Davim J. Paulo (editor). Machining. Fundamentals and Recent Advances
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Contents xi
7.5 Nearly Dry Machining (NDM)...................................................... 201
7.5.1 How NDM Operates ........................................................ 201
7.5.2 Classification of NDM..................................................... 202
7.5.3 Why NDM Works............................................................ 212
7.5.4 Consideration of the NDM System Components............. 217
References................................................................................................. 221
8 Sculptured Surface Machining .............................................................. 225
L. Norberto López de Lacalle and A. Lamikiz
8.1 Introduction ................................................................................... 225
8.2 The Manufacturing Process........................................................... 227
8.2.1 Technologies Involved..................................................... 228
8.3 The CAM, Centre of Complex Surfaces Production ..................... 231
8.4 Workpiece Precision...................................................................... 233
8.4.1 Cutting Forces.................................................................. 235
8.5 Workpiece Roughness ................................................................... 237
8.6 Tool Path Selection Using Cutting Force Prediction..................... 239
8.6.1 Three-axis Case................................................................ 240
8.6.2 Five-axis Case.................................................................. 241
8.7 Examples ....................................................................................... 242
8.7.1 Three-axis Mould............................................................. 242
8.7.2 Five-axis Mould ............................................................... 243
8.7.3 Three-axis Deep Mould ................................................... 245
8.8 Present and Future ......................................................................... 246
Acknowledgements................................................................................... 246
References................................................................................................. 247
9 Grinding Technology and New Grinding Wheels ................................ 249
M.J. Jackson
9.1 Introduction ................................................................................... 249
9.2 High-efficiency Grinding Using Conventional Abrasive Wheels . 250
9.2.1 Introduction...................................................................... 250
9.2.2 Grinding Wheel Selection................................................ 251
9.2.3 Grinding Machine Requirements
for High-efficiency Dressing............................................ 253
9.2.4 Diamond Dressing Wheels............................................... 253
9.2.5 Application of Diamond Dressing Wheels....................... 256
9.2.6 Modifications to the Grinding Process............................. 257
9.2.7 Selection of Grinding Process Parameters ....................... 257
9.2.8 Selection of Cooling Lubricant Type and Application..... 258
8.2.2 Five-axis Milling.............................................................. 229
xii Contents
9.3 High-efficiency Grinding Using CBN Grinding Wheels............... 258
9.3.1 Introduction...................................................................... 258
9.3.2 Grinding Wheel Selection................................................ 259
9.3.3 Grinding Machine Requirements
for High-efficiency CBN Grinding .................................. 264
9.3.4 Dressing High-efficiency CBN Grinding Wheels............ 265
9.3.5 Selection of Dressing Parameters
for High-efficiency CBN Grinding .................................. 266
9.3.6 Selection of Cooling Lubrication
for High-efficiency CBN Grinding Wheels ..................... 266
9.4 Internet Resources............................................................................... 267
References................................................................................................. 269
10 Micro and Nanomachining .................................................................... 271
M.J. Jackson
10.1 Introduction ................................................................................... 271
10.2 Machining Effects at the Microscale ............................................. 272
10.2.1 Shear Angle Prediction .................................................... 275
10.2.2 Plastic Behaviour at Large Strains ................................... 278
10.2.3 Langford and Cohen’s Model .......................................... 278
10.2.4 Walker and Shaw’s Model............................................... 279
10.2.5 Usui’s Model.................................................................... 280
10.2.6 Saw-tooth Chip Formation in Hard Turning ................... 281
10.2.7 Fluid-like Flow in Chip Formation ................................. 281
10.3 Size Effects in Micromachining .................................................... 282
10.4 Nanomachining.............................................................................. 282
10.4.1 Nanometric Machining .................................................... 283
10.4.2 Theoretical Basis of Nanomachining ............................... 284
10.4.3 Comparison of Nanometric Machining
and Conventional Machining ........................................... 294
Acknowledgements................................................................................... 295
References................................................................................................. 295
11 Advanced (Non-traditional) Machining Processes............................... 299
V.K. Jain
11.1 Introduction ................................................................................... 299
11.2 Mechanical Advanced Machining Processes (MAMP)................. 301
11.2.1 Ultrasonic Machining (USM) .......................................... 301
11.2.2 Abrasive Water Jet Cutting (AWJC)................................ 304
11.3 Thermoelectric Advanced Machining Processes........................... 307
11.3.1 Electric Discharge Machining (EDM) and Wire EDM.... 307
11.3.2 Laser Beam Machining (LBM)........................................ 312
Contents xiii
11.4 Electrochemical Advanced Machining Processes ......................... 313
11.4.1 Electrochemical Machining (ECM) ................................. 313
11.4.2 ECM Machine.................................................................. 315
11.5 Fine Finishing Processes ............................................................... 317
11.5.1 Abrasive Flow Machining (AFM) ................................... 317
11.5.2 Magnetic Abrasive Finishing (MAF)............................... 320
11.5.3 Magnetic Float Polishing (MFP)...................................... 323
11.6 Micromachining ............................................................................ 324
11.7 Finished Surface Characteristics.................................................... 325
References................................................................................................. 325
12 Intelligent Machining: Computational Methods
and Optimization .................................................................................... 329
Sankha Deb and U.S. Dixit
12.1 Intelligent Machining .................................................................... 329
12.2 Neural Network Modelling............................................................ 332
12.3 Fuzzy Set Theory........................................................................... 339
12.4 Neuro-fuzzy Modelling ................................................................. 344
12.5 A Note on FEM Modelling............................................................ 347
12.6 Machining Optimization................................................................ 348
12.6.1 Objective Functions and Constraints ............................... 348
12.6.2 Optimization Techniques ................................................. 350
12.7 Future Challenges.......................................................................... 355
References................................................................................................. 356
Index ................................................................................................................. 359
1
Metal Cutting Mechanics, Finite Element Modelling
Viktor P. Astakhov
1
and José C. Outeiro
2
1
General Motors Business Unit of PSMi, 1255 Beach Ct., Saline MI 48176, USA.
