Astakhov V. Tribology of Metal Cutting

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Tribology of the Tool–Chip and Tool–Workpiece Interfaces 147

0.E+00

2.E+06

4.E+06

6.E+06

8.E+06

1.E+07

0.0 0.2 0.4 0.6 0.8 1.0

p(y

)

(a)

(b)

Fig. 3.13. Example of the FEM analysis: (a) tool–chip contact stress distribution and (b) von Mises

stress distributions (A = 0.40; C = 1.99; E = 3.58; G = 5.17 ... O = 11.5; P = 12.3; σ

max

12.7 MPa) in the workpiece and chip (after Astakhov and Outeiro [73]).

Astakhov [36] compared the evolution of shear stress during the cut-in period with that of

stabilized cutting and showed that the shear stresses at the tool–chip interface are almost

30% higher during cut-in period than that in stabilized cutting to achieve the same effect

(for example, to form the stress level corresponding to the beginning of failure of the

work material). This is the prime cause for the reduction of tool life in interrupted cutting.

Figure 3.14(b) shows the evolution of the normal stress up to the beginning of each

chip formation cycle. As seen, the presence of a partially formed chip affects the normal

148 Tribology of Metal Cutting

0.4

0.8

0.4

0.8

Shear stress (GPa)

0 0.27 0.54 0.81

0 0.27 0.54 0.81 0 0.27 0.54 0.81 0 0.27 0.54 0.81

1.08 0 0.27 0.54 0.81 1.08

Distance from the cutting edge (mm)

Normal stress (GPa)

0.4

0.8

1.2

1.6

2.0

Distance from the cutting edge (mm)

(a)

(b)

Rake angle

−18

Rake angle

−18

Rake angle

+18

Fig. 3.14. Dynamics shear (tangential) (a) and normal (b) stress distributions at the beginning of

a new chip formation cycle. Curves 1 to 5 correspond to increasing load with the increment of

250 N, respectively. Work material – AISI 1045 steel, tool material – P20.

stress distribution. The maximum normal stress becomes higher when increasing the rake

angle. Moreover, the location of this maximum shifts towards the cutting edge.

As with the shear stress, a comparison of the results shown in Fig. 3.14(b) with the known

results shown in Fig. 3.1(a) shows that there is no contradiction in the reported results.

In other words, all the reported normal stress distributions (curves 1 to 6 in Fig. 3.1(a))

at the tool–chip interface may occur as being considered at different instants over a chip

formation cycle and under different cutting conditions.

The above analysis of the normal and shear stress distributions at the tool–chip interface

results in two important conclusions:

• Increasing the rake angle leads to the reduction in the contact length that results in

an increase in the maximum shear and normal stresses at this interface. Moreover,

the maximum of the normal stress shifts towards the cutting edge. Because the use

of high positive tool geometry (which stands for high rake angles) has become a new

tendency recently introduced and followed widely by the leading tool producers, the

transfer rupture stress of tool materials for such applications should be increased.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 149

• The ﬂuctuations of the normal and shear stresses at high frequencies [36] explain the

high scatter in the results of using different coatings. Obviously, these ﬂuctuations

should be accounted for in the design of any particular coating.

3.2.4 Experimental study

The basic tribological characteristics of the cutting process determine not only tool wear

or contact temperature but also other physical characteristics of this process. These

tribological characteristics cannot be considered apart from other parameters of the metal

cutting process as they affect these parameters directly. It is very important to establish

the prime and dependent parameters as well as their correlations in order to control the

cutting process. The following considerations are based on the excellent experimental

results obtained by two prominent researchers in the ﬁeld of metal cutting tribology,

namely Poletica [76] and Zorev [2]. In the author’s opinion, these results have never

been properly presented, understood and appreciated. As a result, they were never used

for further developments in the design and optimization of metal cutting processes and

cutting tools although the potential of these ﬁndings is tremendous.

Methodology. In the tests, the contact length was measured on the actual cutting insert

under a microscope. To verify the accuracy of such a measurement, the cutting insert

before the actual testing was plated with a thin copper layer by dipping it in copper

sulfate solution. The comparison of the obtained results showed no noticeable difference

between the results obtained using these two methods of contact length determination.

In special cases, however, when the tests were conducted using soft work materials and

thus, there were no clearly visible wear marks on the tool rake face, a thin layer of a

neutral water-based paint was used to determine the contact length accurately.

