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j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138
j our nal homepage: www. el sevi er . com/ l ocat e/ j mat pr ot ec
A study of computer-assisted analysis of effects
of drill geometry and surface coating on forces
and power in drilling
J. Audy

School of Enterprise and Technology, Edith Cowan University, School of Enterprise and Technology, Bunbury, Western 6230, Australia
a r t i c l e i n f o
Article history:
Received 23 May 2007
Accepted 30 October 2007
Keywords:
Computer-assisted predictions
Drill point geometry
Rake angle distributions
Drill lips
Chisel edge
Surface coatings
Cutting performance
Predicted thrust
Torque
Power
a b s t r a c t
The success of continuous improved drill performance in cutting applications has to date
largely been based on significant advances through tool surface coatings and modifications
of drill point geometry, i.e. optimisation of the rake angle distributions along the drill lips
and the chisel edge. It has been recognised that due to the complexity of equations for
the force and power predictions, computer assistance is needed. Consequently, this paper
presents the results of a systematic – computer-assisted – study focused on determining,
and describing, from a mathematical point of view, the relationship between the drill point
geometrical features and the performance measures as assessed by the cutting forces and
power in drilling. This is followed by a study of predicted influences of drilling variables
on the generated thrust, torque and power. The results are presented for different types
of modern commercial tool surface coatings and work-piece materials. It is suggested that
this sort of information may be used, by both tool manufacturers and users, to assist in the
optimisation, and selection, of the drill point geometrical features for ‘best’ performance.
Crown Copyright © 2007 Published by Elsevier B.V. All rights reserved.
1. Introduction to the effects of drill
geometry on forces and power in drilling
The models and/or software applications for prediction of
thrust, torque and power indrilling for commercially designed
drills are quite complex and include a set of equations which
relate the thrust, torque and power to the drill point features
(D, 2W, ı
0
, , 2P, and Cl
0
), cutting conditions (f, n), num-
ber of elements characterising the lip (M
L
) and chisel edge
(M
C
) regions and the basic cutting quantities (r
l
, ˇ, includ-
ing edge force coefficients K
IP
, K
IQ
) as well as coefficients C
IP
and C
IQ
for discontinuous chip formation obtained from the

Tel.: +61 8 9780 7797; fax: +61 8 9780 7814.
E-mail address: [email protected]
orthogonal cutting data base for a particular tool/work-piece
material combination (Armarego, 1996). It has been stated in
the literature (Armarego, 1996; Zhao, 1994; Armarego et al.,
1997) that values of the geometrical drill point features such
as 2P, ı
0
and 2W vary from manufacturer to manufacturer
and more importantly from batch to batch. The geometry of
the chisel edge region also varies widely depending on the
point sharpening method used and the control of the sharp-
ener settings (Armarego, 1996; Zhao, 1994). Considering more
closely this information it seems to be crucial to obtain accu-
rate data about the actual specified drill point features, and, if
necessary, to use the ‘as measured’ data, rather than the nom-
inal values ‘provided’ by the tool manufacturer, in predictive
0924-0136/$ – see front matter. Crown Copyright © 2007 Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.jmatprotec.2007.10.079
j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138 131
Nomenclature
Symbols
D drill diameter
2W web thickness
f feed rate
r
l
chip length ratio
2P point angle
Cl
0
lip clearance angle
n drill revolutions
ˇ friction angle
chisel edge angle
ı
0
helix angle
ı
w
setting angle of the grinding wheel
shear stress in the shear zone (plane) (N/mm
2
)
drilling models for quantitatively reliable thrust, torque and
power predictions.
The drilling action itself is a complex cutting process con-
trolled principally by the geometry of a given drill dictated
mainly by the positions and lengths of the lips and chisel edge
regions. The cutting action on the drill lips has been reported
to be similar to that of the ‘classical’ oblique cutting process
but with variable cutting speeds, inclination angles and nor-
mal rake angles along the lip from the chisel edge corner to
the outer corner. By contrast, the cutting action at the chisel
edge has been found to be much closer to that of ‘orthogo-
nal’ cutting at relatively high negative rake angles and very
low cutting speeds resulting in discontinuous chip formation.
In the areas very close to the drill axis a type of ‘indentation’
process can be considered to occur where dynamic clearance
angle is zero or negative.
The work presented in the following Sections was under-
taken by the author of this paper and Dr. Armarego, from the
Melbourne University, was the supervisor until his death in
2003. Except where stated the work reported is the results of
the author’s own research work with reference to the source
(Audy, 2002).
2. Analysis of cutting action at drill point
geometry
The investigations outlined in Sections 2.1 and 2.2 were set
up to analyse the lip design and chisel edge region of twist
drills prior examining the effects of drill point modifications
on predicted thrust, torque and power in drilling.
2.1. Lip design and its reported effects on the drilling
forces
Fig. 1 shows the geometry of, and the forces acting on an ele-
ment at, the lip region of a conventional general purpose twist
drill. From the mathematical point of view the drill lip region
can be considered as a sumof a number of different elemental
oblique cuts controlled principally by their own tool geometry
and cutting conditions (V
W
=V,
n
,
s
, t, ␦b
i
, r
i
, f, n). The first
three values – namely V
W
,
n
,
s
– are found from the speci-
Fig. 1 – Geometry of, and the forces acted at, the lip regions
of a conventional drill. Refer Armarego (1996).
fied drill point geometrical features (D, 2W, ı
0
, and 2P) at each
elemental radius r
j
; the oblique cutting forces are determined
from the ‘classical’ oblique cutting analysis for the element
radius of r
j
, areas of cut ␦A(=t␦b) found fromthe cutting condi-
tions, f and b; the fundamental oblique cutting tool geometry,

