7.6 Machining Temperatures Ever since Taylor in 1907, recognised that elevated tool and workpiece temperatures in metal cutting played a crucial role in influencing tool edge wear rates,
Trang 1Figure 169 How the feedrate influences the machined
cusp/surface roughness value ‘Sm’ and its affect on the
wavi-ness parameter ‘Δq’, plus surface topography of actual
nose radii [Courtesy of Joel (UK) Ltd.]
Trang 2the considerably larger effective tool nose radius,
act-ing like a ‘wiper-blade’ blendact-ing-out and obliteratact-ing
the surface’s cusps This technique of utilising a large
tool nose geometry has traditionally been used by
pre-cision turners to improve the overall surface finish
7.5.3 Manufacturing Process
Envelopes
The principal features of manufacturing process
en-velopes and indeed, for many amplitude distribution
curves is that they can be approximated by the
so-called ‘beta-function’ – ‘β’ (Fig 170a) Here, the
func-tion has two parameters that are independent of one
another enabling them to be used as a means of
sur-face characterisation The notation ‘a’ is the allocated
weighting for the profile ordinates measured from the
lowest valley and above, with notation ‘b’ being given
to weighting the profile from the highest peak down
Hence, peaks and valleys have accordingly different
weights One of the problems that has arisen from
util-ising this technique for a topographical profile, which
has somewhat discredited them for certain
applica-tions, is how and in what manner can one determine
‘a’ and ‘b’
The ‘beta-function’ is normally defined within a set
range of: 0→1, being expressed in the following
man-ner:
β (a, b) =�
z a−(a − z) b−dz.
If by changing the range of the ‘beta-function’
equa-tion above, from: 0→1 to Rp + Rv, or indeed with that
of Rt, then substituting σ (i.e the standard deviation
of the distribution) with Rq, the beta-function
param-eters ‘a’ and ‘b’ become:
a = Rv (Rv Rp – Rq/Rt Rq)
b = Rp (Rv Rp – Rq/Rt Rq)
The fact that any dominant peak, or valley within the
assessment length is only raised to a unit power,
in-fers additional stability over the ‘skewness/kurtosis
ap-proach’ The problem with this ‘beta-function’ method
is in accurately determining ‘sound’ results from the
Rv and Rp, which confirms the difficulty that
obtain-ing information from peak/valley measurement and
then deriving valid information is fraught with
com-plications In Figs 170: ‘ai’ it is symmetrical; with ‘aii’
being asymmetrical; for their respective
‘beta-func-tions’ , these relationships are based upon a class of
sta-tistically-derived ‘Pearson distributions’ In the
sym-metrical case (Fig 170ai) the skewness equates to zero; conversely, for an asymmetrical series of results (Fig 170aii), skewness can be either positively, or negatively skewed (i.e see Fig 164bii) Nevertheless, even allow-ing for these limitations, an example of the groups of manufacturing process envelopes for a range produc-tion processes is illustrated in Fig 170b Here, the pro-duction processes can be simplistically classified and grouped into either a ‘bearing’ , or ‘locking’ surface topography The ‘bearing-/locking-groupings’ indicate that certain production processes can achieve specific functional surfaces for particular industrial applica-tions These ‘groupings’ (Fig 170b), also indicate that the general classifications are less distinct than might otherwise be supposed, as certain processes can be provide either a ‘locking’ , or a ‘bearing’ surface condi-tion – termed ‘intermediate groupings’ Typical of such
an ‘intermediate group’ are the P/M drilled compacts
One reason for this is that any P/M ‘secondary ma-chining’ often utilises twist drills, which may produce
‘Pearson product moment correlation coefficient’* – to give
it its full title, is a statistical association utilised when a ‘rela-tionship’ exists between several quantities and it is a measure
of the extent of this affiliation, thus producing its ‘correlation coefficient’ which can then be utilised
*For example, having a sample of pairs of observations ‘x’ and
‘y’ , the value ‘r’ of this ‘Pearson coefficient’ , is given by the
‘generalised formula’ , below:
r = Σ(x – x ) (y – y) /√ Σ(x – x) Σ(y – y)
(Bajpai, et al., 1979):
The calculated ‘Pearson coefficient’ should lie either close
to –1, or +1 If the calculated value is close to –1 then the
‘straight-line trend’ is in a downward direction, conversely, if the calculated value is close to +1 then the ‘straight-line trend’
direction is upward If the value is close to zero (0), then no
correlation exists, so the pairing of the data is disparate and
cannot be utilised With calculated data that is reasonably
close to either –1, or +1, a ‘regression line’ (i.e using linear regression) can be calculated based upon the general straight-line formula:
Y = a + bX
Where a ‘regression line of Y on X’ for the two constants ‘a’ and
‘b’ respectively are:
b = nΣxy – (Σx)(Σy)/n(Σx) – (Σx) a = Σy – bΣx/n Where a ‘regression line of X on Y’ for the two constants ‘a’ and
‘b’ respectively are:
b = nΣxy – (Σx)(Σy)/n(Σy) – (Σy) a = Σx – bΣy/n
NB The ‘regression line’ being the equivalent of the ‘least
squares line’ , allows data on each axes to be compared – with some degree of confidence.(Wild, et al.,1995)
Trang 3Figure 170 The ‘beta-function’ and typical ‘manufacturing process envelopes’
.
