A study of cutting with a CBN tool

ELSEVIER

Journal of Materials ProcessingTechnology49 (1995) 149-164

Journal of Materials Processing Technology

A study of cutting with a CBN tool Z o n e - C h i n g Lin*, D i n - Y a n C h e n Department of Mechanical Engineering, National Taiwan Institute of Technology, 43, Keelung Rd.. Section 4, TaipeL Taiwan, 10772, ROC

Received 31 March 1993; acceptedin revised form 24 January 1994

Industrial Summary The objective of this paper is to study the various cutting characteristics of a CBN tool when it is used in cutting hardened steel, BZN tool inserts of the General Electric Company being used to cut 52100 bearing steel (HRc 64) in the cutting experiments. Based on the resulting experimental data, certain cutting characteristics when a CBN tool is used for cutting this type of hardened material, such as tool life, cutting forces, surface roughness and tool wear, are analyzed. Finally, regressive equations are developed within the experimental applications.

1. Introduction CBN is a type of cubic crystal boron nitride, a CBN tool using a sintered product of CBN that has been treated at high temperature (about 1500°C or above) and high pressure (about 40000 kg/mm2). This product was first developed by the General Electric Company in 1972. At the time, the sintered cement was cobalt. Japan also announced their successful development in using ceramic as the cement of a cutting tool in 1975. Since a CBN tool is a sintered product, the size of the CBN crystals, their distribution, the percentage of CBN and the cement all affect the cutting property of a CBN tool. A CBN tool possesses various characteristics, one of which is its extremely high hardness at room temperature. Amongst all known materials, its hardness is second only to that of diamond. It has an excellent wear durability, which is also second only to diamond. It also has a considerably high hot-hardness, good thermal resistance and a high coefficient of thermal conductivity, its cutting property under high temperature therefore being better than that of diamond. Since it has good thermal stability, it is unlikely to generate a chemical reaction with the workpiece under high thermal

*Corresponding author. 0924-0136/95/$09.50 © 1995 ElsevierScienceS.A. All rights reserved SSDI 0 9 2 4 - 0 1 3 6 ( 9 4 ) 0 1 3 2 1 - Q

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Z-C. Lin, D.-Y. Chen/Journal of Materials Processing Technology 49 (1995) 149-164

conditions. As a result, in industry, CBN tools are used mainly in the processing of hard-to-machine materials. For example, CBN tools can be used for cutting the following materials: alloy steel with a hardness of around HRc 70, forging steel with a hardness of around HRc 45-68, chill iron, nickel-base superalloy, and cobalt-base superalloy. The price of CBN tools is extremely high, about ten to twenty times the price of normal carbide tools or ceramic tools, their economical use therefore being in the machining of hard-to-machine materials and hardened steel or alloy steel. The material remove rate when machining with CBN tool is much greater than that of the grinding process. In this case, if the surface roughness of the workpiece machined with a CBN tool can be kept within an acceptable level, the process of cutting with a CBN tool will be able to replace part of the grinding process, thereby showing economical benefits in using a CBN tool. At present, the commercial use of CBN tools remains, for the most part, in turning or boring processes, although they are also found, but with very limited application, in milling operations: this low application is due to the high hardness but inferior toughness of CBN tools, which makes them less suitable for heavy cuts or milling cutting. Since CBN is a relatively new cutting tool material, information concerning its cutting characteristics, such as tool life, cutting forces, wear and the surface quality of the processed workpiece, is yet to be published in detail. The information provided by various suppliers is usually for general applications, such as the suitable material characteristics and the recommended feed for a particular cutting speed. In most cases, this data does not represent the optimal cutting conditions. Though the potential of CBN tools for application is very much valued by industry, there is a very little information concerning cutting with CBN tools. To improve this lack of information, the Japan Mechanical Research Institute conducted a series of research investigations into the application of CBN tools. The research subjects focused on different materials under the conditions of fixed depth of cut and fixed feed to explore the characteristics of the wear and the life of CBN tools. The materials studied included high-speed tool steel (SKH3, SKH9), structural steel ($45C), highcarbon tool steel (SK3), chromium-molybdenum steel (SNCM8), stainless steel (SUS304, 630), die steel (SKDll), bearing steel (SUJ2) and cast iron with globular graphite. Hodgson et al. [1] used CBN tools to cut hardened steels M2, D2, and D6 in order to compare the cutting force and tool life, whilst Aspinwall et al. [2] compared the tool life of CBN cutting tools of different brands. These latter authors also used CBN tools and carbide tools to machine the Rover 2000 automotive inlet valve seat, finding that a carbide tool needed further grinding after 300 to 350 workpieces, whilst a CBN tool could last for more than 2000 workpieces. Tonshoff et al. [3] concluded that the requirements for cutting hard materials are good thermal conductivity and hardness of the tool, a large horsepower of the machine tool and good stiffness. They mentioned especially that the level of surface roughness of a workpiece cut by a CBN tool should be acceptable in order to be able to replace the time consuming grinding process. There has been very little research in Taiwan on the cutting characteristics, - such as tool life, cutting forces, surface roughness and tool wear - when a CBN tool is used

