Water Jet Conference, Houston, Texas, pp. 219–228.
17.
Shames, I. H., 1962, Mechanics of Fluids, McGraw-Hill, New York.
18.
Tilly
G. P.
, and
Sage
W.
,
1970
, “
The Interaction of Particle and Material Behavior in Erosion Processes
,”
Wear
, Vol.
16
, pp.
447
465
.
19.
Yong
Z.
, and
Kovacevic
R.
,
1997
a, “
Effects of Water-Mixture Film on Impact Contact in Abrasive Waterjet Machining
,”
International Journal of Mechanical Science
, Vol.
39
, pp.
729
739
.
20.
Yong
Z.
, and
Kovacevic
R.
,
1997
b, “
Fundamentals of Constructing Particle-Laden Flow by Fractal Point Sets and Predicting 3D Solid Erosion Rates
,”
International Journal of Chaos, Solitons and Fractals
, Vol.
8
, pp.
207
220
.
21.
Yong, Z., and Kovacevic, R., 1997c, “Feedback Control of Chaotic Point Sets with Arbitrary Velocity Profile,” in press.
22.
Yong, Z., and Kovacevic, R., 1997d, “Modeling of Jetflow Drilling with Consideration of Chaotic Erosion Histories of Particles,” Wear, in press.
23.
Zeng
J.
, and
Kim
T. J.
,
1992
, “
Development of an Abrasive Waterjet Kerf Cutting Model for Brittle Materials
,”
Jet Cutting Technology
, Vol.
13
, pp.
483
501
.
This content is only available via PDF.
You do not currently have access to this content.