Astakhov V. Tribology of Metal Cutting

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Tribology of the Tool–Chip and Tool–Workpiece Interfaces 157

(mm)

200

(MPa)

600

800

400

c−r

(°C)

650

600

550

500

Mean contact temperature

Specific normal contact stress

Fig. 3.22. Inﬂuence of contact length on the speciﬁc normal contact stress and mean contact

temperature at the tool–chip interface. Work material AISI steel 1020, tool material P20 (79% WC,

15% TiC, 6% Co), normal rake angle γ

= 20

◦

, depth of cut d

= 4 mm, cutting feed f =

0.55 mm/rev and cutting speed ν = 60 m/min.

at points A and O. The results of a great number of tests conducted by Zorev [2]

and Klushin [78] with various work materials under a wide range of cutting conditions

conclusively proved this point.

Another important conclusion follows from Fig. 3.22: the mean contact temperature

at the tool–chip interface decreases while the speciﬁc normal stress at this interface

increases. This is in direct contradiction with the known results of friction test where

the temperature increases with the contact stress (for example, see Ref. [79]). It is,

however, in perfect agreement with the above-discussed model of energy distribution in

metal cutting according to which high temperatures in metal cutting are due to contact

processes at the tool–chip and tool–ﬂank interfaces and not due to plastic deformation

in the deformation zone. One more time, the obtained result signiﬁes the importance of

understanding the metal cutting tribology.

Contact stresses. Multiple experimental data obtained by Zorev [2] and Poletica [69]

conclusively proved that the shapes of the normal and shear stress distributions remain

the same under wide variations of cutting conditions, tool and work materials properties

and other parameters and factors of the cutting process. Therefore, it is reasonable to

consider the mean value of these stresses which characterize tribological conditions at

the tool–chip interface. The obtained data also show that the mean shear stress, τ

is the

most stable characteristic of cutting tribology.

Figure 3.23(a) shows results for steel AISI E9310. As seen, the mean shear stress, τ

does

not depend on the cutting speed and on the rake angle. The same results were obtained

using various tool materials, geometry and work materials (Fig. 3.23(b)). These facts

cannot be explained using the traditional notions used today to explain metal cutting

phenomena. For example, although the contact temperature at the tool–chip interface

158 Tribology of Metal Cutting

400

480 320 160 0

320

n (m/min)

240 160 80 0

200

− g

= −10°− g

= 0°− g

= 10°− g

= 20°

200

400

n (m/min)

(a)

(b)

(MPa)

Fig. 3.23. Inﬂuence of cutting speed (ν) on the mean shear stress (τ

): (a) under different rake

angles in machining steel AISI E9310, tool material P20 (79% WC, 15% TiC, 6% Co); (b) for vari-

ous work materials: 1 – beryllium copper UNSC17000, HB320, 2 – beryllium copper UNSC17000,

HB200 and steel AISI O7 (1.2% C) annealed, 3 – steel AISI E9310, 4 – beryllium copper

UNSC17000, HB110, 5 – Armco iron, 6 – copper and 7 – cadmium.

varies considerably over the range of the cutting speeds used in the tests (Figs. 3.23(a)

and (b)), the mean shear stress, τ

does not change. This is in direct contradiction with the

notions on material behavior used in the traditional metal cutting considerations where

the properties of the work material obtained in the standard mechanical testing are used

to judge the cutting parameters. Figures 3.24(a) and (b) explain this issue. As seen, the

mean shear stress, τ

does not depend on the contact temperature over a wide range of

cutting conditions while the same property (the shear strength) obtained in a standard

tensile test is signiﬁcantly temperature dependent.

The experimental results discussed show that the mean shear stress is work material

speciﬁc and does not depend on the rake angle and cutting regime (speed and feed).

This can be easily explained with the generalized model of chip formation (Chapter 1).

According to this model, metal cutting is a cold-working process where the state of stress

in the deformation zone should be sufﬁcient to cause the purposeful fracture of the layer

being removed. The required state of stress in the deformation zone is achieved due to

the spatial arrangements of the components of the cutting system and due to the load

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 159

500 600 700

100

(MPa)

200

900

800

(°C)

f = 0.156 mm/rev f = 0.510 mm/rev

f = 0.205 mm/rev

f = 0.314 mm/rev

f = 0.402 mm/rev

f = 0.610 mm/rev

f = 0.850 mm/rev

f = 1.420 mm/rev

f = 2.380 mm/rev

500 700 900

400

200

f = 0.156 mm/rev

f = 0.510 mm/rev

(MPa)

(a) (b)

(°C)

Fig. 3.24. Comparison of the inﬂuence of contact temperature (θ

) on the mean shear stress (τ

) and on the shear strength in

tensile testing (curves 1 and 2): (a) work material: steel AISI 1050, curve 1 – test results at shear strain 0.15 and curve 2 – test

results at shear strain 0.75, (b) work material: steel ASTM A514 (0.18% C, 1.1% Cr, 1.3% Ni), curve 1 – test results at shear

strain of 0.33 and curve 2 – test results at shear strain of 1.8.

