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International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

Finite element simulation of high-pressure water-jet assisted

metal cutting
Chandrakanth Shet, Xiaomin Deng∗ , Abdel E. Bayoumi
Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208, USA
Received 5 August 2002; received in revised form 16 June 2003; accepted 17 July 2003

Abstract

Experimental studies have shown that improved metal cutting e5ciency can be obtained when a high-pressure
water/coolant jet is injected at the tool–chip interface. The pressure exerted on the chip face by the jet is
expected to reduce, for example, friction along the tool–chip interface, temperature rise in the chip and the
workpiece, the cutting force, and residual stress in the 8nished workpiece, leading to a longer tool life and a
better surface integrity for the 8nished workpiece. This paper presents the results of 8nite element simulations
of high-pressure water-jet assisted orthogonal metal cutting, in which the water jet is injected directly into the
tool–chip interface through a small hole on the rake face of the tool. The mechanical e9ect of the high-pressure
water jet is approximated as a pressure loading at the tool–chip interface. The frictional interaction along the
tool–chip interface is modeled by using a modi8ed Coulomb friction law. Chip separation is modeled by a
nodal release technique and is based on a critical stress criterion. The e9ect of temperature, strain rate and
large strain is considered. Cooling e9ect of the high-pressure jet on the temperature distribution is modeled
with a convective heat-transfer coe5cient. The e9ect of water jet hole position and pressure is studied. Con-
tour plots showing the distributions of steady-state temperature and stress and the residual stress are presented.
The simulation results show a reduction in temperature, the cutting force and residual stresses for water-jet
assisted cutting conditions. The mechanical e9ect of the water jet is found to reduce the contact pressure and
shear stress along the tool–chip interface and also the contact zone length for certain water jet hole locations.
? 2003 Elsevier Ltd. All rights reserved.

Keywords: Metal cutting; Finite element simulation; Water jet; Residual stress

1. Introduction

Metal cutting is a common manufacturing process. It involves complex thermomechanical phenom-

ena, such as high strain rate in the primary shear zone, frictional contact interaction between the chip
∗
Corresponding author. Tel.: +1-803-777-7144; fax: +1-803-777-0106.
E-mail address: deng@engr.sc.edu (X. Deng).

0020-7403/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/S0020-7403(03)00142-5
1202 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

Nomenclature

shear stress

c critical frictional shear stress

th threshold frictional shear stress

f failure shear stress
 coe5cient of friction
p normal pressure
BTp local temperature rise due to plastic work
Bt time interval
p plastic work-heat conversion e5ciency factor
e e9ective stress
˙p e9ective plastic strain rate
J equivalent heat conversion factor
c speci8c heat
 mass density
f percentage of frictional heat into the chip
BTf local temperature rise due to frictional work
ṡ slip velocity
he interface element size normal to the interface
E Young’s modulus
D; m material parameters for a viscoplastic power-law model
 current Fow stress
0 initial yield stress
f stress index for a stress-based chip separation criterion
n normal stress
f tensile failure stress
2 normal stress in 2–2 direction
q heat transfer rate
h heat transfer coe5cient
A cooled surface area
Tw temperature at an exposed surface
Tf coolant bulk temperature
Nu Nusselt number
Re Reynolds number
Pr Prandtl number
v water jet velocity
l characteristic length
K thermal conductivity
 viscocity
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1203

and tool in the secondary shear zone, and elevated temperature in the chip induced by mechanical
energy dissipation. Cutting performance in terms of tool life and workpiece surface integrity depends
strongly on the temperature rise and frictional e9ects at the tool–chip interface. Consequently, cutting
performance can be improved enormously by controlling the tool–chip interfacial temperature rise
and frictional e9ects through the use of a coolant/lubricant.
In conventional metal cutting, a coolant/lubricant Fuid is usually directed onto the back of the chip
(overhead cooling). This is not e9ective in achieving the intended goal of cooling and lubrication, in
that the existence of a high contact pressure at the tool–chip interface will prevent the penetration of
lubricating Fuid into the tool–chip interface. In particular, when water is used as the coolant, it has to
reach into the tool–chip interface through a capillary action, in which the water Fow speed is usually
not high (for example, the speed is only 0:2 m=s even when the water is applied at a fairly high
pressure of 5 MPa [1]). In high-speed machining, however, the chip moves at a speed much higher
than 0:2 m=s, thus preventing the coolant Fuid entering the tool–chip interface. Hence, a conventional
lubrication method does not seem to be e9ective in improving the high-speed cutting process. In
light of this, it is noted that a more e9ective method is to apply a pressurized lubricant/coolant jet
directly to the tool–chip interface. It has been shown [1–7] that, as reviewed below, this method can
reduce temperature rise and contact friction and improves the performance of the cutting process.
Pigott and Colwell [2] conducted experimental studies on metal cutting with a high-velocity cutting
Fuid in the form of a jet. They injected the cutting Fuid at a pressure of 2:76 MPa directly into
the rake face of the tool and they found that the temperature rise dropped by 24◦ C and tool life
increased by eight times, when compared to cases with a conventional cooling/lubrication method.
In addition, it was found that the use of a high-velocity jet led to an improved workpiece surface
8nish, the elimination of a built-up edge, and reduced tool wear.
Sharma et al. [3], in their experimental studies on metal cutting, injected the cutting Fuid directly
into the tool–chip interface through a small hole in the rake face of the tool, where the position of
the hole was varied on the tool face. The Fuid was driven by an air hydraulic pump and impinged
on the chip with a pressure of 41:4 MPa. Their study indicated that the additive chemicals present in
the coolant might block the hole at a high cutting temperature, preventing the required cooling and
lubrication action. However, it was found that sulphur-based lubricants would not cause the blocking
of the jet hole and would escape through longitudinal micro-channels formed on the inner face of
the chip that was in contact with the tool, leading to a reduction of friction by 40%.
Nagpal and Sharma [4] carried out metal cutting by forcing lubricants directly into the tool–chip
interface as a pressure jet from an external nozzle. They used four di9erent lubricants driven at
varying pressures ranging from 0.35 to 3:5 MPa. Of all the lubricants, a water-soluble lubricant
was found to be the most e9ective in reducing the temperature, because of its higher speci8c heat,
higher latent heat of vaporization, and a greater extent of Fuid turbulence. The investigators reported
that the temperature and cutting force decreased with an increase of pressure up to 0:7 MPa, and
then increased with pressure and remained more or less constant for pressures beyond 2:1 MPa. The
chip surface in contact with the tool showed the presence of longitudinal channels, indicating Fuid
penetration into the tool–chip interface.
In the investigation by Ezugwu et al. [5], a pressurized water-based coolant was directed onto the
tool–chip interface from an external nozzle. A pressure of 14 MPa was used to study the performance
of the tool in cutting a Nickel-based alloy under various conditions. Compared to conventional
cutting, a reduction in the tool–chip contact length was observed, which was accompanied by a slight
1204 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

