Metal Machining
Theory and Applications
Thomas Childs
University of Leeds, UK
Katsuhiro Maekawa
Ibaraki University, Japan
Toshiyuki Obikawa
Tokyo Institute of Technology, Japan
Yasuo Yamane
Hiroshima University, Japan
A member of the Hodder Headline Group
LONDON
Copublished in North, Central and South America
by John Wiley & Sons Inc.
New York-Toronto
Childs Prelims 28:3:2000 4:07 pm Page i
First published in Great Britain in 2000 by
Arnold, a member of the Hodder Headline Group,
338 Euston Road, London NW1 3BH

Copublished in North, Central and South America by
John Wiley & Sons Inc., 605 Third Avenue,
New York, NY 10158–0012
© 2000 Thomas Childs, Katsuhiro Maekawa, Toshiyuki Obikawa and Yasuo Yamane
All rights reserved. No part of this publication may be reproduced or
transmitted in any form or by any means, electronically or mechanically,
including photocopying, recording or any information storage or retrieval
system, without either prior permission in writing from the publishers or a
licence permitting restricted copying. In the United Kingdom such licences
are issued by the Copyright Licensing Agency: 90 Tottenham Court Road,
London W1P 0LP.

2.1 Historical introduction 35
2.2 Chip formation mechanics 37
2.3 Thermal modelling 57
2.4 Friction, lubrication and wear 65
2.5 Summary 79
References 80
3 Work and tool materials 81
3.1 Work material characteristics in machining 82
3.2 Tool materials 97
References 117
4 Tool damage 118
4.1 Tool damage and its classification 118
4.2 Tool life 130
4.3 Summary 134
References 135
5 Experimental methods 136
5.1 Microscopic examination methods 136
5.2 Forces in machining 139
5.3 Temperatures in machining 147
Childs Prelims 28:3:2000 4:07 pm Page iii
5.4 Acoustic emission 155
References 157
6 Advances in mechanics 159
6.1 Introduction 159
6.2 Slip-line field modelling 159
6.3 Introducing variable flow stress behaviour 168
6.4 Non-orthogonal (three-dimensional) machining 177
References 197
7 Finite element methods 199
7.1 Finite element background 199

iv Contents
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A2.3 Selected problems, with convection 355
A2.4 Numerical (finite element) methods 357
References 362
3 Contact mechanics and friction 363
A3.1 Introduction 363
A3.2 The normal contact of a single asperity on an elastic foundation 365
A3.3 The normal contact of arrays of asperities on an elastic foundation 368
A3.4 Asperities with traction, on an elastic foundation 369
A3.5 Bulk yielding 371
A3.6 Friction coefficients greater than unity 373
References 374
4 Work material: typical mechanical and thermal behaviours 375
A4.1 Work material: room temperature, low strain rate, strain hardening
behaviours 375
A4.2 Work material: thermal properties 376
A4.3 Work material: strain hardening behaviours at high strain rates and
temperatures 379
References 381
5 Approximate tool yield and fracture analysis 383
A5.1 Tool yielding 383
A5.2 Tool fracture 385
References 386
6 Tool material properties 387
A6.1 High speed steels 387
A6.2 Cemented carbides and cermets 388
A6.3 Ceramics and superhard materials 393
References 395
7 Fuzzy logic 396

