A new approach to cutting temperature prediction considering the diffusion layer in coated tools

A new approach to cutting temperature prediction considering the diffusion layer in coated tools

Zhang Shijun ?,Liu Zhanqiang

School of Mechanical Engineering,Shandong University,Jinan 250061,PR China

a r t i c l e i n f o

Article history:

Received 24May 2008Received in revised form 15January 2009

Accepted 22January 2009

Available online 6February 2009Keywords:

Thermal conductivity Cutting temperature Diffusion layer

a b s t r a c t

A novel approach to the prediction of cutting temperatures within coated tools is presented in this paper.The diffusion layer that results thermal resistance between coating and its substrate is considered.The diffusion layer model was ?rstly developed.Equations for effective thermal conductivity of the diffusion layer were then derived based on three structural models such as the Maxwell–Eucken 1model,the series model,and the equivalent layer model.The in?uences of diffusion layer on cutting temperatures of coated tools were analyzed.Results indicate that the calculated temperature with the new model is more accurate than that of the conventional one compared with measured temperature.The diffusion layer model developed in this work provides a methodology for the design and choice of coated tools in manufacturing industries.

&2009Elsevier Ltd.All rights reserved.

1.Introduction

In metal-cutting operations,the cutting temperature ?eld during cutting determines key process issues such as many parameters including accuracy of the machined surface,tool wear,tool life,mechanics of chip formation,surface quality,cutting forces,and cutting parameters as well as process ef?ciency.The coatings of cutting tools have great in?uence on heat conduction in the tools during machining.The effects of thermal properties of coated tools including coating materials on heat conduction of coated tools become important issues for cases when a very steep temperature gradient can be generated [1].Thus,having a clearer understanding about the temperature distribution in coated cutting tools is very useful and important [2].

A heterogeneous material’s effective thermal conductivity is strongly affected by its composition and structure [3].For example,Kessler et al.[4]investigated the deeper substrate regions and the titanium diffusion.From the carbon pro?les in coatings and substrates,they found a carbon balance was set up for the diffusion from the substrate to the coating during the chemical vapor deposition (CVD)process.The interdiffusion of carbon and titanium between a substrate and coating during CVD in?uences the microstructures and properties of the coating/substrate com-pounds.Dahan et al.[5]investigated the interdiffusion kinetics and the local concentration variations that take place in a Ti/TiC multilayer system in the course of an annealing heat treatment

between 355and 5501C.A diffusion model was developed and the interdiffusion coef?cients were obtained,through measuring the thermal properties of hard coatings with experiments.Thermal contact resistance between the TiN layer and its substrate was measured using thermal waves though the in?uence of the chemical composition,and the thickness remains unclear [6].Li et al.[7]studied the liquid/solid (Zn/Cu)interface diffusion with experiments in high magnetic ?elds (up to 12T).They found that there were no noticeable effects of high magnetic ?elds on the formation of intermetallic phases at the interface.However,the thickness of the diffusion layer changed under different magnetic ?eld conditions.The magnetic ?ux density exerted a non-linear in?uence on the diffusion layer thickness.Grzesik [8]used the energy-dispersive X-ray analysis (EDX)and found that there exists interdiffusion between coatings and their substrates in coated insert (TiC/Al 2O 3/TiN as well as TiC/Ti(C,N)/Al 2O 3/TiN-coated ?at-faced inserts consisting of ISO P20cemented carbide substrate).

However,the researches about the in?uences of interdiffusion between coating and its substrate or two adjacent coatings on heat conduction are far and few-in-between.In this paper,a novel diffusion model was ?rstly developed for coated tools.The formulae for the thermal conductivities among the diffusion layer,the equivalent layer,and diffusion layers of coating were then derived.The model-predicted results were lastly validated by comparing with the measured cutting temperature.