reduction in the cutting force but also by a 40% increase in the contact stress. Their research also
showed a reduction in the tool temperature rise, but not in the chip temperature rise. Shorter metal
chips were also observed with high-pressure cooling, which facilitates easy cleaning and handling.
Mazurkiewicz et al. [1] studied steel cutting using a high-pressure water jet as the coolant/lubricant.
In their study, a water jet was directed at the tool–chip interface from an external nozzle at a high
pressure of 280 MPa. It was observed that the high-pressure water jet reduced friction signi8cantly
by inducing a sliding condition instead of a stick conditions along the tool–chip interface. Compared
to cutting cases with a conventional coolant/lubricant, the use of a high-pressure water jet also
resulted in shorter chips, a reduction of feed force by 50%, an increased material removal rate, and
a reduction of the cutting force by 23%.
Kovacevic et al. [6] compared the e5ciency of two schemes of directing a high-pressure water
jet into the tool–chip interface: (a) through a hole in the tool’s rake face, and (b) from an external
nozzle. In both cases, the pressure of the water jet ranged from 68 to 200 MPa. Their study showed
that, in both cases, the cutting force was lowered considerably and the surface roughness was also
reduced. However, when the pressure was increased from 68 to 200 MPa, the surface roughness
remained constant. The investigators also reported reduced frictional e9ect and improved tool life
and wear characteristics. In a cutting experiment on titanium alloy, the use of a high-pressure water
jet completely eliminated the welding of hot chips to the cutting edge, leading to an improved surface
8nish.
O
Ojmertz and Oskarson [7] carried out metal cutting experiments on Inconel with an injected
high-pressure coolant with pressure in the range of 80 to 380 MPa. The high-pressure jet was applied
directly into the tool–chip interface. It was found that cooling introduced by the high-pressure jet
enhanced the surface 8nish quality with reduced burr. At high pressure the jet was observed to
penetrate deep into the tool–chip interface, which reduced the fracture toughness of the chip material,
resulting in e9ective chip breaking. The test result however indicated an accelerated notch wear rate.
From the experimental studies listed above, it is evident that the use of a high-pressure jet directed
into the tool–chip interface is an e9ective way of providing cooling and improving the performance
of the cutting process. In addition, the enhanced coolant/lubricant e9ectiveness reduces the amount
of Fuid being used in cutting, thus minimizing the amount of waste disposal and making the cutting
process more environmentally friendly. It is noted that when a cutting Fuid contains chemicals, the
chemicals may break down during high-speed machining, which may reduce lubrication e9ectiveness
and increase the cost of coolant disposal. Hence the use of pure high-pressure water jet as the coolant
and lubricant in machining has advantages as it improves the e5ciency of the cutting process and
poses a less environmental concern.
So far studies of high-pressure jet assisted metal cutting seem to be limited to experimental
investigations. Although experimental studies are important and the results so far are encouraging,
they do not provide a complete picture of the process nor an adequate predictive methodology. To this
end, theoretical (analytical and, especially, numerical) techniques o9er complementary investigative
tools capable of predicting the thermomechanical 8elds in metal cutting. In particular, many 8nite
element studies of conventional metal cutting have been reported in the literature. Even though these
studies so far do not speci8cally address the e9ect of using a high-pressure jet, they do shed light
on the types of results that can be obtained from numerical modeling/simulations.
Earliest analytical models on the mechanics of metal cutting include the shear-angle model pro-
posed by Merchant [8,9] and Piispanen [10], and the slip-line model by Lee and Sha9er [11] and
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1205

Kudo [12]. Subsequently these models were extended to include viscoplasticity to address the ef-
fect of work hardening and strain-rate dependency [13,14]. The above models were further modi8ed
by Doyle et al. [15] to include friction at the chip–tool interface. Heating e9ects were considered
in analytical models by Trigger and Chao [16]. The models discussed above were able to provide
helpful information about the cutting force, stress and strain, and the energy involved in the cutting
process under plane strain conditions.
With the advent of digital computers and e5cient numerical techniques such as the 8nite element
method, many numerical models have been proposed in the literature for the metal cutting process.
Usui and Shirakashi [17] developed an early 8nite element model based on empirical data. They
assumed a rate-independent deformation behavior for the material and employed a geometric crite-
rion for chip separation. Strenkowski and Carroll [18] used the general-purpose 8nite element code
NIKE2D with an updated Lagrangian formulation to simulate the orthogonal metal cutting process.
Carroll and Strenkowski [19] developed a 8nite element model based on the Eulerian formulation.
Komvopoulos and Erpenbeck [20] simulated the orthogonal metal cutting process with consideration
of both rate-independent and rate-dependent material constitutive laws. Lin and Lin [21] conducted
8nite element analysis using a coupled thermo-elastic-plastic formulation. They included large defor-
mation e9ects and employed a strain-energy density based chip separation criterion. Shih and Yang
[22] and Shih [23] carried out experimental and 8nite element studies of the orthogonal metal cut-
ting process and investigated the e9ects of viscoplasticity, large strain, high strain rate, temperature,
and friction. Li [24,25] studied the e9ect of coolant jet Fow rate in metal cutting with conventional
overhead and Fank cooling. More recently, Shet and Deng [26,28] and Shi et al. [27] conducted
elaborate 8nite element simulations of the orthogonal metal cutting process for a range of rake angles
and friction conditions at the tool–chip interface. The simulation procedure developed in these two
studies has been validated (see Ref. [29]) with experimental data from the literature as well as by
the recent joint experimental/simulation studies conducted by these authors and their collaborations
(see Ref. [30]).
The purpose of the present study is to model the e9ect of high-pressure water jet in orthogonal
metal cutting using the 8nite element method. Finite element simulation-based studies, such as the
present one, will allow us to gain a basic (albeit qualitative) understanding of various thermal and
mechanical quantities involved in high-pressure water-jet assisted metal cutting, which are often not
accessible experimentally, and to gage the usefulness of such unconventional metal cutting processes.
The 8ndings obtained in this type of study may provide helpful information for the design of such
cutting systems.
In the model problem considered in this study (see details later), a high-pressure water jet enters
the tool–chip interface through a conduit hole in the cutting tool and impinges on the chip face with
a pressure in the range of 200 –800 MPa. In the 8nite element simulations, an Updated Lagrangian
Formulation is employed to handle kinematic issues related to large strains and 8nite strain-rates.
A stress-based chip separation criterion is used to control the chip separation process from the
workpiece. According to this criterion, chip separation occurs when a critical stress state is achieved
at a speci8ed distance ahead of the tip of the cutting tool. The frictional interaction between the chip
and the cutting tool is based on a Modi2ed Coulomb Friction Law. Temperature-dependent material
properties are considered in the analyses. Heat generated by plastic work and friction is allowed to
conduct within the chip and workpiece (thus the usual adiabatic heating condition is not assumed).
Since the chip thickness is small compared to its width, 8nite element simulations are carried out
1206 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

