Astakhov V. Tribology of Metal Cutting

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Tribology of the Tool–Chip and Tool–Workpiece Interfaces 187

Eq. (3.70) becomes

∆

= arccos



0.5 +



(

0.5 − τ

/σ

)

sin ϕ

cos

(

ϕ −γ

)

sin α

≈ 1.25



sin α

, (3.71)

where Br is a similarity criterion, referred to as the Briks criterion [36,68],

Br =

cos γ

ζ − sin γ

(3.72)

The experimental results showed that h

≈ 0.5ρ

is a good approximation when cutting

ductile materials [68]. As such Eq. (3.71) becomes

∆ = ρ



0.5 sin ϕ

cos

(

ϕ −γ

)

sin α



(3.73)

As it follows from Eqs. (3.71) and (3.73), the contact length on the tool ﬂank is a function

of the tool rake angle and CCR.

Using the above considerations and the model shown in Fig. 3.46, one can obtain

expressions for h

and h

= ρ



1 −



1 + Br



(3.74)



1 −



1/1 + Br



cos γ +Br sin γ

(3.75)

According to Poletica [69], the stress distribution at the ﬂank contact surface is as

follows

c−f

(x) = τ

exp



−3



∆





, (3.76)

where τ

is the yield shear strength of the work material and x is the distance from

the cutting edge. Integrating Eq. (3.76) yields the mean shear stress at the tool–ﬂank

interface

c−f

= 0.505τ

(3.77)

188 Tribology of Metal Cutting

which is in excellent agreement with the experimental result obtained by Zorev [2] and

Chen and Pun [83]. Knowing the mean shear stress, one can calculate the mean normal

stress as

0.505τ

, (3.78)

where µ

is the apparent friction coefﬁcient on the tool–ﬂank contact area.

Figures 3.43–3.45 allow to obtain this friction coefﬁcient for various combinations of

the work and tool materials because this friction force is calculated as the ratio of the

shear and normal stresses at the tool–workpiece interface.

Bearing in mind Eq. (3.77), one can obtain the expression for friction force at the tool

ﬂank as

= τ

c−f

ce−a

∆ = 0.505τ

∆ = 0.625τ



sin α

, (3.79)

where b

is the width of cut which calculates depending on the tool geometry as discussed

in Appendix A.

The normal force at the tool–ﬂank interface is then calculated as

0.625τ



sin α

(3.80)

3.3.3 Generalizations

The results of the theoretical and experimental studies on the tribological conditions at

the tool–workpiece interface can be summarized as follows:

• The distribution of the normal and shear stresses have maxima in the region adjacent

to the cutting edge. Then the level of stresses stabilizes over the contact length

becoming zero at the end of the contact. The smaller the curvature of the workpiece

surface, the higher is the level of contact stresses at the end of the contact, where

both stresses may have second maxima.

• There is no or very small region of the plastic part of the interface.

• Adhesion takes place in the region adjacent to the cutting edge while simple friction

is the case on the rest of the interface.

• The normal and shear stresses depend on the mechanical properties of the work

material (primarily on its hardness), while other material characteristics, including

material type, do not seem to have any noticeable effect.

• The stresses at the interface strongly correlate with the processes in the deformation

zone and tool geometry through CCR and Br.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 189

• Although the level of stress, temperatures and strength of adhesion bonds are much

weaker at the tool–workpiece interface compared to those at the tool–chip inter-

face, the sliding velocity at the tool–workpiece interface is much higher (by CCR).

The more ductile or difﬁcult-to-machine material, the higher is the difference in the

sliding velocity. This explains why ﬂank wear is often greater than that on the tool

rake face in machining these types of the work material.

