9.8(a) shows a single locus for fracture,
Figure 9.8(b) shows a family of surfaces T
to U. sc is a critical stress above which
fracture 280 Process selection,
improvement and control Fig. 9.8
Fracture criteria of cutting tools: (a)
Shaws (1984) determinis

or the set of planes h (V, f, di ) = hc. Since
the constants n1, n2 and n3 of Taylors
equation (4.3) have the relation, n1 < n2
< n3 e.g. n1/n2 0.77 and n1/n3
0.37 for HSS tools (Stephenson and
Agapiou, 1997) tool life is most
sensitive to cutting speed

mach (1 n1) Cct ct + Ct d =
( ) n3n1 ( )
n3n1 ( ) n3n1 f n2(n3n1)
Copt Cct load Cc Cn1 (9.29a) Since the
exponents of Taylors equation have
relations n1/n2 0.77 and n1/n3 0.37
for HSS tools, and exponents of the force
model (equations (9.2b), (9.25b) have

290 Critical constraints A constraint, the
limit line of which contains the optimum
point MV or Md, is called a critical
constraint and the limit line a critical
line. Two critical constraints are possible
for each feasible domain in the ( f, d )
and (V,

the assumption that they are sufficient,
are reviewed and developed in Section
9.3.1 before their supplementation by
subjective, fuzzy, optimization, in Section
9.3.2. Tool selection methods (by
heuristic means) and simultaneous
selection of tools and cut

machining space. Starting with the
cheapest Ct combination, they therefore
checked whether any of the constraints
C2 . . . C11 (above) were critical for the
next cheapest. If they were not, the
selection procedure was moved on to
level 5, with the current

and workpiece) to create vibrations
during processing that are known as
chatter. Chatter leads to poor surface
finish, dimensional errors in the
machined part and also accelerates tool
failure. Although chatter can occur in all
machining processes (becaus

a given cutting situation. Figure 9.16
shows the machining of a slender
workpiece, an example for which COATS
has been asked to recommend tool
holders and cutting inserts. In this case,
the reduction of radial force is required
to decrease workpiece defle

magnitude of its amplitude-to-force
ratio, and the phase between the
amplitude and force, vary with forcing
frequency. Figure 9.9 represents a
possible Gs in a polar diagram. It also
shows the compliance transfer function
Gc of the cutting process when th

(9.15d) f where cf is a constant. Chatter
vibration can occur when the chip
formation frequency is close to one of
the natural frequencies of the structure.
Hence, the ratio of cutting speed to feed
that should be avoided in that case is
given by f ni V f

otherwise a large nose radius is selected
to increase strength and wear resistance;
and an insert of lowest acceptable
tolerance is always chosen because of
low cost. Figure 9.18 shows an example
of rough turning, for which the optimum
tool and machining

Ni , is F F1 b F F1 b pf = 1 exp [
( ) ] 1 exp [ a ( ) ]
(9.14b) F0 Fh F1 where Fl and Fh are
forces with a low and high expectation of
fracture after Ni impacts and F0, a and b
are constants. Alternatively, and as
considered further in Section 9.3, pf m

Each segment of the closed lines
represents a limit due to one constraint.
Lines numbered C1 to C10 represent the
corresponding constraints described by
equations (9.18) to (9.26). In the case of
roughing operations, if n passes are
chosen for removing th

be found elsewhere (Shaw, 1984; Tlusty,
1985; Boothroyd and Knight, 1989). The
most commonly studied form of chatter
is known as regenerative chatter. It can
occur when compliance of the machine
tool structure allows cutting force to
displace the cutting

picks up every rule that is even partly
relevant to them. This is the first step of
inference, named matching. Next,
according to some strategy, one rule is
selected from the matched rules. This is
the second step, deciding which is the
most relevant rule

and acoustic emission signals
sometimes in the form of their Fourier or
wavelet transform spectra (or expansion
coefficients in the case of digital wavelet
transforms) as will be considered in
more detail in Section 9.4. In the
absence of a quantitative

type of chip breaker described in Section
3.2.8. Tool geometry and stock
allowance. The depth of cut and feed are
limited by tool geometry and the stock
allowance as well: (C2) d a1l c cos y
(9.19) (C3) f a2rn (9.20) (C4) d da
(9.21) where a1 and a2 are c

finish, avoidance of chatter and excellent
chip control. The dependence of
optimization on heuristic knowledge
implies that the objectives and rules of
machining may not all be explicitly
stated. In that sense machining is a
typical illdefined problem. Re