2.Diffusion layer modeling for coated cutting tools

A diffusion layer is formed between coating and its substrate due to components’diffusion when a cutting tool is deposited or

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International Journal of Machine Tools &Manufacture

0890-6955/$-see front matter &2009Elsevier Ltd.All rights reserved.doi:10.1016/j.ijmachtools.2009.01.010

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International Journal of Machine Tools &Manufacture 49(2009)619–624

there is high temperature increase in machining processes.The diffusion layer is sub-divided into two zones by the interface of coating and its substrate(Fig.1).In diffusion zone I,the coating material is the continuous phase and the substrate material is the dispersed phase.Conversely,in diffusion zone II,the substrate material is the continuous phase and the coating material is the dispersed phase.The effect of the dispersed phase in each zone resists heat conduction within the diffusion layer.So the thermal conductivities of the dispersed phases can be set at zero when the in?uence of the dispersed phase on heat transfer is considered.The next part,the formula of the conductivity of the diffusion layer,will be derived.

3.Thermal conductivity of coated tools

3.1.Effective thermal conductivity of diffusion layer

In this section,a formula of diffusion layer thermal conductiv-ity will be deduced based on three fundamental models.The Maxwell–Eucken1model[3]is a model for continuous phase with one dispersed phase.The physical structure of the series model[9]is of layers of the components aligned perpendicular to the heat?ow.The equivalent layer model that Grzesik mentioned in Ref.[1]is used to calculate the effective thermal conductivity of the multilayer.

The thermal conductivity of diffusion zone I can be obtained using Eq.(1),which is the formula of the thermal conductivity in the Maxwell–Eucken1model[10]:

k e?

k1v1e2k1tk2Tt3k1k2v2

11212

(1)

where k e is the effective conductivity of the two materials in Maxwell–Eucken1model,k1the conductivity of the continuous phase,k2the conductivity of the dispersed phase,and n1and n2 are the volume fractions for the continuous phase and dispersed phase,respectively.

In the diffusion layer model developed in Section2,the dispersed phases in diffusion zones resist heat conduction within the diffusion layer.In order to show the effect of dispersed phase in diffusion I,the thermal conductivity of the dispersed phase is set zero as the following expression:

k21?0(2)

where k21is the thermal conductivity of the dispersed phase in diffusion zone I.So,Eq.(1)can be rewritten as

k e1?

2k11v11

2v11t3v21

(3)

where k e1is the effective conductivity for diffusion zone I,k11is the thermal conductivity of the coating layer,and n11and n21are the volume fractions,which are the continuous phase and the dispersed phase possessed in diffusion zone I,respectively.

Also,the summation of the volume fractions in the two zones is v11tv21?1(4) Applying Eq.(3)to satisfy Eq.(4),the following result is obtained:

k e1?

2k11e1àv21T

2tv21

(5) Similarly,the formula of calculating the conductivity for diffusion zone II can be derived from Eq.(5).The expression for the conductivity for diffusion zone II is

k e2?

2k12e1àv22T

2tv22

(6) where k e2is the effective conductivity of diffusion zone II,k12the conductivity of the substrate,and n22the volume fraction,which is the dispersed phase in diffusion zone II.In the following parts, the effective conductivity of the diffusion layer will be deduced.

Eq.(7)is the expression for the effective conductivity in series model[1,3]:

k es?

1

v1s=k1stv2s=k2s

(7) where k es is the effective conductivity of the two materials in series model,k1s the conductivity of one phase in the model,k2s the conductivity of the other phase in the model,and n1s and n2s are the volume fractions for the two phases.

According to Eq.(7),the formula of effective conductivity of the diffusion layer can be given by

k ed?

1

v1d=k e1tv2d=k e2

(8)

where k ed is the effective conductivity of the diffusion layer,and n1d and n2d are the volume fractions for diffusion zones I and II in the diffusion layer,respectively.

In the diffusion layer model,the volume fractions n1d and n2d are assumed to be equal to the same value.So Eq.(8)is changed into

k ed?

2k e1k e2

k e1tk e2

(9) Applying Eqs.(5)and(6)to satisfy(9),the?nal formula of the diffusion layer effective conductivity can be expressed by

k ed?

4k11k12e1àv21Te1àv22T

k12e2tv21à2v22àv21v22Ttk11e2tv22à2v21àv21v22T

(10) 3.2.Equivalent layer thermal conductivity

The equation of the effective thermal conductivity of the multilayer can be expressed as follows[8]:

P t

i?1

h il

k el

?

h1l

k1l

t

h2l

k2l

tááát

h tl

k tl

(11) where k1l,k2l,y,and k tl is the thermal conductivity of the i th layer.h1l,h2l,y,and h tl is the thickness of the i th layer.S h il is the total thickness of the equivalent layer.k el is the effective conductivity of the equivalent layer.