under plane strain conditions for a typical case in which the coe5cient of friction is 0.2 and the
tool’s rake angle is 20◦ .
As an approximation, only the mechanical e9ect of the high-pressure water jet is modeled in the
present study, while the details of Fuid dynamics of the water jet are left untreated. The simulation
of the mechanical e9ect of the high-pressure jet impinging through a hole in the tool is taken to be
equivalent to a high-pressure loading applied on the chip face at the chip–tool interface. A range
of the jet hole position is considered in order to optimize the mechanical e9ect of the jet. Cooling
provided by the jet is modeled through the use of a convective heat transfer coe5cient for the tool–
chip interface. A 8nite element modeling procedure with deformation-heat conduction coupling has
been developed using various advanced modeling options in the general-purpose 8nite element code
ABAQUS [31] and has been validated previously for cases of orthogonal metal cutting simulations
(see Refs. [29,30]). More details of this study are given in the next section.

2. Finite element modeling details

Fig. 1 shows a schematic diagram of the orthogonal metal cutting process model in this study and
provides a graphical description of some modeling details. In this model, the cutting tool is taken
to be rigid since it is much sti9er than the workpiece material. The tool cuts through the workpiece
along a 8xed path (contact pair #1). A continuous chip is separated from the workpiece at the edge
of the cutting tool and comes into contact with the tool’s rake face, forming the tool–chip interface
(contact pair #2). Possible contact between the tool and the 8nished workpiece surface is handled
by contact pair #3. A friction coe5cient of 0.2 is used (other values can also be considered) and
the tool’s rake angle is 20◦ . Chip separation from the workpiece is controlled by the attainment of

Fig. 1. A schematic diagram of the metal cutting model with contact pairs.
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1207

a critical stress state at a 8xed distance ahead of the tip of the cutting tool. A detailed discussion
of several items of interest is give below.

2.1. Modeling of interfacial friction

During metal cutting, frictional contact occurs along the tool–chip interface, which strongly a9ects
chip formation, stress and strain distribution, and workpiece surface integrity. In the present study,
the interfacial friction is modeled using the Modi8ed Coulomb Friction Law, an option available in
ABAQUS. Suppose
is the shear stress in the chip parallel to the tool–chip interface at a point at
the interface. Relative motion between the tool and the chip takes place at a point along the interface
if
at that point is equal to or above a critical value, say
c ; if
is less than
c , then no relative
motion occurs.
In the Modi2ed Coulomb Friction Law, the critical value
c is determined by

c = min(p;
th ); (1)

where p is the normal pressure across the tool–chip interface,  is the coe5cient of friction, and
th
is a threshold value that de8nes a limit for the product p beyond which the conventional Coulomb
Friction law is taken over by the Modi2ed Coulomb Friction law. In this study,
th is considered to
be governed by the plastic failure of the chip material due to shearing. For example, when the chip
material is AISI 4340 steel,
th is taken to be 549 MPa, a value slightly higher than the materials
shear failure stress
f . A friction coe5cient of 0.2 is used although other values can also be employed
in the 8nite element model.

2.2. Modeling of heating e3ects

During metal cutting, heat is generated due to plastic work done in the primary and secondary
shear zones and due to the frictional work along the tool–chip interface. The rate of plastic energy
dissipation is dWp =dt = e ˙p , where e is the e9ective stress and ˙p is the e9ective plastic strain
rate. The percentage of the dissipated energy that is turned into heat is denoted by p (usually
85% 6 p 6 95%). In this study, p = 90% is taken since it is commonly used value in the literature.
Friction along the tool–chip interface also causes heating of the chip, which is represented by the
frictional heat Fux density q=f
ṡ, where
is the frictional shear stress, ṡ is the relative slip velocity
along the contact interface, and the coe5cient f stands for the portion of the frictional heat Fux
that goes into the chip. For simplicity, the total frictional heat is assumed to split evenly between
the chip and the tool, so that f = 0:5.
Although adiabatic heating is not assumed (a coupled deformation-heat conduction approach is
employed in this study), it is worth noting that, if the adiabatic heating condition is assumed, an
instantaneous local temperature rise can be computed using simple equations. In the active plastic
zones of the workpiece and chip material, the temperature rise BTp induced by plastic work in a
time interval Bt is given by
BTp e ˙p
= p ; (2)
Bt Jc
1208 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

where J is the equivalent heat conversion factor, c is the speci8c heat, and  is the mass density.
Along the tool–chip interface, the chip’s temperature rise BTf caused by friction in a time interval
Bt can be estimated by
BTf
ṡ
=f (3)
Bt Jche
where he is the size of the interface element in the direction normal to the contact interface. The
above expression is equivalent to what was done in Lin and Lin [21] (note that four-node quadrilateral
elements are used along the interface; see Section 2.6).

2.3. Modeling of cutting tool

Since the cutting tool material is expected to be much sti9er than the chip and the workpiece, it is
modeled as a rigid block made of an arti8cial material with an extremely high Young’s modulus (a
value of 2:1×1015 MPa is used in this study). During cutting, the tool tip (hence the tool as a whole)
is made to translate in the cutting direction while the tool is held still in the vertical motion through
constraints along the top edge of the tool block (see Fig. 1). As the tool is displaced horizontally,
its rake face comes into contact with the chip and its clearance face with the 8nished surface of the
workpiece. In order to establish the contact interfaces, a set of contact pairs (contact pairs #2 and
#3 in Fig. 1) is de8ned.