n
and
s
, and the basic cutting quantities, , ˇ and r
l
, and the
edge force coefficients, K
IP
and K
IQ
, obtained from the orthog-
onal cutting data bank.
The thrust force (T
h
) and torque (T
q
) at the drill lip region
can be calculated via the sum of elemental values (␦T
h1j
) and
(␦T
qj
). The required values for both the elemental thrust force
(␦T
h1j
) and elemental torque (␦T
q1j
) can be calculated from
the ‘oblique’ cutting force components (␦F
P
, ␦F
Q
, and ␦F
R
) and
associated ‘edge’ force components (␦F
Pe
, ␦F
Qe
, and ␦F
Re
), the
meanradius (r
i
), the number of selectedelements (M) onthe lip
region, i.e. cutting edge length (

␦L), and the drill geometry
as documented by the same Fig. 1.
Mathematical expressions to calculate drilling forces from
a particular drill lip geometry and cutting conditions are
shown in Eqs. (1)–(18).
Thrust force (T
hl
) and elemental thrust force (␦T
hlj
) at the drill
lip region:
T
hl
=
M

j=1
ıT
hlj
(1)
where the elemental thrust force at the lip region
␦T
hlj
=(␦F
Q
+␦F
Qe
) cos ε sinp−(␦F
R
+␦F
Re
) (cos ␭
s
cos p+sin␭
s
sinpsin␧), and the required angle (ε) canbe obtained by pro-
jecting the speed vector (V
w
) into the normal plane (P
n
), and
132 j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138
calculated as
tanε =
V
W
sinωcos p
V
W
cos ω
= tanωcos p where ω = sin
−1
W
r
i
Torque (T
ql
) and elemental torque (␦T
lj
) at the lip region:
T
ql
= 2
M

j=1
ıT
qlj
where ıT
qlj
= r
i
(ıF
P
+ıF
Pe
) (2)
Cutting edge length (

L) and elemental cutting edge length
(␦L):
L = 2
M

j=1
ıL where ıL =
(D/2) cos ω
0
−Wcot (180

−)
Msinp
(3)

0
) – given by Equation (1.36); and () is ‘as measured’ chisel
edge angle.
Mean radius (r
i
):
r
i
=
_
_
D
2
cos ω
0

