The international journal of advanced manufacturing technology, tập 61, số 1 4, 2012

Int J Adv Manuf Technol (2012) 61:1–13
DOI 10.1007/s00170-011-3684-9

ORIGINAL ARTICLE

Surface roughness and chip formation in high-speed face
milling AISI H13 steel
Xiaobin Cui & Jun Zhao & Chao Jia & Yonghui Zhou

Received: 6 July 2011 / Accepted: 3 October 2011 / Published online: 22 October 2011
# Springer-Verlag London Limited 2011

Abstract Many previous researches on high-speed machining have been conducted to pursue high machining
efficiency and accuracy. In the present study, the characteristics of cutting forces, surface roughness, and chip
formation obtained in high and ultra high-speed face
milling of AISI H13 steel (46–47 HRC) are experimentally
investigated. It is found that the ultra high cutting speed of
1,400 m/min can be considered as a critical value, at which
relatively low mechanical load, good surface finish, and
high machining efficiency are expected to arise at the same
time. When the cutting speed adopted is below
1,400 m/min, the contribution order of the cutting
parameters for surface roughness Ra is axial depth of
cut, cutting speed, and feed rate. As the cutting speed
surpasses 1,400 m/min, the order is cutting speed, feed
rate, and axial depth of cut. The developing trend of the
surface roughness obtained at different cutting speeds
can be estimated by means of observing the variation of
the chip shape and chip color. It is concluded that when
low feed rate, low axial depth of cut, and cutting speed

below 1,400 m/min are adopted, surface roughness Ra
of the whole machined surface remains below 0.3 μm, while
cutting speed above 1,400 m/min should be avoided even if
the feed rate and axial depth of cut are low.
Keywords Cutting forces . Surface roughness . Chip
formation . High-speed face milling . AISI H13 steel

X. Cui : J. Zhao (*) : C. Jia : Y. Zhou
Key Laboratory of High Efficiency and Clean Mechanical
Manufacture of MOE, School of Mechanical Engineering,
Shandong University,
Jinan 250061, People’s Republic of China
e-mail:

1 Introduction
The primary objective of manufacturing operation is to
efficiently produce parts with high quality. The high-speed
machining processes can produce more accurate parts as
well as reduce the costs associated with assembly and
fixture storage by allowing several process procedures to be
combined into a monolithic one [1]. For the purpose of
enhancing machining efficiency and accuracy at the same
time, many significant researches on high-speed machining
have been conducted.
High-speed milling has been widely used in the
manufacturing of aluminum aeronautical and automotive
components so as to generate surfaces with high geometric
accuracy. The tool materials and rigid machine tools have
advanced to be applied in hard milling, which can even be
an alternative for the grinding process to some extent [2, 3].

In order to reveal the effects of cutting conditions especially
cutting speed on the machining efficiency and product
quality in high-speed hard milling, comprehensive and
thorough researches on surface roughness and chip formation should be conducted.
There are relatively few researches relating to surface
roughness in the field of high-speed milling of hardened
steels, and studies on chip formation are scant. As is stated
by Ghani et al. [4], when high cutting speed, low feed rate,
and low depth of cut were adopted, good surface finish can
be obtained in semifinish and finish machining hardened
AISI H13 steel using TiN-coated carbide insert tools. The
effects of cutting parameters on surface roughness in highspeed side milling of hardened die steels were investigated
by Vivancos et al. [5, 6], and mathematical models of
surface roughness were established by means of the design
of experiment (DOE) method. Toh [7] investigated and
evaluated the different cutter path orientations when high-


2

speed finish milling hardened steel, and the results
demonstrated that vertical upward orientation is generally
preferred in terms of workpiece surface roughness. Ding et
al. [8] experimentally investigated the effects of cutting
parameters on cutting forces and surface roughness in hard
milling of AISI H13 steel with coated carbide tools. And
empirical models for cutting forces and surface roughness
were established. The analysis results showed that finish
hard milling can be an alternative to grinding process in the
die and mold industry. Siller et al. [9] studied the impact of

