Influence of regular and random cutting tool deformation on the cutting force of three-dimensional turning operation

Int. J. Machining and Machinability of Materials, Vol. 14, No. 4, 2013 311
Copyright © 2013 Inderscience Enterprises Ltd.
Influence of regular and random cutting tool
deformation on the cutting force of three-dimensional
turning operation
Samy E. Oraby
Department of Manufacturing Engineering,
College of Technological Studies,
The Public Authority for Applied Education and Training,
P.O. Box 42325 Shuwaikh 70654, Kuwait
Fax: +965-24832761
E-mail: se.oraby@paaet.edu.kw
E-mail: samyoraby@hotmail.com
Abstract: The current work emphasises the impact of the various modes
of cutting tool edge wear and failure on the different force components
considering the three-dimension orthogonal continuous machining using
multi-coated carbide tips. Edge force is usually attributed to the ploughing and
rubbing actions on the tool-workpiece interface which, in turn are associated
with the extent of the inevitable wear modes: nose, flank, and notch wear.
Modelling of the experimental results using linear and non-linear regression
analysis is established to qualitatively and quantitatively grasp the functional
interrelation among the involved parameters. Results indicated that all force
components are, to different extents, affected by all edge wear land modes.
However, it is shown that each of the observed edge wear and failure has its
own potential on specific force components and on specific cutting pressure.
Keywords: cutting tool; wear and deformation; carbide inserts; cutting forces;
mathematical models; specific cutting pressure.
Reference to this paper should be made as follows: Oraby, S.E. (2013)
‘Influence of regular and random cutting tool deformation on the cutting force
of three-dimensional turning operation’, Int. J. Machining and Machinability of
Materials, Vol. 14, No. 4, pp.311–341.
Biographical notes: Samy E. Oraby is a Professor at Faculty of Engineering,
Port Said University, Egypt and is currently at the College of Technological
Studies, PAAET, Kuwait. He obtained his PhD in Mechanical Engineering
from the University of Sheffield, England in 1990. He has many publications
covering machining and manufacturing processes. He is a member and
reviewer in many regional and international manufacturing journals and
magazines.
1 Introduction
Machining processes stems its importance from being a major manufacturing method
where some statistics (Astakhov, 2005) indicated that about 15% of all mechanical
components manufactured worldwide are derived from machining operations.

312 S.E. Oraby
Productivity enhancement at lower power requirements usually represents the ultimate
objective of a machining process. While productivity is achieved using higher levels of
operating cutting parameters (speed, feed and depth of cut), the consumed power in the
process depends to great extents on the environment tribological conditions at the
tool-chip-workpiece interfaces. A proper manipulation of the technical junction between
productivity enhancement and power reduction is still required since, as stated by many
investigators, for example (Zemzemi et al., 2007), there is still lack of fundamental
understanding of the phenomenon occurring at the tool-chip and the tool-workpiece
interfaces. One of the most tribological parameters affecting both productivity and
consumed power is the edge wear during machining.
Until early ‘90s of the last century, a tool change policy was entirely based
on the accumulated experience and skills of the machine operators along with the
total efficiency and capacity of the machine tool. Since then there was a transition
from traditional to automated tool change strategy considering the possible
in-process monitoring and/or control the developed wear level on the cutting
tool edges. With the emerging and promising adaptive control AC technology
(http://www.omative.com/173890/ACM), it became possible to optimise, monitor, and
control CNC machine performance to achieve maximum productivity. This basically
depends on the in-process monitoring of the tool wear through analytical and empirical
modelling (Oraby et al., 2003).
Figure 1 Wear and force measurement system in three-dimensional orthogonal cutting
(see online version for colours)
In practice, the cutting edge in machining deforms in an indeterministic fashion that
requires in-process monitoring and/or control techniques to assess the tool performance
during machining. In addition to the regular edge wear that usually develops at both the
tool-chip and tool-workpiece interface surfaces, many random edge fracture types such as
chipping, fracture, breakage, etc., are also common, Figure 1. In practice, many regular
and random wear modes usually take place simultaneously on the cutting edge with the
domination of one or more elements under certain operating conditions. This is expected
to escalate the rate of increase of the cutting forces hence affects the power requirements,

Influence of regular and random cutting tool deformation 313
the system dynamic stability and the surface integrity of the machined product. The
cutting force has been reported as sensitive, credible and reliable measure courier of the
edge wear variations (Okashi and Sata, 1958; Zorev, 1966; Bayoumi et al., 1993; Oraby
and Hayhurst, 2004; Oraby et al., 2005).
The main objective of the current work is to evaluate the impact of various possible
modes of edge wear and deformation during thee-dimension turning process on the
conventionally associated variations in the resulting cutting forces. This includes the
evaluation of the individual and mutual influence of the cutting parameters; speed, feed
and depth of cut. The isolation of the effect of individual and combined edge deformation
mode(s) on forces and on the specific pressure is one of the main considered topics. This
is achieved through the use of the most appropriate and, statistically adequate and
significant non-linear modelling structures together with the relevant experimental data.
2 Orthogonal merchant’s model adaption considering edge wear
Orthogonal force system in metal cutting was first proposed by Merchant (1945),
Figure 2. Merchant’s orthogonal model, assumes a perfectly sharp tool with no
concentrated edge force on the cutting edge, a continuous chip, plane strain, uniform
shear stress distribution on the shear plane, and equilibrium of the action of equal and
opposite resultant force acting at the shear zone and tool-chip interface. The total force is
represented by two equal, opposite forces (action and reaction) Rs and Rs′ which hold the
chip in equilibrium. The force, Rs′, which the tool exerts on the chip, is resolved into the
tool face-chip friction force F and normal force N. The force, Rs, which the workpiece
exerts on the chip, is resolved along the shear plane into the shearing force, FS which is
responsible for the work expended in shearing the metal, and into normal force FN, which
exerts a compressive stress on the shear plane. Force Rs is also resolved along the
direction of tool motion into Fcs, termed by merchant as the cutting force, and into Fst, the
thrust force. Principles of the well-known merchant-type model are:
. . .cos( )
sin .cos( )
c
cs
τ b t γ
F
γ
−
=
+ −
β
φ φ β
(1)
. . .sin( )
sin .cos( )
c
ts
τ b t γ
F
γ
−
=
+ −
β
φ φ β
(2)
arctan arctan ts
cs
F
μ γ
F
⎛ ⎞
= = + ⎜ ⎟
⎝ ⎠
β (3)
1 ( / )cos cos
( ) arctan
4 2 1 ( / ) 1 sin
π t tc γ r γ
γ
t tc r γ
⎧ ⎫ ⎛ ⎞
= − − = =⎨ ⎬ ⎜ ⎟− −⎩ ⎭ ⎝ ⎠
φ β (4)
( )cos sin sin
.
cs ts
c
F F
τ
b t
−
=
φ φ φ
(5)
As early stated by some pioneer studies (Merchant, 1945; Ernst and Merchant, 1941), the
width of cut bc, the undeformed cut thickness t and the normal rake angle γ are usually
considered as given geometrical quantities for a cutting process. However, the shear