160 Tribology of Metal Cutting

applied by the cutting tool which is transmitted to the deformation zone through the

tool–chip interface. Because the combined stress that causes the fracture of the layer

being removed depends primarily on the mechanical properties of the work material,

the mean shear stresses at the tool–chip interface should be the same regardless of the

conditions achieved at the tool–chip interface.

Analyzing numerous experimental results, Poletica concluded [69] that, although the

mean shear stress at the tool–chip interface can be correlated with many mechanical

properties of the work material, the best ﬁt seems to be achieved with the ultimate

tensile strength, σ

UTS

as shown in Fig. 3.25. He concluded that the following empirical

relation shows good correlation

= 0.28σ

UTS

(3.52)

The independence of the mean shear stress at the tool–chip interface on many factors

that affect the cutting process is an important characteristic of this process. Among

other factors, the most surprising and seemingly paradoxical is the independence of this

stress on the mean contact temperature at the tool–chip interface. Zorev [2] and partially

Spaans [80] attempted to explain this paradox by mutual inﬂuence of two reverse-

proportional factors, namely the strain rate and temperature. The following explanation

has been offered: the lowering of the mean shear stress at the tool–chip interface with

the contact temperature is fully compensated by the growth of this stress due to the

0 800

(MPa)

200

400

Beryllium copper, HB320

Beryllium copper,

HB200

Beryllium copper,

HB110

Steel ASTM A514

Copper

Armco iron

Cadmium

Steel AISI 07

UTS

(MPa)

Fig. 3.25. Correlation between the mean shear stress at the tool–chip interface (τ

) and the ultimate

tensile strength (σ

UTS

) for different work materials.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 161

corresponding increase in the strain rate. In other words, the effect of temperature on

the mean shear stress at tool–chip interface is balanced by the strain rate effect in such

a way that this stress remains constant. This idea, however, was criticized by Poletica

[69] who conclusively proved that this is not the case in metal cutting.

The total friction force on the tool rake face (Fig. 3.21(a)) then can be calculated as

F = τ

(3.53)

Substituting Eqs. (3.42) and (3.52) into Eq. (3.53), one can obtain

= 0.28σ

UTS

(3.54)

Bearing in mind that d

= d

and dividing both sides of Eq. (3.54) by A

= t

(the uncut chip cross-sectional area) and rearranging, one can obtain

ζ =

(

0.28σ

UTS

)





(

0.28σ

UTS

)

(

)

(3.55)

This equation establishes the direct correlation between the mean shear stress and CCR,

although some researchers argued that this correlation is linear [69].

On the contrary, to the mean shear stress, the mean normal stress σ

at the tool–chip

interface, is very sensitive to many parameters of the cutting process. Being work material

speciﬁc, this stress depends mainly on the cutting speed, cutting feed and cutting tool

rake angle.

Having conducted a great number of cutting tests, Zorev [2] and Poletica [69] conclu-

sively proved that the mean normal stress at the tool–chip interface increases with the

cutting speed for a wide range of metallic work materials. Figure 3.26 shows the test

results for various steels. As seen, the inﬂuence is more pronounced for high-carbon

steels having higher hardness and strain rate sensitivity. One may argue, however, that

the metallurgy of these steels may also contribute to the obtained result. To show that this

is not the case, Fig. 3.27 presents the results for beryllium copper of different hardness.

As seen, the mean normal stress at the tool–chip interface increases with the hardness of

the work material.

It was found that the mean normal stress at the tool–chip interface decreases with the rake

angle. It can best be illustrated with the experimental results obtained in the machining

of cadmium shown in Fig. 3.28(a) because CCR hardly changes with this work mate-

rial although the rake angle varies in a very wide range, namely from −40 to +60

◦

Therefore, data presented in this ﬁgure may be regarded as that obtained with invariable

CCR. As seen, the mean normal stress decreases with the rake angle. This phenomenon

can readily be explained using the above-discussed deﬁnition of the cutting process.