The average integral contact temperature was measured using the tool–work thermo-

couple technique. Its principle is discussed later in this chapter. The calibration of such

a thermocouple is discussed in Ref. [36,68].

Other characteristics were obtained through the measurements of the cutting force

components [36].

Contact length. As discussed above, the tool–chip contact length known as the length

of the tool–chip interface determines major tribological conditions at this interface as

temperatures, stresses, tool wear, etc. This length is found to be very sensitive to any

change in the parameters and characteristics of the cutting process. Therefore, it is of

great interest to ﬁnd out the correlations between these characteristics and the contact

length because the optimization of tribological processes at the tool–chip interface can

be accomplished only when these correlations are known and well understood.

Figure 3.15(a) shows the correlation between contact length and the uncut chip thickness

for different work materials. As seen, the contact length increases with the uncut chip

thickness for all materials tested although at different rates. This rate is much greater for

soft (HB47) copper having high thermal conductivity than for relatively hard (HB190)

titanium alloy having low thermal conductivity.

150 Tribology of Metal Cutting

0 0.2 0.4

(mm)

0 0.2 0.4

(mm)

(a) (b)

(mm) I

(mm)

Fig. 3.15. Correlation between the contact length and the uncut chip thickness: (a) for different

work materials: 1 – copper, 2 – lead, 3 – aluminum 2014, 4 – steel AISI E9310, 5 – cadmium

and 6 – titanium Grade 1, (b) for different work materials under constant ζ: 1 – copper (ζ = 10),

2 – steel AISI E9310 (ζ = 3.2), 3 – beryllium copper UNSC17000, HB110 (ζ = 4) and 4 – tool

steel O7 (ζ = 2.45).

Analyzing the correlations shown in Fig. 3.15(a), one should keep in mind that the

uncut chip thickness directly affects the chip compression ratio (CCR) which also affects

the contact length. Therefore, it is of interest to separate the inﬂuence of these two

characteristics on the contact length. Figure 3.15(b) shows the inﬂuence of uncut chip

thickness on the contact length under invariable CCR (ζ = Const). As follows from this

ﬁgure, the contact length is directly proportional to the uncut chip thickness for different

work materials. Although Fig. 3.15(b) shows only correlations for four work materials,

this rule was proven to be true for a wide variety of work materials. Therefore, the uncut

chip thickness can be regarded as an independent parameter of the cutting process that

directly affects the contact length.

The contact length decreases with the cutting speed for different work materials as follows

from the data illustrated in Fig. 3.16. As seen, steep dependences hold for relatively low

cutting speeds while the contact length shows a little dependence on the cutting speed in

the range of normal and high cutting speeds. This can be attributed to the corresponding

change in the average contact temperature at the tool–chip interface, which changes

signiﬁcantly with the cutting speed for low cutting speeds and then this change slows

down when the cutting speed increases further. Therefore, the dependences shown in

Fig. 3.16 reﬂect the result of mutual action of the cutting speed and temperature (the

temperature–speed factor as termed by Zorev [2]). Figure 3.17 shows that the same

tendency holds for a wide variety of steels. As seen, the contact length also reduces

with the hardness (the carbon content) of the steel. The scatter in experimental results is

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 151

0 80 160 240 n (mm/min)

(mm)

Fig. 3.16. Correlation between the contact length and the cutting speed for different work mate-

rials: 1 – titanium Grade 1, 2 – beryllium copper UNSC17000, HB200, 3 – beryllium copper

UNSC17000, HB110, 4 – Armco iron, 5 – copper and 6 – aluminum 2014.

120 160

2.0

(mm)

3.0

1.0

200 240

n(mm/min)

Fig. 3.17. Correlation between the contact length and the cutting speed for different steels:

1 – AISI 1010 (0.1% C), 2 – AISI1020 (0.2% C), 3 – AISI 1060 (0.6% C), 4 – AISI 1080 (0.8% C),

5 – AISI 07 (1.2% C). Normal rake angle γ

= 10

◦

, depth of cut d

= 4 mm and cutting feed

f = 0.156 mm/rev.

