Smith G.T. Cutting Tool Technology: Industrial Handbook

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= R cos(φ + τ – α) (i)

and

= τ

/sin φ (ii)

Where:

= Workpiece material’s shear strength – on the

shear plane,

= Shear plane’s area,

= Uncut chip’s cross-sectional area,

τ = Mean friction angle, between too and chip [i.e.

arctan (FT/FN)],

α = Normal rake angle (i.e. working).

From equations (i) and (ii):

R =

sin ϕ



cos(ϕ + τ − α)

(iii)

By geometry:

= R cos(τ – α) (iv)

Hence, from equations (iii) and (iv):

sin ϕ

cos(τ − α)

cos(ϕ + τ − α)

(v).

Now, equation (v) can be dierentiated with respect

to ‘φ’ , then equated to zero to obtain a value of ‘φ’

when ‘F

’ is at a minimum. Hence, the requisite value

is specied by:

ϕ + τ − α =



(vi).

In comparative analysis undertaken by Merchant

(1945), he found close correlation with experimental

results was obtained when machining synthetic plas-

tics, but a somewhat poor theoretical correlation oc-

curred when steel had been machined with cemented

carbide tooling. It needs to be mentioned that when

Merchant dierentiated with respect to ‘φ’ , it was as-

sumed that ‘A

’ , ‘α’ and ‘τ

’ would be independent of

‘φ’ , but on further consideration, Merchant decided to

oer in a ‘modied theory’ the relationship of :

= τ

+ kσ

(vii).

Here, Merchant brought in a modication to the shear

strength of the workpiece material ‘τ

’ which now in-

creased linearly with an increase in normal stress ‘σ

’

on the shear plane, where zero normal stress ‘τ

’ is

equal to ‘τ

’. is new assumption by Merchant was

conrmed by previous work undertaken in the litera-

ture published by Bridgman (1935, ’37 and ’43), where

the shear strength when experimental machining of

polycrystalline metals was shown to be dependent on

the normal stress on the ‘plane of shear’.

Now from Fig. 181, we can obtaing the following

relationship:

= F sin(φ + τ – α) (viii)

and:

= σ

sin ϕ

(ix).

From equations (viii) and (ix):

sin ϕ

R sin(ϕ + τ − α)

(x).

Combining equations (iii) and (x):

= σ

cot(φ + τ – α) (xi)

and, from equations (vii) and (xi):

 − k tan(ϕ + τ − α)

(xii).

is equation (i.e. xii), explains why the value of ‘τ

’

may be inuenced by modications in the shear angle

(‘φ’), which is now inserted into equation (v), to ob-

tain a new equation for ‘F

’ in terms of ‘φ’ , therefore,

the resulting expression becomes:

cos(τ − α)

sin ϕ cos(ϕ + τ − α)[ − k tan(ϕ + τ − α)]

(xiii).

Now, it can be assumed that both ‘k’ and ‘τ

’ are con-

stants for the specic workpiece material, further, that

‘A

’ and ‘α’ are also constants for the machining op-

eration. Hence, equation (xiii) can now be dierenti-

ated to obtain a new value of ‘φ’ , with the resulting

expression:

2φ + τ – α = C

Where:

C = Can be obtained from ‘arccotk’ , which is a con-

stant for the workpiece material.

NB In further more recent experimental work, it has

been shown that ‘τ

’ will remain constant for a speci-

ed workpiece material, across a diverse range of cut-

352 Chapter 7

ting conditions, as such, the value of ‘k’ can be equated

to zero.

When the shear-angle values are compared for the

plotted linear relationships of the earlier theoretical

and experimental work undertaken by Ernst and Mer-

chant, to that of the later comparative work by Lee and

Shaer, then these shear-angle relationships diverge

somewhat. However, one area that these researchers

both agreed upon, was the fact that friction on the

tool’s face was the most important factor during metal

cutting. In the following discussion, the inuence that

frictional behaviour has at the tool/chip interface will

be briey mentioned.

Frictional Effects During Machining

For simplicity’s sake, friction between dry sliding sur-

faces will be concisely reviewed. In 1699 Amontons

‘laws of friction’

were formulated, then veried by

Coulomb

in 1785, with Bowden and Tabor (1954)

contributing greatly to an explanation of these empiri-

cal laws.