Email: astvik@gmail.com
2
Portuguese Catholic University, Faculty of Engineering, Estrada Octávio Pato,
2635-631 Rio de Mouro, Lisboa, Portugal.
Email: jcouteiro@crb.ucp.pt
This chapter presents a short analysis of the basics of traditional metal cutting
mechanics, outlining its components and the basics of finite element modelling
(FEM) of the metal cutting process. Based on a previously proposed definition of
metal cutting, advanced metal cutting mechanics considers the power spent in
metal cutting as the summation of four components: the power spent on the plas-
tic deformation of the layer being removed, the power spent on the tool–chip
interface, the power spent on the tool–workpiece interface, and the power spent in
the formation of new surfaces (cohesive energy). Energy partition in the cutting
system and the relative impact of the parameters of the machining regime are
discussed. Analyzing the basics of FEM and presenting examples, this chapter
considers the errors in such modelling and their major sources. It points out the
importance of the selection, verification and validation of the physically justifi-
able model.
1.1 Advanced Metal Cutting Mechanics
1.1.1 Objective of Metal Cutting Mechanics
The major objectives of metal cutting mechanics are to determine the cutting force
and the cutting power through analyzing the thermomechanical processes involved
in the cutting process.
1.1.2 State of the Art
Although these objectives can reportedly be achieved by analyzing a relevant
model of the cutting process and all available experimental information, this is
2 V.P. Astakhov and J.C. Outeiro
not the case in practice. The old trial-and-error experimental method, originally
developed in the middle of the 19
th
century (well summarized in [1]) is still in
wide use in metal cutting research and development activities. Its modern form,
known as the unified or generalized mechanics approach, has been pursued by
Armarego and co-workers for years [1], then spreading as the mechanistic ap-
proach in metal cutting [2]. It was developed as an alternative to metal cutting
theory because the latter did not prove its ability to solve even the simplest of
practical problems.
One of the most important yet least understood operation parameters of a ma-
chining operation is the cutting force. In general, this force is thought of as a three-
dimensional (3D) vector which is represented by three components, namely, the
power component, the radial component and the axial component in the tool coor-
dinate system as shown in Figure 1.1(a) [3]. Out of these three components, the
largest is normally the power component which is often called the cutting force.
This simplification will be used through the body of this Section. As this force is
of high importance, one might assume that theoretical and experimental methods
for its determination have been developed and thus be available in the literature.
Unfortunately, this is not the case.
When it comes to the possibility of theoretical determination, the foundation of
the force and energy calculations in metal cutting is based on the oversimplified
orthogonal force model known as Merchant’s force circle diagram or a condensed
force diagram [4,
5] shown in Figure 1.1(b). In this figure, the total cutting force
R is resolved into the tool face–chip friction force
F
and the normal force N .
The angle
μ
between
F
and N is thus the friction angle. The force R is also
resolved along the shear plane into the shear(ing) force,
s
F
which, in Merchant’s
opinion, is responsible for the work expended in shearing the metal, and the nor-
mal force
n
F
, which exerts a compressive stress on the shear plane. The force R
is also resolved along the direction of tool motion into
c
F
, termed by Merchant
the cutting force, and
T
F
, the thrust force.
x
y
(a) (b)
z
γ
μ−γ
N
μ
γ
T
F
F
c
R
n
F
F
F
s
y
F
x
F
z
F
R
Figure 1.1. The force system in cutting: (a) turning and (b) the orthogonal force model
proposed by Merchant
Metal Cutting Mechanics, Finite Element Modelling 3
The determination of the cutting force is based upon the calculation of the
shearing force,
s
F
. In 1941 Ernst and Merchant [6] proposed the following equa-
tion to determine this force:
τ
ϕ
=
yc
s
A
F
s
in
(1.1)
where
τ
y
is the shear strength of the work material,
ϕ
is the shear angle and
c
A
is the area of shearing (the uncut chip area, equal to the product of the uncut chip
thickness and the uncut chip width).