a special carbide tool design on the process viability of the
face milling of hardened AISI D3 steel in terms of surface
quality and tool life. It was found that surface roughness Ra
values from 0.1 to 0.3 μm can be obtained in the workpiece
with an acceptable level of tool life.
Previous studies provide much valuable information for
the understanding of surface roughness in high-speed hard
milling. But very few researches were conducted to
investigate the surface roughness in high-speed face milling
of hardened steel. And probably due to the relatively small
tool diameter and the high hardness of the workpiece, the
upper limits of the cutting speed in these studies mentioned
above are much lower than those (1,100 m/min) in the
researches on tool wear in high-speed face milling of
hardened AISI 1045 steel [1].
Because of the great high-temperature strength and
wear resistance, AISI H13 tool steel is widely applied in
extrusion, hot forging, and pressure die casting. In the
present study, characteristics of cutting forces, surface
roughness, and chip formation obtained under different
cutting speeds in high and ultra high-speed face milling
of AISI H13 steel (46–47 HRC) are identified and
compared. For the purpose of experimental investigating
the effects of cutting parameters especially cutting speed
on surface roughness, Taguchi method was used for the
DOE. Because of the dynamic effects, runout, vagaries
of the table feed, and back cutting in the milling process,
the profile of the milled surface can vary substantially in
either the feed or perpendicular directions. Wilkinson
[10] pointed out that, although some profiles were

measured in nonback cutting regions, it still seems that
such variations were realistic. In the present study, for the
purpose of reducing such variation, the milled surface is
divided into four regions, and those regions are investigated separately and integratedly.

2 Experimental procedures
2.1 Workpiece material
A block of AISI H13 steel hardened to 46 to 47 HRC was
used in the present study. The nominal chemical composi-

Int J Adv Manuf Technol (2012) 61:1–13

tion of the H13 tool steel under consideration is shown in
Table 1. Dimensions of the block were designed so as to
avoid back cutting as shown in Fig. 1.
2.2 Cutting tool and machining center
A Seco R220.53-0125-09-8C tool holder with a tool
diameter of 125 mm, major cutting edge angle of 45°,
cutting rake angle of 10°, axial rake angle of 20°, and radial
rake angle of −5° was used in the milling tests. The tool
holder is capable of carrying eight inserts. The tungsten
carbide insert SEEX 09T3AFTN-D09, which is coated with
Ti(C, N)–Al2O3, was used in the experiments. In order to
simplify the analysis, only one of the teeth was used in all
the milling tests. All of the surfaces were milled using fresh
cutting edges. The milling tests were conducted on a
vertical CNC machining center DAEWOO ACE-V500 with
a maximum spindle rotational speed of 10,000 rpm and a
15-kW drive motor without cutting fluid.
2.3 Cutting tests

As has been mentioned, it has been found that the use of
high cutting speed, low feed rate, and low depth of cut
leads to a good surface finish in semifinish and finish
machining hardened AISI H13 steel [4]. Therefore, for the
purpose of acquiring better surface finish at high cutting
speed (upper limit 2,400 m/min), low feed rate (0.02–
0.06 mm/tooth) and low axial depth of cut (0.1–0.3 mm)
were adopted in the milling tests. Symmetric milling was
applied, and the radial depth of cut was fixed as 75 mm as
shown in Fig. 1. In all the milling tests, the feed length was
set to be invariable 112.5 mm so that back cutting can be
avoided.
The effects of cutting speed on cutting forces, surface
roughness Ra, and chip formation are focused on in the
present study. Firstly, experiments with all the cutting
parameters fixed except for the cutting speed v ranging
from 200 to 2,400 m/min with 200 m/min as an interval
were performed. Axial depth of cut ap and feed rate fz
were set to be invariable 0.2 mm and 0.04 mm/tooth,
respectively.
The Taguchi method uses a special design of
orthogonal arrays to study the entire parameters space
with only a small number of experiments [11]. After the
experiments with cutting speed in the range from 200 to
2,400 m/min, in order to distinguish the differences of the
effects of cutting parameters on surface roughness
obtained within different cutting speed ranges, two L9
orthogonal arrays, each of which has four columns and
nine rows, were used in the present study. For both of the
orthogonal arrays, the three influencing factors were

cutting speed, feed rate, and axial depth of cut, and one


Int J Adv Manuf Technol (2012) 61:1–13
Table 1 Nominal chemical
composition of AISI H13 tool
steel (in weight percent)