2.4. Material model and parameters

A rate-dependent elastic–plastic material model of the overstress power-law type is employed to

describe the viscoplastic behavior of the workpiece material (which is AISI 4340 steel in this study),
as given below

m

˙p = D −1 for  ¿ 0 ; (4)
0
where ˙p is the e9ective plastic strain rate,  is the current yield stress, 0 is the initial yield
stress, D and m are material parameters. This rate dependent power law is highly suitable when
the material is subjected to high strain rate deformation as in the case of high-speed metal cutting
being studied here. The numerical values for the constants D and m are taken as 2:21 × 105 s−1
and 2.87, respectively [20]. Temperature-dependent mechanical properties (e.g. Young’s modulus)
given in Shet and Deng [26] and Shi et al. [27] are used. Conventional thermal parameters are used:
c = 502:0 J=kg K for the speci8c heat and  = 7800 kg=m for the mass density.

2.5. Modeling of chip separation

The general-purpose 8nite element code ABAQUS allows two surfaces de8ned by two sets of
separate nodes to interact both mechanically and thermally by means of contact pairs. As shown in
Fig. 1, contact pair #1 de8nes the cutting path, along which the two contact surfaces are in perfect
bond. When a speci8ed chip separation condition is met, the pair of nodes directly ahead of the
tool tip will be released and the contacting surfaces will be separated, enabling the tool to advance
incrementally by one element edge size. With the separation of contact pair #1, the elements forming
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1209

the chip surface will move into contact pair #2 (which refers to the chip–tool interface) and the
elements forming the workpiece surface will move into contact pair #3, as illustrated in Fig. 1.
Note that contact pair #2 is needed to model both the thermal and mechanical interactions along
the tool–chip interface, and that contact pair #3 is de8ned mostly to maintain the contact of the
tool tip with the newly 8nished surface of the workpiece.
A number of physical/geometrical criteria have been proposed to govern the separation of the chip
from the workpiece. Huang and Black [32] made a detailed study of several chip separation criteria
and reported that the geometry of the chip and the distribution of stress and strain in the chip are
not much a9ected by the use of a particular criterion. In the present study, a stress-based criterion
is used because it is an option that can be readily utilized in ABAQUS. According to this criterion,
chip separation takes place when the components of the stress state at a speci8ed distance ahead of
the tool tip (see Fig. 1) reaches a critical combination in terms of a stress index parameter f:



n 2
2
f= + ; where n = max(2 ; 0): (5)
f
f
In Eq. (5),
and n are the shear and normal stress components, and f and
f are the failure stresses
of the material under pure tensile and shear loading conditions, respectively. A critical combination
is reached when f becomes 1.0. In this study, the distance where the criterion is checked is taken to
equal to a few element edge length, which is approximately 80:0 m. For AISI 4340 steel, √ a tensile
failure stress of f = 948 MPa is used, and the shear failure stress is chosen to be
f = f = 3 (based
on the von Mises yield criterion), which is about 548 MPa.

2.6. Finite element mesh and boundary conditions

Plane strain elements are used to model the metal cutting process in this study. As shown in
Fig. 2, the mesh is composed of 1220 four-node elements having a total of 1383 nodes. Since the
chip is expected to undergo severe straining and distortion, the chip portion of the problem domain is
discretized with smaller elements than the workpiece portion. More speci8cally, the chip layer, which

Fig. 2. The 8nite element mesh used in the metal cutting simulations.
1210 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

has a height (the cut depth) of 254 m, is divided into 10 sub-layers of elements. The workpiece
domain, which has a length of 2540 m and a height of 889 m, is divided into 11 layers parallel
to the cutting path, and each layer contains 50 elements in the cutting direction (which have been
shown to be su5cient for the simulation to reach the steady state before the cutting tool reaches the
end). In order to accurately represent the stress and strain 8elds near the chip–workpiece interface,
small elements (50:8 m × 50:8 m) are used in the 8ve layers just below the cutting path. Since
the lower portion of the workpiece is expected to experience relatively little deformation, and the
focus of this study is on the steady-state behavior (hence transient e9ects at the start and end of
simulations may be ignored), the left, right, and bottom boundaries of the workpiece are considered
restrained in the cutting direction.
A simple parallelogram with proper rake and clearance angles is used to represent the cutting tool.
It has a base length of 407 m and a height 762 m. It is meshed with 120 four-node plane strain
elements. During metal cutting simulation, the top edge of the tool is held still in the y-direction
and the tool is made to translate in the x direction. The tool advances incrementally in the negative
x-direction at a constant speed of v = 2:54 m=s (152:4 m=min). The rake face of the tool is bounded
by a contact surface, which will interact with the corresponding contact surface of the chip to form
a contact pair.
It is seen from Fig. 2 that the chip layer is meshed with tilted elements (where the tilt angle is
about 64◦ ). The reason is that the tilted shape will prevent excessive element distortion when the
chip interacts with the tool surface after separation from the workpiece. It is further seen that the
chip is initially separated (with a curved shape) from the workpiece at the right end of the chip layer,
which is used to facilitate a smooth transition of the cutting process from the initial stage to the
steady state. Such an initial mesh design is justi8ed since the focus of this study is the steady-state
behavior. At the left end a triangular portion of the chip layer extends, which is maintained to make
the mesh generation simpler, and this would not a9ect the steady-state simulation results because
the steady-state condition is attained long before the cutting tool approaches the left end. The type
of mesh design described above was originally proposed by Strenkowski and Carroll [18] and has
been adopted by other researchers (e.g. Shih [23], Shet and Deng [26], and Shi et al. [27]).