If two apparent at surfaces are placed together, the

larger asperities (i.e. peaks) on each mating face will

only establish contact. With just normal loading, the

top of these asperities will yeild, creating a real area

of contact until such a time, that they are capable of

supporting an applied load. In the main, for the vast

majority of engineering applications this real contact

area (‘A

’), is normally only a very minute portion of

the apparent real of contact (‘A

’) – even aer the con-

tacting asperities of the soer material has plastically

deformed (i.e. yielded). us:

= F

/σ

(i)

78 ‘Law(s) of friction’ , Amontons in 1699 stated in the main,

that: ‘Friction is independent of the apparent area of contact

and proportional to the normal load between two [mating] sur-

faces.’

79 Coulomb (1785), conrmed these ‘frictional laws’ with the

observation that: ‘e coecient of friction* is substantially in-

dependent of the speed of sliding.’

oecient of friction (µ) = F/N

us, the friction force is proportional to the perpendicular

force between contacting surfaces and is independent of the

surface area, or its ‘rubbing speed’.

Where:

= Normal force,

= Yield pressure of the soer material.

us, for most metallic materials, this close asperity

contact between mating surfaces creates localised ‘cold

welding’. Prior to any sliding with respect to these two

contacting surfaces, a force is necessary to continually

shear potentially contacting and reforming asperity

tips of these ‘welded junctions’. Hence, the total fric-

tional force ‘F

’ is given by:

= τ

(ii)

Where:

= Shear strength of soer contacting material,

= Real contact area.

From equations (i) and (ii), the actual coecient of

friction (‘µ’) between these contacting surfaces will

be:

µ = F

= τ

(iii).

In majority of machining operations typied by the

continuous turning of metallic workpieces, the coef-

cient of friction (‘µ’) at the chip/tool interface can

vary quite considerably. Its frictional variation, being

inuenced by any changes in: cutting speed, feedrate,

rake angle contact regions – this latter factor is par-

ticularly relevant for multi-functional tooling, where

the cutting insert’s top face is not planar (i.e at). In

modern machining practice, the normal pressures ex-

erted at the tool/chip interface are exceedingly high,

typically when machining commercial grades of me-

ium carbon plain steels these pressures are >3.5 GPa.

is high normal pressure at the ‘interface’ causes the

real contact area to approach that of the entire area,

where: A

= unity! is means that under these cir-

cumstances the ordinary laws of friction no longer ap-

ply, and the frictional force ‘F

’ is still represented by

equation (ii), but is now independent of the normal

force ‘F

’. is acute change in the frictional behaviour

during machining, means that the shearing action is

not conned only to the interface asperities, but in-

cludes workpiece material in the local substrate.

In work published by Zorev in 1963, his ‘model’

considered the frictional behaviour in continuous

metal cutting operations where no BUE was present

(Fig. 182). Under these machining conditions, Zorev

Machinability and Surface Integrity 353

noted that the normal stresses at the tool/chip inter-

face were suciently high enough to cause ‘A

’ to

approach unity, over the zone denoted given by length

‘l

’ (Fig. 182) – this being termed the ‘sticking region’

– also see magnied quick-stop photomicrograph in

Fig. 184(top) showing the aect on the resultant chip.

e ‘sliding region’ , extends from from the end of the

‘sticking region’ to a point where the chip loses contact

with the rake face (i.e. ‘l

’-‘l

’), here, the ‘A

’ ratio is

less that unity – meaning that the coecient of friction

is constant. In 1964, Wallace and Boothroyd produced

evidence that the ‘sticking manner’ observed on the

underside of the chip had abruptly stopped. ey ob-

served that in an adjacent vicinity to that of the tool’s

cutting edge, grinding marks on the rake face were im-

printed onto the chip’s underside. is phenomenon

indicated that no relative motion between the chip and

the tool had occurred, suggesting that here, the ‘real’

and ‘apparent’ areas of contact were ‘equalised’ in this

region. erefore, under ‘sticking friction’ conditions,

the ‘mean angle of friction’ on the rake face, depends

on the:

1. Form of the normal stress distribution,

2. Tool/chip contact length (i.e. ‘l

’),

3. Mean shear strength of the chip material – in the

‘sticking region’ ,

4. Coecient of friction – in the ‘sliding region’.

NB It seems apparent that a simple numerical value

for the mean angle of friction, is inadequate when at-

tempting to completely describe the frictional circum-

stances on the rake face.