In this mode,the thickness of the equivalent layer is h1l+1/2h ed (Fig.2).So Eq.(11)becomes

h1lt1=2h ed

k el

?

h1là1=2h ed

k1l

t

h ed

k ed

(12) where h ed is the thickness of the diffusion layer.

Accordingly,the effective thermal conductivity of the equiva-lent layer can be given by Eq.(13):

k el?

k1l k ede2h1lth edT

e2h1làh edTk edt2h ed k1l

(13)

In order to calculate rake face temperature,the formulae used will be introduced in the next section.

4.Average rake face temperature of coated cutting tools

In manufacture processes,it is well established that the heat generation occurs in three zones in the cutting domain:the primary deformation zone(PDZ),the secondary deformation and frictional zone along the tool–chip interface as well as the tertiary or the sliding frictional zone at the tool–workpiece interface. During the cutting process,part of the heat generated at the shear plane?ows by convection into the chip and then through the interface zone into the cutting tool.Therefore,the heat generated at the shear zone affects the temperature distributions of both sides of the tool and the chip.The temperature rise on the tool rake face is due to the combined effect of the heat generated in the primary and secondary zones[11].The details of the steps to calculate the rake face temperature will be elucidated as follows[1,2].

4.1.Calculation of temperature due to plastic deformation in the PDZ

The computation scheme used in this section consists of several steps as follows.In the?rst step,the shear?ow stress[12] is calculated by

t s?F c cos f sin fàF t sin 2f

u

(14) where t s is the shear?ow stress,f the shear angle,t u the depth of cut,w the width of cut,F t the feed force,and F c the cutting force.

Thus,the maximum temperature rise on the chip–tool inter-face caused by shear zone can be obtained using the following formula:

D y s max?

t s

c W r W tan

erf

????????????????

R tan f

4

r

(15)

where erf is the error function.The adequate expression for R can be given by[13]

R?c W r W v c h

l W

(16)

where l W,c W,and r W are the thermal conductivity,the volumetric heat capacity,and the density of the workpiece,respectively.h is the undeformed chip thickness and n c is the cutting velocity.

The average temperature at the shear plane is equal to[13,14]

for R tan f p5;D y s?0:685eR tan fT0:07y s max(17) for5p R tan f p20;D y s?0:620eR tan fT0:13y s max(18) for20p R tan f;D y s?0:820eR tan fT0:04y s max(19)4.2.Calculation of temperature resulting from frictional heat source

The frictional heat?ux can be determined using the formula as follows[15]:

q F?

F g n ch

A c

?

F g n c

h

A c

(20) where l h is the chip thickness compression ratio,F g the friction force,A c the actual area of contact,and n ch the chip velocity.

The value of heat partition coef?cient can be estimated as

R R?

1

1t1:5l T=l W

???????????????

W

=T

p(21)

where R R is the heat partition coef?cient that de?nes the percentage of the heat entering the moving chip from the second deformed zone.l T is the thermal conductivity of the coated tool.

a T and a W are the thermal diffusivities of the coated tool and workpiece,respectively.

The chip maximum temperature at the chip–tool interface due to friction can be computed as

D y f max?

0:565R R q F l c

W

??????

N T

p(22) where D y f max is the maximum temperature rise of the chip resulting from frictional heat source,l c the natural contact length, and N T the thermal number,which can be given by

N T?

v ch l c

a W(23) The chip average temperature at the chip–tool interface due to friction can be computed as

D y f?

0:377R R q F l c

W

??????

N T

p(24) where D y f is the average temperature rise of the chip resulting from frictional heat source.

4.3.Rake face temperature of a coated tool

The maximum rake face temperature of a coated tool is equal to the interface maximum temperature of the chip at the chip–tool interface,namely,

y max?D y s maxtD y f maxty0(25) where y max is the rake face maximum temperature of the coated tool and y0is the environment temperature.

