Astakhov V. Tribology of Metal Cutting

Подождите немного. Документ загружается.

Energy Partition in the Cutting System 87

leads to an increase in the temperature of the chip so that its plastic deformation

increases (curve 1 in Fig. 2.6).

• The work done in the plastic deformation of the chip decreases when the deformation

velocity increases according to Eq. (2.33). It is represented by curve 2 in Fig. 2.6.

• The elastic zone at the tool–chip contact formed at a certain cutting speed leads

to the reduction in the plastic deformation of the chip and thus lowers the CCR,

starting from this cutting speed. Then, the amount of plastic deformation due to the

formation of the elastic zone increases and stabilizes at a certain level as reﬂected

by curve 3 in Fig. 2.6.

Summing up the inﬂuence of these factors caused by and dependent on the cutting speed,

one can obtain the resultant curve 4 (Fig. 2.6), which resembles the known curve of the

inﬂuence of the cutting speed upon CCR obtained experimentally [12]. The analysis

presented, however, allows us to understand the relative impact of different factors

correlated with the cutting speed on the plastic deformation of the chip and thus to

understand the physics of the phenomenon. The inﬂuence of many important external

parameters such as the cutting ﬂuid, pre-heating, cryogenic cooling, MQL technique,

and many others can be evaluated in terms of their inﬂuence on the efﬁciency of the chip

formation process.

2.4.4 Generalization

Other parameters that have a strong inﬂuence on CCR are the cutting feed (f ), tool

cutting edge angle (κ

), cutting edge inclination angle (λ

) and tool rake angle (γ

). As

known [7], the cutting feed (f ), tool cutting edge angle (κ

) and cutting edge inclination

angle (λ

) affect CCR through the uncut chip thickness (t

) which, in turn, may have a

different inﬂuence at different cutting speeds (ν). This probably was the root cause for

many inaccurate conclusions drawn from experimental results in the past. To resolve the

problem, the power of the similarity theory in metal cutting should be utilized [2].

The Péclet criterion. The metal cutting system includes moving heat sources, i.e. the

tool moves relative to the workpiece and the chip moves relative to the tool. As a result,

similarity numbers used in thermodynamics to deal with moving heat sources [23–25]

should be utilized for thermodynamic analyses of metal cutting. Unfortunately, this is

not the case in traditional studies on thermal aspects of metal cutting including tribo-

logical interfaces where traditional steady-state thermodynamic analysis of heat transfer

commonly used today as, for example, in [20,26,27].

The Péclet criterion, often referred to as the Péclet number, is widely used in the thermal

analysis of technical systems subjected to moving heat sources [23–25]. As pointed out

by Astakhov, this criterion should be used in metal cutting [2]. The Péclet criterion

is a dimensionless number expressing the ratio of advection to thermal diffusion. It is

expressed by

Pe =

, (2.34)

88 Tribology of Metal Cutting

where U is the velocity scale, L is the horizontal length scale and w

is the thermal

diffusivity.

Molecular diffusion of heat is negligible when Pe > 10, i.e. a heat source moves faster

than the velocity of heat expansion.

In metal cutting, the Péclet criterion is represented in terms of machining process

parameters as follows [2,28]

Pe =

νt

, (2.35)

where ν is the velocity of a moving heat source (the cutting speed) (m/s) and w

is the

thermal diffusivity of the work material (m

/s),

ρ)

, (2.36)

where k

is the thermoconductivity of work material

(

m ·s ·

◦

))

and (c

ρ)

is the

volume speciﬁc heat of work material



◦



The Péclet number is a similarity number, which characterizes the relative inﬂuence of

the cutting regime

(

νt

)

with respect to the thermal properties of the workpiece material

(

)

.IfPe > 10, the heat source (the cutting tool) moves over the workpiece faster

than the velocity of thermal wave propagation in the work material and so, that the

relative inﬂuence of the thermal energy generated in cutting, on the plastic deformation

of the work material is only due to the residual heat from the previous tool position [8].