3

C

Mn

Si

Cr

Mo

V

Ni

Fe

0.32–0.45

0.20–0.50

0.80–1.2

4.75–5.50

1.10–1.75

0.80–1.20

0–0.30

Bal

column of array was left empty for the error of experiments. Table 2 shows the three levels of the factors in the
two arrays. The experimental layouts ME1 and ME2 are
shown in Tables 3 and 4.
The machined surface of the workpiece material was divided
into four regions as shown in Fig. 2. And the total machined
surface is represented by R5. In region R2 the entrance and
exit angles stay the same, while in the other regions those
angles keep changing. Moreover, for any small time period,
the milling conditions in regions R1 and R2 can still be
considered as symmetric milling, but in regions R3 and R4
they seemed to be two different kinds of asymmetric milling.
It is inferred that these differences will lead to varying
characteristics of the mechanical and thermal loads when
machining different regions, and finally affect the way how
the surfaces generate. Taking these into consideration, in each
test for each region denoted in Fig. 2, surface roughness Ra
was measured three times along the feed direction.
Under given milling conditions, each test was replicated

three times. The surface roughness Ra in different regions
was measured along the feed direction using a portable
surface roughness tester (Model TR200, China). The
sampling length and number of spans were set to be
0.8 mm and five, respectively. As shown in Fig. 3, the
cutting forces were measured using Kistler piezoelectric
dynamometer (type 9257B) mounted on the machine table.
And the charge generated at the dynamometer was
amplified by means of a multichannel charge amplifier
(type 5070A). The sampling frequency of data was set as
7,000 Hz. After the experiments the tool wear was
examined with an optical microscope and the chips were
observed using a Keyence VHX-600E 3D digital microscope with a large depth of field.

3 Results and discussion
3.1 Cutting force
The effects of cutting speed on cutting forces are focused
on in the present study. In the milling tests with cutting
speed ranging from 200 to 2,400 m/min, the cutting force
signatures were picked at the time when the milling cutter
reached the midpoint of region R2. For per cutting force
component, there were 7,000 data points in each recorded
signature. The data point Fm of the resultant cutting force is
calculated from the cutting force components as shown in
Eq. 1:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
À
Á2
Fm ¼ ðFxm Þ2 þ Fym þ ðFzm Þ2

where Fxm, Fym, and Fzm are corresponding data points of
the cutting force components in x, y, and z directions,
respectively. Due to the continuous variability of the
sampled data, the static force component Fsta can be
defined as the mean value of the sampled data point Fm
[12] as shown in Eq. 2:

Fsta

1
¼
N

N
X

!
Fm

ð2Þ

m¼1

where N is the number of the data points. Based on the
research by Toh [13], the dynamic cutting force Fdyn can be
calculated as shown in Eq. 3:
Fdyn ¼ Fmax À Fsta

Fig. 1 The setup of face milling

ð1Þ

ð3Þ

where Fmax is the maximum data value of all the data points
of the resultant cutting force.
Since each test was replicated three times, for each
cutting speed, there exist three values for Fsta and Fdyn,
respectively. Figures 4 and 5 show the developing trends of
the average values of the static cutting force and the
dynamic cutting force with the cutting speed, respectively.
It can be seen from Fig. 4 that as the cutting speed
increases, the static cutting force firstly increases approaching a peak value at a cutting speed of 1,000 m/min and then
begin to decrease. At the cutting speed of 1,400 m/min, the
static cutting force reaches a valley value. When the cutting


4

Int J Adv Manuf Technol (2012) 61:1–13

Table 2 Factors and selected
levels in the face milling
experiments

Factor

Cutting parameter

Unit

Level 1

Level 2

Level 3

A
B
C
D

Cutting speed (v1)
Cutting speed (v2)
Feed rate (fz)
Depth of cut (ap)

m/min
m/min
mm/tooth
mm

350
1,400
0.02
0.10

700
1,750
0.04

0.20

1,050
2,100
0.06
0.30

speed increases over 1,400 m/min, the static cutting force
keeps increasing.
When the cutting speed is relatively low, the cutting
temperature is low and adhesion is less likely to happen
between the tool and the workpiece material. Adhesion peaks
at some intermediate temperature [14]. When the cutting
speed is below 1,000 m/min, the cutting temperature
increases with the cutting speed, leading to the more serious
adhesion. It is inferred that, mainly due to the increase of the
friction coefficient induced by serious adhesion, the static
cutting force increases. As the cutting speed increases over
1,000 m/min, higher cutting temperature occurred. At high
cutting temperature, adhesion is reduced as thermal softening
has greater effect on the interface or on the workpiece
material [14]. Higher cutting temperature arises in the shear
zone, leading to the reduction of the yield strength of the
workpiece material, chip thickness, and tool chip contact
area. Moreover, the increase of cutting temperature results in
the decrease of the friction coefficient between the tool rake
face and the chip. And the shear angle will increase. Finally
the static cutting force will decrease. When the cutting speed
surpasses 1,400 m/min, the tool wear increases greatly with
the cutting speed as shown in Fig. 7. Because of the high