_
i −
1
2
_
ıL sinp
_
2
+W
2
(4)
Cut thickness (t):
t =
f sinpcos ε
2
(5)
Elemental width of cut (␦b):
ıb = ıL cos
s
where
s
=
V
W
sinωsinp
V
W
= sinωsinp (6)
Elemental area of cut (␦A):
ıA = tıb (7)
Elemental oblique cutting force components (␦F
P
, ␦F
Q
and
␦F
R
):
ıF
P
=
ıA[cos (ˇ
n

n
)cos
s
+tanÁ
c
sin
s
sinˇ
n
]
_
cos
2
(
n

n

n
) +tan
2
Á
c
sin
2
ˇ
n
(sin
n
cos
s
)
(8)
ıF
Q
=
ıAsin(ˇ
n

n
)
_
cos
2
(
n

n

n
) +tan
2
Á
c
sin
2
ˇ
n
(sin
n
cos
s
)
(9)
ıF
R
=
ıA[cos (ˇ
n

n
) sin
s
−tanÁ
c
cos
s
cos ˇ
n
]
_
cos
2
(
n

n

n
) +tan
2
Á
c
sin
2
ˇ
n
(sin
n
cos
s
)
(10)
where tanˇ
n
=tan ˇ cos Á
c
and (
n
) can be calculated using
Eqs. (11)–(18).
tan
n
=
tanı[(cos ω +sinωtanωcos
2
p) −tanωcos p]
sinp
(11)
tan
n
=
sin ω
0
tanı
0
[(cot ω +tanωcos
2
p) −tanωcos p]
sinp
(12)
tan
n
=
tanı
0
(r
2
−W
2
sin
2
p) −(D/2)Wsinpcos p
(D/2) sin
_
r
2
−W
2
(13)
Shear angle ()
tan
n
=
r
l
(cos Á
c
/cos
s
) cos
n
1 −r
l
(cos Á
c
cos
s
) sin
n
(14)
tan(
n

n
) =
tan
s
cos
n
tanÁ
c
−sin
n
tan
s
(15)
Elemental ‘edge’ force components (␦F
Pe
, ␦F
Qe
and ␦F
Re
)
ıF
Pe
= K
IP
ıb (16)
ıF
Qe
= K
IQ
ıb (17)
ıF
Re
= K
IR
ıb = K
IP
sin
s
ıb or ıF
Re

= 0 (18)
Other required variables (r
l
, ˇ, and ) and coefficients (K
IP
,
K
IQ
and K
IR
) are taken from the actual database that needs
to be established for a particular tool–work-material–surface
coating combination at different cutting conditions.
2.2. Chisel edge region and its reported effects on the
drilling forces
Fig. 2 shows the geometry of, and the forces at, the chisel edge
region of a conventional drill. Armarego (1996) wrote that it is
possible to create force prediction model for any chisel edge
region if the specific drill point features 2P and 2W are known
or measured.
In such model the chisel edge region is represented by a
number of ‘classical’ orthogonal cutting elements each oper-
ating at its own tool geometry and cutting conditions (V
W
,
ne
,
˛
ne
, t, ␦b, r
k
, f, n, and M
C
) in a particular region (r
limit
<r <r
c
).
The values of the thrust force (T
hc
) and torque (T
qc
) can be cal-
culatedvia summing a number (M
C
) of elemental values (␦T
hck
)
and (␦T
ck
) using Eqs. (19) and (20); and the indentation thrust
force (T
hI
) can be calculated using Eq. (21).
Thrust force at the chisel edge region (T
hc
)
T
hc
=
M

k=1
ıT
hck
where ıT
hck
= ıF
Pc
sinÁ +ıF
Qc
cos Á (19)
Torque (T
qc
) at the chisel edge region and the elemental
torque (␦T
qc
)
T
qc
= 2
M

k=1
ıT
qck
(20)
where ıT
qck
= r
k
(ıF
Pc
cos Á −ıF
Qc
sinÁ) andr
k
= r
c

_
k −
1
2
_
ıb =
Lc
2

_
k −
1
2
_
ıb and
ıb = (r
c
−r
limit
)/M = (L
c
−2r
limit
)/2M
c
The r
limit
is the radius for ˛
ne
(=0), Á (=90