Z.-C. Lin, D.-Y. Chen/Journal of Materials Processing Technology 49 (1995) 149-164

151

FLLllcutting dynom¢k-~

L~ ~II~tT~ERg257A chargeamplifier / KISTLER5006

'rn

J

,,o,

62"

2 Fig. 1.

for cutting a hardened material such as 52100 bearing steel with a hardness of HRc64. The authors hope that this experimental study will assist in the further understand of the cutting characteristics of this type of tool, this being the major objective of the present paper.

2. Cutting with a CBN tool

A MAZAK M-3 NC lathe was used for the carrying out of the cutting experiments in this study, the three-axis cutting forces, the flank wear and the surface roughness of the workpiece being measured and recorded in the experiments. The arrangement of the experimental apparatus and associated equipment in shown in Fig. 1. The NC lathe is used to perform dry cutting on 52100 bearing steel (HRc 64). The process of hard material cutting mostly involves using a negative back-rake angle and a negative side-rake angle, the side cutting angle usually being around 15 °. However, for a CBN tool, a larger nose radius is commonly used to achieve a better cutting effect. Further, experiments on ISO [4] standard tool life often choose quadrate tools. Table 1 shows all of the conditions used in the experiments whilst the specifications of the equipment are presented in Table 2. The CBN tool is used to perform the dry cylindrical turning of 52100 hard steel. The depth of cut is set at 0.20 mm, a dial gauge with an error of less than 0.005 mm being attached to the tool head to measure the actual depth of cut. The cutting speed is derived from the spindle speed and the diameter of the surface of the workpiece. The feed is taken from the actual feed per revolution. The flank wear is observed with a light projecter, with an error of 0.0025 mm, a flank wear of VB = 0.3 mm being the criterion of tool life. Since the depth of cut is only 0.2 mm, only the round part of the tool nose edge has a cutting function; therefore, the flank wear of the tool is the wear on the nose. Fig. 2 shows the relationship between the tool and the workpiece. The greatest amount of wear is used as the measure of flank wear, Fig. 3 presenting the measure of flank wear under different types of wear.

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Table 1 Specifications of the equipment NC lathe

MAZAK M-3 machining center spindle horsepower: 11 k W spindle speed: 68-2000 rpm, 12 speeds feed rate: 1.5-600 mm/min

Dynamometer

KISTLER 9257A three-axis dynamometer largest measuring capacity Fz -- 10000 N linear error under 1, sensitivity Fz = - 3.5 pC/N natural resonant frequency: 4 kHz Fx = Fy = - 7.5 p C / N

Charge amplifer

KISTLER 5006 charge amplifier input charge load between + 10-500000 pC end frequency 180 kHz, sensitivity 0.1-11000 pC/M.U.

A / D interface card

12 bit, input voltage: - 10 V - + 10 V

Digital electric meter

FLUKE 8010A digital electric meter

Dynamic signal analyzer

HP 3562 dynamic signal analyzer frequency between 10.24 mHz ~ 100 kHz

PC/AT

PC/AT compatiable models 10 MHz

Surface roughometer

Surtronic model 3 of TYLOR-HOBSON brand measuring range: 0-9.99 and 0-25 ~tm Ra

Table 2 Conditions of the cutting experiments Tool type

SNMA120408, tool model from GE

Tool angle(°C) Nose radius (mm) Tool-holder type Tool holder Extension length (mm)