3.4 Temperature at the interfaces

3.4.1 Temperatures signiﬁcant to the tribology of metal cutting

Although it is pointed out in almost any book on metal cutting that temperature, and

particularly, its distribution has a great inﬂuence in machining [60], no one study known

to the author quantiﬁes this inﬂuence. Instead, it is stated in very general and qualitative

terms that temperatures in metal cutting affect “the shear properties” of the work material

and, therefore, they affect the chip-forming process itself, and through their effect on

the tool, they determine the limits of the process and mode of tool wear. To address

each of these points, a great number of works on temperatures in metal cutting have

been published. Apart from many contradictive results that can be readily found in the

published works and can be logically explained by the difference in the experimental

methodologies and accuracy of calibration, numerical and analytical models and the

assumptions adopted in both the models, the major concern with these works is their

practical signiﬁcance. In other words, there is no answer to a simple question: “What

should one do with the found temperature and its distribution?”

Trent and Wright concluded [37] that the major objective of heat consideration in metal

cutting is to explain the role of heat in limiting the rate of metal removal when cutting the

higher melting point metals. They concluded that there is no direct relationship between

cutting forces or power consumptions and the temperature near the cutting edge.

Zorev [2] did not consider temperature as an important factor itself. Considering the

energy balance in metal cutting, he calculated that the maximum temperature at the end

of the chip formation zone does not exceed 270

◦

C for plain and alloyed steels while

a considerable reduction in the mechanical properties of these material starts only at

temperatures over 300

◦

According to Childs et al. [58], the two goals of temperature measurements in machining

are: (a) the quantitative measurements of the temperature distribution over the cutting

region is more ambitious, but very difﬁcult to achieve, and (b) is less ambitious to measure

the average temperature at the tool–chip contact. Although the authors presented short

description of various methods of temperature measurements in metal cutting, they did

present results of such measurements and their use in the considerations of tool wear and

other outcomes of the machining process.

Altintas [84] did not consider temperature to be a factor not only in the cutting mechanics

but also in his consideration of dynamic stability and structural errors of the machining

system.

190 Tribology of Metal Cutting

Gorczyca in his book attempted to show the practical application of metal cutting

theory [56]. Unfortunately, he presented only the qualitative inﬂuence of temperature.

He operated with the so-called burnout temperature and cutting temperature. The burnout

temperature is deﬁned as that temperature “at which the tool cannot efﬁciently perform

the cutting process.” Unfortunately, this characteristic is not listed in any speciﬁcation

of tool materials.

Shaw in his book [34] presented a very detailed description of various methods of tem-

perature assessment in metal cutting. He pointed out that there are several temperatures

of importance in metal cutting:

• The shear plane temperature because it may, in his opinion, inﬂuence on the ﬂow

shear stress of the work material and also has a major inﬂuence on the temperature

of the tool face and on that of the tool ﬂank.

• The temperatures on the tool face and ﬂank are very important to crater wear rate

and rate of wear-land development on the tool ﬂank surface. The temperature on

the tool face also plays a major role relative to the size and stability of the built-up

edge.

• The ambient temperature of the workpiece is also important because it directly

affects the above three listed temperatures.

A simple critical analysis of the temperatures listed by Shaw shows that the temperature

of the shear plane cannot play the role assigned by Shaw. First of all, it does not affect

the ﬂow shear stress of the work material as conclusively proven by Zorev’s calculations

based on the experimental results [2] and by Astakhov using direct comparison of cutting

and compression [36]. Second, the temperature at the upper boundary of the deformation

zone (that is the shear plane in the terminology used by Shaw) cannot signiﬁcantly affect

the temperatures at the interfaces. This is because the shear plane temperature does not

exceed 200

◦

C while the temperatures on the tool–chip and tool–workpiece interfaces are

3–6 folds higher.

As others, Shaw did not consider the use of the temperature data in metal cutting

consideration as for example in the assessment of tool wear.

Oxley [35] considered some temperature calculations in the relation of temperature rise in

the deformation zone and its possible inﬂuence on the mechanical properties of the work

material in terms of reduction of the ﬂow shear stress. In his consideration of tool life,

Oxley came to a conclusion that the temperature of the tool ﬂank should be considered

in the tool life calculation. According to Oxley, this average tool ﬂank temperature is

11% lower than that at the tool–chip interface, although the practice of machining and

other available information on the matter do not support this statement.