The average rake face temperature of the coated tool can be obtained from the formula as follows:

y m?D y stD y fty0(26) where y m is the average rake face temperature of the coated tool.

https://www.360docs.net/doc/448106378.html,putation results

5.1.Maximum rake face temperature

To validate the novel method proposed in Sections2and3,the temperature values calculated with the formulae expressed in Section4and measured with a CCD camera in cutting experiment are compared.The camera was calibrated against a black body cavity for which temperature was carefully controlled(resolution 711C)and the emissivity of the work material was calibrated with a thermocouple,which Stuck on the face of the workpiece by Rech[16]and Rech et al.[17].The experimental set-up had been designed on a precision CNC lathe using a thin-walled tube as the

workpiece by Rech[16]and Rech et al.[17].The thickness of the tube was equal to3mm.The workpiece material was27MnCr5. Orthogonal cutting operations were carried out by using a TiAlN (2m m thick)-coated carbide tool(normal rake angle01,inclination angle01,major cutting edge angle901).The cutting speed was 200m/min and feed rate was0.1m/rev.The environment temperature was251C.The measured tool–chip contact width was0.53mm and the average chip thickness was0.26mm.The measured feed force and cutting force were490and615N, respectively.The thermophysical properties of the coating layer and the workpiece in the example are listed in Table1.

The volume fractions of dispersed components are in?uenced by the materials of coatings,substrates as well as deposition processes,and so on[4].The energy-dispersive X-ray analysis was used to determine elemental spectra of a coated tool (TiAlN-coating layer)as presented in Fig.3.The interdiffusion of elements between the substrate and the coating can be found in

Fig.3.To simplify the question,according to Fig.3,the thickness of the diffusion layer is set to1m m and the volume fractions are set to40%in this case study.

Applying the above parameters to Eqs.(10)and(13),the thermal conductivities of the diffusion layer(13.07W/m K)and the equivalent layer(14.64W/m K)can be obtained.When calculating the temperature rise due to plastic deformation in the PDZ,the thermophysical parameters of the workpiece at 2201C should be used.However,the thermophysical parameters of the workpiece at6001C should be used to calculate the temperature rise resulting from the frictional heat source.

Calculation and experiment results of the maximum rake face temperatures obtained for the TiAlN-coated tool are shown in Fig.4.The prediction error of the rake face maximum temperature considering the diffusion layer is12.6%;however,the value is 16.5%when using the conventional way.5.2.Average rake face temperature

In order to validate the novel method proposed in Sections2 and3further,the temperature values calculated with the formulae expressed in Section4and measured with the tool–work thermocouple technique are compared.The components of the resultant cutting force were measured by a biaxial strain-gauge dynamometer.The tube wall thickness was2mm and the outer diameter of a tube was equal to80mm. The orthogonal cutting tests were conducted on a manual lathe without a coolant by Grzesik[18].The feed rate was varied from0.04to0.20mm/rev,while the cutting speed was?xed at220m/min for the carbon steel AISI1045.A single-layer TiC-coated tool consisting of a cemented WC-Co substrate was selected.The cutting parameters and measured parameters in the cutting process are listed in Table2.The thermophysical

Table1

Thermophysical properties of coating layer and workpiece in the example.

Material Thermal conductivity(W/m K)Thermal diffusivity(m2/s)Volumetric heat capacity(J/kg1C)Density(kg/m3)

TiAlN20(6001C) 3.04?10à5

Substrate(P10)37.68(6001C) 1.4?10à5(6001C)

27MnCr545.2(2201C)531(2201C)7.85?103 36(6001C)549(6001C)

TiAlN

Substrate

20 μm

Al

40

30

20

10

W

80

60

40

20

μm

0102030

μm

0102030

Aluminum ka1

Ti

Co

15

10

5

8

6

4

2

10

5

N

μm

0102030

μm

0102030

μm

0102030

Nitrogen ka1_2

Titanium ka1 Fig.3.Spectrum and chemical composition of a coated tool(TiAlN layer).

123

100

200

300

400

500

600

700

T

e

m

p

e

r

a

t

u

r

e

m

/

°

C

Fig. 4.The maximum interface temperature:1—disregarded diffusion layer.