314 S.E. Oraby
stress τ and the frictional angle β can be obtained from literature and the conventional
sliding friction testing, while the shear angle φ is a computational parameter obtained
from the specific shear angle relation.
Figure 2 Orthogonal cutting model allowing for tool flank wear effect
Source: Wang et al. (2003)
As cutting continues, edge wear emerges along the tool clearance face (flank) as a result
of the intimate contact between the cutting edge and the workpiece machined surface.
Therefore, additional forces are inevitable and, a modified Merchant’s model should be
required to consider the emerged situation.
According to many investigators (Kobayashi and Thomson, 1960; Thomson et al.,
1962; Song, 2006), the friction mechanism on the rake face was hardly affected by the
wear land changes at the tool flank. Zorev (1966) stated that the chip formation process
was affected solely by the force on the rake face while the force acting on the flank did
not take part in the process since it produced by the elastic reaction of the layer of the
machined material lying under the tool. This implies that machining with a continuously
developed edge flank wear does not affect the cutting quantities (shear angle, friction
angle, shear stress, etc.), but produces only additional rubbing forces on the wear land on
both the tool flank and workpiece surfaces. Shi and Ramalingam (1991) reported that
flank wear land led to an increase in the cutting force on the flank surface and that was
proportional to the plastic flow in the workpiece machined surface. Additionally, they
studied the shearing and friction processes using a controlled chip breaker and, they
found that these remained unaffected by flank wear.

As generally proposed by many researchers (Wang et al., 2003; Song, 2006;
Milutinović and Tanović, 2011), further parameters should be introduced to merchant’s
model to consider the concentrated force (edge force), or the rubbing and ploughing force
Rw acting at the cutting edge. The edge force is developed as the wedge is not perfectly
sharp and, is manifested by the positive force intercepts when the measured force versus
cut thickness graphs are extrapolated to zero cut thickness. Armarego (1982) claimed that
this was proportional to the engaged cutting edge length and it could be removed from
the measured force data when evaluating the basic cutting quantities using the shin shear
zone model. Consequently, the above equations to evaluate β and τ are modified to
consider the existence of rubbing or ploughing force, Rw, Figure 2.
arctan arctan tm te
cm ce
F F
μ γ
F F
−⎛ ⎞
= = + ⎜ ⎟−⎝ ⎠
β (6)
( ) ( )[ ].cos sin .sin
.
.
cm ce tm te
c
F F F F
τ
b t
− − −
=
φ φ φ
(7)
where Fce and Fte are found from the intercepts of the measured force-cut thickness
graphs. The total cutting force can be represented by:
. . .cos( )
.
sin .cos( )
c
c cs ce c c
τ b t γ
F F F k b
γ
−
= + = +
+ −
β
φ φ β
(8)
. . .sin( )
sin .cos( )
c
t ts te t c
τ b t γ
F F F k b
γ
−
= + = +
+ −
β
φ φ β
(9)
The edge force intensity factors, kc and kt, are obtained from the orthogonal cutting tests.
As shown in Figure 2, by taking into account the secondary rubbing or ploughing force
on the tool wear land:
. . .cos( )
sin .cos( )
c
c cs ce ce c c cw
τ b t γ
F F F F k b F
γ
−
= + + = + +
+ −
β
φ φ β
(10)
. . .sin( )
sin .cos( )
c
t ts te te t c tw
τ b t γ
F F F F k b F
γ
−
= + + = + +
+ −
β
φ φ β
(11)
As concluded by many investigators (Wang et al., 2003; Song, 2006; Milutinović and
Tanović, 2011; Armarego, 1982; Huang and Liang, 2005; Waldorf et al., 1998), there
were some common emerged facts suggesting that the flank wear land significantly
increased the rubbing force on the cutting edge-flank interface, thus the overall cutting
forces, but did not affect the forces required for shear process (chip formation) or the
friction process on the tool-chip interface. In addition, it is claimed that with the existence
of flank wear land, the conventional orthogonal model still applicable to determine the
forces in the shear plane and at the tool-chip interface while the additional edge forces,
rubbing and ploughing forces on the flank wear land are best considered independently.
However, it is indicated (Astakhov, 2006; Popv and Dugin, 2013) that the predicted flank
forces Fce and Fte are usually much higher than those found by extrapolation of the
corresponding components of the cutting force on zero chip thickness. Also, the
consideration of shear stress τ as the only mechanical properties to calculate the forces

316 S.E. Oraby
lacks reality since, in many cases; a material with higher shear stress tends to produce
much lower wear rate and forces than that with lower shear stress.
3 Experimental procedures and setup
Parameters levels and ranges, Table 1, were selected to conform reasonably to practical
rough turning operations. Five levels were specified for each of the cutting parameters;
cutting speed v, federate f, and depth of cut ap. To insure modelling statistical adequacy
and significance, these are arranged according to the central composite design (CCD)
technique to constitute a total of 24-experiment, Table 2. Multicoated carbide inserts
(Sandvik 435 – ISO P35) were employed to cut 709M40 (EN19) high tensile stress
chromium alloy steel. Inserts coating consisted of three layers: the first is a TiN of 1 μm
thickness followed by 3 μm layer of Al2O3 and finally 5 μm layer of TiC over the sintered
carbide substrate. Inserts were of SPUN 12 03 12 configuration (thickness = 3.18 mm
and rn = 1.2 mm and l = 12.7 mm). Inserts were clamped to a Sandvik CSTPRTMAX
tool holder with seat configuration 6°, 5°, 0°, 60°, 30° normal rake, clearance, inclination,
approach and side approach angles respectively. For each experiment, wear value at the
tool-workpiece interface was measured sequentially at three regions: nose VBC, flank
VBBmax, and notch VBN, Figure 1. For each subtest, three cutting force components:
main (tangential) Ft, feed (axial) Fa and radial Fr, Figure 1, were measured using a
three-component dynamometer that replaced the tool post of a Colchester Mascot 1600
turning lathe.
Table 1 Abrasive material and shape properties
Level parameter Lowest Low Medium High Highest
Speed (v) [m/min] 50 72 104 145 206
Feed (f) [mm/rev] 0.06 0.12 0.2 0.3 0.6
DOC (ap) [mm] 1.5 2.0 2.25 2.5 3.0
Table 2 CCD of the entire set of experiments
Test
seq.
Speed (v)
m/min
Feed (f)
mm/rev
DOC
(ap) mm
Test
seq.
Speed (v)
m/min
Feed (f)
mm/rev
DOC
(ap) mm
1 72 0.12 2 13 206 0.2 2.25
2 145 0.3 2 14 50 0.2 2.25
3 145 0.12 2.5 15 104 0.6 2.25
4 72 0.3 2.5 16 104 0.06 2.25
5 104 0.2 2.25 17 104 0.2 3
6 104 0.2 2.25 18 104 0.2 1.5
7 145 0.12 2 19 206 0.2 2.25
8 72 0.3 2 20 50 0.2 2.25
9 72 0.12 2.5 21 104 0.6 2.25
10 145 0.3 2.5 22 104 0.06 2.25
11 104 0.2 2.25 23 104 0.2 3
12 104 0.2 2.25 24 104 0.2 1.5