-6, - 6 , 6, 6, 15, 15 0.8 PSBNL2525M12 SANDVIK T-MAX P 10

Cutting material Proportion (wt%) and Heat treatment

C

Si

Mn

P

S

Cu

Ni

0.96 0.28 0.40 0.02 0.04 0.28 0.14 preheat at 400 °C maintain 850 °C for 30 min

Cr

Mo

V

A1

Sn

Ti

1.34 0.02 0.01 0.03 0.02 0

oil quench for 2 min tempering at 160 °C for 3 h hardness: HRc64

Material sizes (mm)

length: 600; diameter: 118

Experiment serial number Cutting speed (m/min) Feed rate (mm/rev) Depth of cut (mm)

1

2

3

4

5

6

44.5 0.039

44.5 0.210

144.5 0.216

144.5 0.039 0.20

83.0 0.104

83.0 0.104

Z.-C. Lin, D.- Y. Chen /Journal of Materials Processing Technology 49 (1995) 149-164

153

workpiece

Fig. 2.

LLL /vB v~

3

~vB 8

1'

12

Fig. 3. The experimental procedure is listed below: (1) After the machine has been set, the equipment and instruments are examined and tested, following which the lathe is left running for 30 minutes without load, prior to commencing an experiment. (2) The appropriate cutting speed and feed are selected.

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Z.-C. Lin, D.-Y. Chen/Journal of Materials Processing Technology 49 (1995) 149-164

(3) During the actual cutting operation, the cutting force is measured by the dynamometer, and then amplified by the charge amplifier, the analogue signals being converted into digital signals by means of an A / D interface card. The cutting force is then recorded and processed with a PC/AT, the principle of processing being based on taking data at 100 points per second, the cutting force being taken as the average value of the cutting force over a 10 s period. (4) When the cutting force is output from the charge amplifier, signals are sent to the digital electric meter and the dynamic signal analyzer for monitoring cutting force. (5) Each cutting operation lasts for one or two minutes, after which the tool is dis-assembled to show the flank wear, which is also recorded. (6) The tool is replaced with another tool and step 2 is repeated. (7) The experiment on a tool is terminated when its flank wear reaches 0.30 mm. However, to understand what effects a tool may have on cutting force and workpiece surface roughness if it is still in use after its flank wear has reached 0.03 mm, the tools in experiments 3 and 4 are used till serious chipping has appeared on the nose. 3. Results and discussion

Since the effective part of the cutting tool in this experiment involves only the tool nose edge, a very peculiar phenomenon of cutting force was found over the entire cutting process, that is, the thrust cutting force on the tool is, surprisingly, greater than the major cutting force, this phenomenon being found to disappear when the depth of cut is greater (0.40 mm). In other words, when cutting is limited to the tool nose circle, size effects became very obvious. A typical results of flank wear is shown in Fig. 4, whilst typical cutting forces are shown in Figs. 5 and 6. The regressive results of tool life are shown in Fig. 7. The regressive results of tool wear are shown in Figs. 8 and 9, whilst the relationship between surface roughness and flank wear is shown in Fig. 10. The regressive results of cutting force from six cutting experiments are shown in Figs. 11-13, whilst the regressive results of cutting force exclusive of high-speed cutting (V = 144.5 m/min) are shown in Figs. 14-16. The regressive results of the cutting force for fresh tools are shown in Figs. 17-19. From the experimental data, it is found that the cutting parameters of cutting force, flank wear and tool life can all be analyzed regressively with the following equation: y = KoV~'FaX

~

(1)

Since there is limited association between surface roughness and flank wear, it is less practical to use Eq. (1) for the purpose of analysis: the following regressive equations can be acquired after the regressive analysis of Eq. (1). In the regressive equations, V stands for the cutting speed (m/min); F is the feed (mm/rev); TL is the tool life (min); and T is the cutting time (min). All of the units of Fx, Fy and Fz are Newtons (N), whilst the unit for flank wear VB is (mm). (1) Regressive equation of tool life TL ---- 11849.01 V-1.7889 F-0.3863,

(2)

Z-C. Lin, D.- Y. Chen /Journal of Materials Processing Technology 49 (1995) 149-164

155

0.80 o o • +

0.72 0.64

E 0.56 E

v

•

x

0.48 0.40

4

5 6

•

0.32

h

1 2 3

"4"

L 0

E 0

test test test test test test

~t +

0.24

X

+

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,

, i

I

~ ~ ~

i

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31.0

time

i ,

I

41.0

min)

Fig. 4.

