AbstractIn this paper, an erosion-based model for abrasive
waterjet (AWJ) turning process is presented. By using modified
Hashish erosion model, the volume of material removed by impacting
of abrasive particles to surface of the rotating cylindrical specimen is
estimated and radius reduction at each rotation is calculated.
Different to previous works, the proposed model considers the
continuous change in local impact angle due to change in workpiece
diameter, axial traverse rate of the jet, the abrasive particle roundness
and density. The accuracy of the proposed model is examined by
experimental tests under various traverse rates. The final diameters
estimated by the proposed model are in good accordance with
experiments.
KeywordsAbrasive, Erosion, impact, Particle, Waterjet,
Turning.
I. INTRODUCTION
BRASIVE waterjet (AWJ) machining is a well-
recognized technology for cutting variety of materials
such as composites and aerospace alloys [1, 2]. In recent
years, AWJ technique was used in milling [3] and specially
turning operations [4]. In turning operation, the workpiece is
rotated while the AWJ is traversed in axial and radial
directions to produce the required geometry. Some authors
have reported about the volume removal rate [5], surface
finish control [6], flow visualization study [7], and modeling
of the turning process [8], using AWJ technique. Unlike
conventional turning, AWJ turning is less sensitive to the
geometrical workpiece profile. This method is not related to
length-to-diameter ratio of the workpiece and therefore
enables the machining process to turn long parts with small
diameter with close tolerances. This process is ideally suitable
for machining materials with low machinability such as
ceramics, composites, glass, etc. [9]. Useful works by previous
researchers have been done which most of them are based on
experimental investigations. From a visualization study
Hashish reported that the material removal takes place on the
face of the workpiece rather than on the circumference of the
workpiece [7]. Ansari and Hashish conducted experimental
investigations to study various parameters on the volume of
material removed in AWJ turning [10]. The results show that
Iman Zohourkari is PhD student, Faculty of Mechanical Engineering, K. N.
Toosi University of Technology, Tehran, Iran, P. O. Box: 19395-1919,
(corresponding author to provide phone: (+98)-915-306-1870; e-mail:
iman_zohourkari@engineer.com).
Mehdi Zohoor, is associated professor in Faculty of Mechanical
Engineering, K. N. Toosi University of Technology, Tehran, Iran, P. O. Box:
19395-1919, (e-mail: mzohoor@kntu.ac.ir).
the volume of material removed in AWJ turning is similar to
that achieved in AWJ cutting. Zhong and Han [11] studied the
influence of variation in process parameters on turning of
glass with abrasive waterjet. They reported that lower traverse
rate of jet and higher rotational speed of workpiece resulted in
lower waviness and surface roughness for turned specimen.
Many attempts have been conducted to model AWJ cutting of
ductile metallic materials and brittle ceramic materials.
However, attempts on modeling of AWJ turning process are
very much limited. A semi-empirical model to predict radius
reduction in turning using a regression model was presented
by Zeng et al. [12]. Based on an empirical approach to model
AWJ turning presented by Henning [13], the material removal
in AWJ turning process is assumed to be the superposition of
volume removed by single particle impacts on the surface of
the workpiece.
Empirical models do not explain the mechanics of the
process. In addition, To determine the exponents and
coefficient of the empirical models, the regression analysis
should be undergone. An analytical model was suggested by
Ansari and Hashish [5] that relates the volume sweep rate to
material removal rate. This model could predict the final
diameter of specimen in various set of AWJ turning process
parameters. Hashish modified his linear AWJ cutting model
for AWJ turning [14]. He considered that material is removed
from the face of the rotating workpiece and assumed that the
total depth of cut consists of cutting-wear depth and
deformation-wear depth in turning. To estimate the cutting-
wear depth for shallow impact angle zone, Finnies theory of
erosion was used [15]. To calculate the deformation-wear
depth, the Bitters theory of erosion was used [16, 17]. This
analytical model of AWJ, does not consider the continuous
change in impact angle, which is the result of the reduction in
diameter of the workpiece. A different approach considering
the varying local impact angle presented to predict the final
diameter by Manu and Babu [18]. They applied Finnie's
theory of erosion to model AWJ turning of ductile materials.