4 Experimental, analysis, discussions, and evaluation
4.1 Effect of regular wear modes on force variation
Tool edge in machining is subjected to hostile conditions of high contact temperatures,
high contact pressure, cyclic frequent chip-formation-separation mechanism, etc., at the
tool-chip and tool-workpiece interfaces. Such aggressive environment usually leads to
many edge deformation modes such as tool edge softening; diffusion, oxidation, abrasive,
and adhesion wear; cracking due to thermal fatigue; fretting wear; chipping and breakage;
slice fracture of the tool material; wear due to hammering chip, etc. However, most of the
aforementioned wear and deformation mechanisms act simultaneously with predominant
influence of one or more of them. Identification of the most influential and significant
mechanism(s) is still highly subjective (Astakhov, 2006) and, in many situations a
topological approach is widely accepted where the influence of cutting conditions,
temperatures, contact stresses, relative cutting velocities, etc., is experimentally evaluated
and interpreted.
4.1.1 Cutting speed considerations
The effect of the cutting speed on the tool life and on the cutting force may be explained
through the comparison of the experimental results of the tests # 20, 12 and 13 in which
the employed speed values were 50, 104 and 206 m/min respectively.
Figure 3 shows the SEM micrographs together with the experimental wear-time-force
plots Force fluctuations are evident due to the frequent formation and separation
of the built-up edge BUE. At the end of the test, a local edge fracture occurred at the edge
nose leading to force increase especially in the feed and the radial components,
Figure 3(b).
Figure 3 Experimental results of test #20 (v = 50 m/min, f = 0.2 mm/rev, ap = 2.25 mm),
(a) SEM micrographs for entire flank edge chipping (b) Wear-force-time relationships
(a)

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(a) SEM micrographs for entire flank edge chipping (b) Wear-force-time relationships
(continued) (see online version for colours)
(b)
Figure 4 Experimental results of test # 12 (v = 104 m/min, f = 0.2 mm/rev, ap = 2.25 mm),
(a) SEM micrographs of regular edge wear (b) Wear-time-force relationships
(a)
(b)

For a moderate combination of cutting parameters: 104, 0.2 and 2 speed, feed, and depth
of cut respectively, Figure 4, an almost equal gradual wear level developed over the edge
length except for an early random fracture occurred on the notch area. At the end of the
test, wear levels were insignificant enough to produce a noticeable increase in all the
cutting force components.
(a) Edge failure due to plastic lowering (b) Softening reaching the tool face
(c) Wear-time-force relationships (see online version for colours)
(a) (b)
(c)
The use of high speed of about 206 m/min., test #13, Figure 5, ended with a catastrophic
plastic deformation failure after only about 5 minutes cutting. Deformed area was
extended to include the secondary cutting edge, Figure 5(a), and the tool face,
Figure 5(b). As a result, both the feed and the radial force components were enormously
increased while the main cutting component showed a less response, Figure 5(c). Due
to the resulting elevated force values, tool breakage eventually occurred at the

320 S.E. Oraby
tool-workpiece interface. As elaborately explained by Astakhov (2006), the plastic
lowering of the cutting edge is the predominant reason behind such a premature edge
failure at high speeds. Plastic lowering is the plastic deformation of the cutting wedge as
a result of combined plastic flow and spreading of tool material over the chip and tool
contact surfaces. Due to plastic lowering of the cutting edge, tool configuration,
especially rake and clearance angles change leading to an increase in the tool wear rate.
When such a geometrical variation due to plastic lowering reaches a certain limit, the
breakage of the cutting wedge takes place globally or in the form of chipping and
breakage.
To evaluate the effect of the cutting speed on tool life, it is observed that the cutting
time to attain a 0.254 mm average wear (arithmetic mean of VBC, VBBmax and VBN) is
experimentally recorded as 120, 36 and 4 minutes that produces corresponding wear rates
of 2.12, 7.06 and 63.5 μm/min respectively. This indicates that, up to a cutting speed of
104 m/min, the process temperature was still lower or equal to its optimal range while for
the cutting speed of 206 m/min, the resulting high wear rate implies that the process
temperature is far higher than its optimal value (Astakhov, 2007). This was the onset of
thermal lowering and plastic deformation of the cutting wedge which eventually ended
with catastrophic failure and breakage.
Within the specified cutting interval for test #20, Figure 3(b), force increase was
recorded to be 8.2%, 27.3% and 52.9% for the main, the feed and the radial force
components respectively. Counterpart force increase values for test #12, Figure 4(b),
were 15.2%, 32.8% and 35.2% while they were 4.4%, 18.9% and 10.6% for test #13,
Figure 5(c). However, both wear and force rates were drastically increased for test #13 as
thermal lowering and deformation mechanism is activated.
In all cases, the main force component Ft was observed to be the least affected by the
edge wear and failure. The radial force component Fr proved to be the most sensitive to
edge wear at low-to-moderate cutting speeds.
4.1.2 Cutting feed considerations
As explained by Astakhov (2007), the true influence of the cutting feed on tool wear and
its rate should not be assessed in isolation of the entire context of the other parameters of
the cutting process that contributes individually and mutually to the cutting temperature
(Mackarow’s low).
Figure 6 shows SEM and wear-time-force for test #16 were the least feed value of
0.06 mm/rev was employed. Such a low feed value can affect wear rate due to the
formation of the cold worked layer from the preceding pass (revolution) on the machined
surface (Astakhov, 2007). When the cutting feed is smaller than the depth of cold
working layer, the major cutting edge cuts a workpiece that is characterised by a greater
strength and hardness leading to higher tool wear rate. As shown by the relevant
experimental results shown by Figure 6, there was a low gradual wear rate that is
accompanied by many random disturbances in terms of edge chipping, fracture, and
cratering at the rake face.