Trang 4a ‘saw-toothed profile’ to the hole’s surface, along with
pores in the compact that are open to the ‘free-surface’
of the hole The hole topography may have this
‘saw-toothed effect’ present, it being a combination of the
drill’s partial lip and margin occurring at the feed rev–
periodicity, formed by the drill spiralling-down and
around the hole’s periphery Hence, the drill’s passage
creates a positive skewness via drilled ‘saw-toothed
cusps’ , while the pores can introduce negative
skew-ness – creating a potential ‘intermediate group’ to the
manufacturing process envelope groupings
7.5.4 Ternary Manufacturing
Envelopes (TME’s)
In machining operations the dominant factor that
in-fluences surface topography has been shown to be the
tool’s feedrate In Fig 171, the feedrate, in
conjunc-tion with the principal factors such as surface texture
(Ra) and roundness (i.e least squares circle – LSC), are
utilised to define the limits for these ‘Ternary
manu-facturing envelopes’ (TME’s) By using such diverse
factors as: surface texture, roundness and processing
parameters (feedrate), for the major axes on the
ter-nary graph, enables the surface to be characterised in
a unique manner Such TME’s differ quite
consider-ably from the more usual and restricted
‘manufactur-ing process envelopes’ alluded to in the previous section
– the skewness and kurtosis axes of the manufacturing
envelopes, might otherwise mask crucial information
The ‘TME approach’ gives a psuedo three-dimensional
representation on its ternary axes, which can be
ex-ploited to illustrate how the influence of changing a
parameter – such as feedrate – modifies the
relation-ship of the associated surface texture and roundness
values for the final machined result
As an example of the effectiveness of this TME
ap-proach to the complex problem of machining data
analysis, Fig 171 has been drawn from an actual
machinability trial If one observes this TME graph
closely for a pre-selected range of turning and boring
processes, indicated in Fig 171, with specific reference
here, to turning operations – by way of illustrating
the TME’s expediency The TME shows how – for the
turning operations – at low feedrate (0.10 mm rev–)
the surface texture is closely confined to a relatively
small spread of values – nominally around 0.5-1.5 µm
Ra, whereas its associated roundness lies between
approximately 5 and 50 µm LSC As the feedrate
in-creased in an arithmetic progression to 0.25 mm rev–, the range of the surface texture bandwidth propor-tionally expanded to 1.5 at approximately 5-6.5 µm
Ra, with a corresponding roundness ranging from 8 to
48 µm LSC, giving a proportional bandwidth of 1.6 As
the feedrate was raised even higher, to 0.40 mm rev–,
it was not surprising to note that this also produced increases in both the surface texture and its propor-tional bandwidth, with similar values with respect to its roundness These ‘machinability and metrology trends’ allow examination of both the bandwidth vari-ability and the affect of different feedrates on other disparate factors – such as its machined roundness Similar trends occurred for the boring operation, but here only two feedrates were employed, by applica-tion of this analysis technique via the ‘TME-approach’
to a concise machinability trial, complex analysis of the TME is possible The pseudo three-dimensional graph, offers perhaps an unusual insight into the mul-tifaceted inter-relationships that exist after workpiece machining The TME shows that simply examining one metrological parameter in isolation to those that could affect it, may mask vitally important relation-ships and trends that would otherwise remain unseen
By careful selection of the parameters for the respec-tive axes, perhaps based upon the feedrate (i.e here, normally situated along the X-axis), allows an appre-ciation of the whole surface at any instant along the three graph’s axes
7.6 Machining Temperatures
Ever since Taylor in 1907, recognised that elevated tool and workpiece temperatures in metal cutting played
a crucial role in influencing tool edge wear rates, the subject has been one of intensive study Moreover, that the tool/chip interface temperature has a control-ling influence on the rate of crater wear and the fact that tool life can be drastically curtailed by these in-duced machining temperatures, as such, the topic has received considerable research attention Here, space will only allow a brief resumé of this complex temper-ature-induced machining problem
During metal cutting in particular, there are sev-eral temperature effects that need to be considered In Fig 51, an orthogonal single-point cutting operation
is schematically illustrated, indicating the distribution
