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Modelling of the cutting temperature distribution underthe tool ank wear effect

Y Huang1 an d S Y Liang2*1

Department of Mechanical Engineering, Clemson University, Clemson, South Carolina, USA2

George W Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA

Abstract: The understanding of cutting temperature distribution at the presence of tool wear can aid

in addressing important metal cutting issues such as part surface integrity, tool life and dimensional

tolerance under practical operating conditions. The effect of tool wear on the cutting temperature

distribution was rst modelled by Chao and Trigger and there have been very few followers since. In

Chao’s model, the primary heat source was assumed to have no effect on the workpiece temperature

rise and the chip temperatur e rise was treated a s a bu lk quan tity. This paper a nalytically quan ties the

tool wear effect by taking into account the contributions of the primary heat source and consideringthe distribution of chip temperature rise. On the chip side, the primary shear zone is modelled as a

uniform moving oblique band heat source and the secondary shear zone as a non-uniform moving

band heat source within a semi-innite medium. On the tool side, the effects of both the secondary

and the rubbing heat sources are modelled as non-uniform static rectangular heat sources within a

semi-innite medium. For the workpiece side, the study models the primary shear zone as a uniform

moving oblique band heat source and the rubbing heat source as a non-uniform moving band heat

source within a semi-innite medium. The proposed model is veried based on the published

experimental data in the orthogonal cutting of Armco iron. Furthermore, a comparison case is

presented on the temperature variation with respect to cutting speed, feed rate and ank wear length.

Keywords: cutting temperature, ank wear, heat source method

NOTATION

achip thermal diffusivity of the chip

aworkpiece thermal diffusivity of the workpiece

B1… x † [or B1… x 0†]

fraction of the secondary heat source

transferred into the chip

B2… x 00† [or B2… x 000†]

fraction of the rubbing heat source

transferred into the workpiece

F frictional force along the rake face

F c, F t cutting force and thrust forceF cw rubbing force along the tool–workpiece

interface

k chip, k tool thermal conductivities of the chip and tool

K 0 modied Bessel function of the second

kind of order zero

l tool–chip contact length

L length of the shear plane

M point in the medium to be measured about

the temperature rise

qfrictional… x† [or qfrictional … x 0†]

heat intensity of the secondary heat

source

qrubbing… x 00† [or qrubbing… x 000†]

heat intensity of the rubbing heat source

qshear heat intensity of the primary heat source

r chip thickness ratio

R i, R 0i, R

00i distance between the point M and heat

source segments

t undeformed chip thickness or feed rat e inthe ort hogonal cutting

t ch deformed chip thickness

V chip chip velocity

V cutting cutt ing velocity

VB ank wear length

w width of the cut or depth of cut in

orthogonal cutting

X , Y , Z , X 0, Y 0 , Z 0 , X 00, Y 00 , Z 00 , X 000, Y 000 , Z 000

right-handed Cartesian coordinates used

in related gures

a tool rake angle

The M S was received on 25 September 2002 and was accepted after

revision for publication on 26 August 2003.* Corresponding author: George W . W oodruff S chool of M echanical

Engin eering, Georgia Inst itu te of T echnology, A tlant a, GA 30332–0405,

U S A .

1195

C12802 # IM echE 2003 Proc. Instn Mech. Engrs Vol. 217 Part C: J. M echanical Engineering Science

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y0 room temperature

ychip¡friction temperature rise on the chip side due to

the secondary heat source

ychip¡shear temperature rise on the chip side due to

the primary heat source

ytool¡friction temperature rise on the tool side due to

the secondary heat source

ytool¡rubbing temperature rise on the tool side due tothe rubbing heat source

ytoolflank temperature rise along the tool ank face

ytoolrake temperature rise along the tool rake face

yworkpiece¡rubbing

temperature rise on the workpiece side

due to the rubbing heat source

yworkpiece¡shear

temperature rise on the workpiece side

due to the primary heat source

f shear angle

1 INTRODUCTION

The role of the cutting temperature in metal cutting has

been studied in great detail, beginning as early as 1907

by Taylor [1]. Since the early twentieth century, much of

the work on the thermal aspects of metal cutting has

been directly experimental, pr oviding mostly tempera-

ture in an average sense. T hese works can be categorized

as thermo-e.m.f (thermocouples), radiation (pyrometry,

infrared photography, etc.) and thermochemical reac-

tions (thermo-colours) [2]. Other experimental methods

have included the metallographic method [3] an d th e

physical vapour deposition (PVD) lm method [4], to

name just a few. Alternatively, the reverse estimation

scheme has been tried to solve the cutting temperature

prole based on the indirectly measured temperature

information [5]. N umerical metho ds were also a pplied t o

determine the temperature distribution with some

important results documented by Tay et al. [6] an d

Dawson and M alkin [7].