However, their model is not able to predict accurate final
diameter in various traverse rates. Moreover, at angles near to
zero (when the impact angle is very low) it predicts higher
volume of removed material. Hence the objective of the
present work is to develop and experimentally validate a
comprehensive process model for AWJ turning of cylindrical
specimens subjected to various traverse rates.
An Erosion-based Modeling of Abrasive
Waterjet Turning
I. Zohourkari, and M. Zohoor
A
World Academy of Science, Engineering and Technology 62 2010
359
II. MECHANISM OF AWJ TURNING
In abrasive waterjet turning, it is assumed that a jet with a
velocity of V, strikes the surface of the rotating workpiece at a
speed of N revolutions per minute and an initial diameter of D.
The distance between jet centerline and the specimen
centerline is termed as the radial position of jet, x. is the
local impact angle that the jet makes with the tangent of
surface at point of impact (Fig. 1). Where can be computed
as:
o = cos
-1
_
2x
] (1)
Fig. 1 Schematic diagram of AWJ turning
Turning with AWJ is approximately equivalent to the
impact of an inclined jet to a flat surface which moving with a
velocity equal to the tangential linear surface velocity of the
rotating workpiece. The methodology of AWJ turning
involves estimating the volume of material removed by the
impacting abrasive particles by employing suitable erosion
model. The scope of the presented work is limited to AWJ
turning of ductile materials using modified Hashish erosion
model. The workpiece material considered is aluminum 6063-
T6.
III. MODELING OF AWJ TURNING
A. Modeling of Abrasive Waterjet Velocity
1. Velocity of Waterjet
The acceleration of the highly pressurized water through the
orifice generates high speed waterjets where the hydraulic
energy is converted to kinetic energy. According to Bernouli's
law [19]:
P
utm
+
p
w
2
I
th
2
+p
w
gb
1
= P +
p
w
2
I
ppc
2
+p
w
gb
2
(2)
where P
utm
is the atmospheric pressure, p
w
is the water
density which is taken as 1000
kg
m
3
, , I
ppc
is the velocity
before the orifice, I
th
is the theoretical velocity of the water
after the orifice, P is the water pressure before the orifice, b
1
and b
2
are the height of two points after and before the orifice
respectively.
Assume: b
1
-b
2
= u , P > P
utm
and I
th
> I
ppc
The approximate velocity of the exit-water jet is:
I
th
= _
2P
p
w
(S)
Momentum losses occur due to three phenomena which are:
(I) wall friction, (II) fluid flow disturbances, and (III) water
compressibility. To modify (3), a factor C
is added, therefore
the output water velocity "I
w
" becomes:
I
w
= C
_
2P
p
w
(4)
2. Velocity of Abrasive Particles
The abrasive particle acceleration in an abrasive waterjet is
a matter of momentum transfer from the high velocity water to
the abrasive particles injected at low velocities which sucks air
into the mixing chamber. Using a momentum balance
expression:
m
u
I
u0
+m
w
I
w
+ m
L
I
L
= (m
u
+m
L
+m
w
)I
u
(S)
where m
u
, m
w
and m
L
are the mass flow rates for the
abrasives, water and air respectively. I
u0
and I
L
are the input
velocities of abrasives and air respectively. I
u
is the output
velocity of the abrasive waterjet mixture.
