Astakhov V. Tribology of Metal Cutting

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Tribology of the Tool–Chip and Tool–Workpiece Interfaces 177

in the energy of plastic deformation of the layer being removed. Therefore, the

properties of the combination “substrate-coating” should always be considered.

Unfortunately, this fact is not appreciated in the selection of the substrate and

coating materials. As a result, there are many “unexplainable” (by metal cutting

practitioners and coating application specialists) signiﬁcant difference in the results

on the performance of “the same” coating under “similar” conditions.

3.3 Tool–Workpiece interface

3.3.1 Zorev’s results

The contact phenomena on the tool ﬂank surface are of interest because their understand-

ing allows the explanation of tool ﬂank wear and the formation of the major characteristics

of the machined surface. Nevertheless, there are few known studies on the matter avail-

able. Surprisingly, modern books on metal cutting do not consider these phenomena.

The ﬂank wear is considered using the age old Taylor’s tool life equation having a

phenomenological nature.

Another way to look at the problem is to understand the physical processes taking place at

the tool–workpiece interface called the ﬂank contact area. Although the contact processes

on the tool ﬂank are determined by the normal and frictional forces acting at the tool–

workpiece interface, the ratio of the normal and contact forces does not follow those

obtained in the standard mechanical tests due to complexity of the contact process on

this interface. These processes include severe friction and plastic deformation of the

machined surface.

A comprehensive analysis of the attempts to derive analytical expression for the ﬂank

forces is presented by Zorev [2]. He came to a surprising conclusion that if the ﬂank

wear is small, the depth of cut is great and the workpiece hardness is “moderate,” then

the forces on the ﬂank may not be taken into consideration because they are small in

comparison with those on the rake face. On the contrary, if ﬂank wear is large, the depth

of cut is small, particularly when machining hard materials, the ﬂank forces become

comparable with the forces on the tool rake. As such, the normal force on the ﬂank face

of the major cutting edge can be calculated as

= σ

c−f

sin κ

≈

sin κ



kg/mm



(3.60)

The friction force on this face is

= µ

c−f



sin κ



≈ 0.2HB



sin κ





kg/mm



(3.61)

and the normal force on the ﬂank surface of the minor cutting edge calculates as



kg/mm



, (3.62)

178 Tribology of Metal Cutting

where HB is Brinell hardness of the work material, h

and h

are the widths of the ﬂank

contact surfaces of the major and minor cutting edges, respectively, σ

c−f

is the mean

normal contact stress at the tool–workpiece interface and µ

is the apparent friction

coefﬁcient at this interface.

The mean normal (σ

c−f

) and shear (τ

c−f

) stresses on the ﬂank face contact area are

calculated as

c−f

≈

≈ σ

UTS



kg/mm



(3.63)

c−f

≈ 0.2HB ≈ 0.6σ

UTS



kg/mm



(3.64)

According to the initial Zorev’s analysis [2], these stresses do not depend on the cutting

regime and type of tool material. Having noticed this discrepancy later, Zorev carried out

a great number of cutting tests to establish the above-mentioned dependences. More than

20 different work materials having hardness from HB80 (annealed pure iron) to HRC

65 (quench-hardened steel) were tested. Figure 3.41 shows the experimental results for

cutting speeds that correspond to a 90-min tool life. In Zorev’s opinion [2], the reduction

of σ

c−f

with decreasing the cutting speed is attributed to the “secondary shear” on the

100 200 300 400

800

HB (kg/mm

)

c−f

1600

2400

3200

UTS

(MPa)

100 600 800 1000 1200 1400

20 30 40 50 60

HRC

4000

(MPa)

600

1200

1800

Steel - P20 Cast iron - M30

Steel - P01

= 0.1 mm

0.5 mm

1.0 mm

2.0 mm

(MPa)

c−f

Fig. 3.41. Contact stress at the tool–workpiece interface according to Zorev.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 179

rake face, which protects the ﬂank contact surface. The same explanation is provided for

the inﬂuence of depth of cut, d

: if tool life is kept constant, the cutting speed decreases

as the depth of cut increases. This statement is, however, in direct contradiction with

Zorev’s experiments on tool life (criterion – the width of the ﬂank wear land) where

increased cutting speed resulted in a longer tool life [2].

Another important experimental fact should be noted in Fig. 3.41, namely, the inﬂuence

of tool material. For the same tool life, the contact stress σ

c−f

and thus the forces on

the ﬂank contact face for the less wear-resistant carbide P01 are approximately 25%

lower than for more wear-resistant P20 carbide. Nevertheless, Zorev recommended [2]

using the same apparent coefﬁcient of friction µ

= 0.6 for calculating the ﬂank frictional

force regardless of tool material and other cutting conditions.

