Astakhov V. Tribology of Metal Cutting

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Improvements of Tribological Conditions 347

Table 6.5. Thermal conductivity (k

), thermal diffusivity (α

), kinematic viscosity (ν

volumetric expansion coefﬁcient (β

) and Prandtl number (Pr) for dry vapor and water as

functions of temperature.

(

◦

)

×10

(

◦

))

×10





×10





×10

(

◦

)

Air

20 2.59 21.4 15.06 24.10.703

50 2.83 25.7 17.95 30.90.698

100 3.21 33.6 23.13 26.80.688

150 3.56 42.1 28.94 23.60.683

200 3.93 51.4 34.85 21.10.680

250 4.27 61.0 40.61 19.10.677

300 4.60 71.6 48.33 17.40.674

350 4.91 81.9 55.46 16.00.676

Water (along saturation line)

20 59.8 14.3 1.006 1.81 7.02

30 61.8 12.9 0.805 3.21 5.43

40 63.5 15.3 0.659 3.87 4.31

50 64.8 15.7 0.556 4.49 3.54

60 65.9 16.0 0.478 5.11 2.98

70 66.8 16.3 0.415 5.70 2.55

60 67.4 16.6 0.365 6.32 2.21

90 68.0 16.8 0.326 6.95 1.95

100 68.3 16.9 0.295 7.52 1.75

that in this case Re > 0.01

= 170

(

−100

)

1.86

(6.13)

Equations (6.12) and (6.13) are valid only for the temperature difference (∆θ

= θ

−

) corresponding to convective boiling. For water and water-based cutting ﬂuids, this

condition is valid when 105

◦

C ≤ θ

≤ 120

◦

C. For other conditions, the heat transfer

coefﬁcient is calculated as

If 120

◦

C ≤ θ

≤ 235

◦

C, then h

= 3.36 ×10

(

−100

)

−1.43

(6.14)

If θ

> 235

◦

C, then h

= 3 ×10



W/m

2 ◦



(6.15)

Equations (6.13)–(6.15) are valid only when water is boiling under the atmospheric

pressure and under natural convection.

As discussed in the previous section, forced convection often takes place in real cutting

systems. As such, the cutting ﬂuid is forced to move over hot surfaces of tool, chip and

workpiece. Such a movement brings changes in the boiling process. First, the natural

348 Tribology of Metal Cutting

value of the contact angle (Fig. 6.4) is changed. Second, the moving ﬂuid detaches the

partially formed bubbles from the surface being cooled before they reach the diameter

deﬁned by Eq. (6.11). Therefore, the ﬂow of the cutting ﬂuid makes the boiling process

weaker so that heat transfer due to evaporation reduces. When the velocity of the cutting

ﬂuid is high, the heat transfer due to evaporation becomes negligibly small and thus

“normal” heat transfer due to forces of convection takes place as discussed in the previous

section.

The opposite is true, however, when ﬁlm boiling takes place. Here, the ﬂow of the cutting

ﬂuid increases heat transfer because this ﬂow blows a blanket or ﬁlm of vapor which

prevents the liquid from wetting the surface. Under the condition of ﬁlm boiling, Zones

2–4 in Fig. 6.5 shift to the right, i.e. towards higher temperature differences. The higher

the cutting ﬂuid velocity, the greater the shift. To the ﬁrst approximation, the heat transfer

coefﬁcient h

in this case, can be calculated accounting for the combined contribution

of the forced convection and boiling as

If h

< 0.5h

, then h

= h

(6.16)

If 0.5 ≤ h

≤ 2h

, then h

−h

(6.17)

If h

> 2h

, then h

= h

(6.18)

Cooling action of air–cutting ﬂuid mixture (mist). As discussed at the beginning of

this chapter, the cost of cutting ﬂuid is approximately 16–17% of the life-cycle oper-

ational cost of machining. This cost continues to rise. It includes the costs associated

with procurement, ﬁltration, separation, disposal and record keeping. Already the costs

of disposal of a cutting ﬂuid are higher than the initial cost of this ﬂuid, and they are still

rising. Even stricter regulations are under consideration for cutting ﬂuid usage, disposal

and worker protection. As a result of all of this, the cutting ﬂuid in wet machining oper-

ations is a crucial economic issue. An alternative, machining with “minimum quantity

lubricant,” or MQL, is gaining acceptance as a cost-saving and environmental-friendly

option in place of some wet machining processes. For example, spray cooling provides

the beneﬁts of the cutting ﬂuid used in ﬂood applications with the added performance

of a high-velocity air–cutting ﬂuid mixture. Therefore, it is of interest to consider heat

transfer in the interactions of hot tool and workpiece surface and air–cutting ﬂuid mixture.