In the author’s opinion, a confusion with temperatures in machining and their proper

applications to the assessment of the process output parameters stems from non-

tribological considerations, where the temperature considered alone without other

tribological conditions at the interfaces has very little signiﬁcance, particularly when it

is considered apart from the energy balance of the cutting system discussed in Chapter 2.

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 191

The analysis of the energy balance in metal cutting (Chapter 2), heat sources and heat

partition in the metal cutting system [36], results of similarity studies of the metal cutting

process [36,68], and physical aspects of tool wear and tool resource [77,85–87] allowed

to list temperatures that are most relevant in metal cutting tribology:

• The average integral contact temperature as measured by the tool–work thermo-

couple technique. As shown by the practice of metal cutting research [68,85,88,89],

this is the most stable and relevant characteristic that can be measured with high

accuracy, great repeatability and reproducibility. The importance of this temperature

is that this is the only temperature that can be reliably correlated with tool life and

to be used in the optimization of the cutting process, as discussed in Chapter 4.

Hereafter, this temperature is referred to as the cutting temperature.

• The maximum contact temperature. This temperature is of great interest for the

developers of various tool materials as this maximum temperature should not cause

the plastic lowering of the cutting edge (discussed in Chapter 4) or catastrophic

tool failure. The location of the region of maximum contact (normally occurs at the

tool–chip interface) temperature with respect to the cutting edge is also of some

methodological interest.

3.4.2 Assessment of temperatures in metal cutting

There are four basic methods in the assessment of temperature in metal cutting, namely,

analytical, numerical, similarity and experimental.

Analytical and numerical methods. There were a great number of various attempts

to assess the temperature and its distribution in metal cutting using various analytical

(well summarized by Shaw [34], Reznikov [90] and Komanduri [91–93]) and numerical

methods as FEA [94–97] and boundary elements [98] methods. Regardless of the great

diversity of these methods, the following drawbacks make their results of little help in

the consideration of the tribological aspects in metal cutting:

• They cannot predict in principle the cutting temperature (in the sense of the deﬁnition

given above in Section 3.4.1).

• They are based on the single-shear plane model with severe drawbacks as discussed

in Chapter 1.

• They did not account for the signiﬁcant part of energy spent in the deformation zone

as pointed out by Atkins [99,100].

• None of the models used in the analytical and numerical simulations accounts for

the real contact stresses at the tool–chip and tool–workpiece interfaces.

• Numerical methods based on the FEA analysis suffer severe errors when applied to

analyze great plastic deformations. To account for these deformations, dimensional

change cause a complete restructuring of the resulting mesh and the error due to

remeshing would overshadow the changes in the solution.

192 Tribology of Metal Cutting

The following assumptions are common in the known analytical and numerical modeling

of metal cutting:

• The tool is ideally sharp and unworn.

• The chip formation process is continuous without plastic zone attached to the tool

rake face (known as the built-up edge).

• The chip moves as a rigid body relative to the tool.

• Heat ﬂow is steady in the cutting tool and quasi-steady in the chip and the workpiece.

• The deformation of the chip in the shear plane is uniform, so the heat generation is

uniform over the chip cross section.

• The temperature of the chip is uniform as it leaves the shear zone.

• When modeling the chip heating at the tool–chip interface, the chip is viewed as a

semi-inﬁnite solid when modeling the moving heat source effect at this interface.

Likewise, the workpiece is also viewed as a quarter-inﬁnite solid when modeling

the stationary heat source effect at the tool–chip interface.

• When modeling the tool heating at the tool–chip interface, the dimensions of

the cutting wedge are sufﬁciently large, so it can be represented as a quarter-

inﬁnite solid when modeling the stationary heat source effect at the tool–chip

interface.

• Heat losses due to convection and radiation for all surfaces of the chip, workpiece

and tool are negligibly small.

Naturally, such assumptions make the modeling unrealistic.