3.3.2 Assessment of tribological characteristics

Major tribological characteristics. According to a generally accepted hypothesis, the

contact between the tool ﬂank and the workpiece machined surface occurs due to the

elastic recovery (or spring back) caused by plastic deformation of this surface in cutting.

Figure 3.42(a) shows an idealized case where the cutting tool is perfectly sharp as com-

monly assumed in the most known modeling of the metal cutting process (see Fig. 1.1).

The radial cutting force F

(the complete force diagram is considered in Fig. 1.1(c))

causes the plastic deformation of the machined surface which, after the cutting edge

passes over this surface, recovers by δ

causing the contact with the tool ﬂank up to

point A. The elastic recovery, therefore, should be proportional to this radial cutting

force, which, in turn, depends to a large extent on the uncut chip thickness t

The cutting edge of any real tool, however, is not perfectly sharp so that a much real

contact picture is shown in Fig. 3.42(b). In this ﬁgure, the cutting edge radius forms

Workpiece

Tool

(a)

(b)

Fig. 3.42. Contact of the tool ﬂank with the workpiece: (a) ideally sharp tool as assumed in

modeling and (b) real contact with the tool–workpiece interface.

180 Tribology of Metal Cutting

the transition curve BD between the rake and the ﬂank surfaces. This makes the position

of point C uncertain, where the chip separates from the workpiece. The wear land DE

is also present in any real cutting tool or, at least, it forms in the ﬁrst few seconds of

machining. Part EF represents the ﬂank–workpiece contact surface. If the radius of the

cutting edge is small, the normal (F

) and the friction (F

) forces acting on the ﬂank

are results of the interactions between the wear land DE and the machined surface of the

workpiece.

The basic tribological characteristics of the tool–workpiece interface are:

• The sliding velocity which is normally equal to the cutting speed. In some special

tools, where the feed velocity(ies) is signiﬁcant, the magnitude of this velocity is

equal to the magnitude of the resultant velocity of a considered point of the cutting

edge.

• The contact length – the margin and then, after some time of cutting, the margin

and ﬂank wear length of the tool–chip contact, h

• The friction force, F

• The speciﬁc frictional force which is the mean shear stress

c−f

ce−a

, (3.65)

where l

ce−a

is the active length of the cutting edge. Normally, l

ce−a

= d

/sin κ

• The normal force at the tool–workpiece interface, F

• Mean contact stress at the tool–workpiece interface

c−f

ce−a

(3.66)

• Mean contact temperature at the tool–workpiece interface, θ

fl−av

Experimental studies. Any experimental method of evaluation of contact stresses has

its “sensitivity” evaluated by the minimum contact area for which it is yet still possible to

obtain reliable data on contact stress distribution. The area of the contact surface on the

tool ﬂank face of a “sharp” tool is very small, so it is out of range of modern experimental

methods for contact stress distribution. Therefore, the evaluation of contact stresses is

possible for a tool having appreciable natural (due to tool wear) or artiﬁcially made (for

a study) wear land on the tool ﬂank surface.

Poletica [69] studied the contact stresses on the tool ﬂank using the photoelastic method.

A series of turning and orthogonal cutting (shaping on a milling machine) tests were

carried out. Lead discs were used as the work material. The cutting speed was 0.2 mm/s.

The wear land of various widths on the tool ﬂank face was simulated by grinding the

corresponding lands with a zero ﬂank angle.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 181

0.2

x (mm)

c−f

(MPa)

0.4 0.6 0.8

x/h

0 0.2

0.4 0.6 0.8

= 0.55 mm

= 0.15 mm

= 0.10 mm

= 1 mm

= 2 mm

= 1 mm

= 2 mm

(a)

(b)

c−f

(MPa)

c−f

(MPa)

c−f

(MPa)

Fig. 3.43. Normal and shear stress distributions at the tool–workpiece interface in machining of

lead at ν = 0.2mm/s, d

= 3 mm: (a) in turning with different uncut chip thicknesses (t

), x is

the distance from the cutting edge, (b) in shaping with two different widths of the lank on the ﬂank

contact surface (h

The distributions of the normal and shear stresses obtained in the turning test with three

different uncut chip thicknesses are shown in Fig. 3.43(a). As seen, both stresses gradually

decrease with increasing distance from the cutting edge and abruptly decrease in the

vicinity of the end of the modeled land. A comparison of the experimentally obtained

distributions with those obtained in the modeling of punch penetration discussed earlier

shows their similarity although the distribution of the normal stress on the ﬂank face

differs from that on the rake face by the presence of an abrupt segment at the end of

the land.

182 Tribology of Metal Cutting

The distribution of the normal stress at the end of contact (Fig. 3.43(a)) shows that there

is no increase in the contact stress in the vicinity of this end as might be expected. For this

kind, the end condition is similar to that for a punch having sharp corners (Figs. 3.7(a)

and (b)). This, however, can be readily explained by the curvature of the workpiece.