L. B. Oxley (1989, Chichester: Ellis Horwood) which this text might be regarded as
complementing.
It is intended that this book will be of interest and helpful to all mechanical, manufac-
turing and materials engineers whose responsibilities include metal machining matters. It
is, however, written specifically for masters course students. Masters courses are a major
feature of both the American and Japanese University systems, preparing the more able
twenty year olds in those countries for the transition from foundation undergraduate
courses to useful professional careers. In the UK, masters courses have not in the past been
popular, but changes from an elite to a mass higher education system are resulting in an
increasingly important role for taught advanced level and continuing professional devel-
opment courses.
Childs Prelims 28:3:2000 4:07 pm Page vii
It is supposed that masters course readers will have encountered basic mechanical and
materials principles before, but will not have had much experience of their application. A
feature of the book is that many of these principles are revised and placed in the machin-
ing context, to relate the material to earlier understanding. Appendices are heavily used to
meet this objective without interrupting the flow of material too much.
It is a belief of the authors that texts should be informative in practical as well as theo-
retical detail. We hope that a reader who wants to know how much power will be needed
to turn a common engineering alloy, or what cutting speed might be used, or what mater-
ial properties might be appropriate for carrying out some reader-specific simulation, will
have a reasonable chance either of finding the information in these pages or of finding a
helpful reference for further searching.
The book is essentially organized in two parts. Chapters 1 to 5 cover basic material.
Chapters 6 to 9 are more advanced. Chapter 1 is an introduction that places the process in
its broader context of machine tool technology and manufacturing systems management.
Chapter 2 covers the basic mechanical engineering of machining: mechanics, heat conduc-
tion and tribology (friction, lubrication and wear). Chapters 3 and 4 focus on materials’
performance in machining, Chapter 5 describes experimental methods used in machining
studies.

Introduction
Machining (turning, milling, drilling) is the most widespread metal shaping process in
mechanical manufacturing industry. Worldwide investment in metal-machining machine
tools holds steady or continues to increase year by year, the only exception being in the
worst of recessions. The wealth of nations can be judged by this investment. Figure 1.1
shows the annual expenditure on machine tools by each of the most successful countries –
Germany, Japan and the USA. For each, it was between £1bn and £2bn (bn = 10
9
) in the
late 1970s. It fell abruptly in the world recession (the oil crisis) of 1981–82 and has now
recovered to between £2bn and £3bn (all expressed in 1985 prices: £1 was then equivalent
to 300¥ or $1.3). Figure 1.1 also shows similar trends (a growth over the last 20 years from
Fig. 1.1 International demand for machine tools, 1978–88, £bn at 1985 prices (from European community statistics
1988) and projected at that time to 1995
Childs Part 1 28:3:2000 2:32 pm Page 1
50% to 100% in annual expenditure) for the developed European Community countries.
Only in the UK has there been a decline in investment. Over this period, investment in
metal machining has remained at about three times the annual investment in metal form-
ing machinery.
Investment has continued despite perceived threats to machining volume, such as the
displacement of metal by plastics products in the consumer goods sector, and material
wastefulness in the production of swarf (or chips) that has encouraged near-net (casting
and forging) process substitution in the metal products sector. One reason is that metal
machining is capable of high precision: part tolerances of 50 mm and surface finishes of 1
mm are readily achievable (Figure 1.2(a)). Another reason is that it is very versatile:
complicated free-form shapes with many features, over a large size range, can be made
more cheaply, quickly and simply (at least in small numbers) by controlling the path of a
standard cutting tool rather than by investing considerable time and cost in making a dedi-
cated moulding, forming or die casting tool (besides, machining is needed to make the dies
for moulding, forging and die casting processes).

20% of the time: different surveys, however, gave different values. For 40 to 60% of the
time the machine tools were in use but not productively: i.e. they were being set up for
manufacture, or being loaded and unloaded, or during manufacture tools were being
moved and positioned for cutting but they were not removing metal. For 20 to 50% of the
time they were totally unused – idle.
As far as work in progress was concerned, batches of components typically spent from
70 to 95% of their time inactive on the shop floor. So overwhelming was the clutter of
partly finished work that a component requiring several different operations for its comple-
tion, on different machine tools, might find these carried out at the rate of only one a week.
From 10 to 20% of their time components were being positioned for machining and for
only from 1 to 5% of the time was metal actually being removed.
From the late 1960s to the early 1970s both forms of waste – the active, non-productive
and the idle times – began significantly to be attacked, the former mainly by developing
machine tool technology and the latter by new forms of manufacturing organization.
Machine tool technology 3
Fig. 1.3 Idle and active times in batch manufacturing, from surveys
circa
1970
Childs Part 1 28:3:2000 2:33 pm Page 3
1.1.1 Machine tool technology – mainly turning machines
From 1970 onwards, machine tools of new design started to be introduced in significant
numbers into manufacturing industry, with the effect of greatly reducing the times for tool
positioning and movement between cuts. These new, computer numerical control (CNC),
designs stemmed directly from the development of numerically controlled (NC) machine
tools in the 1950s. In traditional, mechanically controlled machine tools, for example the
lathe in Figure 1.4, the coordination needed between the main rotary cutting motion of the
workpiece and the feed motions of the tool is obtained by driving all motions from a single
motor. The feed motions are obtained from the main motion via a gear box and a slender
feed rod (or lead screw for thread cutting). With the exception of machines known as copy-
ing machines (which derive their feed motion by following a copy of a shape to be made)