In Fig. 182, is schematically depicted the ‘frictional

model’ purported by Zorev (1963). Here, Zorev sug-

gested that the normal stress distribution (‘σ

’) on the

tool’s rake face, could be represented by the following

simple expression:

= qx

(iv)

80 ‘Sticking region’ at the tool/chip interface is oen termed the

‘stagnation zone’ , but in this case it appears on the formed/

sheared chip – depicted in Fig. 184 (top). Here, is shown a

magnied and etched view of a quick-stop for an insert cut-

ting carbon steel at 150 m min

–1

. A ‘stagnation zone’ is present,

that follows the insert’s prole, with ‘soened’ workpiece ma-

terial protecting the tool, by a sticking/sliding action. A ‘ow

zone’ occurs aer ‘shear plane’ , visibly dividing undeformed/

deformed material.

Where:

‘x’ = Distance along the rake face – from the

position where the chip losses contact with the tool’s

face,

‘q’ and ‘y’ = are constants.

e maximum normal stress ‘σ

fmax

’ occurs when ‘x’

equals ‘l

’ , so:

fmax

= ql

or, transposing with respect to ‘q’:

q = σ

fmax

–y

(v).

Substituting for ‘q’ in equation (iv), we get:

= σ

fmax

(x/l

)

(vi)

us, in the ‘sliding region’ , ranging from: x=0 to

x = l

– l

the coecient of friction ‘µ’ is constant and,

the distribution of shear stress ‘τ

’ along this region, is

represented by:

= σ

µ = µ σ

fmax

(x/l

)

(vii).

So, in the ‘sticking region’ , the shear stress becomes a

maximum (‘τ

’), therefore from: x= l

– l

to x=l

= τ

(viii).

By integrating equation (vi) to obtain the normal force

‘F

’ acting on the rake face (i.e. from Fig. 181), gives:

= a

�



f m a x

(x�l

)

= σ

fmax

1 + y (ix)

Where:

= Chip width (i.e. width of cut).

e friction force ‘F

’ on the tool’s rake face, is ob-

tained by:

= a

[τ

−l st

�



µ σ

f m a x

(x�l

)

dx]

= τ

+ µ σ

fmax

– l

)

1+y/

(1+y) (x).

At position: ‘x = l

-l

’ , the normal stress ‘σ

’ is given by:

‘τ

/µ’. Moreover, from equation (vi), it is given by:

354 Chapter 7

fmax

-l

)

erefore:

= µ σ

fmax

– l

)

(xi).

By substituting equation (xi) in equation (x), it simpli-

es the expression for ‘F

’ , as follows:

= τ

+ τ

– l

)/1+y (xii).

Hence, the mean coecient of friction on the rake face,

can now be found from both equations (ix) and (xii):

ean friction angle = F

= τ

st/

fmax

(1+yl

) (xiii).

From equation (xi), the mean normal stress on therake

face (σ

fav

) is given by:

fav

= F

= σ

fmax

/1+y

us:

fmax

= (1+y)σ

fav

(xiv).

Substituting for ‘σ

fmax

’ in equation (xiii), produces:

Mean friction angle = arctan{τ

/σ

fav

[1+y(l

)]} (xv).

However, from Zorev’s experimental work, he found

that the term:

[1+y(l

)]/1+y

will remain relatively constant for a specied work-

piece material, across a diverse range of unlubricated

cutting conditions and, as a result, the equation for the

mean friction angle becomes:

ean friction angle = arctan K/σ

fav

(xvi)

Where:

‘K’ =

a constant.