Neglecting the amount of air (m
L
= u) and considering
I
u0
< I
u
m
w
I
w
= (m
u
+ m
w
)I
u
(6)
A moment transfer efficiency term is added for the losses
encountered during the process, therefore the velocity of
abrasive particles are given by:
I
u
=
I
w
_1 +_
m
p
m
w
_ __
(7)
The mass flow rate of water m
w
is estimated using the
expression relating the diameter of waterjet orifice J
0
,
waterjet velocity I
w
, density of water p
w
and velocity
coefficient of orifice C
d
as:
m
w
= C
d
n
4
J
0
2
I
w
p (8)
The typical values of C
, C
d
and are found to be 0.98, 0.7
and 0.8, respectively. [20]
B. Workpiece Diameter after Each Revolution
The local impact angle of jet "
k
" for k
th
revolution is
given by:
o
k
= cos
-1
_
2x
k
] (9)
World Academy of Science, Engineering and Technology 62 2010
360
The volume of material removed during each revolution can
be estimated from the rectangular strip of length equal to
circumference of the workpiece, width equal to jet diameter
and the depth equal to the radial depth of penetration during
that revolution. Thus the radius reduction for the k
th
revolution is given by
Jr
k
=
k
n
k
J
]
(1u)
Where,
k
is the volume of material removed at k
th
revolution,
k
is the workpiece diameter at the beginning of
the k
th
revolution and J
]
is the jet diameter. The Workpiece
diameter after k
th
revolution can be obtained as:
k+1
=
k
-2Jr
k
(11)
C. Erosion Models
1. Finnie's Theory of Erosion
Finnie was the first to derive a single-particle erosive
cutting model. The model assumes a hard particle with
velocity I
u
impacting a surface at an angle . The material of
the surface is assumed to be a rigid plastic one. The final
expression and boundary conditions for the volume of material
removed from the workpiece due to the impact of a single
particle can be obtained from (12) [15].
=
`
1
1
1
1
mI
2
pk
_sin(2o) -
6
k
sin
2
(o)_ , tono
k
6
mI
2
pk
_
kcos
2
(o)
6
_, tono
k
6
(12)
where is the impact angle, k is the ratio of vertical to
horizontal force components, and is the ratio of the depth of
contact l to the depth of the cut y
t
as shown in Fig. 2 , p is the
flow stress of the eroded workpiece material and Q is the total
volume of target material removed. The total volume
removed by multiple particles having a total mass M can be
obtained from (13) [15].
=
`
1
1
1
1
c
mI
u
2
pk
_sin(2o) -
6
k
sin
2
(o)_ , tono
k
6
c
mI
u
2
pk
_
kcos
2
(o)
6
_, tono
k
6
(1S)
The constant c is used to compensate for the particles that do
not follow the ideal model (some particles impact with each
other, or fracture during erosion). Finnie model [15] for
erosion is only valid for ductile materials, and does not include
any brittle fracture behavior of the material.
Fig. 2 Depth of cut and length of contact
2. Hashish Modified Model for Erosion
Hashish [14] modified Finnie model for erosion to include
the effect of the particle shape as well as modify the velocity
exponent predicted by Finnie. The final form of his model,
which is more suitable for shallow angles of impact, is given
in (13):
=
7
n
H
p
p
_
I
u
C
k
]
2.5
sin(2o) sino (1S)
where C
k
can be computed from (14):
C
k
=
_
Sp R
]
3 5
p
p
(14)
where R
]
is the particle roundness factor and p
p
is the abrasive
particle density.
One of the main advantages of this model is that it does not
require any experimental constants. In addition, it is a model
that accounts for the shape of particles.
D. Number of Revolutions to Achieve Desired Diameter
The jet is moved along the axial direction of the part so as
to extend the cutting action along the length of the part. For
acceptable turning results, the axial distance moved by the jet
during one revolution of the workpiece should be a fraction of
the jet diameter. This results in the workpiece surface being
subjected to a definite number of cutting passes during the
turning operation. Number of cutting passes can be calculated
as:
n
p
= N
J
]
u
(1S)
where u is the traverse rate (feed rate) of the jet and N is
rotational speed of the specimen. Further, due to the
interaction between the high velocity abrasive waterjet and the
rotating workpiece, material removal takes place, so an
appropriate erosion model should apply to estimate material
removed at each revolution precisely.
World Academy of Science, Engineering and Technology 62 2010
361
E. Prediction of Final Diameter
During each revolution, the workpiece diameter changes
and this in turn changes the local impact angle. By applying
(2)(14), the volume of material removed, radial depth and the
diameter of work after each revolution can be determined. By
repeating the above procedure till the impact angle tends to
zero, the final workpiece diameter under any given set of
process parameters can be estimated.