2.7. Modeling of high-pressure jet e3ect

In the experimental studies discussed earlier, a high-pressure coolant jet has been applied directly
to the tool–chip interface either through an external nozzle or through a hole out of the rake face
of the tool (see Fig. 3). In particular, Kovacevic et al. [6] demonstrated experimentally that both jet
application methods were e9ective in improving the performance of the cutting process. Intuitively,
it seems more e9ective to eject the coolant through a hole in the tool since it can reduce both the
interface friction and the pressure between the tool and the chip. In addition, the jet may help to
reduce the formation of a built-up edge and eliminate hot-chip welding to the cutting edge, which
has been a major problem in machining titanium alloys. In the present study, the mechanical e9ect
of a high-pressure coolant jet through a hole in the rake face of the tool is modeled. It is noted
that, when the high-pressure coolant jet impinges on the chip surface at the tool–chip interface, it
induces a pressure loading on the chip.
In this study, a Fuid pressure is applied normal to the interacting surfaces at the location of
the coolant-jet conduit hole, which is made possible by a provision in ABAQUS that allows the
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1211

Fig. 3. A schematic showing the high-pressure jet conduit hole location: (a) the hole is just above the tool tip, (b) the hole
is 0:2 mm above the tool tip, and (c) the hole is 0:3 mm above the tool tip. The numbers along the tool–chip interface
refer to 8nite element node numbers in the chip.

simulation of the coolant Fuid penetration into two interacting contact surfaces. The Fuid pressure
loading is applied at three di9erent locations along the tool–chip interface: (1) just above the tool
tip (see Fig. 3(a)), (2) at 0:2 mm (which is about 60% of the contact length along the tool–chip
interface in conventional metal cutting) above the tool tip (Fig. 3(b)), and (3) at 0:3 mm (about
90% of the contact length) above the tool tip (Fig. 3(c)). When the jet is positioned just above the
tool tip, a jet pressure in the range of 200 MPa (equivalent to applying a force of 16 N=mm across
the chip width) to 800 MPa (equivalent to applying a force of 64 N=mm across the chip width) with
an increment of 200 MPa is considered. When the jet is applied at 0:2 mm above the tool tip, the
pressure range is from 200 to 600 MPa, and when the jet is applied at 0:3 mm above the tool tip,
the pressure range is from 200 to 400 MPa. The reason for the reduced pressure range is that, as
the jet conduit hole moves higher along the tool–chip interface, the maximum jet pressure that can
be sustained by the chip is reduced (when the jet pressure is higher than the maximum value, the
chip deformation becomes unbounded).

2.8. Modeling of cooling e3ects

When a high-pressure coolant jet is directed into the tool–chip interface, the Fowing coolant jet
will remove heat from the interface and carry the heat away from the chip–tool–workpiece system.
In this study, the cooling e9ect provided by the jet is described by using a convective heat-transfer
coe5cient, h, as given below
q = hA(Tw − Tf ); (6)
where q is the heat-transfer rate related to the overall di9erence between the temperature at the
exposed surface, Tw , and the bulk temperature of the water jet coolant, Tf , and A is the cooled surface
area. For the forced convective heat transfer, an appropriate heat transfer coe5cient considering the
velocity of the jet is used. The general theory of convective heat transfer due to a boundary layer
1212 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

e9ect of Fuid relates the Nusselt number to the Reynolds number and the Prandtl number through
a power law [33]:
Nu = 0:453 Re1=2 Pr 1=3 : (7)
In the above, the Nusselt number is de8ned by Nu = hl=K, the Reynolds number by Re = vl=,
and the Prandtl number by Pr = c=K, where v, l are the velocity and characteristic length scales,
and K, , , and c are, respectively, the conductivity, density, viscosity and speci8c heat of the
coolant. The impingement of the high-pressure water jet upon the chip face is expected to create a
high-velocity impact with an impact velocity on the order of 370 m=s and above [1]. The amount
of convective heat transfer along the tool–chip interface is computed internally in the 8nite element
model during a cutting simulation using the above information. Other exposed chip and workpiece
surfaces are maintained at a speci8ed room temperature. It is noted that Li [24,25] used a similar
cooling model to study the jet Fow rate e9ect on cooling. Based on the above considerations, an
approximate value of 100 W=(K m2 ) is assigned to the heat transfer coe5cient (h) in the present
study. The bulk temperature (Tf ) of the water jet is set to the room temperature (20◦ C).

2.9. Simulation procedure

In this study, 8nite element simulations have been carried out with a coe5cient of friction 0.2
and a rake angle of 20◦ (other friction coe5cients and rake angles are also possible with the 8nite
element model). To start a simulation, the cutting tool is engaged at the right side of the specimen
(see Fig. 2) and then it moves incrementally towards the left at a velocity of 2:54 m=s until a
steady-state cutting condition is reached, which is usually attained after the tool cuts through 30
–50 elements (corresponding to a distance of 1.5 –2:5 mm along the cutting path). The simulation
is then stopped in order to evaluate the steady-state values of the thermomechanical 8elds during
metal cutting.
Since residual stresses provide good indicators for the quality and integrity of the 8nished work-
piece surface, they are calculated in this study and the e9ect of the high-pressure water jet on the
residual stress distribution is examined. The following computational procedure [28] is used:

Step I. The cutting tool is advanced incrementally in the cutting direction until a steady-state
metal cutting condition is attained.
Step II. The cutting tool is withdrawn incrementally until none of the chip and workpiece nodes
is in contact with the tool.
Step III. Restraining forces at all supporting boundary nodes are released (except for those that
are necessary to prevent rigid body motion).
Step IV. The workpiece is incrementally cooled down until the room temperature is attained. The
resulting stresses in the workpiece are the residual stresses.

3. Results and discussion

Unless stated otherwise, all results presented below are abstracted from 8nite element simulation
solutions obtained after the achievement of the steady-state condition (see Section 3.3 for a discussion
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1213

Fig. 4. Contact pressure variation along the tool–chip interface when the water jet pressure loading is applied just above
the tool tip.

of the steady-state condition in terms of the cutting force variation with the amount of cutting
tool advancement). For comparison purposes, in additional to results for the cases of high-pressure
water-jet assisted metal cutting, those for the case of conventional metal cutting are also included.
Furthermore, as discussed in Section 3.7, the e9ect of convective cooling introduced by the water jet
is signi8cant for the steady-state temperature distribution but is marginal as far as the steady-state
stress and deformation 8elds are concerned. As such, Sections 3.1–3.6 will be focused on the results
obtained with the consideration of only the pressure loading e9ect of the high-pressure water jet, that
is, the e9ect of convective cooling along the tool–chip interface due to the water jet is neglected.
Di9erences caused by the convective cooling are discussed in Section 3.7.