What Zorev’s equation (xvi) indicates, is that the mean

friction angle is somewhat dependent on the mean

normal stress on the rake face, allowing the result to

explain the eect of modications in the working nor-

mal rake to that of the mean friction angle. us, as the

value of ‘α’ (i.e. working normal rake angle) increases,

the resultant component tool force being normal to

the rake face will decrease, so that the mean normal

stress will be reduced. Moreover, from equation (xvi),

an increase in ‘α’ could be expected to increase the

mean friction angle. is observation, has been con-

rmed by experimental work undertaken by Pugh

(1958), where an increase in ‘α’ was shown to result in

a a complementary increase with repect to the mean

friction angle – across an extensive range of workpiece

materials.

Since the passage of time when both of these ‘theo-

retical models’ for the mechanics of machining and the

frictional work produced by Ernst and Merchant and

that of Zorev, respectively, were produced. Consider-

able eort and progress has been made into advances in

our present understanding of: ‘slip-line eld modelling’ ,

‘thermal and frictional modelling of the cutting process’ ,

‘chip-ow analysis’ ,

‘examination of the primary and

secondary shear zones’ ,

non-orthogonal (three-dimen-

sional) machining processes, advances in tool geometries

with their accompanying force and shear relationships

and the advent of applications to machining opera-

tions employing 

nite element analysis (FEA). If all of

these subjects and other not listed, were only concisely

mentioned, then the book would be of epic propor-

tions! defeating the object of reviewing cutting appli-

cations and trends in current practice. However, the

role of FEA, in both machining research and for the

‘dynamic and geometric modelling’ of applied residual

stresses occurring in both the tool and workpiece in

the anticipated cutting processes is worthy of discus-

sion. e topic of ‘computer simulation’ utilising an

FEA approach, has become of increasing importance

of late and several companies have produced products

in this eld. However, to obtain some degree of con-

sistency in the dialogue only one particular company’s

FEA product will now be described.

Computer Simulation of Machining

Processes – an Introduction

By the application of computers to simulate and anal-

yse machining processes, this provides tool manufac-

turers and users alike, assistance in improving machin-

ing eciency and will also predict the likely cutting

response to real-time machinability environments.

Most of the early two-dimensional simulation models

for the mechanics of machining, focussed attention on

shear-zone modelling. ese previous ‘models’ ignored

vital factors such as the frictional conditions along and

between the rake’s tool/chip interface, furthermore,

any potential work-hardening and temperature eects

in this vicinity were also tended to be disregarded.

Machinability and Surface Integrity 355

Over the last two decades, the application of nite ele-

ment analysis (FEA) to that of three-dimensional ma-

chining applications, has been successfully applied to

the cutting process. Major advantages of using FEA,

are its ability to accurately compute: complex material

property denitions; tool/chip interactions; non-linear

geometric boundary conditions – typied by the chip’s

surface; prediction of local variables – such as stress

and temperature distributions in the cutting locality.

Several approaches for the numerical modelling

of machining operations and in particular, for that of

metal cutting have been employed, such as ‘Lagrang-

ian and Eulerian’ techniques. In the former case which

has been utilised for over two decades, ‘Lagrang-

ian methods’ utilise the tracking of discrete material

points. Here, the technique is uses a predetermined

line of separation at the tool’s point, which propagates

a ctitious crack ahead of the tool’s tip. Previously, this

Figure 182. An idealised orthogonal cutting model of chip-tool friction, where:

• σ

= normal stress,

• τ

= shear stress,

• τ

= shear strength of chip material in the sticking region,

• I

= chip-tool contact,

• I

= length of sticking region.

[Source: Zorev, 1963]

356 Chapter 7

routine precluded the resolution of the cutting edge

radius and an accurate resolution of the secondary

shear zone – due to severe mesh distortion. In an at-

tempt to alleviate any form of element mesh distortion

‘adaptive remeshing techniques’ have been employed

to resolve the tool’s cutting edge radius. Whereas the

‘Eulerian approach’ tracks volumes rather than mate-

rial particles, having the advantage of not needing to

rezone any distorted meshes. Moreover the ‘Eulerian

technique’ ,

requires ‘steady-state free-surface tracking

algorithms’ and relied upon a particular bur unrea-

sonable assumption that a uniform chip thickness oc-

curred, further this method precluded the modelling

of either a segmented chip formation, or that of the

milling process. e former technique of a ‘Lagrangian

FEA machining model’ will be reviewed (Fig. 183), as it

has the integrating ability to achieve ‘adaptive remesh-

ing’ with explicit dynamics and tightly coupled tran-

sient thermal analysis, allowing it to ‘model’ the com-

plex interactions between the cutting tool’s geometry

and that of the workpiece.