According to Ernst and Merchant, the work material deforms when the stress
on the shear plane reaches its shear strength. Later researchers published a great
number of papers showing that
τ
y
should be thought of as the shear flow stress,
which is somewhat higher than the yield strength of the work material depending
upon particular cutting conditions. Still, this stress remains today the only relevant
characteristic of the work material characterizing its resistance to cutting.
It follows from Figure 1.1(b) that
()
()
μ
γ
ϕ
μγ
−
=
+−
s
c
Fcos
F
cos
(1.2)
and combining Equations (1.1) and (1.2), one can obtain
()
()
τμγ
ϕ
ϕμγ
−
=
+−
yc
c
Acos
F
sin cos
(1.3)
The cutting power
c
P is then calculated as
=
cc
PFv (1.4)
This power defines the energy required for cutting, cutting temperatures, plastic
deformation of the work material, machining residual stress and other parameters.
However, everyday practice of machining shows that these considerations do
not much reflect reality even to the first approximation. For example, machining
of medium carbon steel AISI 1045 (tensile strength, ultimate
655
σ
=
R
MPa,
tensile strength, yield
02
375
σ
=
y.
MPa) results in much lower total cutting forces
(Figure 1.8 in [7]), greater tool life, lower required power, cutting temperature,
machining residual stresses than those obtained in the machining of stainless steel
AISI 316L (
517
σ
=
R
MPa;
02
218
σ
=
y.
MPa) [8]. The prime reason for that is
that any kind of strength of the work material in terms of its characteristic stresses
cannot be considered alone without corresponding strains, which determine the
energy spent in deformation of the work material [9,
10]. Only when one knows
the stress and corresponding strain, can one calculate other parameters and out-
comes of the metal cutting process [9].
4 V.P. Astakhov and J.C. Outeiro
When it comes to experimental determination of the cutting force, there are at
least two problems:
• The first and foremost is that the cutting force cannot be measured with
reasonable accuracy. Even if extreme care is taken, a 50% variation is
found [11].
• Second, many tool and cutting inserts manufacturers (not to mention
manufacturing companies), do not have adequate dynamometric equipment
to measure the cutting force. Many dynamometers used in the field are not
properly calibrated because the known literature sources did not provide
proper experimental methodology for cutting force measurements using
piezoelectric dynamometers [12].
Therefore, to make practical calculations of the cutting force and thus energy spent
in machining another approach has to be found. This Section is to present such an
advanced approach.
1.1.3 Advanced Methodology
The proposed methodology is based on the definition of the metal cutting process
proposed by Astakhov [10] and on the model of energy partition in the metal cut-
ting system developed using this definition (Figure 2.1 in [7]). According to this
model, the power balance in the cutting system can be written as
==+++
cc pdfRfFch
PFvP P P P (1.5)
from which the cutting force is calculated as
+++
=
pd fR fF ch
c
PPPP
F
v
(1.6)
where
pd
P is the power spent on the plastic deformation of the layer being removed,
f
R
P is the power spent at the tool–chip interface,
f
F
P is the power spent at the tool–
workpiece interface and
ch
P is the power spent in the formation of new surfaces.
The power spent on the plastic deformation of the layer being removed,
pd
P ,
can be calculated knowing the chip compression ratio and parameters of the de-
formation curve of the work material as follows [7,
9]
()
1
115
1
ζ
+
=
+
n
pd w
K.ln
PvA
n
(1.7)
where
K
is the strength coefficient (N/m
2
) and n is the hardening exponent of
the work material,
ζ
is the chip compression ratio [7,
9,
10] and
w
A
is uncut chip
cross-sectional area (m
2
)
=
ww
A
df (1.8)
where
w
d is the depth of cut (m) and
f
is the cutting feed per revolution (m/rev).
Metal Cutting Mechanics, Finite Element Modelling 5
The practical methods of experimental determination of the chip compression
ratio
ζ
are discussed for various machining operation by Astakhov [7,
9].
Power spent due to friction at the tool–chip interface is calculated as
1
τ
ζ
=
fR c c T
v
Plb
(1.9)
where
028
τσ
=
cUTS
. is the average shear stress at the tool–chip contact (N/m
2
)
[7],
σ
uts
is the ultimate tensile strength of the work material (N/m
2
),
c
l is the
tool–chip contact length (m) and
1T
b is the true chip width (m).