Because cracks form at points A and O (Fig. 3.21) due to the combined action of com-

pressive and bending stresses, the maximum combined stress at these points forms due

to compressive force and bending moment imposed by the resultant force R. As such, the

compressive force is determined by the tool–chip contact area while the bending moment

162 Tribology of Metal Cutting

100 180 260

400

200

(MPa)

n(m/min)

600

Fig. 3.26. Inﬂuence of cutting speed (ν) on the mean normal contact stress (σ

) for various steels:

1 – steel 1010, 2 – steel 1020, 3 – steel 1060, 4 – steel HV100 (0.2% C, 3.8% Ni, 1.5% Cr),

5 – steel ASTM A228 (0.8% C) and 6 – tool steel 07 (1.2% C). Tool: carbide P20 (79% WC,

15% TiC, 6% Co), normal rake angle γ

= 10

◦

and cutting feed f = 0.156 mm/rev.

600

300

80 160

900

(MPa)

n(m/min)

1200

f = 0.07 mm/rev

f = 0.15 mm/rev

f = 0.26 mm/rev

f = 0.34 mm/rev

HB110

f = 0.07 mm/rev

f = 0.15 mm/rev

f = 0.26 mm/rev

f = 0.34 mm/rev

f = 0.07 mm/rev

f = 0.15 mm/rev

HB320

HB200

Fig. 3.27. Inﬂuence of cutting speed (ν) on the mean normal contact stress (σ

) for beryllium

copper UNSC17000 of different hardnesses. Tool: carbide P20 (79% WC, 15% TiC, 6% Co),

normal rake angle γ

= 10

◦

and cutting edge angle κ

= 70

◦

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 163

200

−40 −20 0 20 40

(MPa)

Normal stress s

Tangential stress t

400

200

600

6810

= −10°

= 0°

= −10°

= −20°

(°)

100

(a)

(b)

Fig. 3.28. Mean normal contact stress as a functions of: (a) the tool normal rake angle (γ

work material – cadmium, tool material – carbide M30 (92% WC, 8% Co), cutting speed ν =

40.2m/min, cutting feed f = 0.67 mm/rev and depth of cut d

= 2 mm; (b) Po-criterion for

different rake angles tool material – carbide P20 (79%WC, 15%TiC, 6% Co), work material – steel

ASTM A514 (0.18% C, 1.1% Cr, 1.3% Ni), cutting edge angle κ

= 70

◦

, depth of cut d

= 3mm

and cutting feed f = 0.07–0.43 mm/rev.

is determined by both the contact area and the arm of the normal force with respect to

the mentioned points. Because a given work material fails at points A and O under the

same combined stress, the bending in this combined stress is a kind of constant for this

work material. Therefore, if the arm of the normal force creating the bending moment

(stress) increases due to an increase in the rake angle, the normal contact stress decreases

accordingly to keep the same needed bending stress. Figure 3.28(b) provides further

experimental support to the discussed model of the correlation amongst the parameters

of the tool–chip interface.

The relationship between the mean normal stress and the Po-criterion has more general

character than that drawn directly from Fig. 3.27. Figure 3.29 shows the data for different

164 Tribology of Metal Cutting

800

400

1200

161284

Beryllium copper, HB 320, Tool - carbide M30

Steel AISI 07, Tool - carbide P20

Copper, Tool - HSS M42

Beryllium copper, HB 310, Tool - carbide M30

Beryllium copper, HB 200, Tool - carbide M30

Steel ASTM A514, Tool - carbide P10

Steel 1010 HB100, Tool - carbide M30

Steel 1020 HB130, Tool - carbide M30

(MPa)

Fig. 3.29. Inﬂuence of Poletica criterion on the mean normal contact stress for various work

materials. Tools with γ

= 10

◦

work materials. As seen, regardless of a wide range of the mechanical characteristics

of the work materials (HB33–220), all experimental points are close to a single curve.

The same results were obtained by Zorev [2] with AISI steels 1010, 1020 and E9310.

Summarizing the obtained experimental results, one can conclude that not only the uncut

chip thickness and cutting speed but also the mechanical properties of the work material

affect the mean normal stress insomuch as they affect the Po-criterion.

A particular value of the Po-criterion affects the normal stress at the tool–rake face.

As this criterion decreases, the mean normal stress increases. The mean contact stress,

therefore, is a function (and a characteristic) of the state of stress in the contact zone. It

depends on the Po-criterion in the same way as this criterion affects the state of stress in

the contact zone.