2
), feed (f), and
wedge angle
W
=
1
+
2
.
j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138 133
Fig. 2 – Geometry of, and the forces acted at, the chisel edge region of a conventional drill. After Armarego (1996).
Indentation thrust force (T
hI
)
T
hI
= ıT
hck
_
2r
limit
ıb
_
(21)
Cut thickness (t)
t =
f cos Á
2
(22)
The chisel edge length (L
c
) is equal to 2r
c
following a
data associated with the drill tool geometry, i.e. L
c
= 2W/sin
(180

−)
The elemental forces (␦F
Pc
and ␦F
Qc
) can be determined
from Eqs. (23) and (24).
ıF
Pc
= C
IP
ıb (23)
ıF
Qc
= C
IQ
ıb (24)
where C
IP
and C
IQ
are the cutting coefficients (forces per unit
width) for discontinuous chip formation taken from the data-
bank of a particular tool-work-material investigated.
Armarego (1996), for instance, reported that C
IP
and C
IQ
coefficients for a HSS tool – 1020 – steel work-material combi-
nationhadthe mathematical expressions similar those shown
by Eqs. (25) and (26).
C
IP
(N/m) = 1.88.10
6
t
6.51
(90

+
ne
) (25)
C
IQ
(N/m) = 19.14.10
6
t
6.35
(90

+
ne
)
−0.62
(26)
Finally the thrust (T
Ht
) and torque (T
Qt
) for a drill can be
determined by summing all the corresponding values of both
the drill lip region and chisel edge region, as shown in a simple
form in Eqs. (27) and (28).
T
Ht
= T
hl
+T
hc
+T
hI
(27)
T
Qt
= T
ql
+T
qc
(28)
3. Computer-assisted software and
numerical simulation studies for prediction of
forces and power in drilling
Armarego (Armarego, 1996; Armarego and Zhao, 1996;
Armarego and Kang, 1997) and his research scholars (Zhao,
1994; Audy, 2002; Wright, 1981; Wu and Armarego, 1996)
developed the computer software and carried out extensive
numerical simulation studies over a large number of cutting
combinations and drill point geometrical features to study the
effects of these practical variables on the thrust, torque and
power in drilling. The predicted trends have been shown to be
reasonable suggesting that the models were plausible. It has
also been possible to use multivariable regression analysis to
curve-fit the thrust and torque predictions and to establish
‘empirical-type’ equations, which include the cutting condi-
tions, as well as, the many individual drill point features.
Empirical-type equations similar to that given by Eqs. (29) and
(30) have been established for different drill designs modelled
for a given tool–work-piece–material combination.
thrust force (T
Ht
)
T
Ht
= C
1
f
a
1
D
b
1
_
2W
D
_
C
1
2p
d
1
ı
e
1
0
˛
b
1
0
or
m
1
W

n
1
(29)
torque (T
Qt
)
T
Qt
= C
2
f
a
2
D
b
2
_
2W
D
_
C
2
2p
d
2
ı
e
2
0
˛
b
2
0
or
m
2
W

