As can be seen from Table 12, the cutting s[peed has a major impact on the value of ‘CT’ , because an increase in cutting speed normally results in faster tool wear rates, with the tool
Trang 1neering work, then further refined over the years As
can be seen from the graph of flank wear (V B) against
time (T) shown in Fig 176a, tool wear does not
usu-ally follow a straight-line relationship’ Invariably, the
‘V-T curve’ for flank wear initially develops quickly
then settles to a moderate growth over a reasonable
time-period, then has a rapid escalation – almost
ex-ponentially – at an ‘end-point’ as it catastrophically
fails The actual plotted wear curve profile and its
as-sociated inclination angle will vary depending upon
the cutting speed selected, with individual cutting
speeds having specific wear curves (i.e see Fig 176b)
So from the graph in Fig 176b, it can be
visually-es-tablished that the higher the cutting speed utilised, the
greater the flank wear The composite graph depicted
in Fig 176c – left (i.e taking ‘standardised’ flank wear
@ times: T to T – from Graph 176b), shows that a
direct relationship exists between logarithmic time
(logT) and cutting speed (logV C) The features that
characterise this ‘straight-line’ are its position and
gra-dient, these values can be expressed through the
‘gen-eral-case’ tool formula0 developed by Taylor (1907),
as follows:
V Tα = C
‘Cutting time’ (T) here, is the tool-life of the cutting edge,
be-fore a specific amount of flank wear ‘VB’ is established
0 This ‘general case’ Taylor formula, has been expanded and
developed which defines the machining characteristics with
more mathematical rigour, including the effects of:
feed-rate; DOC; as well as component hardness, as follows: V Tα
fm dp Hq = K Tref α fref m dref p Href q Where: ‘f’ = feedrate (mm rev –),
‘d’ = D OC (mm), ‘H’ = Hardness (e.g HR C ), with ‘m’ , ‘p’ and ‘q’
are exponents whose values are experimentally-established
for the production operation, ‘K’ = a constant analogous to
‘C’ , while ‘T ref ’ , ‘f ref ’ , ‘d ref ’ , and ‘H ref’ are the reference values for
feedrate, DOC – when they are <1.0* *This 1.0 numerical value,
indicates the greater effect of cutting speed on tool life, since
the exponent of ‘V’ is 1.0 Moreover, after cutting speed, the
feedrate is the next in importance, so ‘m’ has a value > ‘p’**
**The exponent for work hardness ‘q’ is also <1.0.In reality,
there are difficulties in the application of the above equation
for practical machining operations, due to the vast amount of
machining data that is necessary to determine the parameters
of this equation – producing considerable statistical variance
In order to reduce the variability, while making the overall
equation more manageable, the DOC and hardness parameters,
reduce the equation to the following expression:
V Tα fm = K Tref α fref m
Where: ‘terms’ are the same, but the parameter ‘K’ will have
a slightly different interpretation – see the available literature
for a more rigrous mathematical treatment on the subject of
tool life (Groover et al., 2002)
The two constants (α, C), can be established
graphi-cally from the graph (Fig 176c – right) of the ‘plot-ted’ sloping straight-line gradient Hence, the value
of constant ‘α’ , can be obtained graphically from the
trigonometrically relationship of the respective values
of the ‘X’ and ‘Y’ coordinates Likewise, the other
con-stant ‘C’ , may be found by extrapolating this sloping line down to the cutting speed axis (logV C), for its nu-merical value
Tool Costs
The tool cost ‘CT’ will normally consist of the sum of
the purchase cost, grinding costs – where applicable,
as well as tool-changing cost for each machined
com-ponent In Table 12 (below), it tabulates how
tooling-Table 12 Calculating the cutting-tool cost per cutting edge
Costs for: cutting tool, edges and
Initial cost of tool = (A) Number of cutting edges per tool = (B) Tool cost per cutting edge = (A/B)
= (C)
Number of cutting edges per insert = (E) Insert cost per cutting edge = (D/E)
= (F) Machine charges per hour = (G) Tool changing time (minutes) = (H) Cost per tool change = (G x H/60)
= (I) Regrinding charges per hour = (J) Regrinding time (minutes) = (K)
= (L) Tool cost per edge = (C + F + I + L)
= (M)
Number of components per cutting edge = (N)
Tooling cost/component (i.e Cutting tool
cost per edge)
= (M/N)
= (CT)
.