On analytical modelling, the steady state temperature

in metal cutting has been estimated by Hahn [8], Trigger

an d Ch ao [9–12], Loewen and Shaw [13], Komanduri

and Hou [14–16] and most recently by Huang and Liang

[17] based on the premise of a moving heat source

[18, 19]. This better understanding of the temperature

distribution a long the tool–workpiece interface at the

presence of tool wear helps to provide insight into

several important issues in metal cutting, such as tool

wear progression, dimensional tolerance and workpiece

surface integrity, etc. Unfortunately, most of the

analytical studies documented thus far focus on thermal

modelling only for a fresh tool, except that of Chao and

Trigger [12]. In the work of Chao and Trigger, the

primary heat source was tak en as having no effect on t he

workpiece temperature rise, and the temperature rise on

the chip side was modelled as an average bulk value.

However, the temperature rise due to the primary heat

source on the workpiece surface underneath the tool

ank face can be as high as 200 8C depending on the

thermal number …tV cutting=aworkpiece† in conventional

cutting [14]. Furthermore, the temperature rise due tot he p rim a ry h ea t so ur ce h as b een sh own t o b e

distributed, rather than constant, along the chip side

[14].

The objective of this study is to model the tempera-

ture distributions analytically, especially along the t ool–

workpiece contact length in orthogonal cutting for a

worn t ool. The study ut ilizes the heat source method [18,

19] to treat the effects of heat sources. On the chip side,

the effect of t he primary shear zone is modelled as a

uniform moving oblique band heat source and that of

the secondary shear zone as a n on-uniform moving band

heat source within a semi-innite medium. On the tool

side, the effects of both the secondary and the rubbing

heat sources are considered as non-uniform static

rectangular heat sources within a semi-innite medium.

On the workpiece side, the primary shear zone is

modelled as a uniform moving oblique band heat source

and the rubbing heat source as a non-uniform moving

rectangular heat source within a semi-innite medium.

The proposed model is veried ba sed on the published

experimental data of orthogonal cutting Armco iron. In

addition, a case is presented to analyse t he effects of

cutting speed, feed rate and ank wear length on the

temperature distributions.

2 ANALYTICAL MODELLING

2.1 Introduction and basic assumptions

As shown in Fig. 1, there are three main heat sources in

metal cutting with a tool worn on the ank face, namely

primary, secondary and rubbing heat sources. Tempera-

ture distribution along the tool–workpiece interface at a

location midway across the width of cut is of interest in

this study since temperature assumes its highest level at

that location. Temperatures a t other locations along the

tool–workpiece interface can also be calculated by

applying the appro ach d escribed h erein. T he heat source

method introduced by Jaeger [18] and Carslaw and

Jaeger [19] is applied in this study. Th e temperatu re rises

on the chip side and also on the tool side along the

interface; thus the tool–chip interface boundary is

ad iabatic fo r th e too l an d th e chip r esp ectively.

Similarly, the tool–workpiece interface boundary is

considered to be adiabatic for the tool and the work-

piece respectively. R egarding the adiabatic boundary

conditions along the interfaces, the primary heat source

Y HUANG AND S Y LIANG1196

Proc. Instn Mech. Engrs Vol. 217 Part C: J. Mechanical Engineering Science C12802 # IMechE 2003

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is considered to have no direct effect on the temperature

rise on the tool side, but the determined heat partition

ratios along the interfaces will imply the contribution

from the primary heat source indirectly. To simplify the

problem further, th e effect of t he rubbing heat source on

the chip side and the effect of the secondary heat source

on the workpiece side are taken to be negligible,

considering the relative distance between them and their

partitioned heat intensities [12, 15, 17].

It is also considered that the primary heat source to

the chip is the uniform moving oblique band h eat source

with chip velocity and proper boundary conditions and

the secondary heat source is the non-uniform moving

rectan gular heat source within the semi-innite medium.