Although the results of analytical and numerical modeling cannot be used today in tribo-

logical analyses of the metal cutting process, their further developments should not be

discouraged. The problem is in using the correct physical model and its boundary condi-

tions. In FEA method, the emerging meshless methods (LS Dyna) look very promising

for numerical analysis in metal cutting.

Similarity methods. Similarity methods are much less sensitive to the particular model

used in modeling particularly when applied to the thermal analysis of metal cutting

[36,68]. The results of similarity analysis allow calculating the maximum temperature at

the interfaces as well as the cutting temperature.

The temperature of the tool rake face at point O (Fig. 3.21) can be estimated using the

energy balance approach. The energy E

O−t

released in the vicinity of this point can be

thought of as the sum of the energy of plastic deformation (E

O−pd

) (Eq. (2.24)) and

energy required for the formation of new surfaces (E

O−ns

) [101], i.e.

O−t

= E

O−pd

O−ns

= A

νt

O−ns

(3.81)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 193

On the other hand, the thermal energy generated in this region can be represented as

given in Ref. [68]





erf



PeBr

, (3.82)

where Br is the Briks criterion (Eq. 3.72), Pe is the Péclet criterion (Chapter 2, Section,

Péclet Criterion Eq. (2.35)), erf (z) is the “error function” encountered in integrating the

normal distribution (which is a normalized form of the Gaussian function) [102,103] and





is the speciﬁc heat of the work material. Thus, energy balance E

O−t

= Q

yields in the expression for the maximum temperature at point O



(

O−ns

/νt

)







erf



PeBr

(3.83)

Analysis of Eq. (3.83) shows that the maximum temperature at point O is determined by

the mechanical and thermal properties of the work material as well as by the parameters

of the machining regime. As the cutting speed and uncut chip thickness increase (Pe =

νt

as per Eq. (2.35)), product PeBr increases. When PeBr ≥ 20, erf

√

(PeBr/4) = 1

and the expression for the maximum temperature at point O simpliﬁes to

(

O−ns

/νt

)





(3.84)

In this equation, A

is calculated using CCR (Eq. (2.24)) and E

O−ns

is calculated using

the data presented by Atkins [101]. Calculations, however, showed that in a wide range

of Pe when PeBr ≥ 20, this temperature becomes invariant to the cutting parameters and

can be considered as a characteristic of the work material. For the limiting stabilized

cutting regime, the maximum temperature at point O is determined as

= n

(3.85)

where n

is a proportionality coefﬁcient. For all metallic work materials n

= 0.25 and

is the melting temperature of the work material (Table 3.3).

The maximum temperature at the tool ﬂank, θ

ﬂ−max

occurs in the middle of the tool–

workpiece interface. This temperature is calculated as

ﬂ−max

= θ



0.5 +

0.36 sin

0.25

1.25



PeE

+ψ



, (3.86)

where E

is the relative sharpness similarity criterion,

(3.87)

194 Tribology of Metal Cutting

Table 3.3. Melting points of some work materials.

Material Symbol Melting point

(

◦

)

Aluminum Al 659

Brass (85 Cu, 15 Zn) Cu+Zn 900–940

Bronze (90 Cu, 10 Sn) Cu+Sn 850–1000

Cast iron C+Si+Mn+Fe 1260

Chromium Cr 1615

Copper Cu 1083

Inconel Ni+Cr+Fe 1393

Iron Fe 1530

Lead Pb 327

Magnesium Mg 670

Manganese Mn 1260

Monel Ni+Cu+Si 1301

Nickel Ni 1452

Silicon Si 1420

Stainless steel Cr+Ni+Mn+C 1363

High-carbon steel Cr+Ni+Mn+C 1353

Medium-carbon steel Cr+Ni+Mn+C 1427

Low-carbon steel Cr+Ni+Mn+C 1464

Tin Sn 232

Titanium Ti 1795

Tungsten W 3000

Zinc Zn 419

and

0.6n

α−θ

1.25



PeE

cos α

sin

0.25

α × erf



PeBr

(3.88)

where

α−θ

1 +



0.24F

0.3

sin

0.1

√

PeE

0.2



, (3.89)

where F

is the similarity criterion that accounts for the thermal properties of the tool

and work materials as well as for the tool geometry

, (3.90)

where k

and k

are the thermal conductivities of the tool and work materials,

(

m ×s ×K

))