Trang 2costs can be calculated, for a simple turning operation:
the method can be modified for machining centres
and for most other machining operations
As can be seen from Table 12, the cutting s[peed
has a major impact on the value of ‘CT’ , because an
increase in cutting speed normally results in faster
tool wear rates, with the tool charge per component
increasing as a result Tool costs today, now account
for only a small proportion of the total costs of
pro-duction, owing to the fact that the latest tooling can
operate at higher feeds and speeds than their earlier
counterparts When the tool costs actually rise – due
to greater wear rates as a result of increased cutting
speeds, it naturally follows that associated tool
perfor-mance will also increase
For any machining operation there exists an
‘eco-nomical tool-life’ (T e), which can be calculated from
the following formula:
Te= (
α − )(CT
Cm + tC) Economical tool life
Where:
Te = Economical tool life (minutes),
α = Slope of the V-T curve (i.e measured from
graph),
CT = Cutting tool cost per edge (i.e obtained as
de-scribed above),
Cm = Machine tool, labour, and related overhead costs
– charged per minute,
tC = Tool-changing time per minute for operation in
question*
*This tool-changing time will vary depending upon
whether the chosen cutters are of the ‘conventional‘, or
‘modular quick-change’ tooling varieties
In Fig 177a, the tool-life at ‘maximum production rate’
(T q) is shown, which is a variation of the calculation
given above for ‘economical tool life’ (Te), where the
variables are identical, but in the former case a higher
cutting speed is employed, resulting in shorter
tool-life Even though the lowest possible machining cost
per component can be calculated with the most
eco-nomical cutting speed, it is often desirable to utilise
a faster machining strategy This increased speed, will
involve supplementary costs, although it can only be
warranted if higher production output results If the
number of components per hour (P r) is plotted (Fig
177d) in relation to the cutting speed (V c), a
repre-sentative curve will result This curve is redrawn and
shown in Fig 177e, this now being a ‘composite’ of the
sum of the: machine/labour/overhead costs (Cm); with tooling cost (CT) The zenith of this curve (Fig 177e), represents the highest production rate (P rmax) While the cutting speed (V q) is associated with the peak of the curve, which is greater than the most economical
rate (V e), with the values between these two points,
representing the ‘high-efficiency range’ for a particular
operation
In Fig 177e, the additional vertical axis depicted,
represents the production rate (P r) – this being the number of components machined per hour, it can be calculated in the following manner:
Pr = 60 (1 – tC/T)/tp
Where:
tC = Tool-changing time per minute for operation,
T = Tool life,
tp = Total time per component (i.e including:
ma-chining, handling and down-tome)
The relationships mentioned above represent theoreti-cal associations So, some caution should be applied when using these factors and they need to be treated
as a ‘starting-point’ only for both the values and trends represented here Moreover, they are subject to vari-ability, due to the complex relationships and interac-tions found during machining operainterac-tions
7.7.3 Return on the Investment (ROI)
As an alternative approach to the above mentioned cutting tool costs and production output interactions,
is to relate any productivity improvements to both the actual machinery cost and the total invested capital – to achieve this level of manufacturing yield In the previously described machinability tests, the work seldom considers rates of production, or relates the findings to actual increases in the total economics of production
A significant fiscal argument is that any figures obtained from such testing, should highlight the ‘im-proved’ ROI, which can be obtained by any manu-facturing company utilising the latest tooling, in conjunction with the application of efficient cutting conditions
The following simple formula can be utilised to cal-culate the ROI for a particular: production operation; machine tool; machining cell; etc.:
Trang 3ROI = (TS)(MC)/(MTI)
Where:
TS = Time savings per year (i.e in hours),
MC = Machine tool charge (per hour),
MTI = Machine tool investment
In this section, only a superficial treatment has been
given to the economic argument relating associated
capital equipment costs and their overheads, to
out-put productivity More intricate and sophisticated
eco-nomic models can be obtained in the literature
7.8 Cutting Force
Dynamometry
Introduction
During machining operations, plastic deformation, friction between the tool and workpiece, together with micro-fractures and -fissures occur These mechanical phenomena produce measurable cutting and forming forces with very high-frequency acoustic emissions (AE) The application of AE in association with other
Figure 177 The correlation of typical manufacturing cost factors: machining costs, together with
their resultant productivity [Courtesy of Sandvik Coromant]
.