Figure 6 Experimental results of test#16 (v = 104 m/min, f = 0.06 mm/rev, ap = 2.25 mm),
(a) Edge fracture at tool edge (b) Cratering at the nose (c) Wear-time-force plots
(a)
(c)
When the highest feed of 0.6 mm/rev was employed in test #15, Figure 7, a purely
regular edge wear developed with a local domination impact at the edge nose.
The effect of feed on tool wear and tool life can be evaluated in the light of
wear-force variations curves, Figures 4(b), 6(c) and 7(b) for tests 16, 12 and 15 in which
the employed feed values were 0.06, 0.2 and 0.6 mm/rev respectively. Cutting time to
attain a 0.254 mm average wear was found to be 98, 36 and 10 minutes respectively with
corresponding wear rate values of 2.95, 7.06 and 25.4 μm/min. Within that cutting
interval for test #16, Figure 6(b), force increase was recorded to be 27.5%, 34.7% and
58.5% for the main, the feed and the radial force components respectively. Counterpart
values for test #12, Figure 4(b), were 15.2%, 32.8% and 35.2% while they were 11%,
32.9% and 46.3% for test #15, Figure 7(b). Again, the radial force component showed the
highest sensitivity to the edge wear while the main force component Ft was the least
affected.

322 S.E. Oraby
(a) Entire wear on both tool flank and face (b) Wear-time-force plots (see online version
for colours)
(a)
(b)
Figure 8 Effect of feed and edge wear of the various force ratios (see online version for colours)

The employed level of the cutting feed may affect the dynamic stability of the
cutting process. Astakhov (2007) indicated that increasing feed improved the dynamic
rigidity of the machining process through changing the ratio of the radial and the
axial force components. Verification of the effect of increasing feed on the ratios of
the three considered force components is shown in Figure 8 considering the tests # 16, 12
and 15 which use 0.06, 0.2 and 0.6 mm/rev feed values respectively. Evaluation
includes two cases: the first at the beginning of the test, where zero wear is assumed, and
the second at the considered 0.254 mm criterion average wear level. At both cases the
radial-to-axial (Fr / Fa) force ratio increases with increasing the cutting feed. This
may lead to an improvement in the dynamic rigidity and this reduces the wear rate of
the cutting edge. However, an opposite attitude is observed for each of the
radial-to-tangential (Fr / Ft) and the axial-to-tangential (Fa / Ft) force components. At a
criterion wear level of 0.254 mm, all considered ratios are of higher levels than those at
zero wear. This is expected since the radial and the axial force are frictional, rather than
power (tangential), components that are more sensitive to edge wear. At zero wear, the
(Fr / Ft) is of smaller amplitude than the (Fa / Ft) counterpart. As wear increases, it
increases to reach, and may cross, the level of the corresponding axial-to-tangential one.
This indicates that the radial force is the most sensitive component to edge wear (Oraby
and Hayhurst, 2004).
4.1.3 Depth of cut considerations
Figure 9 shows the SEM micrographs and wear-time-force plots of test #24 where
the lowest depth of cut of 1.5 mm was employed. The test ended with a local nose
fracture that tremendously increased the radial force component Fr, Figure 9(b).
However, when the highest depth of 3 mm was employed in test #23, edge wear was of
almost a regular nature except for a tiny edge fracture at about 10 minutes cutting,
Figure 10.
(a) Edge chipping, breakage and wedge thermal lowering fracture (b) Wear-time-force
plots (see online version for colours)
(a)

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(a) Edge chipping, breakage and wedge thermal lowering fracture (b) Wear-time-force
plots (continued) (see online version for colours)
(b)
For tests # 24, 12 and 23, a 0.254 mm average wear was attained at 48, 35 and 27 minutes
respectively. Within such a cutting interval, Figure 9(b), force increase for test #24 is
found to be 23.6%, 44.9% and 39.6% for main, feed and radial force components
respectively. Counterpart force increases values for test #12, Figure 4(b), are 15.2%,
32.8% and 35.2% while they are 6.8%, 25.2% and 21.2% for test #23, Figure 10(c). This
clearly indicates that increasing the depth of cut reduces the resulting cutting variations
due to the edge wear. For test #24, depth of cut was 1.5 mm which approaches the nose
radius rn = 1.2 mm. This restricts the contact length to the round part of the primary and
the secondary cutting edge. Accordingly, high normal stresses results on the tool-work
and tool-chip interfaces, probably associated with high temperatures and plastic flow.
This complex environment invoked the chipping, breakage and thermal lowering of the
cutting wedge that eventually led to the global plastic catastrophic failure of the cutting
edge. At such a multistage failure mechanism (chipping – breaking – softening) at the
nose zone, force change was accurately reflected as a 260% increase in its original value
prior to failure. A corresponding value for the axial force component was about 100%
while it was just 16% for the tangential component.
In test #23 where the depth was increased to 3 mm, an early edge fracture occurred at
the flank zone, Figure 10. After an instantaneous response to the edge fracture that was
entirely absorbed due to the relatively longer contact length hence, lower stresses.

(a) Wear at flank and rubbing at tool face (b) Edge fracture (c) Wear-time-force plots
(a) (b)
(c)
4.2 Effect of irregular (random) wear modes on cutting force variations
Irregular edge fracture was observed during test #1 where a low cutting speed v value of
70 m/min was employed in combination with low levels of feed and depth of cut of
0.12 mm/rev and 2 mm respectively, Figure 11. Tool edge exhibited local chipping and
fracture on both the nose and the notch regions after about 120 minutes cutting time. All
force components were clearly responded as an increase of 21%, 41.6% and 63.2% for
the main, the feed and the radial force components respectively, Figure 11(c).
In test #3, Figure 12, random wear disturbances were observed in two occasions. An
early edge fracture occurred at the notch region, Figure 12(a), as a result of using a
relatively high depth of cut ap of 2.5 mm. However, following an interval of gradual nose
and flank wear modes, a sudden high rate edge wear occurred at the nose area at cutting
time of 17 minutes, Figure 12(b). This continued until the edge eventually failed four
minutes later due to the accompanied high temperatures and stresses.

326 S.E. Oraby
(a) Nose a flank wear (b) Notch wear (see online version for colours)
(a) (b)
(c)
At the first occasion, the radial force component increased about 15% as it was the most
sensitive to the random wear at the notch area, Figure 12(c). The second stage initiated
as the cutting edge was subjected to a plastic thermal lowering which instantaneously
decreased the depth of engagement depth leading to a force decrease in all components.
As contact area increased at the end of the experiment, the edge failed at the nose
area. Accordingly, both axial and radial force components reflected the effect of the
edge failure as an about 77% increase in their amplitude than that just before failure.
However, tangential force component exhibited only a 19% increase within the same
interval.
For test #4, Figure 13, due to the relative high levels of feed and depth of cut
associated with low cutting speed, a local edge breakage at the nose area initiated after
19 minutes of cutting and continued until the edge failed after 33 minutes cutting,
Figures 13(a) to 13(c). At the end of the first stage, a 49.2% nose wear increase led to
force increase of 10.3%, 30.11% and 37.5% for the main, the feed and the radial force
components respectively. Within the last four minutes of the experiment, the nose wear
increased by 266% and, this escalated the force by 9.95%, 60.5% and 89.7% for main,
feed and radial force components, Figure 13(d).