If 2 <Pe<10, the thermal energy makes its strong contribution to the process of plastic

deformation during the cutting and thus to the tribological conditions at tribological

interfaces. Calculations of Pe for different cutting conditions can be found in [2].

In metal cutting tests, a simpliﬁed form of the Péclet criterion (νt

) can be used for a

given work material.

Experimental results. Figure 2.7(a) shows the inﬂuence of cutting speed on CCR for

different feeds. Figure 2.7(b) shows what happens if the Péclet criterion is used as

the independent variable. Figure 2.8 presents another example of the experimental data

obtained in the machining of tool steel H13. Such a representation allows the reduction

in the number of cutting tests needed to study the amount of plastic deformation in the

metal cutting process. Moreover, it helps in revealing the mutual inﬂuence of the cut-

ting regime, tool geometry and physical properties of the work material on this plastic

deformation. For example, it is clearly shown that the amount of plastic deformation in

cutting a work material having low thermoconductivity is greater, compared to that in

cutting a work material having higher thermoconductivity, if the other cutting param-

eters remain the same. It can be stated that the experimental results obtained, for the

ﬁrst time, reveal the correlation of the thermoconductivity of the work material and the

amount of plastic deformation in its machining. In other words, the results obtained

quantify one of the most important qualitative characteristics of the work material,

Energy Partition in the Cutting System 89

0 70 140 280

1.8

2.0

2.2

2.4

2.0

1.8

1.00 3.02.0

2.4

2.2

n (m/s)

0.125 mm/rev

0.200 mm/rev

0.280 mm/rev

0.390 mm/rev

0.500 mm/rev

0.75 mm/rev

(a)

(b)

Fig. 2.7. The chip compression ratio vs. cutting speed for different feeds (a) and generalized

correlation between CCR and Pe criterion (b). Work material – steel AISI 1030, tool material –

carbide P20, rake angle γ

= 10

◦

, cutting edge angle κ

= 60

◦

, depth of cut d

= 2 mm (after

Astakhov [28]).

i.e. “machinability.” Using the work of plastic deformation which is the sole property

of the work material involved in the cutting process, one can determine machinabilities

of various work materials quantitatively.

Analyzing the results discussed, one may argue that the inﬂuence of tool geometry is

not accounted for. To address this concern, the following should be explained. The tool

rake angle is the only tool geometry parameter that might affect the work of plastic

deformation. The inﬂuence of the tool rake angle on CCR is shown in Fig. 2.9. As

shown, CCR does not depend on the tool rake angle.

Based upon the results obtained, the following generalizations can be made:

• Plastic deformation is a nuisance for the metal cutting process and thus it should be

reduced in order to increase the efﬁciency of the process. The rule of thumb here

is: less the plastic deformation, better the cutting process.

• The ﬁnal shear strain used to assess plastic deformation in metal cutting is not a

relevant characteristic because it does not correlate with the known properties of

90 Tribology of Metal Cutting

2.0

3.0

70 140

2.0

3.0

n(m/s)

f = 0.1 mm/rev

0.2 mm/rev

0.3 mm/rev

(b)

(a)

Fig. 2.8. CCR vs. Pe criterion. Work material – tool steel H13, tool material – carbide M10, rake

angle γ

=−10

◦

, cutting edge angle κ

= 60

◦

, depth of cut d

= 2 mm (after Astakhov [28]).

70 140 210

1.2

2.0

2.8

+20°+10° 0°

−10°

−20°

g :

Fig. 2.9. CCR vs. Pe criterion for different rake angles. Work material – steel AISI 1045, tool

material – carbide P20, cutting edge angle κ

= 60

◦

, depth of cut d

= 2 mm (after Astakhov [28]).

the work material. CCR represents the true strain in plastic deformation and can

be used to calculate the elementary work spent over plastic deformation of a unit

volume of the work material. Knowing the elementary work, the total work done by

the external force applied to the tool can then be calculated. As a result, CCR can

be used as the prime parameter for the optimization of the metal cutting process.