Trang 4sensors, such as: force transducers, accelerometers can
be coupled to neural networks to give a psuedo-form
of articial intelligence (AI) – more will said relating to
cutting tool monitoring and analysis in a succeeding
chapter Many of the early attempts at cutting force
monitoring were by using several strategically-placed
resistance-type of strain-gauged mechanical elements
These strain-elements were designed so that at a
par-ticlur portion of their geometry they could either
minutely: buckle, bulge, or twist – well within their
elastic limit At the positions of greatest sensitivity
on these mechanical elements, strain-gauges were
se-curely placed and wired into a ‘Wheatstone bridge
re-sistance circuit’ , which as the gauges distorted they
changed their micro-resistance, which could then be
fed through suitable instrumentation These
strain-gauged elements could be calibrated against ‘known’
mechanical devices (e.g ‘proving-rings’, or similar),
‘Wheatstone bridge resistance circuits’ – invented by Sir
Charles Wheatstone: circa 19th Century, for accurately
measuring resistance in an electrical circuit Simply, a ‘bridge
circuit’ consists of: four resistances; a galvanometer; with a d.c
power supply In essence, in these highly sensitive resistance
‘bridges’ they are used to detect minute changes in strain gauge
resistance A typical ‘full-bridge’ consists of the four resistors:
‘R ’; ‘R ’; ‘R ’; ‘R ’; suitably coupled to the galvanometer and
d.c supply Typically, the most simple strain-gauged circuit
would consist of: a resistance ‘R ’ which here for argument,
is the gauge used for strain measurement Resistance ‘R ’ is
a second strain gauge which here, could remain at constant
resistance The other ‘half of the bridge’ , resistances ‘R ’ and
‘R ’ are variable resistors which by adjustment, are utilised to
‘balance’ and ‘rebalance’ the bridge (i.e employed to reduce
the current across the galvanometer arm to zero) Therefore,
when the ‘bridge’ is ‘balanced’ , the ratio of the gauges and the
variable resistances are equal, thus:
R/R = R /R
∴ R = R × R /R (Collet and Hope et al., 1974)
‘Proving-rings’ , are laboratory calibrated and certificated
me-chanical device, normally consisting of: a steel ring; dial gauge
and loading pads It is usually employed in the calibration of
force-measuring systems – only within its maximum
permis-sible load Such ‘proving-rings’ can be manufactured for either
high sensitivity – for strain-gauge applications, or for more
robustness – when calibrating tensile testing machines In
practice, the steel ring if compressed, allows the diameter to
minutely contract in direct proportion to the applied force,
with its deflection accurately measured by a dial gauge located
across the centre of the internal portion of the proving-ring’s
diameter Changes in the dial gauge readings, can be converted
to force measurement by means of a suitable calibration graph,
or more simply, by multiplying the gradient of the graph – as
the graph produced has a straight-line relationship (Ramsey
et al., 1981)
allowing the resolved cutting forces during subsequent machining to be data-logged, for suitable in-depth analysis by the user Strain gauge dynamometers based upon the Shaw and Cook (1954) model, normally re-quire several design criteria to be addressed, if they are
to perform satisfactorily, these factors are:
1 That the dynamometer should have a sensitivity of 1% of its mean designed force,
2 Such a dynamometer requires a natural frequency
of at least 4 times the ‘forcing frequency’ ,
3 The strain-gauged circuit elements should produce the minimum of cross-coupling (i.e ‘cross-talk’ is
<2%) – when calibrated
NB This latter point, can be assessed by a range
of calibrated ‘proving rings’ , or ‘torque arms’ – if required to measure torque effects in the circuit, thegraphical calibration should indicate: both
plot-ted linearity and also be coupled to minimal
hys-teresis Today, most multi-axes cutting force dynamometers
utilise sensing elements, based upon the piezoelectric
effect and these ‘active sensors’ , will now be more