IV. CASE STUDY
In order to check the accuracy of the proposed model, an
aluminum cylindrical stepped bar (6063-T6) as shown in Fig.
3 was considered. The Process parameters employed for the
proposed model are listed in Table I. Waterjet orifice of 0.25
mm diameter and mixing tube (nozzle) of diameter 0.76 mm
were assumed for the cutting head. Garnet with a mesh size
of 80, roundness factor of 0.4 and particle density of 4000
kg m
3
was used as the abrasive material. Water pressure is
set to 250 Mpa and abrasive mass flow rate is assumed to be
5g s .
Fig. 3 Geometry of desired specimen
TABLE I
AWJ TURNING PARAMETERS
Parameter Level
Pressure, MPa 250
Nozzle diameter, mm 0.76
Abrasive mass flow rate, g/s 5
Rotational speed, rpm 200
Axial traverse rate, mm/min 2, 2.5, 10, 20
V. RESULTS AND DISCUSSION
Since flow stress is an important parameter in Finnie and
Hashish erosion models, so this parameter was determined
through 12 tests which are listed in Table II. Also material
removed predicted by Finnie and Hashish models are shown in
Fig. 4.
TABLE II
DETERMINATION OF FLOW STRESS
Hashish 's
prediction
of Flow
stress,
MPa
Finnie's
prediction
of Flow
stress,
MPa
Jet
contact
time, s
Volume
removed,
mm3
Surface
speed of
workpiece,
mm/min
Nozzle
Diameter
(mm)
7567.91 1136.68 21.38 587.91 1000
1.6
5397.96 744.67 11.30 474.04 2000
4803.19 643.44 7.02 340.76 3000
4887.97 657.70 3.93 186.64 4000
5960.88 843.09 17.85 661.49 1000
1.2
5493.27 761.57 9.39 385.39 2000
4433.92 582.85 5.37 288.08 3000
7219.33 1071.42 3.28 95.67 4000
8359.51 1285.18 27.69 673.36 1000
0.76
6010.45 852.04 12.40 454.79 2000
6830.42 999.32 11.54 360.72 3000
6223.56 889.98 8.28 290.74 4000
6099 874 Average
Fig. 4 Material removed predicted by Finnie and Hashish models
In Table III final diameter predicted by the proposed model
and Manu model [18] are compared and related errors are
described. The results were obtained under traverse rate equal
to u=2 mm min . To investigate the effect of traverse rate and
to check the efficiency of the propose model, the predicted
diameters obtained by proposed model and Manu model and
the comparison with experimental data are inscribed in Table
IV.
TABLE III
PREDICTION OF FINAL DIAMETER
Initial
diameter
Target
diameter
Manu
model
Error(mm) Presented
model
Error
(mm)
25.40 22.640 23.089 0.449 22.640 0
25.40 20.640 20.879 0.239 20.640 0
25.40 18.640 18.711 0.071 18.642 0.002
25.40 16.640 17.110 0.470 16.643 0.003
25.40 14.640 14.943 0.303 14.654 0.014
1 2 3 4 5 6 7 8 9 10 11 12
0
200
400
600
800
1000
1200
Test number
R
e
m
o
v
e
d
v
o
l
u
m
e
(
m
m
3
)
Finnie
Hashish
experiment
World Academy of Science, Engineering and Technology 62 2010
362
TABLE IV
COMPARISON OF THE EXPERIMENTAL, PROPOSED AND MANU MODELS
Traverserate
(
mm
min
, )
2 2.5 10 20
Experiment[18]
Manumodel
Presentedmodel
VI. CONCLUSION
In contrast with reported results obtained by other
researchers, the proposed model in this paper, predicts desired
geometry of specimen in various traverse rates, successfully.
Different flow stress values obtained by Finnie and Hashish
erosion models show that the flow stress may even be
considered as an empirical constant which accounts for the
material property and all other effects which are not accounted
in the erosion models. Since the proposed model does not
consider the jet divergence, so further attempts should be done
to model abrasive waterjet turning more precisely.
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