(a) Notch and nose wear (b) Catastrophic softening failure (c) Wear-time-force plots
(a) (b)
(c)
(a) Edge softening at nose (b) Entire flank deformation (c) Wear-time radar distribution
(d) Force-time radar distribution (see online version for colours)
(a) (b)

328 S.E. Oraby
(a) Edge softening at nose (b) Entire flank deformation (c) Wear-time radar distribution
(d) Force-time radar distribution (continued) (see online version for colours)
(c) (d)
The experimental results indicated that the common edge failure took place over the
region of the edge that surrounds the edge nose starting from the flank at the primary
edge and extends to the secondary cutting edge. This was basically due to the thermal
softening of the cutting wedge as a result of the high temperatures and pressure in
the tool-chip and tool-workpiece interfaces. This substantially affected the frictional
force components especially the radial component. The tangential force, as a power
component, was the least affected by the edge wear and deformation. Edge deformation
at the nose usually affects the dimensional accuracy of the produced part (larger
diameter) and, this is undesirable in finish machining. This is the reason behind the
concern (Astakhov, 2004) to suggest the use of the radial wear parameter normal to the
cutting direction as an alternative wear criterion measure.
Whenever the edge wear is evenly distributed over the entire flank contact area, an
almost equal response was observed for the radial and the axial force components.
However, when the cutting edge is randomly deformed, the type of the deformation is
found to differently affect the various force components. Notch wear, for instance,
basically affects the axial force component.
Deformation of the cutting edge is inevitable as a result of the interaction of the
thermal, mechanical and tribological features involved in the process. It is practiced in
forms of regular wear and irregular random modes and, in reality; both modes cannot be
dealt with individually but, should be simultaneously considered in the general context of
the regime under study. For instance, the effect of the cutting feed on the emerged edge
wear and deformation should be considered taking the level of the employed cutting
speed as a cutting heat generation prime factor. The cutting speed, as an input parameter,
may be judged without the consideration of the expected process variations as cutting
continues. While it is known that the cutting forces decreases marginally as speed
increases when the cutting edge is primarily sharp, the situation is reversed at advanced
stages when edge wear increases. Too many parameters affect the process and its
symptoms and, these are associated with the effect of each of system elements

(tool-workpiece-machine tool). Among the workpiece influential parameters affecting the
process are the material properties as well as the geometry of the workpiece and its
relative dimensions. Among the geometrical parameters of the workpiece that causes
variability in machining is the workpiece diameter. For a given surface speed in turning,
decreasing diameter requires more rotational speed and, this affects the dynamic
characteristics of the process. Also, it is shown (Al-Khalid et al., 2012) that material
hardness varies as different diameters of the same workpart. While hardness slightly
decreased at smaller diameters of AISI 4140 and AISI 1020, an opposite outcome was
observed for AA 6082 aluminium alloy. Moreover, it is explained (Astakhov, 2007) that
thermal and deformation waves interaction usually takes place during machining. For
given cutting speed and feed, the time elapsed for one revolution affects such an
interaction in such a way that a bigger workpiece diameter pumps less residual thermal
energy from the past pass then, reduces tool wear and its rate.
Due to the complexities involved in metal cutting, the tool state diagnosis through the
symptoms associated with the problem under study has been adopted. The symptoms are
linked to the associated phenomena through the examination of an easy response. Edge
deformation in machining usually represents the symptoms of the problems involved in
the cutting process.
Cutting parameters (speed – feed – depth of cut) have long been considered to
evaluate and analyse the state of the cutting edge. Due to the unexpectedly edge random
deformation modes, the dependence on only cutting parameters is insufficient strategy to
in-process monitor and/or control policies recently required in adaptive control systems.
One approach is to relate the immeasurable process symptoms (wear and deformation) to
measurable parameters. Cutting force variations may represent smart and credible
information carrier about the instantaneous state of the cutting edge. The challenge,
however, is to approach a versatile technique that is universal and material properties
independent. The current study is just a step forward toward that direction.
5 Empirical force-wear models considering edge, rubbing and ploughing
force elements
As indicated by equations (10) and (11), the overall cutting forces can be attributed to
three independent fundamental elements each of which have its own individual source
and features. The first depends on cutting configuration and work material properties; the
second (edge force) depends on edge configuration and specific cutting pressure while
the third represents the extra wear influence imposed on the process. The first two
elements may be combined to represent a wear-independent force component Fwi that
may be expressed as:
. .( . ) [ ]wi o c oF a ap f N= =β β (12)
βo is the cut coefficient that depends on specific cutting pressure (N/mm2
), ac is the cut
area (mm2
), ap is the depth of cut (mm) and f is the feed (mm/rev). As wear propagates
on the flank face, an additional rubbing and ploughing force component Frp evolves:
( )1 1. . . .cot [ ],rp c i r iF b VB ap κ VB N= =β β (13)