Thus the temperature rise on the chip side can be

expressed as ychip¡shear ‡ ychip¡friction [17]. Additionally,

the secondary heat source to the tool can be considered

as the non-uniform static rectangular heat source within

the semi-innite medium and the rubbing heat source

due to ank wear the non-uniform static rectangular

heat source within the semi-innite medium. Therefore,

the temperature rise on the tool side along the tool–chip

interface can be expressed as ytoolrake, wh ile t he

temper atu re r ise o n th e too l sid e alo ng th e to ol–

workpiece interface can be expressed as ytoolflank . Also

considered are the primary heat source to the workpiece

as the uniform moving oblique band heat source with

cutting velocity within the semi-innite medium and the

rubbing heat source due to ank wear as the non-

uniform moving band heat source within the semi-

innite medium. It follows that the temperature rise on

the workpiece side can be expressed as yworkpiece¡shear ‡yworkpiece¡rubbing.

In calculating the above temperature rises along the

interfaces, the heat partition ratio of the secondary heat

source going to the chip is specied as a function B1… x †[or B1… x 0†] along the rake face contact length. Thus t he

remaining heat size 1 ¡ B 1… x † [or 1 ¡ B 1… x 0†] goes to the

tool. The heat pa rtition ra tio of the rubbing heat source

going to the workpiece is specied as a function B2… x 00†[or B2… x 000†] along the ank wear land, so the remaining

heat size 1 ¡ B 2… x 00† [or 1 ¡ B2… x 000†] goes to the tool.

These are shown in Fig. 1 as well.

The basic assumptions involved in the study are:

1. The generated heat ow and temperatur e distribution

are in steady states.

2. All of the deformat ion energy within the deformation

zones is converted into heat. A negligible amount is

stored as latent energy in the deformed metal. Heat

loss along the interfaces and at all surfaces of the

tool, chip and workpiece is insignicant.

3. The dimensions of the t ool are so large compared to

the chip cross-section that the tool size can be

considered a s innite.

4. Primary, secondary and rubbing heat sources are

plane heat sources and the nature of the secondary

heat source is not affected by the possible crater

wear.

5. It is assumed that there is no redistribution of

thermal shear energy going into the chip during the

very short time when the chip is in contact with the

tool. This assumption appears to be well founded for

the normal cutting operation involving continuous

chip formation without a built-up edge [13].

6. The effect of the rubb ing heat source on th e chip and

th e effect o f th e seco nd ary h eat so ur ce o n th e

workpiece a re considered to be negligible.

Fig. 1 Heat sources and h eat part itions along the tool–chip and t ool–workpiece interfaces

MODELLING OF THE CUTTING TEMPERATURE DISTRIBUTION UNDER THE TOOL FLANK WEAR EFFECT 1197


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7. For simplicity, both heat partition ratios B1… x 0† an d

B2… x 00† are assumed to be unchanged along the Y 0 or

Y 00 directions respectively, if applicable [12].

8. A cutting wedge angle of 908 is considered to simplify

the problem, which is reasonable for most cutting

tools.

The coordinates X Y Z in Fig. 2 are attached to the

chip to model the chip t emperature while the coordi-nates X 000Y 000 Z 000 are attached to the workpiece while

modelling the temperature rise in the workpiece. To

model the heat partition along the tool–chip and tool–

workpiece interfaces, two coordinates X 0Y 0 Z 0 an d

X 00Y 00 Z 00 are adopted for the tool as

X 0 ˆ l ¡ Z 00

Y 0 ˆ ¡Y 00

Z 0 ˆ VB ¡ X 00

…1†

For the coordinates used here, X overlaps with X 0 an d

X 00 overlaps with X 000, so B1… x † a nd B1… x 0† are the same

an d B2… x 00† an d B2… x 000† are the same in this study.

2.2 Chip side temperature modelling

2.2.1 Eff ect of the primary heat source

As proposed by Huang and Liang [17], by considering

the primary heat source as the obliquely moving band

heat source with a velocity V chip , in the coordinates X Y Z

the temperature rise on the chip side due to the primary

heat source can be expressed as

ychip¡shear… X , Z †

ˆ qshear

2pk chip

… L0

e¡… X ¡ X i †V chip=…2achip †

6 K 0V chip

2achip … X ¡ X i†

2 ‡ … Z ¡ Z i†2

q µ ¶‡

1

2K 0

V chip

2achip

… X ¡ X i†

2 ‡ …2t ch ¡ Z ¡ Z i†2

q µ ¶

‡1

2K 0

V chip

2achip

… X ¡ X i†

2 ‡ … Z ‡ Z i†2

q µ ¶¼dli

…2†

where

X i ˆ l ¡ li sin…f ¡ a†

Z i ˆ li cos…f ¡ a†

L ˆ t ch

cos…f ¡ a†

2.2.2 Eff ect of the secondary heat source

By considering the secondary heat source as the non-

uniform moving band heat source with a velocity V chip,

in the coordinates X Y Z the temperature rise on the chip

side due to the secondary heat source can be expressed

Fig. 2 The used right-handed Cartesian coordinates and associated heat sources in thermal modelling