of heat sources within the three deformation zones In
Trang 5Figure 171 ‘Ternary manufacturing envelopes’ for the production processes of turning and boring,
axes: feedrate, roundness and surface texture
.
Trang 6particular, the heat generated in the main ‘body’ within
the cutting region via both the primary and secondary
zones is a result here, of the workpiece’s plastic
defor-mation Still more intensive heat is generated at the
tool/chip interface – along the rake face, with the
ma-jority of heat being swept away with the chips, while
the remainder of heat is either conducted through the
tool, or conducted/convected into the workpiece
As-suming that no coolant application is present in the
machining operation, then any heat loss to the
ambi-ent air becomes insignificant An equation has been
developed that governs the temperature distribution –
via its isothermal gradients – in machining (Fig 172),
this being an ‘energy-based equation’ as follows:
ρC (∂T�∂t + V � ∇T) − k∇T − ˙q =
(Source: Tay, et al., 1993)
Therefore, in steady-state machining operations, the
transient term will disappear and at the region of the
tool (i.e insert) only the conduction term remains
∴ Rate of heat generation (˙q) = σ ˙ε
Where: ‘σ’ was obtained from an emprical function of:
‘ε’ , ‘˙ε’; plus ‘T’
NB This rate of heat generation only exists within the
primary and secondary deformation zones
By way of example of how the temperature
genera-tion/distribution occurs in orthogonal cutting, in the
more-easily understood ‘Boothroyd machining model’
(i.e being in a slightly modified form – by the author),
this workpiece material is in a state of ‘continuous
motion’ during cutting (Fig 172) If specific points
are selected to show how temperatures occur as they
pass along/through these deformation zones then,
the points: ‘X, Y and Z’ can be considered for special
observation So, as the workpiece material enters the
cutting region at point ‘X’ , it begins to move toward
the cutting insert It approaches and passes through
the primary deformation zone where it is heated-up
until it leaves this zone, it is then swept-away by the
formed chip Equally point ‘Y’ , passes through both
the primary and secondary deformation zones (i.e
see Fig 51 for these deformation zones) and
contin-ues to heat-up until it leaves the secondary
deforma-tion zone In both of the above cases, these points (i.e
namely: X and Y) are cooled as heat is conducted into
the chip’s body (as it exit’s the cut), where it eventually achieves a uniform temperature right the way through Prior to this occurring, the maximum temperature occurs along the cutting insert’s rake face, some dis-tance from the actual cutting edge (i.e see Fig 172)
Conversely point ‘Z’ , which remains attached to the
workpiece, is heated by conduction from the primary deformation zone and some heat is also conducted from the secondary deformation zone into the body
of the cutting insert, while the tertiary deformation zone will also impart some heat into the machined surface of the workpiece
Many thermal and thermographical techniques have been developed over the years to obtain accurate isothermal temperatures within the: cutting zones: tool/insert interface plus rake face vicinity; together with the machined surface region of the workpiece Moreover, ‘indirect methods’ have been utilised to obtain similar thermal historical data from within these dynamic and harsh environments, but only one
of these techniques will be mentioned in the next sec-tion
7.6.1 Finite Element Method (FEM)
The popular approach today, to obtaining ‘simulated’
thermal data is by employing the ‘Finite element method’ (FEM), to calculate temperature distributions
in the vicinity of the cutting regions (Fig 173) Typical
of this approach and worth mentioning in some de-tail, was that conducted and described by Tay (1993), where he experimentally-obtained information re-garding: velocity, strain and strain-rate distributions,
by utilising a printed-grid and quick-stop technique The rate of heat generation within the primary defor-mation zone was determined from the equation: (˙q) = σ ˙ε
From the deformed grid pattern (Fig 173a), the ac-tual dimensions of the triangular deformation zone,
as well as the velocity distribution along the tool/chip interface can be established and analysed By this FEM technique, it is possible to determine the shear-strain rate within the secondary deformation zone at the tool/chip interface:
(˙γint) has been found to be approximately constant
and equal to: V c/ δt The shear strain-rate within the
Trang 7Figure 172 Typical temperature distributions (isotherms) during machining, illustrated across the: chip, insert and
work-piece; at relatively low cutting speed
.