Lagrangian FEA Simulation

Machining Modelling

In Fig. 183, just a few images of the Lagrangian FEA

machining model are depicted for several applica-

tions of machining operations. is simulation mod-

elling technique contains a tightly coupled thermo-

echanical material response capability, this being a

vital factor for any elevated temperatures that occur

at the tool/chip interface, furthermore, having a fully

adaptive mesh generation ability. Hence, the material

modelling facility forms an intergral part when at-

tempting to predict the workpiece’s material behav-

iour, under high strain and increased stress condi-

tions. is advanced modelling capability ensures the

accurate capture of any strain-hardening, or thermal

soening eects coupled to rate sensitivity properties,

for a given set of material conditions. Many of today’s

ferrous and non-ferrous materials, together with ‘ex-

otic materials’ such as nickel and titanium alloys can

also be successfully simulated, across a diverse range

of single- and multi-point cutting tools (e.g. turning,

milling, drilling, broaching, sawing, etc.).

Machining Simulation – Validation

Not only can simulation techniques of the type shown

in Fig. 183 be utilised for workpiece material machin-

ing modelling: work-hardening; thermal-soening

eects; machining-induced residual stresses; induced

temperature eects and heat-ow analyses with the

‘adaptive’ ‘Lagrangian FEA machining model’. e

‘model’ can also reasonably accurately predict: both

two- and three-dimensional cutting force magnitudes.

Invariably, the individual cutting force components

can be closely validated to actual machining working

practice, the same can also be said for a comparison

of a ‘dynamically-modelled chip’ to that of an actual

chip’s morphology – including both its chip-curling

tendency and any chip segmentation occurring. ese

validated simulation capabilities enable the cutting

process to be improved, by using the:

•

Force and temperature information – to reduce

overall production cycle times,

•

Temperature and thermal eects – can be utilised

to improve tool life and part quality,

•

Tool wear analysis – predicts the eects of tool

ank wear and how this wear land inuences sub-

sequent: temperatures, pressures and forces,

•

Chatter and vibration prediction – indicating the

onset and magnitude of these unwanted eects,

•

Residual stress information – helps alleviate poten-

tial machined component fatigue and aids in part

deformation analysis.

NB 

e inuence that tool coatings have on the

dynamic machining eciency can also be reviewed,

plus the capability to customise the tooling with

chip-breakers to improve chip-curl, or chip evacu-

ation abilities.

Computer machining simulation of the type illus-

trated in Fig. 183, can be integrated into an overall

CAD/CAM package, enabling a range of signicant

advantages to accrue, without having to operate a

costly and time-consuming task of undertaking an

extensive machinability trial. is o-line machining

simulation facility, allows: realistic cycle-time calcula-

tions including cut-and non-cut timings; visualisation

of tool paths to high-light and then avoid any localised

‘power-spikes’ occurring during a machining opera-

tion and many other useful production features.

e use of a dynamic FEA machining simulation

package similar to the one mentioned and illustrated

in Fig. 183, adds a scientic element to the understand-

ing of the overall machinability of specic workpiece

materials and associated tooling. Such machining

simulation oers not only a visual interpretation to

Machinability and Surface Integrity 357

Figure 183. Simulated machining processes. [Courtesy of Third Wave Advant Edge].

358 Chapter 7

the machining operation, but it also provides the user

with validated and relevant data analysis. ese posi-

tive benets enable tool designers and users alike, to

design and develop advanced cutting tools and to un-

dertake ecient and optimised machining operations.

Beyond the positive advantages of tool optimisation,

simulation can signicantly reduce tooling develop-

ment costs and lead times to bring a newly-developed

product to market. e role of machining simulation

is likely to rapidly grow, as more tooling and produc-

tion engineers become aquainted with these soware

packages.