152 Tribology of Metal Cutting

0.2

−40

(°)

4020

−20

1.0

1.8

(mm)

Fig. 3.18. Inﬂuence of rake angle on the contact length: 1 – cadmium, 2 – steel AISI E9310

= 0.16 mm, ν = 22 m/min), 3 – steel AISI E9310 (t

= 0.28 mm, ζ = constant = 2.5).

much smaller for harder steels. Analysis of Figs. 3.16 and 3.17, however, shows that the

dependence of the contact length on the cutting speed directly resembles the dependence

of CCR on the cutting speed (Fig. 2.5 and Ref. [77]).

Figure 3.18 shows the inﬂuence of normal rake angle on the contact length for different

work materials. As seen, the contact length decreases with the rake angle. Moreover,

this conclusion is true even when the CCR is kept invariable. Therefore, the rake angle

affects the contact length in two ways, namely, directly and through CCR. One should

notice, however, that the inﬂuence of rake angle on the contact length is not signiﬁcant.

As follows from the foregoing considerations, among the three considered factors (the

uncut chip thickness, cutting speed and rake angle), only the uncut chip thickness affects

the contact length directly. The other two factors affect the contact length through CCR.

This allows to introduce a similarity criterion to be used in metal cutting tribology,

namely the Poletica criterion (Po-criterion)

Po =

(3.40)

The Po-criterion, strongly depends on CCR and weakly depends on the rake angle as

follows from the experimental data presented in Fig. 3.19(a). As seen, the inﬂuence of

rake angle is within the normal experimental scatter. Moreover, it was found that the

Po-criterion remains invariant to changes in the mechanical and physical properties of

the work material. As can be seen in Fig. 3.19(b), the hardness of the work material

does not affect the dependence of Po-criterion on CCR. Considering this test, one should

note that beryllium copper is an excellent test material because its mechanical properties

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 153

513

2 4 21

HB110

HB200

HB320

f = 0.07

0.15 0.26 0.34

(mm/rev)

Po Po

g = −10°

g =0°

g =10°

g =20°

(a) (b)

Fig. 3.19. Inﬂuence of chip compression ratio on Po-criterion: (a) in machining steel AISI E9310,

tool material P20 (79% WC, 15%TiC, 6% Co), cutting feed f = 0.07 −0.43 mm/rev and cutting

edge angle κ

= 70

◦

; (b) in machining beryllium copper UNSC17000 of different hardnesses. Tool

material – HSS M30 (92% WC, 8% Co).

can be changed in a wide range by heat treatment while the phase composition and

microstructural parameters remain practically unchanged.

Figure 3.20 presents the results of cutting tests with various work and tool materials

having a wide range of physical and mechanical properties. In this ﬁgure, the normalized

chip compression ratio, ζ

is used instead of ζ. It is calculated as

, (3.41)

where d

is the chip width. This is done to include into consideration the results of

the cutting test with copper and Armco iron. When cutting these two materials, the chip

width changes considerably compared to the width of cut (the depth of cut), whereas for

many other work materials, the ratio d

≈ 1 if measured properly [36].

Although some scatter of experimental results can be observed in Fig. 3.20, it can be

concluded that a single-valued functional relationship Po = f

(

)

exists within a wide

variety of cutting parameters. Statistical evaluation of the obtained experimental results

allows obtaining the following relationship for the Po-criterion

Po =

= ζ

, (3.42)

where k

= 1.5 when ζ

< 4, and k

= 1.3 when ζ

≥ 4.

154 Tribology of Metal Cutting

1 5 9 13 17

Armco iron, g = 10°

Steel E9310,M30 cutter, g = −10°, 0°, 10°, 20°

Steel O7, annealed, g = 10°

Beryllium copper, HB110, g = 10°

Beryllium copper, HB200, g = 10°

Beryllium copper, HB320, g = 10°

Copper, HSS M35 cutter, g = 10°

Copper, UNSC17000 cutter, g = 25°

Copper, Ti Grade 1 cutter, g = 25°

Fig. 3.20. Inﬂuence of chip compression ratio on Po-criterion in machining various work materials

using different tool materials and tool rake angles.

The correlation between the Po-criterion and CCR obtained experimentally and expressed

by Eq. (3.42) represents the condition of static equilibrium of the chip. Figure 3.21(a)

shows the simpliﬁed model of chip formation at the last phase of a chip formation

cycle for the cutting tool with the full rake face. In this picture, ϕ is the angle of ﬁnal

inclination of the surface of maximum combined stress approximated by a plane, point

B is the coordinate of application of normal force N (which can be thought of as the

coordinate of the center of gravity of the distribution of the normal stress along the tool–

chip contact), point D is the coordinate of application of normal force F

on the surface

of maximum combined stress approximated by a plane, OC = l

is the contact length.