an average. Individual time savings increase with part complexity and the number of set-
ups that can be eliminated. Centres are also much more expensive than more simple tradi-
tional machine tools and need to be heavily used to be cost effective. The implications of
this for the development of metal cutting practice – a trend towards higher speed machin-
ing – will be developed in Section 1.4.
4 Introduction
Childs Part 1 28:3:2000 2:33 pm Page 4
Machine tool technology 5
Fig. 1.4 A mechanically controlled lathe and (below) partly-built and complete views of a numerically controlled
machine with individual feed drive motors
Childs Part 1 28:3:2000 2:33 pm Page 5
The increased versatility of machine tools (based on turning operations as an example)
has been briefly considered: the freedom given by CNC to create more complicated feed
motions, both by path and speed control; and the evolution of multi-function machine tools
(centres). The cost penalty has just been mentioned. As part of the continuing scene setting
for the conditions in which metal cutting is carried out, which will be combined with
systems and materials technology considerations in Section 1.4, some broad machine tool
mechanical design and cost considerations will now be introduced – still in the context of
turning.
Figure 1.7 sketches a turning operation, in which, in one revolution of the bar, the tool
moves an axial distance f (the feed distance) to reduce the bar radius by an amount d (the
depth of cut). The figure also shows the cutting force F
c
acting on the tool, the diameter D
at which the cutting is taking place and both the angular speed W at which the bar rotates
and the consequent linear speed V (in later chapters this will be called U
work
) at the diam-
eter D. Material is removed, in the form of chips, at the rate fdV. (More detail of cutting
terminology is given in Chapter 2).

preferred linear cutting speed V. Equation (1.2b) suggests that for a constant area of cut
the required motor power should be independent of diameter cut. Observing what motors,
with their torque and power capacities, are fitted to production machine tools can give
insight into what duties the machine tools are expected to perform; and what forces the
cutting tools are expected to withstand. This is considered next.
Machine tool manufacturers’ catalogues show that turning machines are fitted with
motors the torques and powers of which increase, respectively, with the square of and
linearly with, the maximum work diameter. A typical catalogue specifies, among other
things, the main motor power, the maximum rev/min at which the work rotates and the
maximum diameter of work for which the machine is designed. Figure 1.8(a) plots the
torque at maximum rev/min, obtained from P = WT, against maximum design diameter,
both on a log scale, for a range of mechanically controlled and CNC centre lathes and
chucking turning centres (as illustrated in Figures 1.4 and 1.6 respectively). Apart from
two sets of data marked ‘t’, which are for lathes described as for training and which might
be expected to be underdesigned relative to machines for production use, both the mechan-
ical and CNC classes of machine show the same squared power law dependence of torque
on maximum work diameter.
It seems that machines are designed to support larger areas of cut, fd, the larger the work
diameter D. Not only are larger diameter workpieces stiffer and able to support larger
forces (and hence areas of cut), but usually they require more material to be removed from
them. A larger area of cut enables the time for machining to be kept within bounds. A
Machine tool technology 7
Fig. 1.7 The turning process – not to scale
Childs Part 1 28:3:2000 2:33 pm Page 7
design specification that the maximum depth of cut d should increase in proportion to the
maximum work diameter D would, from equation (1.2a), give the observed squared power
law.
Design cutting forces may be deduced from the torque/diameter relationship shown in
Figure 1.8(a). For example the lowest torque of 10 N m in Figure 1.8(a) would be caused
by a cutting force of 140 N at the diameter of 145 mm, while the upper limit around 50