330 S.E. Oraby
β1 is the wear land intensity coefficients per unit wear land area, bc is the cut width, κr is
the approach angle, and VBi is the wear land height. Combining equations (12) and (13)
yields the total force model for the worn edge Fi:
( )1( . ) .cot . [ ]i VBi rp o r iF F F ap f ap κ VB N= + = +β β (14)
( ) . [ ]i o c j jF a ap VB N= + ∑β β (15)
where suffix i refers to the type of force component: main Ft, feed (axial) Fa, radial Fr or
thrust Far force components while suffix j that refers to the type and the mode of the edge
wear: nose wear VBC, flank wear VBBmax and notch wear VBN. The natural form of
equation (15) takes the form:
( ) ( ) ( ) ( )1 2 3. . max .i o c C B NF a apVB apVB apVB= + + +β β β β (16)
Mathematical models were established using the experimental data according to
model (16). Multiple regression procedures are used to estimate the equations’
coefficients (predictors) β’s. Results of all possible models structures along with their
statistical and significance measures are as follows:
5.1 Main (tangential) cutting force component Ft
( ) ( ) ( ) ( )2,178.13 ( ) 177.16 261.02 max 269.18t c C B NF a ap VB VB VB⎡ ⎤= + + +⎣ ⎦ (17a)
( ) ( ) ( )2,186.03 ( ) 227.42 459.0 maxc C Ba ap VB VB⎡ ⎤= + +⎣ ⎦ (17b)
( ) ( ) ( )[ ]2,193.95 ( ) 263.81 407.87c C Na ap VB VB= + + (17c)
( ) ( ) ( )2,187.18 ( ) 405.95 max 327.84c B Na ap VB VB⎡ ⎤= + +⎣ ⎦ (17d)
( ) ( )[ ]2,243.44 ( ) 550.3c Ca ap VB= + (17e)
( ) ( )2,200.71 ( ) 715.50 maxc Ba ap VB⎡ ⎤= + ⎣ ⎦ (17f)
( ) ( )[ ]2,230.20 ( ) 683.7c Na ap VB= + (17g)
Models set (17) indicate the all-possible force-wear interrelationships using multiple
regression analysis using ‘ENTER’ technique where the required parameters are forced
into the final model. The adequacy and the significance are examined throughout many
statistical criteria as indicated in Table 3. These include the adjusted correlation factor
Adj. R2
, the F_ratio and the standard error of estimate SE in addition to the partial
standard error and the corresponding t_value for the individual coefficients. All statistical
criteria confirm the significance and the adequacy of all models. Models coefficients
indicate that the main cutting force Ft is affected, to different extents, by the various wear
modes with the highest impact of the flank wear VBB while it is least affected by the nose
wear VBC. This is further examined with STEPWISE regression routine, which uses some
statistical measures to specify the merit and the priority of each variable to include in the
final model. According to ‘stepwise’ routine, all wear modes deserved the inclusion in
the final model (17a) with the significance inclusion sequence: the flank wear followed

by the notch wear and finally the nose wear. This is supported by the statistical criteria
for individual models (17e) to (17g). However, all models indicate that the main force
component Ft, as a power rather frictional component, is strongly associated to the
shearing process which, is represented by the cut area ac.
Table 3 Statistical criteria and measures for models of main force component
Model statistical criteria Partial predictors t_value(3)
Model
no. Adj. R2(1)
F_ratio(2)
Model (SE) t_βo t_β1 t_β2 t_β3
(17a)(4)
99.5% 35,564 85.10 154.0 6.92 6.50 7.85
(17b) 99.5% 43,374 88.95 148.6 8.75 13.94 -
(17c) 99.5% 44,615 87.71 153.0 11.7 - 14.8
(17d) 99.5% 44,228 88.10 150.0 - 11.4 9.53
(17e) 99.4% 50,143 101.0 139.6 40.9 - -
(17f) 99.4% 58,295 93.94 142.6 - 45.0 -
(17g) 99.4% 55,414 96.34 145.3 - - 43.8
Notes: (1)
Adj. R2
= [1 – (Residuals Sum Squares / Total Sum Squares)]
(2)
F_ratio = [Regression Mean Squares / Residuals Mean Squares]
(3)
t_value = [Predictor Value / Predictor Standard Error]
(4)
STEPWISE estimation for Ft.
The Ft-wear relations may be simplified, without affecting their predictability by using
the average wear VBav as the arithmetic mean of the three wear modes.
Additionally, the notch wear mode VBN is observed to have the least influential
impact on the cutting force and is thought to use the average wear considering only the
nose and the flank wear.
( ) ( )
1
2
2,179 649.923 .
99.5%, 85.65, 70,185, 160, 51o
t c avF a apVB
R SE F t t
= +
= = = = =⎡ ⎤⎣ ⎦β β
(18)
( ) ( )
1
max
2
2,192.51 657.67 .
99.5%, 92, 60,782, 152.5, 46.5
C B
o
t c av VB VBF a apVB
R SE F t t
− −= +
= = = = =⎡ ⎤⎣ ⎦β β
(19)
5.2 Feed (axial) force component Fa
Models set (20) represent the estimation procedures for the feed force component Fa.
Stepwise procedures, model (20c), indicate that the nose wear VBC is the most influential
factor with better statistical criteria and measures, Table 4.
( ) ( ) ( ) ( )338.3 ( ) 739.76 0.672 max 82.11a c C B NF a ap VB VB VB⎡ ⎤= + − +⎣ ⎦ (20a)
( ) ( ) ( )341.24 ( ) 754.95 59.72 maxc C Ba ap VB VB⎡ ⎤= + +⎣ ⎦ (20b)
( ) ( ) ( )[ ]338.79 ( ) 739.54 81.75c C Na ap VB VB= + + (20c)
( ) ( ) ( )376.50 ( ) 602.98 max 326.43c B Na ap VB VB⎡ ⎤= + +⎣ ⎦ (20d)

332 S.E. Oraby
( ) ( )[ ]348.71 ( ) 796.96c Na ap VB= + (20e)
( ) ( )389.98 ( ) 911.20 maxc Ba ap VB⎡ ⎤= + ⎣ ⎦ (20f)
( ) ( )[ ]440.410 ( ) 855.01c Na ap VB= + (20g)
Table 4 Statistical criteria and measures for models of feed force component
Model statistical criteria Partial predictors SE and t_valueModel
no. Adj. R2
F_ratio Model (SE) t_βo t_β1 t_β2 t_β3
(20a) 95.1% 3,157 127.5 16.0 19.0 –.011 1.6
(20b) 95.1% 4,198 127.6 16.2 20.2 1.26 -
(20c)(1)
95.1% 4,216 127.4 16.3 22.5 - 2.04
(20d) 92.3% 2,610 159.5 14.3 - 9.33 5.24
(20e) 95.1% 6,290 127.7 17.2 47.0 - -
(20f) 92.0% 3,751 162.7 14.6 - 33.3 -
(20g) 91.3% 3,422 169.6 16.3 - - 31.1
Note: (1)
Stepwise estimation for Ft.
Models considering the average wear; either VBav or max ,C Bav VB VBVB − − are as follows:
( ) ( )
1
2
326.87 925.85 .
93.0%, 151.7, 4,360, 15.8, 37o
a c avF a apVB
R SE F t t
= +
= = = = =⎡ ⎤⎣ ⎦β β
(21)
( ) ( )
1
max
2
321.78 900.996 .
93.2%, 149.6, 4,492, 16.6, 37.8
C B
o
a c av VB VBF a apVB
R SE F t t
− −= +
= = = = =⎡ ⎤⎣ ⎦β β
(22)
5.3 Radial force component Fr
Models (31) to (37) represent the estimation procedures for the radial force component Fr
with statistical measures listed in Table 5. Stepwise procedures, model (23), indicate that
the radial force is affected by all wear elements. Data show an opposite action for each of
the flank and the notch wear modes to that imposed by the nose wear VBC.
( ) ( ) ( ) ( )300.88 ( ) 1,082.19 142.25 max 166.79r c C B NF a ap VB VB VB⎡ ⎤= + − +⎣ ⎦ (23a)
( ) ( ) ( )295.99 ( ) 1,051.34 264.93 maxc C Ba ap VB VB⎡ ⎤= + +⎣ ⎦ (23b)
( ) ( ) ( )[ ]292.26 ( ) 1,035.22 242.37c C Na ap VB VB= + + (23c)
( ) ( ) ( )356.00 ( ) 740.83 max 190.64c B Na ap VB VB⎡ ⎤= + +⎣ ⎦ (23d)
( ) ( )[ ]262.86 ( ) 864.98c Ca ap VB= + (23e)
( ) ( )363.87 ( ) 920.38 maxc Ba ap VB⎡ ⎤= + ⎣ ⎦ (23f)