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as [17]

ychip¡friction … X , Z †

ˆ 1

2pk chip

… l0

B… x †qfrictional … x†e¡… X ¡ x †V chip=…2achip †

6

µ2K 0

R iV chip

2achip

´‡ 2K 0

R 0iV chip

2achip

´

‡ 2K 0 R 00

i V chip

2achip

´¶d x

ˆ 1

pk chip

… l0

B… x †qfrictional … x †e¡… X ¡ x †V chip=…2a†

6

µK 0

R iV chip

2achip

´‡ K 0

R 0iV chip

2achip

´

‡ K 0 R 00

i V chip

2achip

´¶d x …3†

where

R i ˆ

… X ¡ x †2 ‡ Z 2

q

R 0i ˆ

… X ¡ x †2 ‡ …2t ch ¡ Z †2

q

R

00

i ˆ

… X ¡ x †

2

‡ …2t ch ‡ Z †

2q

2.2.3 Chip side temperature

Th e temper atu re r ise o n the ch ip side, wh ich is

ychip¡shear … X , Z † ‡ ychip¡friction … X , Z †, is attributed to the

primary and the secondary heat sources. Along the tool–

chip interface, the temperature rise on the chip side can

be given as ychip¡shear… X , 0† ‡ ychip¡friction … X , 0† in th e

coordinates X Y Z .

2.3 Workpiece side temperature modelling

2.3.1 Eff ect of the primary heat source

Komanduri and Hou [14] considered that the primary

shear heat source was a band heat source obliquely

moving under the workpiece surface of a semi-innite

body with a velocity V cutting. The right part next to the

shear zone is imaginary and is extended for continuity in

modelling. The boundary condition for the workpiece

surface is considered to be insulated in this study. An

imaginary heat source HH with the same heat intensity

as that of the primary heat source is considered in this

model [19]. As shown in Fig. 3, the temperature rise due

to the primary heat source on the workpiece, which

contacts the tool worn ank face, can thus be shown as

yworkpiece¡shear … X 000, Z 000†

ˆ qshear

2pk workpiece

… L0

e¡… X 000 ¡li sin y¡VB†V cutting=…2aworkpiece †

6

K 0

µ V cutting

2aworkpiece

6

…VB ‡ li co s f ¡ X 000†2 ‡ … Z 000 ‡ li sin f†2

q ¶

‡ K 0µ V

cutting2aworkpiece

6

…VB ‡ li co s f ¡ X 000†2 ‡ …2t ‡ Z 000 ¡ li sin f†2

q ¶¼dli

…4†

2.3.2 Eff ect of the rubbing heat source

The rubbing heat source is considered as the band heat

source moving along the workpiece surface within a

semi-innite body with a velocity V cutting. The boundary

condition for the workpiece surface is considered to be

insulated in this study. It is a classical Jager’s moving

Fig. 3 Heat transfer model of the primary heat source relative to the workpiece side



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heat source conguration within a semi-innite medium.

An imaginary heat source II with t he same heat intensity

as that of the rubbing heat source is considered in thismodel [19]. As shown in Fig. 4, the temperature rise due

to the rubbing heat source on the workpiece, which

contacts the tool worn ank face, can be expressed as

yworkpiece¡rubbing… X 000, Z 000†

ˆ 1

pk workpiece

… VB

0

B2… x 000†qrubbing … x 000†

6e¡… X 000 ¡ x 000 †V cutting =…2aworkpiece †

6 K 0V cutting

2aworkpiece

… X 000 ¡ x 000†2 ‡ … Z 000†2

q µ ¶ ¼d x 000

…5†

2.3.3 W orkpiece side temperature

The temperature rise o n the workpiece, yworkpiece¡shear

… X 000, Z 000† ‡ yworkpiece¡rubbing… X 000, Z 000†, is m ainly co n-

tributed by primary and rubbing heat sources. Along

the tool–workpiece interface, the workpiece temper-

atur e r ise can b e wr itten as yworkpiece¡shear… X 000, 0† ‡yworkpiece¡rubbing… X 000, 0† in the coordinates X 000Y 000 Z 000 .