Let us introduce the dimensionless coordinates of points B and D as follows:

(3.43)

sin ϕ

(3.44)

Because the chip is in static equilibrium, the sum of the moments of the normal forces

is zero, i.e.

Po =

sin ϕ

(3.45)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 155

(a) (b)

Fig. 3.21. Simpliﬁed model of chip formation at the last phase of a chip formation cycle: (a) for

the cutting tool with the full rake face and (b) with the restricted length rake face.

Normal forces N and F

can also be expressed through the resultant force R using the

angle of action, ω

(Fig. 3.21(a)) as

N = R sin

(

+γ

)

(3.46)

= R sin

(

+ϕ

)

(3.47)

Substituting Eqs. (3.46) and (3.47) into Eq. (3.45), one can obtain

Po =



1 + tan ω

tan

−1



(

cos γ −sin γ tan ω

)

(3.48)

Dimensionless coordinate

is deﬁned by the shape of distribution of the normal stress

because the location of point B is determined by the position of the center of gravity

of the distribution area. As proven by Zorev [2], the shape of this distribution curve

is stable depending weakly on the process parameters. It means that

varies within

very narrow range so, to the ﬁrst approximation, it can be accepted that

= constant.

Then, it follows that

= constant. Using these approximations (which, in fact, quite

accurately resemble the reality of the cutting process), one can represent Eq. (3.48) as

Po =

= f

(

ϕ, ω

)

(3.49)

i.e. the Po-criterion is a function of two angles, namely ϕ and ω

Zorev showed [2] that, for a given work material, ϕ and ω

are directly correlated.

As such, the Po-criterion is a function of only one angle, say ϕ. It follows from the

156 Tribology of Metal Cutting

model shown in Fig. 3.21(a) that

ϕ = arctan

cos γ

ζ − sin γ

(3.50)

where, by deﬁnition, CCR ζ = t



. It directly follows from Eq. (3.50) that ϕ depends

on CCR, ζ, and on the rake angle, γ. However, the inﬂuence of γ is not signiﬁcant as

follows from the structure of Eq. (3.50). Therefore, it can be written with reasonable

accuracy

Po =

= f

(

)

(3.51)

The same conclusion follows from the above-discussed experimental results represented

by Eq. (3.42).

Although the obtained result is known for years, it has never been explained. In the

author’s opinion, a possible explanation is rather simple as it directly follows from the

generalized model of chip formation discussed in Chapter 1. Because cracks form at

points A and O (Fig. 3.21(a)) due to the combined action of compressive and bending

stresses, the maximum combined stress at these points forms due to compressive force

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

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

by both the contact area and the distance l

. When the cutting parameters (primarily

the properties of the work material) are changed so that CCR increases, a much higher

contact area and l

are needed to achieve the same critical combined stress at points A and

O because the cross-sectional area of the partially formed chip–cantilever increases with

CCR. This explanation can be easily veriﬁed experimentally using tools with restricted

contact length.

When the tool rake face is straight, the contact length l

sets itself to the value required

by the static equilibrium condition (Eq. (3.48)). This contact length is termed as the

natural contact length. If the length of the rake face is made smaller than the natural

contact length, then the resultant contact length known as restricted contact length, l

is as shown in Fig. 3.21(b). As shown in this ﬁgure, the restricted rake face is made

with the normal rake angle, γ

while the secondary rake face is made with γ

.Itis

understood that according to the explanation provided, if the contact length (the contact

area in reality) decreases, the contact stress must increase to provide the same combined

stress at points A and O.

When a tool with restricted contact length is used, the equilibrium condition set by

Eqs. (3.48) and (3.49) should be justiﬁed with this new contact length. However, this

length is no more a function of ϕ and ω

but rather becomes an independently controlled

parameter.

Some representative experimental results are shown in Fig. 3.22. As seen, the reduc-

tion of the contact length leads to the corresponding increase in the contact stress as

was predicted above. Moreover, this increase exactly corresponds to an increase in the

compressive force and bending moment needed to keep the critical combined stresses