cutting speeds from 215 m/min to 450 m/min. It will be seen later (Section 1.3 and Chapter
3) that speeds in the range 100 to 1000 m/min are indeed practical for turning steels with
cutting tools made from cemented carbides (tungsten and titanium carbides bonded by
cobalt), which are the workhorse tools of today.
The dissipation of up to 5 to 20 kW through cutting tools results in them becoming
very hot: 1000˚C is not unusual (this is justified later). For the tools to carry kN forces
(or rather the associated stresses, approaching 1 GPa) at such temperatures requires high
temperature strength. It is this that ultimately limits the productivity of cutting tools.
Obsolete machine tools – from the 1960s and earlier – were provided with lower power
motors (line A–A in Figure 1.8(b)) because they were designed for use with less produc-
tive tools made from high speed steels, with a lower high-temperature strength than
cemented carbides. Some modern machine tools, designed for use with ceramic tooling
and higher cutting speeds, are being fitted with higher power motors (line B–B in Figure
1.8(b)).
These ‘facts of life’ of the turning process – forces up to 2 or 3 kN and cutting speeds
up to 1000 m/min – are set by the material properties of the work and tool materials as well
as the mechanics of the process. Later chapters will be devoted to the details of why these
‘facts of life’ are so. They, and the functional versatility considered earlier, determine the
price of turning machine tools. Machines must have a sufficient bulk and mass to be stiff
and stable when cutting the high speed rotating mass of the workpiece. Figure 1.10(a)
shows, for the same machine tools as in Figure 1.8, how their masses increase in propor-
tion to motor power (the maximum workpiece lengths are in the range 500 mm to 1 m;
machine mass increases with workpiece length as well as diameter capacity). Mass turns
out to be one practical measure of value in a machine tool, the other being versatility.
Figure 1.10(b) shows the list price of machine tools (without tax) as a function of mass
(the data were gathered in 1990).
Machine tool technology 9
Fig. 1.9 The torque and power characteristics of a typical 15 kW AC variable speed motor used in CNC turning
machines
Childs Part 1 28:3:2000 2:33 pm Page 9

Childs Part 1 28:3:2000 2:33 pm Page 10
time, investment in CNC machines was growing, equally spread between turning and
milling. Post-1980, investment in mechanically controlled machines collapsed and that in
CNC turning machines held steady, while CNC milling machine investment increased to
the stage where it was twice that of turning machines. This increase was mainly due to the
influence of machining centres.
At first sight it is surprising that pre-1980 investment in substituting mechanically
controlled for CNC-controlled milling machines equalled that for lathes, because there is
less to be gained from reducing non-productive cycle times. The obvious difference
between turning and milling processes is that, in turning, the main power is used to rotate
an essentially cylindrical workpiece, with feed motions applied to the tool; whereas in
milling the main power rotates a cutting tool, with the prismatic workpiece undergoing
feed motions. Milling cutting tools have many cutting edges, and are more complicated
than turning tools (Figure 1.12) and each edge cuts only intermittently. The cost of the
tools makes it prudent to remove metal more slowly, and vibrations set up by the inter-
mittent tool contacts reinforce this. The longer cutting times make the non-productive time
less significant.
However, investment in milling machines in the pre-1980 period was not only in order
to take advantage of the reduced non-productive time due to numerical control. A revolu-
tion was taking place, not only in machine control but also in machine structure. When
mechanical feed drives were replaced by individual ball-screw feed drives, it was found
that the accuracy of the cut was no longer limited by the accuracy of the drive but by elas-
tic deflection of the milling machine frame. The introduction of CNC control led directly
to a mechanical redesign of milling machines in order to produce machines of higher stiff-
ness and hence accuracy. Figure 1.13 compares the new type of design with the earlier one.
In addition, the freedom to vary x–y feed motions simultaneously to create curved feed
paths opened up the possibilities for free-form shape generation by milling that existed
before only with difficulty.
After 1980, machining centres attacked the long set-up and tool change times associ-
ated with milling. The number of set-ups was reduced by developing machines with more