2.4 Tool side temperature modelling

2.4.1 Eff ect of t he secondary heat source

For a fresh tool, the boundary condition on the ank

can be considered to be insulated [17]. For a worn tool,

it is considered as adiabat ic because the t emperature rise

on both sides of the tool–workpiece interface should be

equal. The heat transfer model for the effect of the

secondary heat source on the to ol side is the same as tha t

for the fresh tool, except for the adiabatic boundary

condition along the tool–workpiece interface. The

temperature rise on the tool side due to friction can

thus be expressed as [17]

ytool¡friction … X 0, Y 0 , Z 0†

ˆ 1

4pk tool

… l0

‰1 ¡ B1… x 0†Šqfrictional … x0† d x 0

6

… w=2

¡w=2

2

R i

‡ 2

R 0i

´d y 0

ˆ 1

2pk tool

… l0

‰1 ¡ B1… x 0†Šqfrictional … x0† d x 0

6

… w=2

¡w=2

1

R i

‡ 1

R 0i

´d y 0 …6†

where

R i ˆ

… X 0 ¡ x 0†2 ‡ …Y 0 ¡ y 0†2 ‡ Z 02

q

R 0i ˆ

… X 0 ¡ 2l ‡ x 0†2 ‡ …Y 0 ¡ y 0†2 ‡ Z 02

q

2.4.2 Eff ect of the rubbing heat source

I t fo llows fr om sect io n 2.1 t ha t 1 ¡ B 2… x 00† [or

1 ¡ B 2… x 000†] of the rubbing heat source is transferred

to the tool as the non-uniform static rectangular heat

source. Both interface boundaries are considered as

adiabatic, considering the assumptions that temperature

rises are equal along both the tool–chip and tool–

workpiece interfaces. Thus, there are two main imagin-

ary heat sources JJ and KK [12, 19]. The heat intensity

of the imaginary heat source JJ is equivalent to that of

the rubbing heat source, and the heat intensity of the

imaginary heat source KK is twice the rubbing heat

source. The related heat transfer model is shown in

Fig. 5.

Fig. 4 H eat tran sfer model of th e rubbing heat source relative to the workpiece side



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The temperature rise at any point M … X 000, Y 00 , Z 00† on

the tool side due to rubbing can thus be shown to be

ytool¡rubbing… X 00, Y 00 , Z 00†

ˆ 1

4pk tool

… VB

0

‰1 ¡ B2… x 00†Šqrubbing … x 00† d x 00

6

… w=2

¡w=2

2

R i

‡ 2

R 0i

´d y 00

ˆ 1

2pk tool

… VB

0

‰1 ¡ B2… x 00†Šqrubbing … x 00† d x 00

6

… w=2

¡w=2

1

R i

‡ 1

R 0i

´d y 00 …7†

where

R i ˆ … X 00 ¡ x 00†2 ‡ …Y 00 ¡ y 00†2 ‡ … Z 00†2

q R 0

i ˆ

…2VB ¡ X 00 ¡ x 00†2 ‡ …Y 00 ¡ y 00†2 ‡ … Z 00†2

q

2.4.3 T ool rake and ank temperature rises

The temperature rise on the tool is mainly attributed

t o t he seco nd ar y a nd t he r ub bin g h ea t so ur ces

…ytool¡friction ‡ ytool¡rubbing†. When considering the effect

of the rubbing heat source on the tool temperature rise

in the coordinates X 0 Y 0 Z 0 , the temperature rise due

t o t he ru bb in g h ea t so ur ce ca n b e r ewr it t en a s

ytool¡rubbing …VB ¡ Z 0 , ¡ Y 0 , l ¡ X 0† based on the coordi-

nate transformation given in equation (1). Therefore the

temperature rise in the middle of the t ool rake face along

the tool–chip interface …Y 0 ˆ 0 a nd Z 0 ˆ 0) ca n b e

estimated by

ytoolrake … X 0, 0 , 0† ˆ y tool¡friction … X 0, 0, 0†

‡ ytool¡rubbing …VB, 0, l ¡ X 0† …8†

The effect of the secondary heat source on the tool

temperature rise can be given as ytool¡friction …l ¡ Z 00 ,

¡Y 00 , VB ¡ X 00† followed from the coordinate transfor-

mation. Thus, in the middle of the tool ank face side,

the temperature rise along the tool–workpiece interface

…Y 00 ˆ 0 and Z 00 ˆ 0) can be expressed as

ytoolflank … X 00 , 0 , 0† ˆ ytool¡friction …l,0 ,V B ¡ X 00†

‡ ytool¡rubbing… X 00, 0 , 0† …9†

2.5 Solution method for temperature distributions

It is assumed that the temperature rise on the chip side

and on t he tool side along the to ol–chip interface should

be equal as follows:

ychip¡shear … X , 0† ‡ ychip ¡friction … X , 0†

ˆ ytoolrake … X 0, 0 , 0† …10†

Similarly, on the workpiece side and on the t ool side

along the tool–workpiece interface the temperature rise

Fig. 5 Heat transfer model of the rubbing heat source relative to the tool side



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should be equal, i.e.