fully discussed
Piezoelectric Dynamometers
These high-rigidity force transducers provide an elec-trical output signal under the effect of direct element deformation Hence, element deformation can be kept several degrees of magnitude smaller than that of the
‘passive systems’ – such as those utilising strain-gauged
elements With most ‘dynamic systems’ such as those
employing quatrz-based elements, their inherent de-gree of rigidity and a broad measuring frequency range creates smaller measurement interference and
‘Hysteresis loop’ is an area bound between the loading and
unloading paths (i.e typically found in a stress-strain curve), indicating energy dissipation, or damping
‘Piezoelectric effect’ , was discovered by Pierre and Jacques
Curie in 1880 A piezoelectric material (e.g quartz, or Ro-chelle salt) is a special kind of insulator which, if compressed along one of its axis, acquires an electrostatic charge on the material’s opposite faces Hence, when such material is ac-curately and precisely cut to the desired shape, it acts as a piezoelectric transducer, hence its input is force and its output
is charge These piezoelectric elements, can be suitably posi-tioned and arranged and thus, used in dynamometers for dy-namic cutting force measurement.
Trang 5as a result, offer extremely fast process response, in
comparison to those of the of the ‘non-rigid type’
– having long measurement paths (i.e found in
con-ventional strain-gauged elements) Unlike ‘passive
sys-tems’ utilising strain-gauges, it is virtually impossible
to perform static measurements by using piezoelectric
transducers, even though an electric charge delivered
under static load can be registered, it cannot be stored
for any realistic time period
The design of most of today’s multi-component
dynamometers use piezoelectric elements which are
quintessentially comprised of a stack of quartz discs,
or plates with accompanying electrodes being installed
into a stainless steel housing (Fig 178ai and aii) Every
disk, or plate has been precisely cut in a definite
crys-tal axis, with their sensing orientation coinciding with
that of the axes of the force components to be measured
(Fig 178) In practice, the electrodes can collect the
‘charge’ on their respective quartz disk’s surfaces, these
being suitably ‘hard-wired’ to their appropriate and
corresponding plug connectors As shear forces can
only be transferred by frictional contact, a certain
minimum of friction is essential between the quartz
disks, electrodes and housing Depending upon the
shear force magnitude (i.e measured) a more-or-less
high pre-loading of the system must be generated by
a pre-loaded bolt This act of preloading the system is
absolutely essential and is usually undertaken when
the force transducer is initially installed into the
dyna-momoter by the manufacturer
A typical three-component dynamometer (Fig
178ai), consists of sensors with two shear quartz pairs
– namely for ‘F X ’ and ‘F Y’ , plus one pressure quartz pair
– for ‘F Z’ , assembled in a suitable housing Each quartz
pair has two identical plates stacked with a common
‘Piezoelectric storage’ – for static loading, this cannot be
achieved because an insulating material would have to have
infinitely high resistance, together with amplifiers that are
perfectly free from any form of leakage and ‘non-operate
cur-rents’ , with an amplification factor of infinity! The drift in
today’s charge amplifiers is below ±0.03 pC s– In static
mea-surements performed with ‘load washers’ , this means that in
practice, the zero-shift is limited to within ±10 mN s– For
example, if a static load of 10 kN is measured for one
min-ute, then after this time, the result of the measurement can
only be invalidated by a maximum ±0.6 N, that is by ±0.006%
Hence, it is a simple task to piezoelectrically measure large
forces for minutes, or hours, but small forces can only be
mea-sured ‘statically’ for very short time-periods Thus,
piezoelec-tric transducers are normally referred to as being: ‘quasistatic
measurement elements’.