n
2
(30)
The associated constants (regressioncoefficients) are given
inTable 1 for both‘general’ and‘plane’ flankmodels anda Type
1020 steel work-material (Armarego, 1996).
134 j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138
Table 1 – Regression coefficients for Eqs. (29) and (30) valid for ‘general’ (a), and ‘plane’ (b) flank models and a Type 1020
steel work-material
(a) Drill: general flank model Work-material: 1020 steel
C
(1, 2)
a
(1, 2)
b
(1, 2)
c
(1, 2)
d
(1, 2)
e
(1, 2)
h
(1, 2)
m
(1, 2)
n
(1, 2)
T
Ht
47.5 0.545 1.036 0.339 0.168 −0.206 – 0.311 0.266
T
Qt
4.56 0.660 2.004 0.149 −0.241 −0.263 – −0.008 −0.188
(b) Drill: plane flank model Work-material: 1020 steel
C
(1, 2)
a
(1, 2)
b
(1, 2)
c
(1, 2)
d
(1, 2)
e
(1, 2)
h
(1, 2)
m
(1, 2)
n
(1, 2)
T
Ht
99.7 0.546 1.027 0.279 0.518 −0.210 – – 0.05
T
Qt
3.71 0.661 2.004 0.113 −0.226 −0.263 – – −0.177
After source Armarego (1996).
Armarego (1996) further mentioned that the thrust and
torque characteristics exhibited monotonic trend, and their
prediction has been possible for any particular drill/work-
material combination after determining the coefficients
required for Eqs. (29) and (30). These equations were exper-
imentally verified (Verezub, 1996) and found to be reliable for
prediction purposes rather than running the more complex
analyses and computer software.
Audy (2002) established empirical force equations for the
general purpose twist (GPT) drill force model and web pro-
file ground (WPG) drill design model (see Fig. 3a and b)
when drilling a Type Bisalloy 360 steel work-piece mate-
rial.
In the study (Audy, 2002) the six drill point variables
(D, 2W/D, , 2P, ı
0
and f) were considered giving the total
3
6
or 729 combinations of thrust and torque values indi-
vidually for a particular database used, see the evaluated
Eqs. (31) and (32). For WPG drill force model the helix angle
was replaced with the two extra variables – the ˛
g
and the
ı
w
– giving such 3
7
or 2187 computed values of predicted
thrust and torque for each database chosen, see Eqs. (33) and
(34).
Uncoated general purpose twist drills (Audy, 2002, 2006a)
T
h
= 101.892f
0.67
D
0.967
_
2W
D
_
0.379
2P
0.397

0.265
ı
−0.233
0
(31)
T
q
= 28010.23f
0.732
D
2.004
_
2W
D
_
0.202
2P
−0..388

−0.282
ı
−0.427
0
(32)
Uncoated web profile ground drills (Audy, 2002, 2006a)
T
h
= 354.5f
0.691
D
0.964
_
2W
D
_
0.577
2P
0.313

0.295
˛
−0.313
g
ı
−0.0779
w
(33)
T
q
= 20944.68f
0.718
D
2.001
×
_
2W
D
_
0.309
2P
−0.288

−0.128
˛
−0.469
g
ı
−0.119
w
(34)
It has been shown experimentally (Audy, 2002, 2006a) that
the web profile ground drill design produced lower force levels
than the general purpose twist drill design. The quantita-
Fig. 3 – The GPT drill design (a) after Audy (2002), Audy et al. (2002a,b); and the CNC stub – web profile ground (WPG) – drill
design (b) after Audy (2002), Audy et al. (2001, 2002b).
j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138 135
tive comparison of such improvement has been determined
from the thrust and the torques values predicted using the
force models (Audy, 2002, 2006a; Audy et al., 2002b). When
comparing the thrust forces from the uncoated web pro-
file ground drill force model with those produced by the
uncoated general purpose twist drill force model the aver-
age percentage decrease (improvement) in the thrust values
was −13±4%. For the torque values the percentage difference
associated with decrease (improvement) in the torque values
was −15±2%.
In addition, Audy’s research (Audy, 2002, 2006a; Audy et al.,
2002b) has shown that the cutting action (drilling forces and
power) generated by the drill point geometry (D, 2W/D, , 2P,
and ı
0
) and feed rate is influenced by the elemental distribu-
tion of rake angles along the lip region and the chisel region.
This is outlined in Section 4.
4. Elemental rake angle distribution at the
lip and the chisel edge regions of GPT and WPG
drill designs
The elemental distribution of rake angles of each GPT and
WPG drill design has been studied separately for the lip region
and the chisel edge region by changing the values of the
drill point features, namely, the point angle 2P, the chisel
edge angle , the lip spacing to drill diameter ratio 2W/D,
the helix angle ı
0
, and the grinding wheel features, namely,
˛
g
and ı
w
. The drill specifications used were: D
(GPT)
=6.35mm;
D
(WPG)
=6mm; ı
0(GPT)
=25