Function σ

= f

(

)

shown in Fig. 3.29 has the hyperbolic shape and with reasonable

accuracy can be approximated as

180

(

)

0.95

(3.56)

which, in the general case, can be represented as

(

)

(3.57)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 165

where coefﬁcient A

and power m

are determined by the rake angle. As such, normally

< 1 and A

decreases with the rake angle.

Substituting Eq. (3.42) into Eq. (3.57), one can obtain

(

)

(3.58)

N = A

(

1−m

)

(3.59)

Because m

is close to 1, the power of CCR is very small. Therefore, for a given uncut

chip cross-sectional area (t

×d

), the normal force on the tool–rake face is primarily a

function of the tool–rake angle and only weakly depends on CCR.

Inﬂuence of tool material. Of the many properties of the work material, elastic

characteristics, thermophysical properties (primarily, thermoconductivity) and chemi-

cal properties play the most signiﬁcant role in the contact process at the tool–chip and

tool–workpiece interfaces. Elastic deformation of the cutting wedge due to the normal

contact stress may play a signiﬁcant role for wedges having high rake angles. Normally,

it does not affect signiﬁcantly the distribution of the normal and shear stresses on the

tool–chip interface.

Experimental studies of the inﬂuence of various thermophysical properties of the tool

material on the tribology of the tool–chip interface are very complicated, so it requires

vast experience and knowledge on the relevant properties of the work and tool materials.

This is because the selection of the pairs “tool–work” materials has to be accomplished in

a certain sequence when one property is altered while the other remains the same. It can-

not be accomplished within the tool and work materials normally used in the practice of

machining. Therefore, copper, lead and aluminum were used in the experimental studies

as work materials to obtain tool materials with various desired properties, which normally

cannot be used as tool materials due to their insufﬁcient hardness and low hot hardness.

To evaluate the separate inﬂuence of thermoconductivity and chemical properties of the

tool material on the contact characteristics, Poletica [69] proposed to use lead as the work

material. The prime cause for this selection is because lead is chemically passive. More-

over, it does not form solid-state solutions with materials used in machining. Exceptions

are some “soft” materials as magnesium, tin, cadmium and antimony as well as noble

materials as gold and silver. Therefore, lead can be considered as chemically inactive

(inert) with respect to the tool material. Among similar soft materials, lead is charac-

terized by low thermoconductivity that assures relatively high cutting temperatures and

it allows clearly distinguishing the inﬂuence of thermoconductivity of tool materials on

the contact process.

Tests with lead as the work material were carried out using the same tool geometry,

cutting feed and the depth of cut. Figure 3.30(a) shows the results obtained using vari-

ous tool materials. The experimental points correspond to the invariable cutting speed.

166 Tribology of Metal Cutting

4.0

034

(W/mK)

(a)

(b)

4.5

2.0

1.5

Beryllium

copper

HSS M42

Carbide P20 (79%WC, 15%TiC, 6%Co)

Carbide M30 (92%WC, 8%Co)

Ti Grade 1

Carbide M30

Carbide P20

Carbide P30

Carbide P10

Fig. 3.30. Inﬂuence of thermoconductivity of the tool material (k

) on CCR: (a) work material –

lead and (b) work material – steel AISI 1055.

Figure 3.30(b) shows the results for steel AISI 1055. As seen, CCR, and thus the amount

of work of plastic deformation in metal cutting, increases when the thermoconductivity

of the tool material increases. When this is the case, the mean temperature at the tool–

chip interface increases. Therefore, it can be suggested that the relationships shown in

Figs. 3.30(a) and (b) represent the dependence of CCR on the mean contact temperature.

Unfortunately, the experimental results presented in Fig. 3.31(a) do not support this sug-

gestion. As seen, if the mean contact temperature is kept invariable, CCR still depends on

the thermoconductivity of the tool material (Fig. 3.31(b)). It can be concluded, therefore,

that the thermoconductivity of the tool material has a more complicated physical mech-

anism of inﬂuence on CCR and hence on the work of plastic deformation in cutting. The

trend, however, is still the same: the greater the thermoconductivity of the tool material,

the higher is the CCR.

Any change in the mean contact temperature leads to the corresponding change in the

contact pressure at the tool–chip interface. Moreover, this pressure also changes when the

distribution of the contact temperature changes. The thermoconductivity of the tool mate-

rials has the greatest inﬂuence on the distribution of the contact temperature. The results

of a great number of cutting tests with diamond tools showed [69] that a great increase

in the thermoconductivity of the tool material leads to a signiﬁcant shift of the maximum