2
. For a given cutting speed, from equation (1.2b), the machine power to provide that
force would also increase as D
2
. Manufacturers’ catalogues show that milling machine
tools do have different power-to-capacity relations than turning machine tools, which can
be explained on the basis that spindle failure or deflection limits their use, as just outlined.
They also have different mass to power characteristics. However, the price of milling
machines per unit mass is similar to turning machines. All this is developed in Figure 1.16.
12 Introduction
Fig. 1.12 Examples of turning and milling solid, brazed and insert tools
Childs Part 1 28:3:2000 2:33 pm Page 12
In Figures 1.16(a) and (b) the capacity of a milling machine is measured by its cross-
traverse capacity. This defines maximum workpiece size in a similar manner to defining
the capacity of a turning centre by maximum work diameter (Figure 1.8). Figures 1.16(a)
and (b) show that torque and power increase as cross-traverse cubed and squared respec-
tively. An assumption that machines are designed to accommodate larger diameter cutters
in proportion to workpiece size yields the D
3
and D
2
relations derived in the previous
paragraph.
Machine tool technology 13
Fig. 1.13 A traditional – column and knee – design and (right and below) partly-built and complete views of a modern
(bed) design of milling machine
Childs Part 1 28:3:2000 2:34 pm Page 13
If Figure 1.16(b) is compared with Figure 1.8(b) it is seen that for given workpiece size
(cross-traverse or work diameter) a milling machine is likely to have from one fifth to one
half the power capacity of a turning machine, depending on size. This means that milling

power availability implies a much lower material removal rate capacity. It is perhaps a
saving grace of the drilling process that not much material is removed by it. This too is
taken up in Section 1.4.
1.2 Manufacturing systems
The attack on non-productive cycle times described in the previous section has resulted in
machine tools capable of higher productivity, but they are also more expensive. If they had
been available in the late 1960s, they would have been totally uneconomic as the manu-
facturing organization was not in place to keep them occupied. The flow of work in
progress was not effectively controlled, so that batches of components could remain in a
factory totally idle for up to 95% of the time, and even the poorly productive machines that
were then common were idle for up to 50% of the time (Figure 1.3). Manufacturing tech-
nology has, in fact, evolved hand in hand with manufacturing system organization, some-
times one pushing and the other pulling, sometimes vice versa.
Manufacturing systems 15
Fig. 1.15 A milling machine tooling magazine
Childs Part 1 28:3:2000 2:34 pm Page 15
In the late 1960s there were two standard forms of organizing the machine tools in a
machine shop. At one extreme, suitable for the dedicated production of one item in long
runs – for example as might occur in converting sheet metal, steel bar, casting metal, paint
and plastics parts into a car (Figure 1.17) – machine tools were laid out in flow lines or
transfer lines. One machine tool followed another in the order in which operations were
performed on the product. Such dedication allowed productivity to be gained at the price
of flexibility. It was very costly to create the line and to change it to accommodate any
change in manufacturing requirements.
At the other extreme, and by far the more common, no attempt was made to anticipate
the order in which operations might be performed. Machine tools were laid out by type of
process: all lathes in one area, all milling machines in another, all drills in another, and so
on. In this so-called jobbing shop, or process oriented layout, different components were
16 Introduction
Fig. 1.16 (a) Torque and (b) power as a function of cross-traverse capacity and (c) mass/power and (d) price/mass rela-