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1
Effect of cutting conditions on temperature generated in drilling process:
A FEA approach
R. Muhammad
1a*
, N. Ahmed
2b
, Y.M. Shariff
2c
, V.V. Silberschmidt
1d
Loughborough University, Wolfson School of Mechanical and Manufacturing Engineering
Loughborough University, Leicestershire, UK LE11 3TU
2
Department of Mechanical Engineering, Taibah University, Saudi Arabia
a
*R.Muhammad@lboro.ac.uk,
b
Dr.N.Ahmed@hotmail.com
c
yshariff@taibahu.edu.sa,
d
V.Silberschmidt@lboro.ac.uk
Abstract
Heat generated during a drilling process has a major influence on the tool life and the
workpiece material behaviour that are significantly affected by cutting conditions (cut-
ting speed, feed rate). In this paper, the effect of cutting conditions on temperature
generated in drilling process is investigated by means of finite element (FE) simulations
using commercially available code MSC MARC MENTAT. A Johnson Cook material
model is used to describe elasto-plastic deformation behaviour. The updated Lagran-
gian procedure is used to implement the transient analysis for the elasto-plastic mate-
rial in the model. A modified shear friction model is employed to model friction at the
tool tip-workpiece interface. The effect of friction on chip shape is investigated with FE
simulations. Experiments were carried out to verify the FE results.
1. Introduction
Friction plays a very important role in metal cut-
ting. It determines the energy required to re-
move a given volume of metal, as well as de-
termining the surface quality of a finished prod-
uct, chip shape, surface hardness and the rate
of wear of the cutting tool. Friction is the main
source of heat generated at the tool-workpiece
interface, and most of the problems relating to
machining are caused directly or indirectly by
the amount of heat generated at the cutting
edge. Of all the machining processes, drilling is
one of the commonly used machining proc-
esses in creating a hole in finished compo-
nents. Most of the drilling operations are nor-
mally performed at the final steps of manufac-
turing. Understanding thermal effects in drilling
process is critical in predicting the effect of the
machining technique on the workpiece as well
as the consequences for the tool wear.
The finite element method (FEM) is a reliable
computational technique in the modelling of
mechanics of materials and drilling in particu-
larly. In order to expedite the numerical compu-
tation most of the drilling simulations in the past
were performed with a certain level of simplifi-
cations such as reducing a three-dimensional
problem to a two-dimensional formulation [1] or
by assuming the cutting lips as a combination
of small elementary cutting tool performing or-
thogonal cutting operation [2].
In this study a 3D finite element model of drilling
process is performed to investigate the effect of
cutting condition on the temperature generated
during drilling process. The three key material
response are strain hardening, strain rate and
thermal softening which are incorporated in the
model. The influence of cutting parameter
(spindle speed, feed rate), on the temperature
generated during the drilling process is investi-
gated in the model.
For the modelling of the drilling process an up-
dated Lagrangian formulation of FEA is utilized
in the model. In the updated Lagrangian formu-
lation, the element shape changes with the ma-
terial flow, and the calculation embeds a com-
putational mesh in the material domain and
solves the problem for the discrete points of the
mesh in time. The formulation accounts for all
non-linear kinematics effects due to large dis-
placements and rotations.
The thermal processes in drilling comprise of
heat generation due to plastic deformation, fric-
tion heating at the tool-chip interface, contact
heat conduction between the tool and chip as
well as convective heat transfer from the free
surface of the workpiece, tool and chip to the
environment which are incorporated in the FE
model.
1.1. Johnson Cook Material Model
Parameters such as strain, strain rate, tem-
perature and strain hardening have a major in-
fluence on flow stresses or instantaneous yield
strength, at which the materials start to deform
plastically. Accurate and reliable flow stress
models are necessary to represent the mate-
2
rial’s constitutive behaviour under different cut-
ting conditions. The Johnson Cook material
model [3] is used to describe the mechanical
behaviour of AISI 1010 steel at high strain,
strain rate and elevated temperature in simula-
tions of drilling process. In this model, strain,
strain rate and strain hardening effects are
combined in a multiplicative manner. The mate-
rial response is represented as
1
1
,1
where
is flow stress,
is the effective plas-
tic strain,
·
,
is the plastic strain rate,
·
1
is the reference strain rate,
is the homologous temperature, is the
absolute temperature,
is the melting tem-
perature of mild steel,
is the room tempera-
ture, =250 MPa is the initial yield stress at the
reference strain rate, =275 MPa is the hard-
ening modulus, =0.078 is strain rate sensitivity
coefficient, =0.36 is the hardening coefficient
and the term T^(*m) is assume to zero. All
these parameters were determined experimen-
tally using the Split Hopkinson Pressure Bar
method and were adopted from [4].