This curvature “weakens” the contact in the vicinity of point E (Fig. 3.42(b)) that, in

turn, lowers the contact stresses at the end of the contact. The wider the width of the

wear land, the smaller is the diameter of the workpiece and the weaker is the contact at

point E.

The distributions shown in Fig. 3.43(b) obtained in orthogonal cutting (shaping), where

the machined surface is ﬂat, conﬁrm this point. As seen, the stress distribution in this

case is more uniform and the distinctive stress maxima are observed in the vicinity of

point E. Increasing the width of the ﬂank land results in the smoothing of the maxima

in the vicinity of point E, while the maxima at the cutting edge end remain sharp.

The analysis of the distribution of the stress on the tool–workpiece interface results in

the following conclusions:

• The distribution of the shear stress over the tool–workpiece interface does not have

the same ﬂat region as the shear stress distribution over the tool–chip interface

does over the plastic part of the tool–chip contact (adjacent to the cutting edge).

It suggests that there is no or little small plastic contact zone at the tool–workpiece

interface.

• The ratio of the shear and normal stresses at the region adjacent to the cutting edge

(which could be thought of as the apparent friction coefﬁcient) reaches 1 or even

higher. In this respect, it is similar to that found at the elastic part of the tool–chip

interface. This creates conditions for adhesion to occur at this interface.

• Over the rest of the tool–workpiece contact length, the ratio of the shear and normal

stresses stabilizes approaching 0.5–0.7. In this respect, the tribological process at

the tool–workpiece interface is closer to the classical hard pin-on-soft disc case than

that at the tool–chip interface.

A good coincidence of the normal and shear stresses distributions obtained for various

uncut chip thickness (Fig. 3.43) is an important experimental result. This is the ﬁrst

experimental evidence that the stresses at the tool–workpiece interface do not depend on

the uncut chip thickness.

Experiments also showed that the stress distribution curves do not change with the rake

angle while the mean contact stresses do. For example, an increase in the rake angle

leads to a decrease in the mean contact stresses at this interface. The introduction of

the cutting ﬂuid at the tool–workpiece interface reduces the mean shear contact stresses

while the mean normal contact stress is not affected. The shape of the stress distribution

curve does not change in this case either.

In parallel with the discussed photoelastic tests, the actual cutting force has been mea-

sured and the total forces acting on the tool ﬂank were determined as the force intercept

at zero uncut chip thickness. In these tests, the vertical (F

) and radial (F

) components

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 183

Table 3.2. Comparison of normal and shear forces at the tool–workpiece interface found using

various experimental methods.

Cutting conditions Rake angle Forces at the tool–workpiece interface

Photo

elasticity

Extrapolation Photo

elasticity

Extrapolation

Dry 0 15.6 14.5 16.2 16.0

15 12.1 12.0 12.9 13.5

With the cutting

ﬂuid (kerosene)

0 13.9 13.0 12.0 11.0

15 12.9 11.5 9.5 8.5

of the resultant cutting force have been measured using a dynamometer. Then the normal

) and shear (F

) forces acting at the tool–workpiece interface have been determined.

Table 3.2 shows these forces in comparison with those obtained using the method of pho-

toelasticity. A fairly good agreement of the normal and shear forces at the tool–workpiece

interface obtained using these two methods conﬁrms the validity of the force intercept

at zero uncut chip thickness method.

The stresses at the tool–workpiece interface are parts of the general state of stress in the

formation zone. Because the angle of action, ω

(Fig. 3.8) is directly determined by the

work in the plastic deformation of the work material, there should be direct correlation

between CCR, ζ and F

. Moreover, this correlation should be more vivid for a small

ﬂank wear land.

Zorev pointed out [2] that there is a correlation between CCR and F

. He explained it

by the correlation between CCR and the workhardening of the work material. As such,

the correlation between ζ and F

should be stronger for work materials with a greater

ability for workhardening. Poletica argued [69] that if it is so, the correlation between

ζ and F

due to workhardening of the work material should be the same for the entire

length of the tool–workpiece interface while the correlation between ζ and F

due to

the ﬁeld of stress around the cutting edge shows up at this interface in the vicinity of the

cutting edge.

To clarify the issue, the study of the correlation between ζ and F

was conducted for a

wide range of work materials and cutting conditions [69]. The cutting tests were carried

out using “sharp” tools having no signiﬁcant ﬂank contact land. To accomplish this,

the cutting tool edge preparation was used before each run and the test time did not

exceed several minutes. This time was more than sufﬁcient to reach thermal balance in

the cutting system. The wear land after the test did not exceed 0.05–0.07 mm even for

the hardest work materials.