yworkpiece¡shear … X 000, 0† ‡ yworkpiece¡rubbing … X 000, 0†

ˆ y toolflank … X 00, 0 , 0† …11†

To solve the heat pa rtition ratios B 1 an d B2 along the

interfaces numerically, the contact length along the

tool–chip interface is divided into n1 sections and the

heat partition ratio in each section is represented as

B1, 1, . . . , B1, n1, as shown in Fig. 6. Similarly, the contact

length along the tool–workpiece interface is divided inton2 sections and the heat partition ratio in each section is

also represented as B2, 1, . . . , B2, n2, as shown in Fig. 6.

Equations (10) and (11) can be described by a set of

linear equations as

A 1 A 2

A 3 A 4

µ ¶…n1 ‡n2†6…n1 ‡n2†

B1

B2

µ ¶…n1‡n2 †61

ˆ A 5

A 6

µ ¶…n1 ‡n2†61

…12†

where

B1 ˆ ‰ B1, 1, . . . , B1, n1Šn161, B2 ˆ ‰ B2, 1, . . . , B2, n2

Šn261

an d A 1, . . . , A 6 are dened by ychip¡shear, ychip¡friction ,

ytoolrake, yworkpiece¡shear, yworkpiece¡rubbing, ytoolflank , a n d

positions along the X … X 0† or X 00… X 000† axis accordingly.

The temperatures at every section are inuenced not

only by the effect of the heat source of this section but

also of the heat sources of all the other sections. The

partition ratios B1 an d B2 can be estimated by solving

equation (12). Subsequently, the temperature rises

ytoolrake a nd ytoolflank can be predicted based on equations

(8) and (9) respectively. Finally, the temperature

distributions can be determined by including the room

temperature y0.

3 MODEL VALIDATION

3.1 Process parameter estimation for the chip formation

process

Given the cutting conditions in the orthogonal cutting,

namely, the cut ting speed V cutting, width of cut (as of thedepth of cut) w, undeformed chip thickness (as of the

feed ra te) t and material properties of the workpiece and

tool for a fresh tool, th e process information, such as the

cutting forces, shear angle and shear ow stress, can be

estimated with acceptable accuracy by applying Oxley’s

predictive ma chining th eory [20] or its modication [21].

Then the input variables required by the proposed

thermal model, including the chip velocity V chip,

frictional force on the rake face F and primary heat

intensity q shear can be calculated as follows:

V chip ˆ rV cutting

F ˆ F c sin…a† ‡ F t co s…a†

qshear ˆ ‰F c cos…f† ¡ F t sin …f†Š‰V cutting cos…a†= cos…f ¡ a†Š

t ch rw csc…f†

…13†

The heat intensity of the secondary heat source can be

determined based on the frictional force F , as discussed

in reference [17].

As the tool wears, neither the shear angle nor the chip

thickness cha nges noticeably [22]. The rubbing force F cw

due to ank wear can be modelled based on the process

information of chip formation and ank wear length VB

Fig. 6 Schematic for numerical computation o f the temperature rise in thermal modelling



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[22, 23]. If there is only an elastic contact under the tool

ank face, the heat source is uniform along the tool–

workpiece interface. Then the rubbing heat source

density a long the tool–workpiece interface can be simply

expressed as

qrubbing ˆ F cwV cutting

w VB…14†

Figure 7 depicts the modelling process of the tool–

workpiece temperature distribution.

3.2 Results and validation

3.2.1 M odel validation

To acquire the temperature distribution a long the tool–

workpiece interface, Boothroyd [24] applied an infrared

photographic technique in orthogonal cutting of a

tubular workpiece. The cutting conditions were an

Armco iron workpiece, cemented carbide t ool with a

208 rake angle, 0.60mm/rev feed, 6.35mm depth of cut

and 0.17 m/s cutting velocity. T he tools had articial

wear lengths (VB) of 0.381, 0.762 and 1.143mm.

Thermal conductivity of both the workpiece and the

chip is taken as 0.762J/cm(s) 8C and thermal diffusivity

is 0.220 cm2 /s, th e sam e as th at of a pu re iro n. Cemen -

ted carbide t ool thermal conductivity is considered to

be temperature independent in cutting [12] as 0.57

J/cm(s) 8C (K series carbide) [13].