, 30

, and 35

; ˛
g(WPG)
=25

, 30

, and
35

; ı
w(WPG)
=25

, 30

, and 35

; Cl
0(GPT)
=14

, Cl
0(WPG)
=12

; then
for both drill designs: 2P=110

, 120

, and 145

; =115

, 125

,
and 145

; 2W/D=0.1, 0.18, and 0.3 were used. Furthermore, the
nominal cutting conditions were the speed of 4.33m/min, the
feedof 0.1mm/rev andthe work material was Bisalloy 360 high
abrasive and wear resistant steel.
The distribution of elemental rake angles at the drill lips
and the chisel edge region for GPT drill design and WPG drill
design has been studied for different values of 2P, ı
0(GPT)
,
˛
g(WPG)
, ı
w(WPG)
, , and 2W/D, and the patterns obtained were
similar to that shown in Fig. 4(a and b) for different 2P values.
From Fig. 4 it appears that for the GPT twist drill design the
normal rake angles,
n
, will vary from negative value(s) of
ni
at i =1 close to the outer chisel edge corner to highly positive
value(s) of
ni
at i =25 close to the lip outer corner radius. The
chisel edge represents series of negative rake angles that cut
from the smallest negative
ni
at i =1 close to the drill axis to
the highest negative
ni
at i =25 close to the outer chisel edge
corner. Comprehensive stresses created by the chisel edge will
contribute to the large percentage of the total thrust force in
drilling, while the drilling torque will, however, be not as great.
The lip region of WPG drills appears to be more favourable
for lower forces and power than that of GP-twist drills. This
is due to higher normal rake angles at radii along the drill
lip as seen in Fig. 4(a). The reduced chisel edge lengths of the
WPGdrills from1.24 to 0.75 contribute to the lower percentage
of the total thrust force and the torque values than expected
to be produced by the much longer chisel edges of the GP-
twist drills. Moreover, the normal rake angle distributionalong
the chisel edge region for the WPG drill design appears to be
qualitatively and quantitatively similar to that for the GPTdrill
design, as shown in Fig. 4(b).
The ‘as observed’ effects of different 2P, ı
0(GPT)
, ˛
g(WPG)
,
ı
w(WPG)
, , and 2W/D on the pattern of elemental rake angles
in the lip region and the chisel edge region can be described
as follows: (a) the larger values of 2P, for the whole drill, may
result in a small increase in the thrust and a little decrease
in the total torque; (b) the values increase the total thrusts
and the total torques are expected to decrease a little; (c) the
lower values of 2W/D reduce the drilling forces due to the pat-
tern of elemental rake angles on the lip and in the chisel edge
region which increases into less negative and more positive
values; (d) the increases in the ı
0
angle will result in lowering
the drilling forces along the whole lip region only because the
helix angle does not affect the geometry of the chisel edge; (e)
the feed is not expected to change the distribution of elemen-
tal rake face angles at the lip region, while the elemental rake
angles at the chisel edge may slightly decrease as the feed
values increase causing the thrust and the torque values to
increase approximately linearly with the feed due to the lin-
ear increases in the area of cut. The above rule was described
in more detail in sources (Audy, 2002, 2006b) and it has been
found, and reported, to be valid for the standard – GPT – drill
design (Armarego, 1996; Zhao, 1994; Audy, 2002, 2006b) and
point thinned drill design (Armarego, 1996; Zhao, 1994), and
also applied for the WPT drill design (Audy, 2002).
From the above it is evident that the drill point geometry
and cutting conditions control the distributions of the rake
face angles and their mutual relationship can be studied by
varying the magnitudes of different influencing variables in
the input of the software. The value of corresponding angle
of WPG and/or GPT drills as well as other drill designs can
be determined for each particular element at the lip and
the chisel edge region so the illustrated trends may them-
Fig. 4 – Effect of the point angle 2P on the elemental normal rake angle distribution along the lip (a) and the chisel edge (b)
regions of GPT and WPG drill designs; after Audy (2002).
136 j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138
selves indicate expected thrust and torque trends as described
earlier.
5. Studies of predicted influences of drilling
variables on the generated thrust and torque
Literature shows that the drilling action depends on the drill
point features, a large variety of tool–work-piece–material