Trang 8secondary deformation zone tends to be linear in
na-ture from:
(˙γ int) – at the interface, → zero – at the boundary of
the triangular secondary zone
The frictional stress along the tool/chip interface
can be assumed to be constant along the first half of
the contact region, then linearly decreasing to zero at
its end The frictional heat source distribution at this
interface, can be obtained from stress and velocity
dis-tributions at this location
In Fig 173a, the basic ‘FEM mesh’ is shown, with
typical temperature distributions obtained from this
being illustrated in Fig 173b The accuracy of this
particular example for the ‘Tay-model’ for the total
sum of all heat sources was within 2.6% of actual
mea-sured power consumption (F c U) Moreover, the values
of ‘β’ calculated from the temperature distributions
closely-agreed to those obtained some years earlier
by Boothroyd (1963) The FEM approach to
machin-ing data capture and analysis covers these and other
related parameters and clearly indicates the power of
simulation – more will be mentioned on this subject
later in the chapter
7.7 Tool Wear and Life
Introduction
The working environment for most machining
pro-cesses is extremely harsh, with pressures exerted
onto a minute area of tool tip being of the order of
>1600 MPa, with localised temperatures reaching over
750°C creating a sterile surface at the tool/chip
inter-face, making this an ideal state for a pressure-welding
condition In attempting to minimise this affinity
be-tween the work-hardened chip – often this plastic
de-formation making the chip >5 times harder than that
of the parent workpiece material, means that there are
several ways of relieving this tool/chip affinity The
ob-vious one is to use a cutting tool material that is
in-ert to the workpiece such as a either a: ceramic, or
mixed-ceramic cutting insert composition, or
some-thing similar, but this may not prove to be satisfactory,
particularly if interrupted cutting conditions are
antic-ipated In this situation above, perhaps by utilising a
multi-coated cemented carbide insert this may reduce
this ‘adherence-tendency’ Lastly, the correct grade of
‘flood-coolant’ may: lower the interface temperature,
reduce friction here, while somewhat improving the machined surface texture When only partial success
is achieved by employing the above tooling strategies, the last resort may be to adjust the cutting data to
en-hance and provide a ‘less-abusive machining regime’ , while simultaneously improving the ‘steady-state’ wear
conditions
So far, no mention has been made here concern-ing frictional effects in the cuttconcern-ing process Friction is very complex subject which relates not only to: chip
flow-stress and ‘stiction’ 0 problems at the chip/tool
in-terface, but concerns the tribological conditions along this interface Cutting tool rake and flank faces are never perfectly smooth, as even when faces and edges have been either been ground, or super-finished the abrasive nature of the super-finishing process pro-duces an abraded surface that approaches the grit size
of the abrasive medium Therefore, to the naked eye the insert’s surface looks smooth, but at the ‘micron-level’ of surface magnification (i.e 1 × 10– m), the cut-ting insert’s surface has localised ‘high-spots’ , or as-perities present These asas-perities significantly reduce the contact area produced between the forming chip and its contact at the interface on the tool’s rake face Not only can these asperities considerably decrease the
‘real area of contact’ and as a result increase the coeffi-cient of friction here, but the asperities may be either
‘plastic’ , or ‘elastic’ in nature In Table 11 (i.e exper-imental data extracted from: Childs, et al., 2000, con-cerning surface texture assessment of cutting insert faces), comparison is made between a small sample of
0 ‘Stiction’ , is sometimes confused with its ‘close alternative’ this being: ‘stick-slip’ These terms are worth stating, to
ex-plain their respective differences and have been defined in the
following manner: ‘Stiction’ is: ‘The phenomenon at an
inter-face where the frictional stress is equal to the shear yield stress of the softer material.’