300 C

(A) Thrust cutting force (B) Main c u t t i n g f o r c e (C) Feed c u t t i n g f o r c e

250

c

2OO (A)

o D3 C

150

u

I00

(B) (C)

50

00

1.0

20

30

40

50

60

Cutting time

Z0

80

90

10

(sec)

Fig. 5.

correlation coefficient ? = 95.6%. (2) For a fresh tool (i.e. a tool with very little wear): c u t t i n g force

Fz =

12.2538 V 0"78567 F 0"538,

(3)

156

Z-C. Lin, D.-Y. Chen/Journal of Materials Processing Technology 49 (1995) 149-164 600 50C

(A) Moin c u t t i n g f o r c e (B) T h r u s t c u t t i n g f o r c e (C) Feed cutting f o r c e

400

v ¢# u L

~o

30C

O~ r-

20C (A)

(J

--

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(B)

(C) 10~

,

,

~

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I

2.5

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I

~

I

I

i

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i

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Cutting time

(sec)

N

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~o

speed

Fig. 7.

I

10.0

Fig. 6.

Cutting

I

(mlmin)

t

,

J

i

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12.5

Z.-C Lin, D.-E Chen/Journal of Materials Processing Technology 49 (1995) 149-164

O80/[0.70~~Q60 u

h

157

[] t e s t 1 +

0 • + x ~

test 2 test 3 test 4 test 5 test 6

I il l l l

~I l l l

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1.0

[l i l l l l l. l.l.1l.l.i .l .l l

1l i

6.0

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1 I I I I I 1 1[ 1 1 1 ' 1

16.0

21.0

Cutting

time

I I I ~I I I I

26 0

II1'

310

36.0

(min)

Fig. 8.

0.80~~

L

0.70~- u o 0.60~- • 0.50~-L +

test 1 test 2 test 5 test 6

I3

0.40 r-

1:3

~

030

0.00

~

o

1o I

_~.a~---u

n,.,.--O'''-u

,,I+ ~.~'0

t" . . . .

1.0

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L ,

6.0

,

,

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,

,

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16.0

t

t I

t

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Cutting

i t

i I

26.0

time

t

I

,

,

I

t

31.0

t

,

,

I

36.0

I t

,

t

I

41.0

(rain)

Fig. 9.

correlation coefficient: 7 = 98.8%; feed force F r = 2.7554

V

0"7714

F

0"2101,

(4)

correlation coefficient 7 = 97-5%; thrust force Fx = 34.329 V °'432 F °'2~°3, correlation coefficient 7 = 97. 70/0.

(5)

158

Z-C Lin, D.-Y. Chen/Journal of Materials Processing Technology49 (1995) 149-164 o o • + x t

2.5C

2.0C

test test test test test test

I 2 3 4 5 6

x _ . . ~ x

X

n,-

X~ X

/

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o

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°

+

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d')

0.50

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o o

0.00 , 0.00

,

1

,

I

i

,

,

0.10

i

I

020

i

i

i

i

1

~

i

+

,

1

i

0.30 Flank

I

1

,

i

0.40 wear

i

I

,

0.50

I

i

,

I

,

i

,

0.60

i

I

0.70

(mm)

Fig. 10.

"E 6OO n ¢J

500

o • o 400 : + O3 C -'x u L

...Fa :3 'J

300

test test test test test

I 2 3 4 5

/

.

~

0 testO

•

_o

+ ~

f

200

c

~E

100 -

O

0 ",~,,,,,J,l,l,lJ~,lllal,i,,,lil,,i,,,,,,l,,t, 000 0.10 0.20

,,,

0.30

Flank wear

0.40

,I

0.50

(ram)

Fig. 11.

(3) The cutting force is derived from the regressions of six sets of experimental data of a tool with wear, including high-speed cutting: F= = 233.01 V °'351s F °'224s Vb °'694, correlation coefficient 7 = 96.4%;

(6)

Z.-C. Lin, D.- Y. Chen /Journal of Materials Processing Technology 49 (1995) 149-164

159

600 E

500

U test o test

1 2

ou

400

E

300

3 4 5 co

u

200

• test + test x test test

u

"t3

100 u_

~ O0 r

,

,

i

,

,

,

i

i

i

l

i

l

l

l

i

l

,

i

0.10

l

i

,

,

i

,

i

,

,

i

i

i

i

0.20

l

i

i

l

i

,

i

,

l

,

i l l l l l J

,

0.30

Flank

wear

0.40

0.50

(mm)

Fig. 12.