In cooling using an air–cutting ﬂuid mixture, it becomes a case of two-phase cooling

medium. Figure 6.6 shows spherical droplets having diameter d

that moves with veloc-

ity ν

air

towards a hot surface [47]. It is assumed that the concentration of droplets in the

unit volume of the mixture is uniform. The temperature of the hot surface is θ

and that

of the mixture is θ

. When a droplet meets the surface, it deforms so that the diameter

of contact is D

= m

. As such, m

 1.

The thermal energy entering a droplet ﬁrst heats it to the saturation temperature, θ

and then causes its evaporation. For the ﬁrst part, heating, of this two-stage process the

Improvements of Tribological Conditions 349

air

Fig. 6.6. Graphical representation of droplets moving towards a hot surface.

balance equation is

πD

(

−θ

)

= C

p−cf

πd

(

−θ

)

, (6.19)

where τ

is the time of heating. Thus this time can be expressed as

p−cf

(6.20)

For the boiling and evaporation

πD

(

−θ

)

πd

, (6.21)

where τ

is the time of boiling and evaporation, which can be expressed as

(

−θ

)

(6.22)

As the mean heat transfer coefﬁcient for the whole process can be represented as

1−2

+τ

(6.23)

350 Tribology of Metal Cutting

then substituting Eqs. (6.20) and (6.22) into Eq. (6.23), one can obtain

1−2



p−cf

(

−θ

)



p−cf

(

−θ

)

(6.24)

The number of droplets falling simultaneously on the hot surface having an area A

depends on the concentration K

of liquid in the two-phase mixture. As it was assumed,

the concentration of droplets in the unit volume (m

) of the mixture is uniform, this

number is calculated as

dr−V

πd

(6.25)

and on the surface of unit area (m

)itis

dr−A



√

dr−V







(6.26)

As the area of the total surface A

taken by one droplet is 0.25πm

, the total area

taken by all the droplets at any time instant is

hs−dr

= 0.25πm

dr−A

(6.27)

The heat transfer process with the heat transfer coefﬁcient

1−2

takes place over the

area A

hs−dr

of the total surface area A

. On the rest of this surface (over the area

− A

hs−dr

), the heat transfer takes place with the air contained in the two-phase

mixture. The heat transfer coefﬁcient in this process is designated as h

air

. The total

combined heat transfer coefﬁcient for the two-phase mixture is calculated as

c−mix

1−2

hs−dr

−h

air



−A

hs−dr



(6.28)

c−mix

= 1.2K



1−2

−h

air



air

(6.29)

Heat transfer coefﬁcients in this equation are calculated using the above-described

methodologies.

When boiling takes place in rather thin surface ﬁlms of the cutting ﬂuid, whose thick-

ness is close to the diameters of bubbles formed on boiling (d

, Eq. (6.11)), then the

heat transfer coefﬁcient h

would depend on the thickness of the surface ﬁlm, δ

Improvements of Tribological Conditions 351

Reznikov and Resnikov [47], for the surface ﬁlms having a thickness δ

≤ 5 ×10

−3

proposed the following correction factor

cor

= 1.25 exp



−40δ



(6.30)

which is to be used as a multiplier in Eqs. (6.13)–(6.15). Because in the practice of

machining the thickness δ

= (0.5–10) ×10

−3

m, then for many practical cases χ

cor

1.20–1.23.

Cooling action due to heat pipe embedded in the tool. Heat pipes are sometimes

used to cool down the cutting tools [48,49]. Although the theory of heat pipes is well

developed [50,51], there is no simple methodology to calculate the cooling action of heat

pipes that can be used in the practice of tool design.

The heat pipe (Fig. 6.7) basically consists of a thick-walled hermetic container (1) made

up of a high thermal conductivity material. The container encloses some amount of the

easy-to-evaporate working ﬂuid. One end (often called as the evaporator) of the container

is embedded in the unit to be cooled (2) while the other end (often called as the condenser)

contains a heat exchanger (radiator) (3) to release the thermal energy to the surrounding.

Heat applied by a heat source at the evaporator region vaporizes the working ﬂuid in that

section. This also creates a pressure difference that makes the vapor to ﬂow from the

out

h−ex

h−in

hs2

hs1

Fig. 6.7. Model of a vertical heat pipe.

352 Tribology of Metal Cutting

evaporator to the condenser where it condenses releasing the latent heat of vaporization.

The condensed working liquid then returns to the evaporator. This process is capable of

transporting the heat from a hot region to a cold region. The heat pipe transports large

amount of heat with a small temperature difference.