Oxley’s predictive machining theory [20] is used to

estimate the required process information for the chip

formation process of cutting 0.03 per cent carbon

Armco iron. Waldorf’s worn tool force model [22, 23]

is applied to estimate the rubbing force at the tool–

workpiece interface. In the cutting steel workpiece, if the

ank wear length is greater than a particular value,

elastic contact and plastic contact coexist along the

tool–ank interface; otherwise, there is only elastic

contact [25]. As no information exists regarding this

particular value for Armco iron, it is assumed that there

was only uniform elastic contact along the interface for

these selected ank wear lengths. The predicted process

information is summarized in Table 1.

The estimated temperature distributions and the

measured temperature for the above conditions are

shown in Figs 8 to 10. The comparisons are within 10

per cent of error and the distribution predictions

resemble tho se of the measurements. Since the contribu-

tions of both the secondary heat source on the work-piece side and the rubbing heat source on the chip side

are ignored in this study, this simplication leads to the

temperature underestimation and it needs to include

these contributions for a more accurate prediction. The

observed error may also come from the estimated

process information, which is indispensable in predicting

the tool–workpiece temperature distribution. The aver-

age temperature information along the rake face and

ank face is listed in Table 2. The ratio between the

average rake face temperature and average ank face

temperature in kelvin is also shown in Table 2, which

ranges from 78 to 81 per cent under t he investigatedcutting conditions. This range is reasonable when

Fig. 7 Approach o f thermal modelling of the tool–workpiece interface

Table 1 Process information under the conditions of Booth-

royd [24]

VB (mm) F c…N† F t…N † f l (mm)Shear owstress (MPa) F cw…N †

0.381 18 616 20 196 5.5 16.5 414.3 563.80.762 18 616 20 196 5.5 16.5 414.3 1127.51.143 18 616 20 196 5.5 16.5 414.3 1691.2

Table 2 Temperature information under the conditions of Boothroyd et al. [24]

VB(mm)

Average

rake facetemperature( 8C)

Average

ank facetemperature( 8C)

Ratio between average

rake face temperatureand average ank facetemperature in kelvin (%)

0.381 888.9 638.3 78.40.762 890.8 652.8 79.6

1.143 893.5 664.9 80.4



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compared to the ratio of 82–95 per cent determined

from measurements [20, 24, 26].

3.2.2 Case study

To stu dy th e ap plicab ility o f th e mod el, ano ther

orthogonal machining case is researched here. The

cutting conditions were an AISI 1018 steel workpiece,

K3H carbide tool with a 78 rake angle and 5.16mm

depth of cut. As suggested in reference [12], this paper

considers a temperature value intermediate between the

bulk workpiece material and the average interface

temperature for evaluation of the workpiece thermal

properties. For simplicity, thermal conductivity of both

the workpiece and chip is taken as 0.489J/cm(s) 8C and

thermal diffusivity as 0.121cm2 /s at 200 8C [27]. C arbide

tool thermal conductivity is considered to be tempera-

ture independent in cutting [12] as 0.57J/cm(s) 8C (K

series carbide) [13].

Oxley’s predictive machining theory [20] is used to

estimate the required process information for the chip

formation process of cutting AISI 1018. Waldorf’s worn

tool force model [22, 23] is applied to estimate the

rubbing force a t the tool–workpiece interface. T hree

scenarios are investigated herein: (a) varying t he feed

Fig. 8 Temperature comparison along the tool–workpiece interface with a 0.381mm ank wear length




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rate when VB ˆ 0.1 mm and cutting speed ˆ 1.32m/s;

(b ) v ar yin g th e an k wear len gth VB wh en feed

rate ˆ 0.28mm/rev and cutting speed ˆ 1.32m/s; (c)

varying the cutting speed when VB ˆ 0.2mm and feed

rate ˆ 0.28mm/rev. Under the selected ank wear

length, only t he un iform elastic contact along the tool–

workpiece interface is expected. The predicted process

information is summarized in Tables 3 to 5.