Considered together with the work of plastic deformation, CCR reveals the energy

spent in cutting. Moreover, CCR is a post-process parameter and thus there are a

number of simple, though forgotten, ways to measure this parameter accurately in

metal cutting.

Energy Partition in the Cutting System 91

• The cutting speed inﬂuences the energy spent on the deformation of the chip through

the temperature, dimensions of the deformation zone adjacent to the cutting edge and

the velocity of deformation. For the ﬁrst time, the relative impact of each of these

parameters on the chip compression ratio is revealed, and thus the experimental

dependence of CCR on the cutting speed is explained.

• To avoid the typical misrepresentation of the experimental data on CCR, it is pro-

posed to determine this parameter as a function of the Péclet criterion. Such a

representation allows accounting for the combined inﬂuence of the cutting regime

and physical properties of the work material.

2.5 Practical Analysis of the Physical Efﬁciency of the Cutting System

A series of turning tests were carried out to reveal the inﬂuence of various parameters of

the cutting system on its efﬁciency. General purpose cutting inserts made of P20 carbide,

having the shape SNMM 150612 SN-HT were selected for the test. A special tool holder

was designed and made to provide these inserts with various rake angles. Figure 2.10

shows the inﬂuence of rake angle. As shown, the efﬁciency of the cutting system increases

with the rake angle, this result was anticipated because it follows the usual machining

practice. More pronounced effect of the rake angle is observed when the depth of cut,

cutting speed and feed are increased. This inﬂuence is greater for difﬁcult-to-machine

materials (as an example, the results for steel AISI 52100 are presented).

Figure 2.11 shows the inﬂuence of depth of cut. As shown, the depth of cut may affect

the efﬁciency of the cutting system in considerably different ways depending upon the

particular combination of the cutting parameters and properties of the work material.

The results obtained are in contradiction to the common belief that the cutting process

becomes “better” as the depth of cut increases.

Figure 2.12(a) shows the inﬂuence of cutting speed on the efﬁciency of the cutting system.

As shown, although this inﬂuence depends on many cutting parameters, the inﬂuence of

work material is of prime importance. This is natural because a great part of the energy

“wasted” in the cutting process is spent on the plastic deformation of the chip and the

workpiece surface. Therefore, machining of more brittle work materials is more efﬁcient

than that of the ductile ones. Although this fact is well known in machining practice,

the existing metal cutting theory, operating with shear strength and ﬂow-shear stress,

cannot explain it. However, when one accepts the approach discussed, this problem

disappears (as well as many other problems in understanding and implementation of the

metal cutting theory). Although the inﬂuence of cutting speed according to Fig. 2.12(a)

seems to be at odds with the existing perception of machining, it is correct because

increasing the cutting speed causes higher heat generation on the tool–chip and tool–

workpiece interfaces. Moreover, because CCR decreases with the cutting speed (Fig. 2.9),

the relative tool–chip velocity increases even further causing the intensiﬁcation of heat

generation at the tool–chip interface and thus additional energy losses.

The cutting feed has a marked effect on the system efﬁciency (Fig. 2.12(b)) for difﬁcult-

to-machine and brittle materials, while the inﬂuence of cutting speed and depth of cut

92 Tribology of Metal Cutting

Efficiency, η

(%)

Steel 52100, n = 0.5 m/s, d

= 1 mm

−10 0 +10

Rake angle, g(°)

f = 0.17 mm/rev

f = 0.11 mm/rev

f = 0.07 mm/rev

Steel 52100, f = 0.11 mm/rev, d

= 1 mm

Steel 52100, n

= 0.5 m/s, f = 0.11 mm/rev

n = 0.3 m/s

n = 0.5 m/s

n = 0.6 m/s

= 1.0 mm

Rake angle, g(°)

0−10 +10

−10 0

Rake angle, g(°)

+10

= 1.5 mm

= 0.5 mm

Fig. 2.10. Inﬂuence of rake angle on the efﬁciency of the cutting system. Work material – steel

AISI 52100 (after Astakhov [3]).