3.1. Contact pressure and shear stress along the tool–chip interface

Figs. 4–6 show the variations of the contact pressure along the tool–chip interface for three di9erent
pressure-loading locations. In these 8gures, the contact node numbers along the chip–tool interface
are those at a particular time step after the steady-state cutting condition is reached and refer to
nodes on the chip side of the interface. Speci8cally, Node 1232 is next to the tool tip and has just
arrived at the tool–chip interface (also see Fig. 3), while Node 1352 is near the end of the tool–chip
interface and is on its way out. It can be seen from Fig. 4 that, when the water jet is absent (the
conventional cutting case), the contact pressure between the tool and the chip begins with a value
of 800 MPa at a point where newly formed chip enters the interface; it then rises sharply to the
maximum of 1300 MPa and drops quickly to 1100 MPa and remains there along most part of contact
length (which is about 0.34 mm). The contact pressure drops further to a value around 700 MPa
just before the chip leaves the contacting interface. However, when the water jet in the form of a
pressure loading is applied just above the tool tip (see Fig. 3(a)), the contact pressure experiences
a substantial reduction (more than 28%) throughout the contacting interface when compared to the
conventional cutting case. Furthermore, the contact pressure reduction is almost independent of the
1214 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

Fig. 5. Contact pressure variation along the tool–chip interface when the water jet pressure loading is applied at 0:2 mm
above the tool tip.

Fig. 6. Contact pressure variation along the tool–chip interface when the water jet pressure loading is applied at 0:3 mm
above the tool tip.

magnitude of the applied pressure loading (which varies between 200 and 800 MPa). It must be
pointed out that, although the contact pressure is reduced when a water jet is applied, the contact
zone length (indicated by the location of the right-most node) is essentially the same as in the
case of conventional cutting, which suggests that the tool tip area may not be the best location for
applying the water-jet pressure loading.
To evaluate the e9ect of the water jet hole location, the results of moving the pressure loading
point are presented in Figs. 5 and 6. When the water jet pressure loading is applied at 0:2 mm above
the tool tip (see Fig. 3(b)), it is found (see Fig. 5) that, in addition to substantial reduction in the
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1215

contact pressure, the size of the zone with the high contact pressure and the size of the entire contact
zone (indicated by the location of the right-most node) are also reduced considerably, especially in
the case with the highest pressure loading. It is noted that pressure loading higher than 600 MPa
is not possible in this case because when the pressure loading goes beyond 600 MPa, the chip will
completely lose contact with the tool, leading to numerical instability in the FEM analysis.
When the pressure loading is moved further up along the tool–chip interface and is applied at
0.3 mm above the tool tip (see Fig. 3(c)), the bene8ts of the water jet seem to begin to decrease
compared to the preceding case. As seen in Fig. 6, while the reduction in the contact pressure is
still substantial, the zone with high contact pressure is about twice of that in Fig. 5. Similar to the
preceding case, when the pressure loading is beyond 400 MPa, the chip will completely lose contact
with the tool and a numerical solution cannot be obtained.
The variations of the contact shear stress along the tool–chip interface for the cases of high-pressure
water-jet assisted metal cutting are quite similar to those presented for the contact pressure distri-
bution. This is expected because the maximum shear stress is well below the threshold shear stress

th in the Modi8ed Coulomb Friction Law (see Section 2.1), and hence the conventional Coulomb
friction law is active and the contact shear stress in the chip is equal to the product of the contact
pressure (normal stress) with the friction coe5cient.
In summary, the most bene8cial e9ects of the water-jet pressure loading through a conduit hole
in the cutting tool are the reduction in the contact pressure (and hence in the frictional shear stress)
and reduction in the contact zone length.

3.2. Tool–chip interface opening displacement

A plot of the opening displacement along the tool–chip interface will clearly reveal the interface
contact zone in which the opening displacement is zero. To this end, Figs. 7–9 present the variation
of the opening displacement along the interface for the cases of high-pressure water-jet assisted

Fig. 7. Interface opening displacement variation along the tool–chip interface when the water jet pressure loading is applied
just above the tool tip.
1216 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

Fig. 8. Interface opening displacement variation along the tool–chip interface when the water jet pressure loading is applied
at 0:2 mm above the tool tip.

Fig. 9. Interface opening displacement variation along the tool–chip interface when the water jet pressure loading is applied
at 0:3 mm above the tool tip.

metal cutting and conventional metal cutting. In particular, Fig. 7 shows the variation of the opening
displacement when the pressure loading is applied just above the tool tip. In this case, the size of
the contact zone is reduced by about 9% when conventional metal cutting is assisted with a water
jet with a pressure in the range of 200 –800 MPa. When the pressure loading is applied at 0:2 mm
above the tool tip, as can be seen from Fig. 8, the reduction in the contact length is, respectively,
7%, 14 %, and 22 % for the pressure value of 200, 400, and 600 MPa. When the pressure loading
is applied at 0.3 mm above the tool tip, the reduction in the contact length is, respectively, about
8% and 10% for pressure value of 200 MPa and 400 MPa (see Fig. 9).
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1217

Fig. 10. Cutting force variation with tool displacement when the water jet pressure loading is applied just above the tool
tip.

From the above observations it is evident that, from the point of view of maximizing the reduction
of the contact zone, positioning the water-jet conduit hole near the tool tip (which is the lower end
of the contact zone) or at 0:3 mm above the tool tip (which is the upper end of the contact zone) is
not as good as placing the hole at 0:2 mm above the tool tip (which is approximately in the middle
of the contact zone).

3.3. Cutting force and steady-state condition

The cutting force is de8ned as the horizontal force experienced by the cutting tool. In this study,
this force is computed by summing horizontal reaction forces at the constrained nodes on the cutting
tool. In the case of conventional metal cutting when the high-pressure water jet is absent, this
“calculated” cutting force is the actual cutting force. However, when the e9ect of the water-jet
pressure loading is included, this “calculated” cutting force is equal to the actual cutting force plus
a force due to the pressure loading (which equals, approximately, 15 N=mm when the water-jet
pressure is 200 MPa and 60 N=mm when the pressure is 800 MPa). As such, the “cutting force”
data presented below must be interpreted properly.
The variation of the calculated cutting force with the amount of tool displacement is given in Figs.
10–12 for several cases. The case in which the water jet pressure loading is applied just above the
tool tip is shown in Fig. 10. It is seen that the cutting force is basically constant after the cutting tool
has advanced about 0:5 mm, indicating the achievement of a steady-state cutting condition. Moreover,
when compared to conventional metal cutting, the introduction of a high-pressure water jet leads
to substantial reduction (more than 30%) in the cutting force. It is noted that the di9erence in the
steady-state cutting force values for the pressure loading cases is mostly caused by the inclusion of
the e9ect of the pressure loading in the cutting force (as discussed in the preceding paragraph)—the
actual di9erence is very small.
1218 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

Fig. 11. Cutting force variation with tool displacement when the water jet pressure loading is applied at 0:2 mm above
the tool tip.