The estimated temperature distributions for the above

conditions are shown in Figs 11 to 13 and the average

temperature information along the rake face and ank

face is l isted in Tables 6 to 8. Th e temper atu re

distributions resemble those of Boot hroyd [24]. Th e rat io

between the average rake face temperature and average

ank face temperature in kelvin is investigated here for

the purpose of model validation. Tables 6 to 8 list the


Table 3 Process information under the conditions VB ˆ 0.1mm and cutting speed ˆ 1.32m/s

Feedrate t (mm/rev) F c…N† F t …N† f l (mm) Shear ow stress (MPa) F cw…N†

0.17 2365.9 2050.5 12.6 1.1 469.6 136.30.19 2515.1 2095.7 13.5 1.1 465.8 135.20.28 3112.1 2262.5 16.2 1.3 455.2 132.0

Table 4 Process information under t he conditions feedrate ˆ 0.28mm/rev and cutting speed ˆ 1.32m/s

VB (mm) F c…N† F t …N † f l (mm) S hear o w st ress (M P a) F cw…N†

0.1 3112.1 2262.5 16.2 1.3 455.2 132.00.2 3112.1 2262.5 16.2 1.3 455.2 264.10.35 3112.1 2262.5 16.2 1.3 455.2 396.1

Table 5 Process information under the conditions VB ˆ 0.2mm/rev and feedrate ˆ 0.28mm

Cutting speed (m/s) F c…N† F t …N † f l (mm) Shear ow stress (MPa) F cw…N†

1.32 3112.1 2262.5 16.2 1.3 455.2 264.1

2.03 2812.5 1828.1 18.4 1.1 457.0 265.33.05 2561.1 1472.3 20.7 0.9 458.8 266.4



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comparisons. The ratio ranges from 75 to 82 per cent

under the investigated cutting conditions. Again t his

range is reasona ble when compared to the ra tio of 82–95

per cent acquired from measurements [20, 24, 26].

Based on the presented results, several conclusions

can be drawn:

1. The progression of ank wear changes the average

rake face temperature only slightly, as seen from

Tables 2 and 7.

2. Both the average ank temperature and average rake

temperature increase with ank wear length and

cutting speed.

Fig. 12 Temperature pro le under the different ank wear lengths along the tool–workpiece interface (feedrate ˆ 0.28mm/rev and cutting speed ˆ 1.32m/s)

Fig. 11 Temperature prole under th e different feed rat es along the tool–workpiece interface (VB ˆ 0.1mmand cutting speed ˆ 1.32m/s)



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3. It is found that both average temperatures decrease

with feed rate. Since shear ow stress decreases with

feed rate, as estimated here and by Oxley [20], the

rubbing force, which is a function of shear ow

stress, decreases with feed rate as well. Then heat

intensities of both the secondary a nd the rubbing

heat sources are expected to decrease with feed rate

accordingly. However, the conicted phenomena

were observed in orthogonal cutting of the AISI

1018 steel by Chao et al. [28].

4 CONCLUSIONS

This study investigates the temperature distributions by

considering the effect of the tool wear land. On the chip

side, the effect of the primary shear zone is modelled as

the uniform moving oblique band heat source and that of

the secondary shear zone as the non -uniform moving

band heat source within the semi-innite medium. For

the tool side, the effects of both the secondary and the

rubbing heat sources are mo delled as no n-uniform static

rectangular heat sources within the semi-innite medium.

On the workpiece side, the effect of the primary shear

zone is modelled as the uniform moving oblique band

heat source a nd that of the rubbing heat source as the

Fig. 13 Temperature prole under the different cutting speeds along the tool–workpiece interface(VB ˆ 0.2mm and feed rate ˆ 0.28mm/rev)

Table 6 Temperature information under the conditions

VB ˆ 0.1mm and cutting speed ˆ 1.32m/s

Feedrate t

(mm/rev)

Averagerake facetemperature

( 8C)

Averageank facetemperature

( 8C)

Ratio betweenaverage rake facetemperature andaverage ank facetemperature in kelvin

(%)

0.17 820.1 608.7 80.70.19 813.0 593.1 79.80.28 791.4 547.5 77.1

Table 7 Temperature information under the conditionsfeedrate ˆ 0.28mm/rev and cutting speed ˆ 1.32m/s

VB (mm)


( 8C)


( 8C)

Ratio betweenaverage rake face

temperature andaverage ank facetemperature in kelvin

(%)

0.1 791.4 547.5 77.10.2 791.6 586.9 80.80.35 793.5 596.1 81.5

Table 8 Temperature information under the conditionsVB ˆ 0.2mm a nd feedrate ˆ 0.28mm/rev

Cutting

speed (m/s)


( 8C)


( 8C)

Ratio between averagerake face temperatureand average ank facetemperature in kelvin

(%)

1.32 791.6 586.9 80.82.03 851.4 603.4 77.93.05 931.4 630.4 75.0



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