seen that there is an intermediate space
with feasibility 0 < f m < 1 between the
fully feasible (f m(x) = 1) and unfeasible
(f m(x) = 0) spaces. Like constraints, the
objective function (9.16c) is represented
by a fuzzy set R 0 with membership
functions:

n1 CcC 1 n1 Vopt = (
) (9.28b) 1 n1
(Cct ct + Ct )f mach f 1/n2 opt d1/n3 opt
It is assumed that the optimum point Md
(Vopt, f opt) is not outside the feasible
domain. The insertion of equation
(9.28b) in Taylors equation (4.3) and
equation (9.16c) lead

expert system for the design of turning
operations, with three modules for tool
selection, cutting condition design and
learning and given the name SAM
(Smart Assistant to Machinists) is shown
in Figure 9.20 (Chen et al., 1995). The
systems inputs Optimiz

improvement and control Childs Part 3
31:3:2000 10:38 am Page 284 t mach t
mach t total = t load + + t ct
f mach T (9.16d) pDLda 1 V1/n1f
1/n2d1/n3 = t load + ( + t
ct Vfd f ) mach C Constraints
For a given combination of tool,
workpiece and machine too

component and maximum resultant
force permissible for factor i,
respectively, and mincfw_. . . is the
minimum operator. For tool breakage,
equation (9.14a) may be used for a set of
deterministic constraints. Other limits.
There may be other constraints,
d

recommendation exists. The elimination
and eventual search strategy is split up
into six stages or levels, as listed in Table
9.2. Levels 1 to 3 and 6 use heuristic
knowledge and levels 4 and 5 are
modelbased. Starting with level 1, only
tool holders that

described in this section are if (a
condition is met) then (take an action)
rule-based (or production) expert
systems. They all have three essential
elements: a workpiece description file
(or working memory), to hold a
description of a required shape chan

tool geometrical design and tool making
technologies decrease the cost of
consuming cutting edges Ct . This results
in increases in the optimal cutting speed.
The lines of minimum cost LcV and Lcd
are respectively shown schematically in
Figures 9.11(a) an

(as considered in Appendix 3). The
temperature distributions in Figure
9.7(a) and the flank contact
temperatures and stresses in Figure
9.7(b) Process models 277 Childs Part 3
31:3:2000 10:37 am Page 277 have been
obtained from an FDM simulator, Q
FDM, of

y)kd] where kd is called the cutting
stiffness. This periodic force will in turn
cause periodic structural deflection of
the machine tool normal to the cut
surface. If the amplitude of the
deflection is greater than a0, the surface
waviness will grow and

y ymax to give a sub-total score S(y):
S(y) = si (y) (9.33b) i To continue with
the same example, COATS also has rules
for the normal relief angle gn, normal
rake angle an, cutting edge inclination
angle ls , tool included angle er (er = p/2
+ y k r ), n

load + ( ) t max (9.23b) VFd
fmach Maximum rotational speed Nmax.
This limits the cutting speed. Writing
spindle speed as Ns : (C8) V = 2pDNs
2pDNmax (9.24) Maximum spindle
motor power Plim. This also provides
constraints (C9) FcV Plim (9.25a) When
a reg

route of reasoning, ending up with a
right answer. In the second case,
methods of compromise are necessary
and different experts might reach
different answers. They also, like experts,
have a range of points of view. Some
(most simple) systems are workpie

VNMG160408 53 P10 38 0.40 0.70 4 11
17 35 0.8 Childs Part 3 31:3:2000 10:39
am Page 298 system, only that holder
with the stiffest clamping system is
considered further (unless the clamp
interferes with the work, when the next
stiffest is chosen). At leve

of this type has already been considered
in Chapter 3, supported by Appendix 5,
to relate a tools required cutting edge
included angle to its materials
transverse rupture stress. A more
detailed approach is to estimate, from
surface contact stresses obtai

tool do?): the first and last examples just
considered are at the extremes of the
span; while COATS offers a balanced
view. The range of skills covers
monotonic and non-monotonic heuristic
and rational reasoning. It is a real
problem to replace real exper

rule, the tool selected and, as a result of
its action, the start and end features of
the machined plate, i.e. hole shape, hole
diameter and surface finish. The tools
selected are, in operation order, a centre
drill 2 mm, two drills 11.7 mm and
19.5 mm, a