Figure 3.44(a) shows a typical correlation of the ﬂank forces F

, F

and CCR ζ for

ductile materials. As seen, both forces increase with ζ. When CCR is small, the shear

force F

is less than the normal force, F

so the apparent friction coefﬁcient is less

than 1. When ζ increases, the shear force F

increases becoming ﬁrst equal to and

then greater than the normal force F

, so the apparent friction coefﬁcient exceeds 1.

184 Tribology of Metal Cutting

100

200

F(N)

100

F(N)

200

HB220

HB320

HB110

(a)

(b)

Fig. 3.44. Correlations between CCR and forces on the tool ﬂank: (a) for copper, rake angle

γ = 10

◦

, tool cutting edge angle κ

= 70

◦

and depth of cut d

= 3 mm, (b) beryllium copper

of different hardness, rake angle γ = 10

◦

, tool cutting edge angle κ

= 70

◦

and depth of cut

= 2 mm.

This can only be explained by the corresponding increase in the stress in the vicinity of

the cutting edge. In other words, the zone of the work material brought to the plastic

state in the vicinity of the cutting edge increases. This leads to the condition where the

greater part of the ﬂank land is in contact with the work material brought to the plastic

state.

When the hardness of the work material increases, the ratio of the shear and normal

stresses (the apparent friction coefﬁcient) decreases although both forces F

and F

f 1

grow (Fig. 3.44(b)). Each hardened state of beryllium copper yields in the group of

experimental points shifted along the ζ axis. Compiling these data, Poletica concluded

[69] that there is a correlation between the apparent friction coefﬁcient at the tool–

workpiece interface and CCR.

Figure 3.45 shows the experimentally obtained normal and shear forces on the tool ﬂank

surface as functions of CCR for a wide variety of work–tool material combinations.

The increase in the tendency of force with the hardness of the work material is especially

noticeable for the normal force (F

). The greater the hardness, the higher is the location

of the corresponding curve F

= f(ζ).

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 185

200

400

600

04 8121620

048121620

(N)

200

400

600

(N)

Fig. 3.45. Correlations between CCR and forces on the tool ﬂank for various combination of the

work and tool materials: 1 – beryllium copper HB320-carbide M30, 2 – beryllium copper HB200-

carbide M30, 3 – steel 07-carbide P20, 4 – Ti Grade 1-carbide M10, 5 – steel A514-carbide P20,

6 – Armco iron-carbide P20, 7 – cadmium-HSS M42, 8 – Lead-HSS M42, 9 – Al 2014-HSS M42,

10 – beryllium copper HB110-carbide M30, 11 – copper -Ti Grade 1, 12 – HSS M42 and 13 –

Al-HSS M42.

It is important to note that for three materials having similar mechanical properties

characterized by their hardness (steel 07, beryllium bronze tempered to HB200 and Ti

Grade 1), the experimentally obtained relationships F

= f(ζ) are very close. At the

same time, the chip-formation and tribological parameters at the tool–chip interface as

the contact length, CCR, apparent friction coefﬁcient, etc. are considerably different

(Figs. 3.16, 3.25, 3.26, etc.).

Similarity methods. To estimate the forces acting on the tool ﬂank and contact stresses,

consider the model shown in Fig. 3.46. According to this model, the cutting tool has the

cutting edge radius, ρ

. Due to this radius, the total uncut chip thickness (t

) is separated

into the actual uncut chip thickness (t

) and the layer of thickness (h

) to be burnished

by the round part adjacent to the tool ﬂank face. The arc distance between points A and

D is designated as ∆ and is given by

∆ =

(

∪AC

)

(

∪CD

)

= ρ

ψ +

sin α

, (3.67)

186 Tribology of Metal Cutting

Workpiece

Chip

Tool

∆

Fig. 3.46. Model of the chip–workpiece interface.

where ψ is the central angle corresponding to arc AC and h

is the elastic recovery of

the machined surface.

Because ψ = arccos

(

1 − h

/ρ

)

, then ψ =arccos (1 – h

/ρ

) and

∆ = ρ



arccos



1 −



sin α



(3.68)

It is known [68] that the cutting process ceases and the layer to be removed undergoes

plastic deformation similar to burnishing when

≤ 0.5 −

, (3.69)

where σ

is the yield strength of the work material, τ

is the strength of adhesion

bonds at the tool–workpiece interface determined using results of the adhesion tests [82].

As discussed above, the strength of the adhesion bonds depends on the mutual adhesion

properties of the tool and work materials.

Substituting Eq. (3.69) into Eq. (3.68), one can obtain

∆

= arccos



0.5 +





0.5 −



sin α

(3.70)

The plastic deformation of the surface layer can be characterized by the burnishing factor

m = h

which according to Poletica [69] can be approximated by CCR. As a result,