~.

6OO

v

500 u L

o

4oo

.-=

300

u

200

[] o • +

test 1 test 2 test 3 test 4

x

test 6

~--~-'~°~

~

~

Ln

u

L

100

0 i 0.00

Iiii

ill

11

i i i i i i

0.10

I iii1

i i I I i ] i I i I I I i I I I i I

O. 2 0 Flank

O. 3 0 wear

0.40

I l l l l ]

0.50

(ram)

Fig. 13.

feed force Fy = 373.44 V °'°3564 F 0"06498 VB 0"6748,

(7)

c o r r e l a t i o n coefficient y = 92.6%; thrust force Fx = 334.09 V °'1718 F °'374° c o r r e l a t i o n coefficient y = 95.5%;

VB0"6199,

(8)

160

Z . - C Lin, D.-Y. Chen/Journal o f Materials Processing Technology 49 (1995) 149-164

600 E ID I..) L o O3 r-

50C

test 1 t o est 2 test 5 0

500

300

+

+ test e

J

/

/

.i..I

u

20O

rID

100

Z Or,,,,

0.00

0 II

Illlll

IIII

I IIIIIIIlll

0.10

IIII

O. 20 Flank

IIIIIII

O, 30 wear

II

II

IIIIII

0.40

0.50

(mrn)

Fig. 14.

600 E 0 U [_

5O0

o

400

(33 C

300

U

2O0

o test 1 o test 2 • test 5 + test 6

100 LL

0 Jtllll 0.00

IIII

IIII

0.10

III

Ii II IIII

iii

0.20 Flank

iiii

0.30 wear

II Iiiiiiiii

0.40

IIIII

I

0.5O

(mm)

Fig. 15.

flank wear VB = 0.002233 V 0"902¢ F °'1781 T 0"5448,

(9)

correlation coefficient 7 = 90.9%. (4) From Figs. 11-13 and 8, it is found that Eqs. (6)-(9) are not suitable in high-speed cutting. Therefore, low-speed cutting (i.e. exclusive of high-speed cutting), is performed. The cutting force is derived from the regressions of experimental data: Fz = 144.82 V °'5°87 F 0"2751 VB0"7200, correlation coefficient y = 99.3%;

(10)

Z-C. Lin, D.- Y. Chen /Journal of Materials Processing Technology 49 (1995) 149-164

161

600

C

500

[_

o O3 C

40C 300

o o • +

test test test test

1 2 5

• +

6

/

~

{J

200 :3

L .17. I--

100 0 ililillliillllil 0.00 0.10

liliilllll

II1

0.20

0.30

Flank

wear

IIIlillllllillllll

I I

0.40

0.50

(mm)

Fig. 16.

n 0 250 ~-. !+ 200 _---x 300

v

test 1 test 2 test 3 test 4 test 5

150 u C

8

100

5O 0 40

0" IIII

Iiii

[11 i i i i i

GO

IiIiIIliillllllllllililli

80

100

Cutting speed

iiiiiil[lllllll

120

140

ill

160

(m/rain)

Fig. 17.

feed force Fy = 777.05 V °'°°41 F 0"01745 VB0"0053,

(11)

c o r r e l a t i o n coefficient ? = 92.6%; t h r u s t force Fx = 215.22 V °'234° F °-°238 VB°'s478, c o r r e l a t i o n coefficient ? = 95.1%;

(12)

162

Z-C. tin, D.-Y. Chen/Journal of Materials Processing Technology 49 (1995) 149-164 300

Q)

u o • ÷ x •

250

(.9

20O %,-

o~ 150 C

~oo

test test test test test test

1 2 3 4 5 6

5o ~ ,

.......

~0

. .

.......

6O

. _

........

8O

, .........

100

Cutting

speed

, .........