electrode between them, offering twice the sensitivity This three-component dynamometer is constructed with four of these three-component sensors mounted
in parallel between the base and top plate, being as-sembled with a high preload Given that the outputs from the four sensors are in the form of an electrical charge, they are able to be interconnected within the dynamometer body With this particular sensor ar-rangement, it is possible to obtain up to eight charge outputs from the dynamometer
The four-component dynamometer shown in Fig 178aii, has several shear quartz plates arranged in a cir-cle (i.e top circular element), with their sensitive axes being tangential, allowing an element to be formed
responding to a moment ‘M Z’ In this dynamometer, the four-component sensor is obtained by assembling
this element (i.e ‘M Z’) in a housing, together with two
shear quartz pairs – for ‘F X ’ and ‘F Y’ , plus one pressure
quartz element pair for ‘F Z’ So, by mounting this sen-sor assembly under a high preload between the base and the top plate, it results in a four-component dy-namometer, capable of simultaneous measurement of:
‘F X ’ , ‘F Y ’ , ‘F Z’ and ‘MZ’
For both accurate and precise machinability and data-gathering assessment, these invaluable piezoelec-tric dynamometers offer the following advantages and typical properties:
• High rigidity (‘cx ’ , ‘c y’: >1 kN µm– , ‘c z’: >2 kN µm–),
hence producing a high natural frequency (‘f o’: ≈3.5 kHz),
• Wide measuring range (-5 to 10 kN),
• Extreme linear sensitivity (‘FX ’ , ‘F Y’: ≈-7.5 pC N–,
‘F Z’: ≈–3.7 pC N–) and virtually free from
hyster-esis (≤0.5%FSO),
• Minimal cross-talk (≤±2%),
• Environmentally-protected (IP67), typically sealed
against of both cutting fluids and debris ingress
NB Such high-quality apparatus is not cheap to
purchase, therefore it should be carefully main-tained and looked after, to ensure an extremely long life and fail-safe operation
Piezoelectric dynamometers can have their quartz sensing elements arranged to fit into platforms (Fig 178b), for fitment onto a turning machine tools turret with the cutting tool suitably arranged for turning op-erations These type of dynamometer platforms can be located on the machine tool’s bed, with the workpiece clamped onto the dynamometer for milling, drilling,
or grinding operations to be used for specific types of machinability investigation In the former case, it is
Trang 6Figure 178 Multi-axis non-rotating dynamometers, used for: milling, drilling and turning
experimental data-gathering and analysis [Courtesy of Kistler Instrumente AG]
.