combinations and the cutting conditions. It has also been
noticed that the experimental testing could not provide such
flexibility as computer simulations using an appropriate pre-
dictive force and power model. The most complete research
concerning qualitative trends in the predicted thrust force
and torque for different drill geometry and uncoated drills
have been presented by various members of the research
group at the University of Melbourne supervised by Armarego
over 40 years. Whenever comparison of forces was possible,
considerable agreement between Melbourne’s research and
‘international’ research has been found.
Armarego (1982) and his research scholar Whitfield
(Whitfield, 1986) – studied a mechanics of cutting approach
for the prediction of forces and power in some commer-
cial machining operations. A part of his research work was
dedicated to study the general effects of drilling variables
on the thrust and torque. Noteworthy Fig. 5(a–h) has been
adopted from the study of these researchers (Armarego, 1982;
Whitfield, 1986) because of illustrating the representative
thrust and torque predictions as influenced by drill geometry
(D, 2W, ı
0
, 2P, , and 2
W
) and drilling conditions (v, f) when
drilling a Type S1214 free machining steel work-material. Both
thrust andtorque increasedwiththe drill diameter, Fig. 5(a), as
a consequence of increases in the area of cut. Increases in the
web thickness 2W caused increases of both thrust and torque
values, as shown in Fig. 5(b), with the major increase occur-
ring on the thrust due to the wider and inefficient chisel edge
region, whereas the torque is the largest at the lips where the
lever arm is largest. Whitfield further reported that increases
in both the chisel edge angle and the chisel edge wedge
angle 2
W
increase the thrust but have only marginal effect
on the torque as illustrated in Fig. 5(c and d). Increases in
the point angle 2P had little influence on the predicted torque
but increased the predicted thrust as shown in Fig. 5(e). Both
the thrust and torque values were reduced with increases of
the helix angle ı
0
as shown in Fig. 5(f). Finally both thrust
and torque decreased little with increases in drilling speed,
Fig. 5(g). Increase in the feed, Fig. 5(h), resulted in increases
in both thrust and torque. Interestingly both the thrust force
and torque patterns similar to those shown in Fig. 5(a–h) were
achieved when the analysis was applied to the drilling of a
Type CS1040 steel work-material, and in this connection it has
been concluded that the pattern should remain qualitatively
the same for other common work-piece materials.
Armarego(1996) extendedthe researchinthis area. He used
a database for a Type 1020 steel work-material and predicted
thrust (T
Ht
) andtorque (T
Qt
) values as a functionof cutting con-
ditions (n, f) and drill point features (D, 2W/D, ı
0
, 2P, and ). A
set of typical graphs derived from the study of this researcher
were published in reference source (Audy, 2006b) and indi-
cated strong similarities to the qualitative trends pictured in
Fig. 5.
The knowledge and basis of the ‘Mechanics of Cutting
Approach’ primarily developed and examined by Armarego
(1996, 1982) has been extensively studied in recent years by
other scholars such as, for example, Audy (2002, 2006a), Audy
et al. (2002a, 2001, 2002b), Whitfield (1986), Kata (1997), Gong
(1989) and Zhao (1994), Armarego and Zhao (1996). These
researchers confirmed that this method can successfully be
applied for prediction of thrust force and torque in drilling
operations with general purpose, web-modified, four plane
facet point and circular centre edge drill point designs.
In addition, Audy (2002) has shown that the above method
for force and power predictions in drilling with uncoated
drills outlined in sources (Armarego, 1996, 1982; Zhao, 1994;
Whitfield, 1986; Kata, 1997) will produce similar qualitative
trends for the effects of the individual, and common drill
point features, the tool substrate and more importantly tool
surface coatings (Audy, 2006b) on the thrust and torque val-
ues. These trends are reproduced in Fig. 6. The experiments
were conducted with TiN, Ti(C,N) and Ti(Al,N) coated drills.
Fig. 5 – Some reported predicted effects of the drilling thrust (T
Ht
) and torque (T
Qt
) on the drill geometrical features, D, 2W,
2P, ı
0
, , 2
w
, (a–f); drilling speed, v, (g); and drilling feed, f, (h). Unless indicated otherwise D=10mm, 2W=1.5mm,
=135