‘Stick-slip’ is: ‘A jerky motion between sliding members due to
the formation and destruction of junctions.’ (Kalpakjian, 1984)
‘Plastic asperities – on a plastic chip’ , these are ‘high-spots’
that will sink into the chip and how they achieve this action, does not depend on local conditions at interface contact, but
on the bulk plastic flow field Specifically, the lower the
hydro-static stress in the bulk flow field, the less effort is required for
these asperities to sink.‘
Asperities – on an elastic foundation’ , this situation is
ex-tremely complex phenomena and put simply, in conditions of low contact stresses, the chip beneath these asperities is elas-tic (Childs, et al., 2000)
Trang 9cutting insert surface conditions, clearly illustrating
that even when ‘super-finishing’ an insert’s face it still
has asperities present
7.7.1 Tool Wear
Introduction
On a single-point turning tool’s cutting insert, the
main regions of wear are normally confined to the:
rake face; flank; trailing clearance face; together with
‘Super-finishing’ , is based on the phenomenon that a lubricant
of a given viscosity* will establish and maintain a separating
film between two mating surfaces, if their roughness does not
exceed a specific value and, if certain critical pressure –
keep-ing them apart – is not exceeded Thus, as minute peaks occur
on the cutting insert’s surface, they are then cut away by the
abrasive (e.g minute diamond abrasive in a lubricant – oil –
suspension) this being applied with a controlled pressure –
until a required level of smoothness has been achieved.
NB The maximum stock removed from the insert will be
ap-proximately 50 µm.(Degarmo et al., 2003)
*Viscosity relates specifically to oils, which will vary with
temperature Different oils vary by dissimilar amounts for the
same temperature, this is why the ‘viscosity index’ (VI) has
been developed
the actual nose radius (Fig 174) Likewise, the type
of wear pattern provides important information as to the effectiveness of the overall machining operation Considerable time and effort has been spent by both researchers and tooling companies, ensuring that tool wear mechanisms and their respective classifications for specific machining operations are understood So,
by knowing the anticipated wear behaviour for a cut-ting insert for a specific machining operation, this al-lows the user to optimise productivity by ensuring that the ‘ideal’ tool grade and its associated geometry, will produce the desired machining conditions with the correct type of cut for the chosen workpiece materi-al’s composition A range of factors can influence tool wear when component machining, these are: material removal rate; efficient chip control; machining eco-nomics, precision and accuracy demanded; plus the machined surface texture requirements
If one magnifies then inspects the wear pattern on
a worn cutting edge, then it is reasonably straightfor-ward to establish both the cause and remedy for the indicated type of wear (i.e see Appendix 11), this will allow subsequent tooling to be more adequately con-trolled during following machining operations In order to ensure that the correct tool has been selected,
it is really only down to basic ‘good engineering prac-tices’ , namely:
• that the initial selection of criteria for the cutting data is sound;
Table 11 Cutting insert surface texture and contact stress severity data.
← 10k local /E* [°] →
Ra [µm] ∆q [°]
* When s/k is <0.5, an asperity is totally elastic – if the plasticity index is <5 and totally plastic if its >50.
As s/k increases to 1, these critical plasticity index values reduce In large s/k conditions of metal machining, an asperity would normally be
‘fully-plastic’ , if: ∆q ≥ 10klocal/E*.
NB ‘s’ = Shear strength and ‘k’ = local shear stress.
[Source Childs, et al., 2000]
.