Trang 7not possible to index the turning centre’s turret, due
to the nature of the electrical couplings to the
plat-form, but this problem can be overcome by mounting
a different dynamometer configuration, situating the
sensing equipment within the turret – as depicted in
Fig 179a Here, the installation of an acoustic emission
sensor (AE) behind the turret in combination with
a multi-component force sensor mounted in the
tur-ret’s pocket – this force equipment having previously
required the necessary of preloading which was
pro-vided by a suitable ‘preload wedge’
In Fig 179b, are exhibited the measuring results
from the sensor installation decribed in Fig 179a – for
a longitudinal (external) turning operation, with the
cutting force components and the AE signals being
simultaneously recorded The resulting graphs
pro-duced in both Figs 179bi and bii, show the AE rms
and force signals in the case of a tool breakage The
tool breakage can be readily seen in both signal traces
Figs 179biii and biv, show the AE and force sensor
sig- Acoustic emission sensors (AE), in metal machining
applica-tions usually capture frequencies in the range of 50 kHz to
>1 MHz in range, this being a usual aid for any form of
in-process monitoring operations By using a combination of AE
and force monitoring, this has been shown to be a means of
condition monitoring of the cutting tool’s state – more will
be said on this topic later In metal cutting operations AE
oc-curs due to plasto-mechanical processes of crack formation
and chip removal, in combination with surface friction Any
form of tool wear alters the contact surfaces between the tool
and workpiece, influencing and increasing the AE signal
in-tensity Hence, advanced warning of potential tool breakage
sometimes results in the appearance of micro-fissures in the
tool, which cause an escalation of the AE signals – allowing
a basic form of tool and process monitoring to be achieved
AE generation in metallic machining operations, can extend
over frequencies of several MHz, although the signal intensity
is normally very low and diminishes with increasing distance
from its source Any form of machine vibrations and
inter-ferences from the local environment introduce signals from
a low frequency range, meaning that any form of significant
analysis is normally only possible above 50 kHz Machine tool
interference sources are usually the result of either electrical,
or hydraulic main and feed drives, as well as from bearing
noise, spindles and gears These unwanted interferences can
be suppressed by utilising suitable high-pass filters, or
alterna-tively a well-designed AE sensor(s), with inherent high-pass
frequency characteristics
‘Root mean square’ (rms), is a measure of the effective mean
current of an alternating current Its actual rms value is
de-rived from the power dissipation by an ac current.
nals respectively, on the ‘over-turning’ of transversal holes present in the external turning of the workpiece Hence, the interrupted cut can clearly be seen peri-odically in the resultant force traces In Fig 179biii, the AE rms signal shows this interference, albeit not very well pronounced, unlike that of the force trace produced in Fig 179biv, where a definite noise spike can be seen This combination of two complementary sensing elements and their sensor signals, allows the reliable detection of a process fault, such as tool break-age detection
Until approximately the mid-1990’s, commercial versions of cutting force monitoring equipment for the measurement of a rotating cutting tool, or an edge was not readily available for: drilling, reaming, tapping and milling applications A major advantage of these rotating cutting force dynamometers, is that they can
be used for multi-axes contour milling applications,
or simply for an investigation of a discrete tool’s cut-ting edge geometry and its anticipated machining per-formance An early version of such a rotating cutting force dynamometer, is depicted in Fig 180a
In Fig 180b, graphs have been produced showing the cutting force and torque results respectively, pro-duced by the rotating cutting force dynamometer In-terest frequently centres on the forces and moments acting on the rotating tool A rotating cutting force dynamometer (Fig 180a), allows measurement of
three orthogonal forces: ‘F X ’ , ‘F Y ’ , ‘F Z’ , together with
the moment ‘M Z’ The data measured by the rotating dynamometer occurs via miniature charge amplifiers, which are then transferred by telemetry to an appro-priately positioned stationary antenna The telemetry involves a bi-directional transmission, with measured data being transmitted to the ‘stationary side’ of the monitoring system and any control commands for the integral charge amplifiers transmitted to the appropri-ate section of the rotating dynamometer The power supply to the electronics in the rotor, occurs by the same antenna, but having a different carrier frequency
to that of the data transfer Typical resultant signals produced by the rotating dynamometer are shown in Fig 180b and have been ‘zoomed’ for the investigation
of a single drill’s cutting edge
Cutting force dynamometers of various configu-rations, are invaluable tools for any form of in-depth machinability study, as they indicate the precise condi-tions at the cutting tool’s edge(s), in a truly dynamic situation All dynamometers that are purchased from the manufacturer must come with an appropriate
Trang 8cali-Figure 179 A Rotating Cutting-force Dynamometer (RCD), utilising piezoelectric sensor systems
[Courtesy of Kistler Instrumente AG]
.
Trang 9Figure 180 A Rotating Cutting-force Dynamometer (RCD), utilising piezoelectric sensor systems
[Courtesy of Kistler Instrumente AG]
.