2—considered diffusion layer.3—CCD camera measurement.

S.Zhang,Z.Liu/International Journal of Machine Tools&Manufacture49(2009)619–624

622

properties of the coating layer [19]and the workpiece [11]in the example are listed in Table 3.

In this example,the thickness of the diffusion layer is assumed to be 2m m.The conductivities of diffusion layer (12.55W/m K)and equivalent layer (24.08W/m K)can be obtained using Eqs.(10)and (13).When calculating the temperature rise due to plastic deformation in the PDZ,the thermophysical parameters of the workpiece at 3001C should be used.However,the thermo-physical parameters of the workpiece at 7001C should be used to calculate the temperature rise resulting from the frictional heat source.

Calculation and experiment results dealing with the average rake face temperatures obtained for the TiC-coated tool are shown in Fig.5.The calculated temperature considered diffusion layer is more accurate than that of the disregarded one.The charts in Fig.6show the relative errors of calculated values considered and disregarding diffusion layer compared to the measured temperatures.The prediction errors of the average rake face temperature considered diffusion layer are not higher than 10.2%;however,the maximum value is 18.25%when using the conventional way (Fig.6).A similar experiment was conducted by Grzesik [15].The relative errors of calculated temperatures considered diffusion layer and disregarded diffusion layer compared with the measured results at cutting speeds 60,100,

and 160m/min are shown in Fig.7.The relative errors of calculated temperatures considered diffusion layer are much lower than that of the disregarded one.So the calculated temperatures of the considered diffusion layer are more accurate than that of the disregarded diffusion layer.

Table 2

Cutting parameters and measured parameters in the cutting process.Feed rate (mm/rev)Cutting force (N)Feed force (N)Contact length (mm)Chip thickness compression ratio Shear angle (1)Contact temperature (1C)0.04563.8616.710.523 2.77419.198701.20.08847.81706.580.634 2.76319.267774.90.1989.81751.010.703 2.70519.636790.50.141273.82838.850.871 2.5620.626828.50.161415.82882.270.968 2.47921.214835.20.2

1699.83

968.08

1.192

2.312

22.554

841.9

Table 3

Thermophysical properties of coating layer and workpiece in the example.Material Thermal conductivity (W/m K)Thermal diffusivity (m 2/s)Volumetric heat capacity (J/kg 1C)

Density (kg/m 3)

TiC

37(5001C)14.5?10à6(5001C)

Substrate 15(6001C)AISI 45

44.83(3001C)573.2(3001C)7.844?103

30.1(7001C)

772.8(7001C)

0.04

0.060.080.10.120.140.160.180.2

500

600700800900Feed rate f/mm/rev

T e m p e r a t u r e m a x / °C

1

3

2

Fig. 5.Calculation average rake face temperatures with different method and experiment results:1—measured temperature.2—calculated temperature con-sidered diffusion layer.3—calculated temperature disregarded diffusion layer.

0.02

0.040.060.080.10.120.140.160.180.20.22

05101520

Feed rate f / mm / r ev

R e l a t i v e e r r o r / %

Fig. 6.The relative errors of calculated average temperatures compared with

measured results with different feed rates.

60

100

160

-5

0510********

Cutting speed v c / m / m i n

R e l a t i v e e r r o r / %

Fig.7.The relative errors of calculated average temperatures compared with measured results with variable cutting speeds.

S.Zhang,Z.Liu /International Journal of Machine Tools &Manufacture 49(2009)619–624

623

6.Conclusions

A new approach has been proposed to improve the prediction of coated cutting tool temperature.A diffusion layer model is developed to determine the relationship between the diffusion layer and the thermal effective conductivity.The results of the case studies using the developed models to predict the rake face maximum temperature and average temperature in turning processes indicate that the developed models are more accurate than the conventional one.The model developed in this paper can be used for designing coated tools not only for monolayer coated tools but also for multilayer coated tools with predictable performance.

Acknowledgements

This project was supported by the National Basic Research Program of China(no.2009CB724401),the National Great Project of Scienti?c and Technical Supporting Programs of China during the11th Five-year Plan(no.2008BAF32B01),and the National High Technology Research and Development Program of China (no.2008AA042405).

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