Fig. 12. Cutting force variation with tool displacement when the water jet pressure loading is applied at 0:3 mm above
the tool tip.

When the location of the pressure loading is moved up to 0:2 mm above the tool tip, the attainment
of the steady-state condition is delayed, especially for the 600-MPa loading case (see Fig. 11). The
actual steady-state cutting force (see discussion in the 8rst paragraph) for the pressure loading cases
is about 36% or more below that of the conventional cutting case. When the pressure-loading hole
is further moved up to 0:3 mm above the tool tip, the steady-state condition seems to be reached
earlier than in the preceding case, and reduction in the cutting force from the conventional cutting
case is around 27% (see Fig. 12).
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1219

Fig. 13. Temperature contours in the chip and workpiece for the case of conventional metal cutting.

Fig. 14. Temperature contours in the chip and workpiece for the case of high-pressure water-jet assisted metal cutting
with a 200-MPa pressure loading just above the tool tip.

Reduction in the cutting force is expected in the cases of high-pressure water-jet assisted metal
cutting. This is because the addition of a water-jet pressure loading along the tool–chip interface
lessens the amount of frictional resistance (because of reductions in contact stresses and in the
contact length) along the interface, as evidenced by the results of the previous sections.
1220 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

Fig. 15. Temperature contours in the chip and workpiece for the case of high-pressure water-jet assisted metal cutting with
a pressure loading at 0:2 mm above the tool tip: (a) pressure = 200 MPa; (b) pressure = 400 MPa; (c) pressure = 600 MPa.

3.4. Temperature contours in the chip and workpiece

Steady-state temperature (actually, temperature rise) contours for cases of conventional metal cut-
ting and high-pressure water-jet assisted metal cutting are shown in Figs. 13–15. The reference case
of conventional metal cutting is given in Fig. 13. It is seen that the maximum contour level (level
10) occurs near the middle portion of the tool–chip interface (the secondary shear zone), where
the actual maximum temperature rise is about 552◦ C. The temperature contours for the case of a
200-MPa pressure loading just above the tool tip are shown in Fig. 14. In this case, the maximum
temperature rise is about 503◦ C, a reduction of 9% from the conventional metal cutting case. A
further reduction in the maximum temperature rise is not observed when the water-jet pressure is
further increased.
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1221

Fig. 16. Contours of 11 in the chip and workpiece for the case of conventional metal cutting.

The case of high-pressure water-jet assisted metal cutting with a pressure loading at 0:2 mm above
the tool tip is di9erent from the preceding case. Figs. 15(a), (b) and (c) provide the temperature
contours when the applied pressure loading is, respectively, 200, 400, and 600 MPa. It is observed
that the contour level 8 is getting closer to the tool–chip interface as the applied pressure is increased,
suggesting an increasing reduction in the maximum temperature rise. The actual maximum temper-
ature rise for a 200-, 400- or 600-MPa pressure loading is, respectively, 470◦ C, 463◦ C and 449◦ C
(the corresponding temperature rise reduction relative to the case of conventional metal cutting is,
respectively, 15%, 16% and 19%).
A maximum temperature rise of about 482◦ C is found for the case of a 200-MPa pressure loading
applied at 0:3 mm above the tool tip, which corresponds to a temperature rise reduction of 13%
when compared to the case of conventional metal cutting. The change in the maximum temperature
rise is negligible when the water jet pressure is increased from 200 to 400 MPa.
An interesting observation is that the pressure loading e9ect alone leads to a sizable reduction in
the temperature rise. The reason for this reduction is that the water jet pressure loading causes a drop
in the cutting force as well as in the contact pressure, the contact shear stress and the contact length
along the tool–chip interface, which in turn lowers the level of the heating source due to plastic
energy dissipation in the chip and workpiece and due to frictional work along the tool–chip interface.
As discussed in Section 3.7, the inclusion of the additional water jet e9ect of convective cooling
along the tool–chip interface will result in further reduction in the temperature rise.
1222 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

Fig. 17. Contours of 11 in the chip and workpiece for the case of high-pressure water-jet assisted metal cutting with a
200-MPa pressure loading just above the tool tip.

3.5. Steady-state stress distribution in the chip and workpiece

The steady-state distribution of the normal stress 11 is chosen for discussion in this paper because
it is the dominant stress component and is in the cutting direction. Fig. 16 shows the stress contours
for the case of conventional metal cutting. Two observations can be made. The 8rst is that stress in
the chip is mostly compressive. In particular, it is noted that chip materials just ahead of the tool
tip experience a high level (about twice the yield stress) of compression against the tool, which
serves as a good indicator of the abrasive action of the chip upon the tool tip. Abrasive action and
high temperature are known to cause tool wear, such as the formation of a built-up edge, tool Fank
wear, and tool cratering (see e.g. Ezugwu et al. [5]). The second observation is that stress in the
workpiece just below and behind the tool tip is tensile and its magnitude is also about twice of the
yield stress. This stress is expected to have a strong inFuence on the formation of residual stresses
in the workpiece.
When a water-jet with a 200-MPa pressure is applied just above the tool tip, the magnitude of
the compressive stress in the chip region immediately ahead of the tool tip is reduced (see Fig. 17).
A similar reduction is also observed in the workpiece. When the location of the water jet is moved
up to 0:2 mm above the tool tip, a progressive stress reduction in the chip (relative to Fig. 17) is
observed as the water-jet pressure is increased from 200 MPa to 600 MPa (see Figs. 18a–c), but
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1223

Fig. 18. Contours of 11 in the chip and workpiece for the case of high-pressure water-jet assisted metal cutting with a
pressure loading at 0:2 mm above the tool tip: (a) pressure = 200 MPa; (b) pressure = 400 MPa; (c) pressure = 600 MPa.

there is little change in the tensile stress in the workpiece. Moving the water jet further up to 0:3 mm
above the tool tip does not seem to be bene8cial in terms of stress reduction. The conclusion is
that it is better to place the water-jet in the middle (rather than the lower or upper) portion of the
contact zone along the tool–chip interface. Reduction of the compressive stress in the chip ahead
of the tool tip and of the tensile stress along the 8nished surface of the workpiece is expected to
reduce abrasive wear of the tool and enhance the quality of the 8nished workpiece surface.