, 2
w
, =110

, 2P=118

, ı
0
=35

, v=20m/min, f =0.2mm/rev; after source Whitfield (1986).
j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138 137
Fig. 6 – Effects of specified drill point features and feed on predicted thrust, T
h
, and torque, T
q
, values when drilling Bisalloy
360 steel with the uncoated and the coated GP twist drill(s): D=12.7mm, 2P=118

, 2W/D=0.12, =125

and ı
0
=30

, at a
speed of 12.5m/min and a feed of 0.1mm/rev (Audy, 2002, 2006b).
For the prediction purposes the coated tools were treated as
one group (Audy, 2002). It was because when comparing the
effect of different coatings, one with another, in orthogonal
cutting tests (Audy, 2002) the quantitative differences in var-
ious performance measures namely, forces, power, friction
angle, shear angle, shear stress and chip length ratio values
were statistically equal at 95%and higher confidence level, i.e.
there were no qualitative or quantitative differences between
the three coatings (Audy, 2002). Moreover, the group of coated
tools reduced, on average the torque by 24.9% and the thrust
by 14.5% indicating that the highest reductions were in the
thrust force not in the power force (Audy, 2002). This allowed
establishment of one combined database for coated tools and
use it for prediction of drilling forces and power.
Comparison of the predicted total thrusts and the total
torques for the relevant drill point geometry of the WPT-jobber
and the GP-twist drills has shown that the WPT drills reduced
the total thrust by ∼13% for the uncoated drills and by ∼20%
for the coated drills. The total torque reductions due to more
suitable WPT drill design were ∼15% for the uncoated drills
and ∼13%for the coated drills. Comparison of the total thrusts
and the total torques produced by a standard point geome-
try of the GP-twist drills and the WPT drills examined over a
wide range of the feed rates confirmed again that the WPT
drill produced lower forces (and power) than the GP drills.
Moreover, in the same groups the coatings lowered the total
thrust by ∼20% and the total torques by ∼13% for both drill
designs.
The drilling force experiments were also carried out to con-
firm the validity of predictions. The results generated in this
way showed that all the three different coatings produced sta-
tistically equal variances and mean of the lip thrusts and the
lip torques at the 95% and higher confidence levels, indicating
that the effects of each coatings have the same importance
in drilling Bisalloy 360 steel. This pattern has been proved
for the two different speeds one of 5.33m/min and another
of 12.5m/min supporting such knowledge that the speed has
no significant effect on the drilling forces and power. Finally
it has been experimentally proved that the group of differ-
ently coated – TiN, Ti(Al, N) and Ti(C, N) – GP-twist drills of a
nominal diameter of 10mm was able to reduce the lip thrust
and the lip torque by a factor of ∼1.7 and ∼1.3, respectively
comparing to the uncoated drills when drilling Bisalloy 360
steel at a feed of 0.15mm/rev employing speeds of 5.33 and
12.5m/min. The predicted values and trends matched reason-
ably well with the experimental data, and the force tests have
confirmed the advantage of various – single layer – coatings
over unprotected/uncoated tool substrate material.
6. Conclusions
This study has briefly reviewed the concept and modelling
approach of the ‘Unified’ approach with particular reference
to drilling operations which have commonly been set to study
the effects of drill point geometry and tool surface coating
on cutting performance. Results showed that the computer-
assisted modelling allowed studying the changes in the drill
point geometry, namely, the rake angle distributions along the
drill lips and the chisel edge. In addition, this approach has
been shown to provide reliable means of quantitatively pre-
dicting all the force components, thrust, torque and power
for different drill design with particular reference to differ-
ent GPT and WPG drill geometries, and tool surface coatings.
Finally it has been shown that computer-assisted modelling
allowed to establish simpler predictive equations for forces
and power in drilling with different drill designs which oth-
erwise would needed to be estimated by direct experimental
138 j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138
or ‘empirical’ approaches, reported for being time consuming
and expensive.
Acknowledgements
The author would like to thank the Edith Cowan University
(ECU) and Professor Bill Louden and Dr. Elaine Chapman from
the University of Western Australia (UWA) for supporting his
research work on ‘Designing Technology Enriched Pedagogy in
Higher Education’.
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