, β

is the cutting wedge angle in the normal plane (rad) (Appendix A),

is the angle between the major and the minor cutting edge in the reference plane (rad)

Tribology of the Tool–Chip and Tool–Workpiece Interfaces 195

that calculates through the tool cutting edge angles of the major (κ

) and minor (κ

)

cutting edges (Appendix A) as

= π −

(

+κ

)

(3.91)

D is the similarity criterion that accounts for the parameters of the uncut chip thickness

(Appendix A)

D =

ce−a

(3.92)

As before, l

ce−a

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

ce−a

= d



sin κ

The distribution of temperature over the contact length ∆ (Fig. 3.46) is deﬁned as (the

axis is perpendicular to the cutting edge)

ﬂ

(

)

= θ

⎛

⎜

⎝

0.5 + 0.25

sin

0.25

1.25



PeE

∆

+2.12ψ



∆



1 −

∆



⎞

⎟

⎠

(3.93)

The second additive in brackets in Eq. (3.93) is a decreasing function within

0 ≤ x

/∆ ≤ 1 while the third additive is a function having its maximum at x

/∆ = 0.5.

Therefore, the maximum contact temperature at the tool–chip interface is in the range of

0 ≤ x

/∆ ≤ 0.5. The exact location of the point of maximum is found by differentiating

Eq. (3.93) and setting the differential to zero. The obtained result is



∆



max

= 0.25 +



0.0635 −

0.1 sin

0.5

erf



PeBr

α−θ

PeE

2.5

cos α

(3.94)

Analysis of Eq. (3.94) shows that with increasing the cutting speed (Pe), the second

term under the square root decreases which leads to increasing

(

/∆

)

max

. This second

term is equal to zero in the limit, so the maximum

(

/∆

)

max

= 0.5. Conversely,

when the cutting speed decreases, the maximum temperature on the tool–workpiece

interface shifts towards the cutting edge. In the limit,



0.1 sin

0.5

erf



PeBr

α−θ

PeE

2.5

cos α

= 0.0625



that the minimum

(

/∆

)

max

= 0.25. Therefore, for a wide range of practical machining

conditions, 0.25 ≤

(

/∆

)

max

≤ 0.5.

Analysis of Eq. (3.94) also shows that the higher the thermoconductivities of the tool and

work materials and the smaller the radius of the cutting edge, the smaller is

(

/∆

)

max

i.e. the closer is the point of the maximum temperature to the cutting edge.

196 Tribology of Metal Cutting

1.0

0.2

1.2

0.4 0.6 0.8

/∆

0.75 0.25 0.50 1.00

1.4

1.6

1.8

2.0

0 0 1.25

1.0

1.5

2.0

2.5

3.5

3.0

(

)(

)

Fig. 3.47. Temperature distributions: (a) over the tool–ﬂank interface, ψ

= 1.415, Pe = 35,

Br = 0.715 and α = 10

◦

, (b) over the tool–chip interface, ψ

= 2.0.

An example of the calculations of the temperature distribution over the tool–workpiece

interface using Eq. (3.93) is shown in Fig. 3.47(a).

The distribution of temperature over the tool rake face can be calculated as (the x

axis

is perpendicular to the cutting edge):

(

)

= θ



1 + ψ





, when 0 ≤ x

≤ l

/2, (3.95)

(

)

= θ



1 + ψ





0.6



, when x

/2, (3.96)

where

0.9675n

γ−θ

√

PeBr

erf



PeBr

cos γ +sin γ −Br

(

cos γ −sin γ

)

cos γ +Br sin γ

(3.97)

and

λ−θ



1 +

0.25FD

0.3

√

sin γ+Br cos γ

√

PeBr

0.3



cos γ+sin γ−Br

(

cos γ−sin γ

)

0.2





(3.98)