1.2. Friction Modelling
Various friction models are available to model
the interaction at the tool chip-workpiece inter-
face: these models include the Coulomb friction
model, with friction stress proportional to the
normal interface stress
, 2
where τ is the shear stress, is the coefficient
of friction and
is the normal stress [5-7]. The
shear friction model
, 3
where is the shear yield strength [8], the
modified Coulomb friction model
min
µp,
, 4
where is Coulomb shear stress, p is the
normal pressure and
is the thresholds value
for conventional Coulomb model [9], stress-
based polynomial model [10] and modified
shear friction model [11] for friction modelling in
metal cutting.
When the normal force or stress becomes
large, the Coulomb friction model may not cor-
relate well with experimental observations. This
is due to the fact that the Coulomb model pre-
dicts frictional shear stresses to increase to a
level that can exceed the flow stress or failure
stress of the material. As this is not physically
possible, a different friction model should be
applied. There are several choices available to
correct for this unphysical prediction: (i) to use
a nonlinear coefficient of friction; (ii) introduce a
friction stress limit in a bilinear model or (iii) to
use a modified shear friction model. Therefore,
the modified shear friction model is imple-
mented using approximations of the theoretical
step function [12]. Because this step function
causes numerical difficulties in FE simulation of
the process, the arctangent function used in the
modified shear friction model is used to smooth
out the step function in order to avoid numerical
difficulties:
√
3
2
sgn
V
artan
5
Where is the equivalent stress,
is the rela-
tive sliding velocity,
is the critical sliding ve-
locity below which sticking is simulated, is the
friction coefficient and sgn
x
is the signum
function.
2. Finite Element (FE) Model Description
A commercially available FEA code MSC Marc
Mentat (2007r) is used for modelling the drilling
process; a schematic of this process with rela-
tive movement of the workpiece and drill bit is
shown in Figure 1. The drill bit has a complex
geometry and is a challenge in representing it
in current FEA packages; however, it demands
a significant computational cost in FEA simula-
tions of drilling process. To reduce the compu-
tational cost, only one cutting lip of the drill bit
(MZS0980S-DIN) having a diameter of 9.89
mm is considered in the FE simulation. The
model is simulated for only one revolution of
the drill bit. A cylindrical workpiece with outer
diameter of 8 mm, with a 3 mm diameter pre
hole and 1 mm thickness is used in FE simula-
tion. Eight-nodded, isoperimetric, three-
dimensional element with linear interpolation
are used to model the workpiece. However,
due to the poor representation of shear behav-
iour and lack of support for remeshing tech-
nique these elements were automatically con-
verted into approximately 5000 five-nodded tet-
rahedral element. An eight-nodded isoperimet-
ric brick element with tri-linear interpolation is
used for descritization of the cutting tools. The
ambient temperature is selected as 20°C for
the cutting tool and workpiece.
In the present FE model of drilling process the
cutting tool rotates with different spindle speeds
(300 rpm, 650 rpm and 1000 rpm) and the
workpiece is moved against the cutting tool with
constant feed rates of 0.12 mm/rev, 0.175
mm/rev and 0.24 mm/rev (Table 1). The prop-
erties of the workpiece used in the FE simula-
tion are that of AISI 1010 steel and those for
the cutting tool are of tungsten carbide.
3
Chip separation is determined by the plastic
flow. Due to severe deformation of the process
zone and of chip, the elements near the cutting
lip of a drill bit distort significantly, leading to
some well-known computational problems. As a
result re-meshing technique is used frequently
to replace those distorted elements with geo-
metrically consistent ones. Figure 2 shows the
chip formation after the successful implementa-
tion of the remeshing technique.
In FE simulation two contact condition contact
with friction ( 0.5 ) and contact without fric-
tion ( 0 ) is used to investigate the effect of
friction on chip shape.
Figure 1: Scheme of relative movements of
workpiece and cutting tool in 3D simulations of
drilling process
3. Experimental Setup
For experimental verification of temperature
distribution in the cutting region during the drill-
ing process various experiments were con-
ducted using CYL 6240 conventional lathe ma-
chine with a maximum spindle speed of 2000
rpm and 7.5 horse powers (HP) drive motor.