0.5

AISI 1045

1.5

AISI 52100

n= 0.5 m/s, s= 0.11 mm/rev

n =1.2 m/s, s=0.11 mm/rev

Depth of cut, d

(mm)

1 − g = −10°

2 − g = 0°

3 − g = +10°

Efficiency of the cutting system, η

(%)

Fig. 2.11. Inﬂuence of depth of cut on the efﬁciency of the cutting system for different work

materials (after Astakhov [3]).

Steel AISI1035,

=1.5m/s, d

=1 mm

Gray cast iron,

=3m/s, d

=1 mm

0.8

AISI 1045

1.5

0.3 0.6

AISI 52100

f=0.11 mm/rev, d

=1 mm

f=0.11 mm/rev, d

=1 mm

−

g =

−

g = 0

−

g =

Efficiency of the cutting system,h

(%)

Cutting speed, n (m/s)

0.170.07

Cutting feed, f (mm/rev)

Steel AISI1035,

=1.5m/s, d

=1 mm

0.07

0.17

Gray cast iron,

=3m/s, d

=1 mm

g = 0

−

g =

−

g = 0

−

g =

AISI 52100

AISI 1045

f=0.11 mm/rev, d

=1 mm

0.07

0.17

=0.5m/s, d

=1 mm

(a)

(b)

g = 0

Fig. 2.12. Dependence of the efﬁciency of the cutting system on: (a) cutting speed and (b) cutting

feed (after Astakhov [3]).

94 Tribology of Metal Cutting

are more noticeable for easy-to-machine materials. These results also reﬂect the well-

known practical ﬁnding that one should use as high feed as allowed by the strength of

the tool, quality of machining and other constraints in order to increase the efﬁciency of

the cutting system.

It follows from the data presented in Figs. 2.10–2.12 that the efﬁciency of the cutting

system depends to a large extent on the properties of the work material. For a wide range

of commonly machined steels, this efﬁciency is in the range of 25–60%. It means that

40–75% of the energy consumed by the cutting system is simply wasted. Most of this

wasted energy is spent at the tool–chip and tool–workpiece interfaces. Naturally, this

energy lowers the tool life, affects the shape of the chip produced, and leads to the neces-

sity of using different cooling media that, in turn, lowers the efﬁciency of the machining

system as more energy is required for the cooling medium delivery and maintenance.

The results obtained are of enormous signiﬁcance in metal cutting as they primarily

quantify the margin allowed for process improvements. Even in machinery, where the

waste of resources (energy) due to the ignorance of tribology hardly exceeds single digit,

this waste is estimated to be approximately one-third of the world’s energy consumption

[1]; so the study and optimization of tribological process are considered as having great

importance. Today, more money is spent for the research in tribology. The objective

of this research is understandably the minimization and elimination of losses resulting

from friction and wear at all levels of technology where rubbing of surfaces is involved.

As claimed [1], research in tribology leads to greater plant efﬁciency, better performance,

fewer breakdowns and signiﬁcant savings.

In metal cutting, the situation is entirely different from that of the design of tribological

joints in modern machinery. In the latter, a designer is rather limited by the shape of

the contacting surfaces, materials used, working conditions set by the outside operating

requirements, use of cooling and lubricating media, etc. In metal cutting, practically any

parameters of the cutting system can be varied in a wide range. The modern machine

tools do not limit a process designer with the selection of cutting speeds, feeds and depth

of cut. The tool materials, geometry of cutting inserts and tool-holder nomenclature avail-

able at his disposal is very wide. The selection of cooling and lubrication media and their

application techniques are practically unlimited. Although the chemical composition of

the work material is normally given as set by the part designer, the properties of this

material can be altered in a wide range by heat treatment, forging and casting conditions.