3.6. Residual stress distribution in the workpiece

The preceding section reveals that the steady-state stress in the workpiece in the cutting direction
is tensile and the stress level can be lowered if a high-pressure water jet is directed through the tool
1224 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

Fig. 19. Contours of residual stress 11 in the workpiece for the case of conventional metal cutting.

Fig. 20. Contours of residual stress 11 in the workpiece for the case of high-pressure water-jet assisted metal cutting with
a 200-MPa pressure loading just above the tool tip.

into the tool–chip interface. This section discusses the e9ect of the water jet on the residual stress
distribution in the 8nished workpiece. The residual stress distribution is expected to have a more
direct inFuence on the quality of the 8nished workpiece surface than its steady-state counterpart.
Again, the focus here is on 11 since it is the dominant residual stress component and it is parallel
to the 8nished surface.
Fig. 19 shows the sub-surface residual stress distribution for the reference case of conventional
metal cutting. The residual stress is tensile near the freshly 8nished surface of the workpiece, achieves
its maximum value (about 400 MPa) right at the surface, drops quickly away from the surface, and
becomes compressive beyond a certain distance. When a high-pressure water jet of 200 MPa is
applied just above the tool tip, a marginal reduction in the tensile stress level is observed (see
Fig. 20), in which the maximum tensile stress is 387 MPa. An increase in the applied pressure
loading does not seem to make a di9erence.
When the water jet hole is moved to 0:2 mm above the tool tip, an increasing reduction in the
maximum tensile stress is observed as the value of the pressure loading is increased (see Figs. 21a–c).
The percentage reduction (relative to the case of conventional metal cutting) in the maximum tensile
stress is, respectively, 16%, 30% and 34% when the applied pressure is 200, 400, and 600 MPa. A
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1225

Fig. 21. Contours of residual stress 11 in the workpiece for the case of high-pressure water-jet assisted metal cutting with
a pressure loading at 0:2 mm above the tool tip: (a) pressure = 200 MPa; (b) pressure = 400 MPa; (c) pressure = 600 MPa.

relative maximum stress reduction of 18% or more is also achieved when the pressure loading is
applied at 0:3 mm above the tool tip.

3.7. E3ect of water-jet induced convective cooling

In the preceding sections only the mechanical e9ect of the high-pressure water jet is considered.
This section describes what happens if the convective cooling e9ect of the water jet is also included,
which is done for the case of a water jet pressure loading at 0:2 mm above the tool tip. As discussed
in Section 2.8, the cooling e9ect of the water jet is modeled in terms of a convective heat transfer
coe5cient for the tool–chip interface.
Figs. 22a–c show the steady-state temperature contours in the chip and workpiece for water jet
pressures of 200, 400, and 600 MPa, respectively. When the water jet pressure is 200 MPa (Fig. 22a),
a 25%-reduction in the maximum temperature rise is observed when compared to the counterpart
case that includes only the mechanical e9ect of the water jet (see Fig. 15a), which corresponds to
a reduction of 36% when compared to the case of conventional metal cutting (Fig. 13). When the
water jet pressure is 400 MPa (Fig. 22b), the reduction in the maximum temperature rise is similar
to the 200-MPa case, which is 25% and 37% when compared to, respectively, the counterpart case
with mechanical e9ect only (Fig. 15b) and the case of conventional metal cutting. The case of a
600-MPa pressure is also similar (Fig. 22c), in which the corresponding reductions in the maximum
temperature are 24% and 38%.
An examination of the e9ect of convective cooling on the steady-state stress and deformation
8elds reveals that inclusion of convective cooling along the tool–chip interface only leads to marginal
1226 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228

Fig. 22. Temperature contours in the chip and workpiece for the case of high-pressure water-jet assisted metal cutting
with a pressure loading at 0:2 mm above the tool tip and with the e9ect of convective cooling: (a) pressure = 200 MPa;
(b) pressure = 400 MPa; (c) pressure = 600 MPa.

changes in these 8elds. In order to understand this phenomenon, it is noted that during high-speed
machining, the e9ect of removing heat from the tool–chip interface is expected to be felt only locally
due to the existence of an adiabatic heating condition, which is con8rmed by the observation that,
from the case with mechanical e9ect only (Fig. 15) to the case with both mechanical and convective
cooling e9ects (Fig. 22), the temperature rise 8eld is signi8cantly modi8ed only in the tool–chip
interface region. Another factor may be due to the limitations of the metal cutting geometry model
(Fig. 1) and the cooling model, in that they cannot realistically simulate real-life situations (e.g.
turning) in which cooling e9ect provided by a water jet may be felt by materials away from the
tool–chip interface. Clearly a full evaluation of the cooling e9ect requires further studies in which
more realistic models are employed.
 C. Shet et al. / International Journal of Mechanical Sciences 45 (2003) 1201 – 1228 1227

4. Concluding remarks

This paper has presented the results of a 8nite element simulation model for a high-pressure
water-jet assisted metal cutting process. To make the problem tractable, a number of idealizations
have been employed, but the trends revealed by the simulations should provide useful insights into
this type of unconventional metal cutting processes.
To summarize, the simulation results show that the use of a high-pressure coolant jet is e9ective
in improving the performance of the metal cutting process, which is consistent with the 8ndings
of limited experimental studies in the literature. In particular, when a high-pressure water jet is
injected into the tool–chip interface through a conduit hole in the tool, substantial reductions in the
steady-state interface contact pressure and shear stress, the contact zone size, the temperature rise,
and the residual stress in the 8nished workpiece are observed. The location of the jet hole is found
to be an important factor. Simulation results suggest that somewhere in the middle of the tool–chip
interface will be the best location for the jet hole.
It is also worth noting that another e9ect of the high-pressure water jet in metal cutting is that
enhanced lubrication due to the water jet will lead to reduced friction along the tool–chip interface,
which is expected to further reduce the maximum temperature rise and residual stresses. This e9ect
can be modeled by using a smaller friction coe5cient value in the simulations. Insights about this
e9ect can be obtained from a related study for the conventional metal cutting process [27], and, as
such, simulations of this e9ect are not repeated here.

Acknowledgements

The authors gratefully acknowledge the support of the Mechanics and Materials Program of the
National Science Foundation (NSF Grant #: CMS-9700405).

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