The balance equation for internal surface of the container is constructed assuming that

this container is thermo insulated so that there is no heat exchange with the surrounding

regions between the “hot” and “cold” zones. Thus,

(

hs1

−θ

)

= h

(

−θ

hs2

)

, (6.31)

where h

and h

are the heat transfer coefﬁcients in the boiling and condensation

zones, respectively, θ

hs1

and θ

hs2

are the average temperatures in the boiling and con-

densation zones, respectively, A

and A

are the areas of boiling and condensation

zones, respectively.

The left side of this equation is the amount of thermal energy that enters from the walls

of the container into the boiling liquid in the “hot” zone while the right side is that released

through the walls in the “cold” zone. For the vertical container shown in Fig. 6.7

= πd

h−in

ν1

+0.25πd

h−in

(6.32)

= πd

h−in

ν2

+0.25πd

h−in

(6.33)

To determine the heat transfer coefﬁcient in the boiling zone, one can use Eq. (6.12)

representing it in the following form

= Θ

(

hs1

−θ

)

(6.34)

where

= c

eq−wf





(6.35)

Values of the physical characteristic of working liquid and its vapor in Eq. (6.35) are

taken at temperature θ

The heat transfer coefﬁcient on condensation can be determined using a simpliﬁed model.

The condensed liquid usually appears as liquid droplets (poor wetting) or ﬁlm. In the

cooling of cutting tools, good wetting surfaces for heat tube are usually used so as

to consider the surface condensation. All the thermal energy formed on condensation

of vapor is transferred into the surface (of temperature θ

which is lower than the

temperature of vapor, θ

) through the ﬁlm of condensed liquid. Because the ﬂow in this

ﬁlm is normally laminar, it can be accepted that heat transfer takes place due to thermal

conductivity. Consider an inﬁnitively small element ∆x of the surface ﬁlm condensed on

a vertical surface of a body (Fig. 6.8). As thickness of the ﬁlm, δ

is small, the temperature

Improvements of Tribological Conditions 353

∆x

Fig. 6.8. Model of ﬁlm condensation.

gradient across this ﬁlm can be thought of as

(

−θ

)

and thus, according to the

Fourier law of heat conduction, the speciﬁc heat ﬂux through this ﬁlm is

= k

(

−θ

)

, (6.36)

where k

is the thermal conductivity of the working ﬂuid corresponding to the average

temperature 0.5

(

−θ

)

Because the speciﬁc heat ﬂux is q

= h

(

−θ

)

, the heat transfer coefﬁcient is

calculated as

= k

/δ

(6.37)

As it follows from Eq. (6.37), the determination of the heat transfer coefﬁcient reduces

to that of the thickness of the ﬁlm condensed on the surface, δ

. Nusselt, compiling a

great body of experimental data, proposed the following equation [47]



(

−θ

)



, (6.38)

where µ

is dynamic viscosity of the working ﬂuid, µ

= ν

354 Tribology of Metal Cutting

Substituting Eq. (6.38) into Eq. (6.37), one can obtain

= 1.25



(

−θ

)



(6.39)

For practical calculations, it is necessary to determine the average heat transfer coefﬁ-

cient,

over the total length L

ﬂ

, of the hot surfaces in contact with the condensed ﬁlm

of the cutting ﬂuid as

ﬂ



dx = 1.67



ﬂ

(

−θ

)



(6.40)

As before, ρ

, and µ

in Eq. (6.40) should be considered at the temperature

0.5(θ

−θ

Equation (6.40) is obtained for a vertical wall. If vapor is condensed on a surface inclined

at an angle ϕ

to a horizontal plane, then the heat transfer coefﬁcient is calculated as

= 1.67



sin ϕ

(

−θ

)



(6.41)

and for a horizontal tube having diameter d

it is calculated as

= 1.28



(

−θ

)



(6.42)

By analogy with Eqs. (6.34) and (6.35), the heat transfer coefﬁcient for condensation

can be represented as

= Θ

(

−θ

hs2

)

−0.25

(6.43)

where

= 1.67



sin ϕ

ν2



, (6.44)

where ϕ

is the inclination angle of the heat pipe, ρ

and µ

are considered at

the temperature 0.5(θ

−θ

hs2

Improvements of Tribological Conditions 355

Substituting Eqs. (6.34) and (6.43) into Eq. (6.31), one can obtain

hs1





(

−θ

hs2

)

0.75

+θ

, (6.45)

where the ratio

depends on the properties of the evaporated ﬂuid, saturation temper-

ature and the temperature on the inner wall of the hot tube in the condensation zone.