The tool–chip contact length is calculated as [7]
15
1
ζ
=
.
cT
lt (1.10)
where
1T
t is the true uncut chip thickness (m) [7].
The true uncut chip thickness and the true chip width depend on the configura-
tion of the projection of the cutting edge into the main reference plain. Formulae
to calculate
1T
t and
1T
b for various configuration presented by Astakhov [7,
10].
The most common case of machining is when the cutting insert, with tool cutting
edge angle
κ
r
and tool minor cutting edge angle
1
κ
r
, is made with a nose radius
r
n
and set so that the depth of cut
w
d is greater than the nose radius, as shown
Figure 1.2. If the following relationships are justified
()
1
κ
≥−
wn r
dr cos,
1
2
κ
≤
nr
f
rsin (1.11)
then the formulas for calculation of
1T
t and
1T
b are as follows
[]
1
1
11 11
11
κκ κ
=
−− + +
T
rr r
fc
tsinarctan
c e ( cos ) cot e (sin g )
(1.12)
and
[]
1
1
1
111
11
κκ κ
=
−− + +
w
T
rr r
cd
b
c
sin arctan
e ( cos ) cot e (sin g )
(1.13)
where
1
2
=
n
f
g
r
,
1
=
n
w
r
e
d
,
()
11 1
111=− − −ce g (1.14)
Power spent due to friction at the tool–workpiece interface is calculated as
=
f
FfF
PFv (1.15)
where
f
F
F
is the friction force on the tool–workpiece interface
0 625
τρ
α
=
fF y ce ac
*
Br
F. l
sin
(1.16)
6 V.P. Astakhov and J.C. Outeiro
where
τ
y
is the shear strength of the tool material (N/m
2
),
ρ
ce
is the radius of the
cutting edge (m),
α
* is the normal flank angle (deg) and
ac
l is the length of the
active part of the cutting edge (the length of the cutting edge engaged in cutting)
(m). In the considered case (Figure 1.2)
0018
κ
κ
κ
+
⎞
⎛
=+
⎜⎟
⎝
⎠
n
ac n
rcos
lr.
sin
(1.17)
Br is the Briks similarity criterion [7, 10],
γ
ζ
γ
=
−
cos
Br
s
in
(1.18)
where
γ
is the normal rake angle (deg).
The power spent in the formation of new surfaces
ch
P is calculated as the prod-
uct of the energy required for the formation of one shear plane and the number of
shear planes formed per second, i.e.,
=⋅
ch fr cf
PEf (1.19)
where
cf
f
is the frequency of chip formation, i.e., the number of shear planes
formed per second and
f
r
E is the energy of fracture per shear plane.
The frequency of chip formation determines how many shear planes form per
second of machining time. This frequency depends primarily on the work material
and on the cutting speed, as discussed by Astakhov [10]. Figure 1.3 provides some
data for common work materials.
Workpiece
Tool nose
radius
Direction of feed
motion
(a)
Chip
Tool
A
Transient surface
Direction of prime
(speed) motion
Work surface
Machined surface
Workpiece
Cutting
insert
(b)
A
SECTION A-A
ENRARGED
Chip
n
d
w
κ
r
r1
κ
r
ρ
ce
α
*
Figure 1.2. Visualization of terms used in the considered case of machining
Metal Cutting Mechanics, Finite Element Modelling 7
0.05
0.05 0.10 0.40 1.00 2.00 v, m/s
0.10
0.20
0.40
1.00
2.00
4.00
f, KHz
1018
1045
Cr-Ni-Mn
steel
steel
Alloy
303 steel
Figure 1.3. Effect of the cutting speed on the frequency of chip formation
The work of fracture per a shear plane is
−
=⋅
f
rfrufr
EE A (1.20)
where
ch
E is the cohesive energy (J/m
2
) [13] and
ch
A
is the area of fracture (m
2
).
The area of fracture is the area of the shear plane determined as
1
=⋅
f
rshT
A
Lb (1.21)
where the length of the shear plane
s
h
L is calculated as
1
=
T
sh
t
L
s
in arc tan Br
(1.22)
1.1.4 Combined Influence of the Minor Cutting Edge
The influence of the minor cutting edge (Figure 1.2(b)) on the cutting force and
power consumption is seldom considered in the literature on metal cutting. At
best, the influence of the tool minor cutting edge angle
1
κ
r
is mentioned in the
consideration of the theoretical roughness of the machined surface or the geomet-
ric component of roughness [14,
15]. In the authors’ opinion, the term minor
probably misled many researchers in the field, causing a common perception that
this cutting edge does not affect the cutting process to any noticeable degree.
Everyday practice of machining and even simple observation of the chip formed in
a common machining operation show that the chip side formed by the minor cut-
ting edge is always more deformed and has a darker colour. Zorev [3] provided
a detailed analysis of the chip formation by the minor cutting edge. Zorev studied