The only problem in the selection of the optimal tribological cutting parameters is the

lack of knowledge on the metal cutting tribology. Therefore, the study and optimization

of the tribological conditions at these interfaces have a great potential in terms of reduc-

tion in the energy spent in cutting, increase in tool life, reduction and elimination of

coolants, etc.

2.6 Energy Balance of the Cutting System

To improve the analysis and optimization of the cutting system, one should ﬁrst analyze

the energy ﬂows in it, besides determining its efﬁciency. Because any alteration of the

system parameters leads to a change in the energy distribution within the cutting system.

Energy Partition in the Cutting System 95

Although the distribution obtained may not affect the physical efﬁciency of the cutting

system, it might change the outcomes of the cutting process. For example, the use of

coating applied on the tool contact surfaces may improve the tool life. At the same time, it

changes the distribution of thermal energy in the cutting system. Because many coating,

particularly multi-layered, have low thermal conductivity, and a greater portion of the

thermal energy generated in the cutting process goes into the workpiece creating higher

machining residual stresses compared to uncoated tools. This is a typical example of

the non-system consideration of the cutting process to improve a single outcome while

others may get much worse. Therefore, a special master program should be developed

not only to calculate the efﬁciency of the cutting system, but also to analyze the energy

ﬂows in this system.

In the author’s opinion, such a program should use a ﬂowchart of energy ﬂows in the

cutting system similar to that shown in Fig. 2.13. Using this ﬂowchart, the correlation

between these energy ﬂows and the properties of the cutting system can be established

in order to evaluate the efﬁciency of this cutting system.

Energy losses due to friction and deformation of the cutting wedge (Q

) and the chip

) are unavoidable. As such, the energy loss in the cutting wedge can be thought of as

= f



,υ

,σ



, (2.37)

where f

is the known function explained in [29–32], A

is the potential energy of

the cutting wedge and E

,υ

and σ

are the in-process mechanical characteristics of

the cutting wedge material (tool material) (the modulus of elasticity, Poisson’s ratio,

strength). These energies depend on the original mechanical characteristics of the cutting

wedge material and the thermal energies accumulate in the cutting wedge

= f



tγ

tα



(2.38)

= f



tγ

tα



(2.39)

= f



tγ

tα



, (2.40)

Fig. 2.13. Flowchart of energy ﬂows in the cutting system.

96 Tribology of Metal Cutting

where f

and f

are the functions described in [33], E

,υ

and σ

are the standard

mechanical characteristics of the cutting wedge material (tool material), Q

is a part

of Q

accumulated in the tool and Q

tγ

tα

and Q

are the thermal energies shown

schematically in Fig. 2.13.

tγ

= f

(

)

(2.41)

tα

= f





(2.42)

= f

(

)

(2.43)

= f



tγ

tα



, (2.44)

where f

–f

are the functions described in [30,31,34–38], k

and k

are the ther-

moconductivities of the tool material, workpiece material and material of the chip,

respectively, V

and V

are the volumes of the tool, workpiece and chip, respectively,

and d

are the tool–chip contact length and width, and A

is the ﬂank contact area.

The heat generated due to friction on the tool rake face is calculated as

= f



tγ



(2.45)

and the heat generated due to friction on the tool ﬂank surface is

= f

(

tα

)

(2.46)

Functions f

and f

are described in [2,12,27,30,31].

The potential energy of the tool,

= U

−Q

(2.47)

is spent on the friction work done on the rake and ﬂank surfaces

tγ

= f



,υ



(2.48)

tα

= f



,υ



(2.49)

and on the work done over the chip. The energy loss in chip deformation is cal-

culated as

= f



,υ

,σ



, (2.50)

where f

–f

are the functions described in [11,12,27,30], U

= U

− W

tγ

− W

tα

a part of W

which is spent on the work done over the chip, and E

,υ

and σ

are the