The experiments were carried out in a 3 mm
pre-hole drilled workpiece and the temperature
values were recorded when it was reached to a
steady state condition.
3.1. Cutting Conditions
Table 1 shows the detail of machining parame-
ters used in experimentation such as feed rate,
cutting speed. Temperature was experimentally
measured in dry drilling conditions.
3.2. Temperature Measurement
To measure the temperature of a drill bit during
the dry drilling process, a standard Teflon
coated K-type thermocouple is inserted into the
coolant hole of a drill bit.
The diameter of the thermocouple is 127 μm
and can measure temperature up to 600°C with
a response time of 10 µs. HH501DK 4-channel
K-type thermometer is used to record the
measured temperature values;
the Fourier's law
is then used to calculate the estimated tem-
perature at the centre point of the cutting lips of
the drill bit. The setup used for the measure-
ment of a drill-bit temperature is shown in Fig-
ure 3. Figure 4 demonstrate the experimental
results obtained at various cutting conditions.
Figure 2: Chip formation
Parameters used
in analysis
Magnitude of parameter
Spindle Speed
(rpm)
300, 650, 1000
Feed Rate
(mm/rev)
0.12, 0.175, 0.24
Table 1: Cutting parameters of drilling
Figure 3: Experimental setup for temperature
measurement
Figure 4: Experimentally measured tempera-
ture in drilling process at various cutting condi-
tion
4. Results of Simulation
In this section we present the result obtained
with FE simulation of drilling process with dif-
ferent cutting conditions. Varying cutting
speeds (rpm) and feed rates (mm/rev) are used
4
in the FE simulation of the drilling process. The
FE simulation results are in good quantitative
agreement with the experimental results.
4.1 Effect of Feed Rate
Variation of feed rate has a significant effect on
the temperature generated during the drilling
process. In all the FE simulations the cutting
speed and other parameters are kept constant
and only the feed rate is varied.
From the FE simulations of the drilling process
it is observed that the temperature increases
with the increase of feed rate (Figure 5), which
is in good agreement with [13-15]. The possible
reason is that increasing the feed rate in-
creases the penetration into the workpiece
leading to higher plastic deformation resulting
in a higher heat generation at the cutting re-
gion. Increasing the feed rate from 0.175 to
0.24 mm/rev (approx. by 37%) causes a 5%
increase in temperature.
4.2 Effect of Cutting Speed
Temperature generated during the drilling
process is also greatly affected by the cutting
speed. In the following FE studies, the feed rate
is kept constant and the cutting speed is varied.
A rise in temperature is observed with an in-
crease of cutting speed (Figure 5). For in-
stance, an increase in cutting speed from 300
to 650 rpm (approx. by 116%) can cause an
average increase of about 15% in temperature
during the drilling process [2, 13, 14, 15].
4.3. Chip Shape
A visible difference in chip shape is observed in
numerical simulations for dry and frictionless
drilling conditions. Figure 6 shows chip shape
for both cases. The radius of curvature of a
chip under frictionless contact condition was
approximately 60% smaller than that for contact
condition with friction at the tool tip-workpiece
interface. The ratio of thickness of the uncut
chip to that of the deformed one is equals to 0.7
with friction (0.5 ) and 0.45 without friction
( 0.5 ).
5. Conclusions
A numerical study of the process of drilling is
carried out to analyse the effect of various cut-
ting conditions on the temperature generated. A
comparison of feed rate shows that tempera-
ture grows with its increase. A 37% increase in
the feed rate causes a 5% increase in tempera-
ture.
The effect of cutting speed on temperature
generated during drilling process is also stud-
ied. A 116% increase in cutting speed causes a
Figure 5: Effect of feed rate and cutting speed
on temperature generated in drilling process:
(a) 1000 rpm, 0.24 mm/rev, (b) 1000 rpm,
0.175 mm/rev, (c) 650 rpm, 0.24 mm/rev, (d)
650 rpm, 0.12 mm/rev, (e) 300 rpm, 0.24
mm/rev and (f) 300 rpm, 0.12 mm/rev, at t =
0.035 s.
Figure 6: Effect of friction on chip shape (a)
without friction (w=0), (b) with friction (w=0.5)
15% increase in temperature.