plowing forces induced by the increased contact area of the
larger flank wear face of the cutter acting on the workpiece,
the static cutting force increases with the cutting speed when
the cutting speed is above 1,400 m/min.
Figure 5 shows that when the cutting speed increases, the
dynamic cutting force keeps increasing until it reaches a peak
value at about 1,000 m/min. Then it decreases until the cutting
speed is 1,400 m/min. As the cutting speed surpasses

1,400 m/min, the dynamic cutting force will increase. It
seems that the developing trends of the static and dynamic
cutting forces are similar. This can be attributed to the
profound effect of the static cutting force on the occurrence of
cutter vibration. Since the tool wear increases rapidly with the
cutting speed when the cutting speed is above 1,400 m/min as
shown in Fig. 7, it is inferred that besides the effects of the
fixturing elements and the machine tool system, the higher
tool wear also has great contribution to the increasing trend of
the dynamic cutting force when the cutting speed increases
over 1,400 m/min. The evolution of the dynamic cutting force
with the cutting speed indicate that for the cutting parameters
under consideration, relatively stable cutting condition can
still be obtained at a high cutting speed of 1,400 m/min. The
relatively stable cutting condition is beneficial to the surface
finish of the workpiece. It is concluded that the cutting speed
of 1,400 m/min can be considered as a critical value for both
of the static and dynamic cutting forces.

Table 3 Experimental layout ME1 using an L9 orthogonal array

Table 4 Experimental layout ME2 using an L9 orthogonal array

Exp. no.

Exp. no.

1
2
3
4
5
6
7
8
9

A (v1)

C (fz)

D (ap)

1
1
1
2
2
2
3
3

3

1
2
3
1
2
3
1
2
3

1
2
3
2
3
1
3
1
2

E (error)

3.2 Surface roughness
Figure 6 shows the surface roughness in different regions
vs. cutting speed v. The surface roughness yi in region Ri is
calculated by means of the following equation:
1
yi ¼

n

n
X

!
ð4Þ

yij

j¼1

where n is the number of repeated test, namely three; yij is
the average value of Ra in region Ri at the jth test (i=1, 2,

10
11
12
13
14
15
16
17
18

B (v2)

C (fz)

D (ap)

1
1
1
2
2
2
3
3
3

1
2
3
1
2
3
1
2
3

1
2
3
2
3
1
3
1
2

F (error)


Int J Adv Manuf Technol (2012) 61:1–13

5

Fig. 4 Static cutting force Fsta vs. cutting speed v (fz =0.04 mm/tooth,
ap =0.2 mm)
Fig. 2 Division of the machined surface

3, 4, 5; j=1, 2, 3). The average surface roughness y5j of the
total machined surface is determined by Eq. 5:
y5j ¼ y1j S1 =S5 þ y2j S2 =S5 þ y3j S3 =S5 þ y4j S4 =S5

ð5Þ

where Sk is the area of the region Rk (k=1, 2, 3, 4, 5).
It can be seen from Fig. 6 that the curves (solid line) of
the surface roughness in regions R1 and R2 with cutting
velocity are similar, while those in region R3 and R4 are
similar. For surface roughness in all the regions, cutting
speed v=800 m/min is the optimum one, and v=1,400 m/
min can be considered as a transition value above which the
surface roughness in the five regions increase rapidly. It
must be pointed that when the cutting speed v is at a rather
high value of 1,400 m/min, as for the total machined
surface R5 good surface quality (0.068 μm) can still be
obtained.