120

, ....

tJJl

160

140

(m/rain)

Fig. 18.

t-

300

u test -o test

1 2

test 3 - test 4 2 0 0 -× t e s t 5 25Q

L

:. .~

test

6

150

.._..J3

e-J

u

100

u

50

t._ t"F-

iii

%0 . . . . . . . 86 . . . . . . . ~ 6 . . . . . . . 1S6 . . . . . Cutting

speed

tilllllllllllil

120

lit

140

I

160

m/rain)

Fig. 19.

flank wear VB = 0.00718 V 0"5991 F 0"1532 T 0'5247,

(13)

correlation coefficient ? = 98.3%. The phenomena in Figs. 4 - 1 9 m a y be explained in terms of the following aspects: (1) It can be seen from the relationship between flank wear and time in Fig. 4 that the flank wear rate is usually greater at the beginning. For low-cutting speed experiments such as tests 1 and 2, the wear grows steadily after a certain period of time. However, for cutting at greater cutting speeds, wear rate is generally quite great, under the situations of greatest wear, reaching 0.31 m m in only two minutes. It can be seen very clearly from the figure that the wear characteristics m a y not be fully

Z.-C. Lin, D.- Y. Chen /Journal of Materials Processing Technology 49 (1995) 149-164

163

described by the simple Eq. (1). Therefore, a distinct phenomenon appears in the regressive curve in Fig. 8. The error between the regressive curve and original data is smaller in low-speed cutting, but this error becomes much greater in high-speed and high-feed situations. As a result, the wear regressive equation (9) used in this study is not applicable in high-speed and high-feed situations. Nevertheless, the results of Eq. (13), shown in Fig. 9, derived from the regression of low-speed situations only, indicate that wear can be predicted in low-speed cutting. (2) Fig. 7 shows the tool-life curve. There are a total of six tests on tool life in this experiment, amongst which, tests 5 and 6 share exactly the same conditions and generated the same tool life. It can be seen from the regression results that the Taylor tool-life equation is, on the whole, applicable in this test environment. (3) Fig. 5 shows the typical three-axis cutting forces at a cutting depth of 0.20 mm. The experimental results show that the thrust force is always greater than the cutting force, this phenomenon clearly indicating the size effects. Due to only the tool nose circle of the cutting chin being engaged in cutting, and the tool squeezing into the workpiece almost by pushing, the thrust force is greater than the cutting force. (4) As shown in Fig. 6, in the cutting force is greatest when the depth of cut is larger (0.40 mm), whilst the thrust force becomes smaller than the cutting force. In other words, the size effect is smaller with a greater depth of cut. (5) Figs. 11-13 show, respectively, the relationship between the flank wear and the cutting force, the feed force and the thrust force. It can be seen from these three figures that the relationship between thrust force and the flank wear is not very clear. Without consideration of the high-speed cutting data, the regressive results are as those shown in Figs. 14-16. It is obvious that, under these circumstances, the cutting data is closer to the regressive results. The reason behind this phenomenon may be that the cutting force of the tool with chipping at the nose is different from that of the tool without chipping. From Figs. 12 and 15, it was found that the relationship between the feed force and the flank wear is almost unrelated to the cutting speed and feed, only to VB. (6) Fig. 10 shows the relationship between the workpiece surface roughness Ra and the flank wear VB, the results of the various regressions performed on VB in the same experiment being shown in solid lines. Generally speaking, the greater the feed, the greater the value of Ra. However, this relationship stops short of being absolute. If nose chipping or surface cratering occurs, there will still be a great difference in the surface roughness, even under the same experimental conditions, as is the case in tests 5 and 6. Therefore, surface roughness can not be expressed simply by Eq. (1): the detailed causes should be studied further. (7) The regressive and experiment results of the cutting of fresh tools are very similar (Figs. 17-19). However, due to the limited experimental data available, it can not be guarantee that they are applicable in all kinds of situations.

4. Conclusions

These experiments used CBN tools to cut 52100 bearing steel of HRc 64. From the results of the experiments the following conclusions can be drawn.

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(1) A CBN tool can be used for cutting hardened hard-to-machine materials. In view of its superior quality in terms of the resultant surface roughness, it can replace a portion of the grinding work. Therefore, it possesses considerable economic potential. (2) The resultant workpiece surface roughness can not be expressed simply by the rudimentary equations of cutting speed, feed and flank wear. (3) The flank wear rate becomes quite large with a greater cutting speed. Therefore, it does not comply with the economic purpose of cutting under a high cutting speed. (4) When a CBN tool is used to cut hardened hard-to-machine materials, with a shallow depth of cut the thrust force is greater than the cutting force. Contrarily, with a greater depth of cut the cutting force is greater than the thrust force.

Acknowledgements We would like to express our deep gratitude to the National Science Foundation for granting the project expenditure (project code: NSC 77-0401-E011-02), which made this study possible.

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