( ) ( )[ ]434.52 ( ) 840.05c Na ap VB= + (23g)
Table 5 Statistical criteria and measures for models of radial force component
no. Adj. R2
(23a)(1)
93.3% 2,272 150.8 12.0 23.8 -2.0 -2.7
(23b) 93.2% 2,998 151.6 11.8 23.7 -4.72 -
(23c) 93.3% 3,015 151.2 11.8 26.6 - -5.1
(23d) 87.5% 1,524 206.0 10.5 - 8.9 2.4
(23e) 93.0% 4,345 154.0 10.7 42.3 - -
(23f) 87.4% 2,268 206.8 10.7 - 26.5 -
(23g) 86.0% 2,008 217.9 12.5 - - 23.8
Note: (1)
Stepwise estimation for Fr.
Models considering the average wear are as follows:
( ) ( )
1
2
281.833 956.388 .
90.5%, 179, 3,130, 10.7, 33.9o
r c avF a apVB
R SE F t t
= +
= = = = =⎡ ⎤⎣ ⎦β β
(24)
( ) ( )max
2
259.158 949.849 .
91.4%, 170.4, 3,493, 11.1, 36.6
C B
o t
r c av VB VBF a apVB
R SE F t t
− −= +
= = = = =⎡ ⎤⎣ ⎦β β
(25)
5.4 Thrust force component Far
As shown in Figure 1, the thrust force Far is the component normal to the cutting edge
and, is considered as the resultant of the feed and the radial components. Models (26)
indicate the global and the individual influence of wear modes on the thrust force
variation with statistical criteria listed in Table 6. Model (26b) is selected by the stepwise
procedures with only the nose and the flank wear modes to enter into the final equation.
( ) ( ) ( ) ( )451.80 ( ) 1,310.95 112.62 max 70.21ar c C B NF a ap VB VB VB⎡ ⎤= + − −⎣ ⎦ (26a)
( ) ( ) ( )449.74 ( ) 1,297.96 164.26 maxc C Ba ap VB VB⎡ ⎤= + −⎣ ⎦ (26b)
( ) ( ) ( )[ ]444.97 ( ) 1,273.76 130.05c C Na ap VB VB= + − (26c)
( ) ( ) ( )518.56 ( ) 957.13 max 362.77c B Na ap VB VB⎡ ⎤= + +⎣ ⎦ (26d)
( ) ( )[ ]429.19 ( ) 1,182.42c Ca ap VB= + (26e)
( ) ( )533.54 ( ) 1,299.66 maxc Ba ap VB⎡ ⎤= + ⎣ ⎦ (26f)
( ) ( )[ ]620.01 ( ) 1,201.8c Na ap VB= + (26g)

334 S.E. Oraby
Table 6 Statistical criteria and measures for models of thrust force component
no. Adj. R2
(26a) 94.6% 2,873 189.8 14.4 23.9 –1.25 –0.92
(26b)(1)
94.6% 3,832 189.77 14.3 23.4 –2.33 -
(26c) 94.6% 3,827 189.87 14.4 26.0 - –2.2
(26d) 90.3% 2,030 254.70 12.3 - 9.3 3.6
(26e) 94.6% 5,706 190.42 14.2 46.7 - -
(26f) 90.1% 2,983 257.00 12.6 - 30.0 -
(26g) 89.0% 2,657 270.73 14.4 - - 27.4
Note: (1)
Stepwise estimation for Ftr.
Models considering the average wear are as follows:
( ) ( )
1
2
429.331 1,336.69 .
92.3%, 227, 3,915, 13.4, 36.6o
ar c avF a apVB
R SE F t t
= +
= = = = =⎡ ⎤⎣ ⎦β β
(27)
( ) ( )
1
max
2
408.82 1,315.269 .
92.9%, 218.4, 4,251, 14, 38.7
C B
o
ar c av VB VBF a apVB
R SE F t t
− −= +
= = = = =⎡ ⎤⎣ ⎦β β
(28)
The developed models present qualitative and quantitative evaluation of the wear-force
interrelations. This is a necessity in any computerised monitoring and/or control of the
machining process especially the assessment of the tool performance. In addition to that,
the models are used to analyse and evaluate many of the cutting quantities. In the
following sections, two different, but technically related, topics are discussed: the specific
cutting pressure and the friction at the tool-workpiece interface.
6 Effect of edge wear on the specific cutting pressure
Performance of the machining process and the quality of the machined surface are largely
dependent on the geometrical stability of the cutting edge. This, to great extent, is
influenced by the continuous variation of the cutting force and temperature. The specific
cutting pressure or, the nominal cutting stress gives a direct indication of the state of the
tool wedge. It is defined as the main cutting force, Ft, divided by the cross section area of
the undeformed chip. For sharp edge, the specific cutting pressure depends on the cutting
parameters specially cutting speed (Thakur et al., 2009). The specific cutting pressure is
affected as wear increases on the cutting edge:
( ) 1 2 max 3. . .C B Nt o c VB VB VBF a a a a= + + +β β β β (29)
In which βo is the nominal specific cutting pressure (stress) due to shearing process
(rubbing and ploughing actions) while β1, β2 and β3 represent the individual added
pressure due to nose wear, flank wear and notch wear elements respectively.
Accordingly, the instantaneous state of the specific pressure β can be represented as:

( ) ( ) ( ) ( ) ( )1 2 3
max. . .
.
t t C NB
o
c
F F VB VBVB
a ap f f f f
= = = + + +β β β β β (30)
Equation (30) explains that the extra pressure imposed on the process depends mainly on
the wear land-feed ratio. This ratio introduces a controlling variable of the process to
indicate that more pressure is expected as wear land height exceeds the employed cutting
feed.
The individual impact of each wear mode on the specific pressure is explained in the
light of the wear-time-force experimental results of test #16 which are earlier presented
by Figure 6. The cutting edge attained a low gradual wear rate along with random
chipping, fracture at both the tool-chip and tool-workpiece interfaces. Due to the sudden
nose deformation from 0.218 to 0.284 mm (≈30%), Figure 6(a), a corresponding increase
in the pressure from 4,133 to 5,192 N/mm2
(≈26%) was resulted. As indicated by
Figure 14, the initiation of edge nose deformation is very well detected as the pressure
increases reaching a high value at wear level of 0.226 mm after which it remains constant
retaining most of its rise gain. At later stage, the tool edge experienced chipping and
fracture at both the flank and the notch areas with almost constant level of nose wear
VBC, Figure 6. This has led to a sudden increase of about (10%) in the value of specific
pressure, Figure 14, revealing that only 20% pressure increase should be attributed to the
effect of the nose wear. Again, both flank and notch disturbances are well detected by the
increase in the specific pressure, Figure 14. However, it is observed that the onset of all
deformation modes occurred at an almost similar wear-feed factor of about (4).
Figure 14 Experimental data for specific pressure-wear-feed for test #16 (see online version
for colours)
In test #3, where a low feed of 0.12 mm/rev is used in association with high values of
cutting speed and depth of cut of 145 m/min and 2.5 mm respectively. As shown in
Figure 12, an early edge fracture at the notch zone occurred, Figure 12(a). At later stages,
however, a sudden high edge wear rate occurred at the nose area that eventually led to the
edge failure, Figure 12(b). As show by Figure 15, the early notch deformation increased
the specific pressure by about 6% and then kept constant until it was strongly invoked by

336 S.E. Oraby
the sudden increase at the edge nose at the end of the test. Although the early notch
disturbance is detected, Figure 15, the overwhelming increase in the pressure of about
20% at the end support the existence of a strong impact of the edge nose deformation
mode. While the wear-feed ratio at ultimate edge nose fracture was found to be around
the value (3.5), a less values were observed considering the notch and flank modes,
Figure 15.
for colours)
for colours)
As shown by Figure 4, a moderate speed-feed-depth combination was employed in
test #12 where an almost equal gradual wear level developed over all edge zones except
for an early random fracture occurred on the notch area. At the end of the test, wear
levels were insignificant enough to produce a noticeable increase in either of the pressure

or the wear-feed ratio. Nevertheless, the early notch fracture was noticed to increase the
specific pressure by about 8%, Figure 16.
As indicated in Figure 5, a catastrophic failure due to the use of high cutting speed
occurred at the nose area without affecting any of the flank or the notch edge zones. As
shown in Figure 17, an increase of about 24% in the specific pressure as a result of
attaining a wear-feed ratio of about 4.9, 1.2 and 1.2 for nose, flank and notch wear modes
respectively.
for colours)
Experimental results for test #4, Figure 13, give additional evidence that the wear
domination along the nose area, including the partial extension along the secondary
cutting edge, may have the most impact on the specific cutting pressure. It is observed
that, Figure 18, about 27% increase in the specific pressure corresponds to a wear-feed
ratio of 2.33, 0.65 and 0.65 for nose, flank and notch wear level respectively.
for colours)

338 S.E. Oraby
Non-linear regression procedures using the entire experimental data have led to relate the
specific cutting pressure to all constituents as:
( ) ( ) ( )0.345 0.332 0.114
1,991.003 950.406 maxC B Nβ VB f VB f VB f= + (31)
Nose wear-feed ratio indicates a slight bigger impact on the specific cutting pressure than
that of the flank wear-feed ratio while the notch wear-feed ratio showed the least
influence. During machining, the machined work surface is plastically recovered
(Astakhov, 2006) imposing an extra frictional pressure on the cutting edge. To reduce
computational complication without affecting modelling accuracy, the average wear, as
the mean value of the three edge wear modes, may be used in the form:
( )0.828
2,037.5 904.63 avVB f= +β (32)
Figure 19 Response surface and contours of the specific pressure-feed-average wear (see online
version for colours)

In Figure 19, the response surface pressure-wear-feed interrelation is illustrated in both
three-dimensional and surface contours graphs. The response surface shows three
distinguished functional regions considering the wear-feed ratio (VBav / f). The
customised practical domain may be determined as (VBav / f) ≥ 1. At this technically
feasible region, the cutting parameters, which are represented by feed and depth of cut,
may be optimised according to a certain objective function and operational constraints.
Lower values of cutting feed usually are accompanied by higher levels of specific cutting
pressure especially at elevated wear values. Additionally, for a criterion wear level, the
metal removal rate (productivity) and the specific pressure can be enhanced through
increasing the cutting feed. At the other side, for a given feed value, increasing pressure
through decreasing depth of cut may lead to higher wear scars especially at the nose area.
This information may be exploited in any proposed adaptive control strategy to increase
productivity of a rough turning operation using the measured cutting forces as an indirect
way to assess, monitor and/or control tool wear (Liang et al., 2004).
7 Conclusions
The wear and deformation on the cutting edge is the result of a complex
mechanical-thermal-chemical process involved in metal cutting. The edge deformation is
usually developed in different modes each of them is attributed to one or more of the
aforementioned, usually correlated causes. It has long been accepted to use the cutting
parameters in machining (speed-feed-depth of cut) as a prior input to design and optimise
the machining process, and to prior judge the state of the cutting edge and its
performance. Although the cutting parameters may produce a general vision of the
relationship between the deformation causes and its symptoms, the functional interaction
among these parameters makes it even more difficult to determine the individual
influence of a parameter in isolation of the effect of the others. For instance, the effect of
the cutting feed on the emerged edge wear and deformation should be evaluated taking
the level of the employed cutting speed as a cutting heat generation prime factor into
consideration. Also, the effect of the cutting speed, as an input parameter, should be
judged considering the expected process variations as cutting continues.
The experimental results indicated that the common edge failure takes place over
region of the edge that surrounds the edge nose initiated at the primary edge and extends
to the secondary cutting edge. This was basically due to the thermal softening of the
cutting wedge as a result of the high temperatures and pressure in the tool-chip and
tool-workpiece interfaces. This affected the frictional force components especially the
radial component. The tangential force, as a power component, was the least affected
by the edge wear and deformation. Random wear disturbances were found to have a
localised influence and sometimes changed the radial-to-axial force ratio.
Robust non-linear mathematical models were established to isolate the effect of
different wear and deformation modes on the cutting force components. Most the
aforementioned experimental findings were grasped by the developed models. Also,
wear-feed ratio was mathematically related to the cutting pressure producing a good
measure to determine the onset of edge failure as well as other random wear types.

340 S.E. Oraby
Acknowledgements
The author would like to thank the Public Authority for Applied Education and Training
PAAET, KUWAIT for supporting this study under the research support agreement:
TS-11-11.
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