Because for a given type of the working ﬂuid, the saturation temperature θ

is completely

determined by the pressure in the container, p

in−c

(MPa) then

= f(p

in−c

hs2

), i.e. the

efﬁciency of the hot pipe is determined by the level of vacuum inside the container, type

of the working ﬂuid and by cooling intensity of its condensation zone. Approximation

of the available experimental data allowed [47] to obtain the following relation

hs2

−θ

≤ 14.2p

−0.15

in−c

(6.46)

It is understood that Eq. (6.45) is an approximation because the real thermal process

in the heat pipe is more complicated compared to that considered in the derivation of

this equation. However, it can be used in many engineering calculations involved in the

cutting tool design. An example of a tool design with the heat tube is shown in Fig. 6.9.

The cutting insert (1) is cooled by the heat pipe (2) imbedded in the holder (3). The heat

from the cutting insert is transferred to the “hot” end of the heat pipe and then transferred

by the vapor of the working ﬂuid to the “cold” end of the heat pipe, where it is dissipated

by the radiator (4). As seen, the tool design is very simple. The use of such tools can be

very efﬁcient in dry cutting. Moreover, the efﬁciency of such tool can be signiﬁcantly

improved if radiator (4) is a part of the machine tool circulation cooling system.

Embrittlement action. The embrittlement action of the cutting ﬂuid reduces the strain at

fracture of the work material. This action is based on the Rebinder effect [52]. This effect

was invoked as early as in 1936 as the basis of “oiliness” of boundary lubricants. Con-

ducting tension studies of tin specimens, Rebinder observed that a boundary-lubricant

ﬁlm of oleic acid lowered the stress and stress at fracture. Microscopic examination of

Fig. 6.9. Tool with a built-in heat tube.

356 Tribology of Metal Cutting

the test specimens showed a great increase in the number of active slip planes. He con-

cluded that this resulted from the penetration (absorption) of the surface active acid into

microcracks which lowered the strength of the specimen.

Rebinder’s studies were directly concerned with the metal cutting process. Conducting a

great number of cutting tests under different cutting conditions and with different cutting

ﬂuids, he observed microcracks formation and “healing.” The latter was particularly

pronounced in machining ductile materials, where great plastic deformation of the layer

being removed is observed. The results of Rebinder’s study showed that the absorbed

ﬁlms prevent the closing of microcracks (healing due to plastic deformation of the work

material). Because each microcrack in the machining zone serves as a stress concentrator,

smaller energy was required for cutting. Pursuing this direction, Epifanov [53] found

that the penetration of the foreign atoms (from cutting ﬂuid decomposition) produced an

embrittlement effect in a manner similar to hydrogen embrittlement. He concluded that

it thus facilitated by a resulting decrease in plasticity.

Our current understanding of the Rebinder effect is that the alternation of the mechanical

and physical properties of materials is due to the inﬂuence of various physiochemical

processes on the surface energy [52]. The energies of the process which lead to the

formation of a new fracture surface was considered by Grifﬁth [54], who developed the

equation which deﬁnes the thermodynamic requirements for fracture

2γ

πc

, (6.47)

where σ

is the fracture stress, γ

is the surface energy, E is the Young’s modulus and

is the length of some pre-existing crack.

Grifﬁths’ equation assumes that the only process that absorbs energy during fracture is

the energy required to form a new surface. As follows from this equation, the surface

energy reduces from a certain level γ

sf −1

to a new level γ

sf −2

due to the penetration of

the foreign atoms (from cutting ﬂuid decomposition) then the energy required for fracture

reduces by



sf −1

/γ

sf −2



1/2

. At this point one may wonder if pre-existing cracks exist

at the surface of ductile work materials. Multiple observations on the surface conditions

show that there are many cracks existing on the surface of even very ductile materials. For

example, Fig. 6.10 shows a micrograph of partially formed chip (ductile work material –

AISI steel 4330), where a number of very deep cracks exists on the surface of the layer

being removed.

The Rebinder effect takes place for practically all solids and structures. Its occurrence

depends on many physiochemical factors like the chemical composition of solid and

ﬂuid, deformation and fracture conditions (strain, velocity, state of stress, material struc-

ture), etc. Depending upon a particular combination of the conditions, the Rebinder

effect manifests itself in different ways: from lowering the shear ﬂow stress to a signif-

icant reduction of strength (both the stress and strain at fracture). The thermodynamic

condition for the Rebinder effect to lower the strength of a material is that the inten-

sity of surface interactions should be comparable with the energy of atomic, ion and/or