Figure 184. The insert’s cutting edge: illustrating the ‘rounding eect’ (exaggerated) or, a manufacturer’s ‘edge preparation’ and

the material ow conditions that arise as a result

Machinability and Surface Integrity 359

7.10 Surface Integrity of

Machined Components –

Introduction

Previously in Section 7.5 concerning machined sur-

face texture, the discussion was principally concerned

with the resultant surface topography where the topo-

graphical information was valid, but disguised the fact

that potential sub-surface material layers might have

compromised and altered the machined component.

e concept of the overall functional performance of

a surface and its accompanying sub-surface condition

was recognised by Field and Kahles (1971), where they

used the term ‘Surface Integrity’ to describe its poten-

tial state. e overall concept of surface integrity ant

its various generating mechanisms in conjunction with

the production process is known as the ‘

unit event’

is unit event has now been reclassied into ve

discrete generating mechanisms: chemical, mechani-

cal, mechano-thermal, thermo-mechanical and ther-

mal – the order they are listed reects their respective

power density per unit area. For example, increases in

the power density from the chemical end of the series,

results in an augmented level of thermal energy enter-

ing the surface leading to greater thermal damage and

poorer part surface integrity. e chemical mechanism

is dominant across all classes of production process to

some degree and that surfaces react with their imme-

diate environment, via absorbates, oxidation, etc., as

illustrated in Fig. 185 – more will be said on these ef-

81 ‘Unit event’ , is a complex interrelated series of reactions with

the potential for distinct zones to be present within the sur-

face vicinity, including a:

Chemically aected layer (CAL) – resulting from chemical

surface changes by the production process, or from post-

production exposure to a local environment,

Mechanically aected layer (MAL) – this may be due to

factors such as material bulk transportation: deposits; laps;

folds and plastic deformation,

Heat aected layer (HAL) – principally concerned with

factors such as: phase transformation; thermal cracking and

retempering,

Stress aected layer (SAL) – is in the main, the result of

residual stresses being a combination of the above. (Field

and Kahles, 1971)

–

fects when discussing the machined surface condition

in the following section.

7.10.1 Residual Stresses

in Machined Surfaces

A machined surface is the product of either ‘abusive’ ,

or ‘gentle’ machining regimes, these being the direct

result of the cutting process and its chosen machining

data. us, machining being a complex relationship of

many interrealated factors, aects the outcome of the

production process – see Fig. 144. Here, a simplistic

schematic diagram attempts to show the complexity

of a machining operation, with the surface integrity

grouping indicating for a turning operation the fol-

lowing features:

•

Surface condition – surface texture and its associ-

ated roundness,

•

Micro-structural changes – micro-cracks, disloca-

tions and ssures, etc.,

•

Surface displacement – bulk transportation of ma-

terial and residual stresses,

•

Surface/sub-surface micro hardness – plastic de-

formation and localised residual stress layers.

Machined surfaces are even more complex than seem-

ingly at rst glance, as their performance can be in-

uenced by either external layers (chemical transfor-

mations and plastic deformations) and internal layers

(metallurgical transformations and residual stresses).

By way of example, the anisotropic – periodic

– longitudinally turned surface illustrated in Fig. 185,

is aected by the cutting insert’s tool tip geometry

and the regularity of the cusps (i.e. peaks and val-

leys) – the surface topography being dominated by

the pre-selected feedrate. A series of other micro-tech-

nological features can also occur, these oen being

superimposed onto the machined surface, typically

the result of: tool wear, vibrational inuences and to

a lesser extent, machine tool-induced errors. In the

circumferential direction the ‘Lay’ is both periodic

and regular, albeit this round generated surface by

the turning operation, will probably have some form

of harmonic eects present: departures-from-round-

ness characteristics (i.e. a combination of harmonic

inuences present). e exposed sterile surface (Fig.

185), is the result of highly localised temperatures and

transients, which when turned the machined surface

will be instantaneously oxidised and adsorb contami-

360 Chapter 7

Figure 185. The cross-section of an anisotropic (i.e. periodic) surface, illustrating surface contaminants (oxides and adsorbates),

together with some sub-surface plastic deformation (the residual stress zone) and an unaected substrate

Machinability and Surface Integrity 361