Though the machined surface has been divided into four
regions and each test was replicated three times, for the
surface roughness in each region, there still seems to be some
randomness. In order to reveal the developing trends of
surface roughness in a more clear way, the curves of the
surface roughness with the cutting speed are fitted as shown in
Fig. 6 (dotted line). It can be seen from these fitted curves
that as the cutting velocity increases, the surface roughness
in different regions all exhibit similar developing trend: they

Fig. 3 Photos of the experimental setup

all decrease firstly and then increase. Equations 6, 7, 8, 9,
and 10 are the fitted formulas for the surface roughness in
regions R1, R2, R3, R4, and R5, respectively.
y1 ¼ 1:29 Á 10À7 v2 À 2:25 Á 10À4 v þ 1:27 Á 10À1 ðmmÞ

ð6Þ

y2 ¼ 8:68 Á 10À8 v2 À 1:06 Á 10À4 v þ 8:51 Á 10À2 ðmmÞ

ð7Þ

y3 ¼ 1:18 Á 10À7 v2 À 2 Á 10À4 v þ 1:65 Á 10À1 ðmmÞ

ð8Þ

y4 ¼ 8:13 Á 10À8 v2 À 1:36 Á 10À4 v þ 1:21 Á 10À1 ðmmÞ

ð9Þ

y5 ¼ 9:08 Á 10À8 v2 À 1:18 Á 10À4 v þ 9:07 Á 10À2 ðmmÞ

ð10Þ

The R squares (the coefficient of multiple determination,
measuring how successful the fit is in explaining the
variation of the data) for the five formulas are 0.92, 0.93,
0.91, 0.89, and 0.95, respectively. According to the fitted
formulas, for different regions, the cutting speeds at which
the optimum surface quality can be obtained are between
600 and 900 m/min. The surface quality is expected to be
optimal when the cutting speed adopted is in this speed
range.
Since both the cutting forces and the surface roughness
are low at an ultra high cutting speed of 1,400 m/min,

Fig. 5 Dynamic cutting force Fdyn vs. cutting speed v (fz =0.04 mm/
tooth, ap =0.2 mm)


6

Int J Adv Manuf Technol (2012) 61:1–13

Fig. 6 Surface roughness Ra in
different regions vs. cutting
speed v (fz =0.04 mm/tooth, ap =
0.2 mm). a Ra in R1 vs. cutting
speed. b Ra in R2 vs.

cutting speed. c Ra in R3
vs. cutting speed. d Ra in R4 vs.
cutting speed. e Ra in R5 vs.
cutting speed

(a) Ra in R1 vs. cutting speed

(b) Ra in R2 vs. cutting speed

(c) Ra in R3 vs. cutting speed

(d) Ra in R4 vs. cutting speed

(e) Ra in R5 vs. cutting speed
relatively low mechanical load, good surface quality, and
high machining efficiency are expected to arise at the same
time for the cutting parameters under consideration.
Though the machining efficiency is a little lower, cutting
speeds below 1,400 m/min can still be used to obtain good
surface finish, but the cutting speeds above 1,400 m/min
should be avoided.
Figure 7 shows the evolution of the average flank wear
VB after one pass of the workpiece surface with the cutting
speed. It can be seen that when the cutting speed is below
1,400 m/min, the tool wear rate is relatively small. As the
cutting speed surpasses 1,400 m/min, the tool wear rate
increases rapidly with the cutting speed. Taking the
developing trend of the surface roughness with cutting
speed into consideration, it is inferred that when the cutting
speed is below 1,400 m/min, the effect of tool wear on

surface roughness is small. But as the cutting speed
surpasses 1,400 m/min, the higher tool wear rate contributes greatly to the increase of the surface roughness with
the cutting speed.

Fig. 7 Flank wear of the cutting tool after one pass of the workpiece
surface vs. cutting speed v (fz =0.04 mm/tooth, ap =0.2 mm)


Int J Adv Manuf Technol (2012) 61:1–13

7

As 1,400 m/min is a transition cutting speed for surface
roughness, two experimental layouts ME1 and ME2 are
designed to investigate the effects of cutting parameters on
surface roughness within two different cutting speed
ranges, namely <1,400 and ≥1,400 m/min, as shown in
Tables 3 and 4. The results of surface roughness show that
for all the regions surface roughness Ra remains below
0.3 μm can be obtained using the cutting parameter
combinations listed in the experimental layout ME1.
Surface roughness below 0.3 μm is an acceptable value
for the comparison with other finishing process like
grinding [15], while the surface roughness Ra obtained
under some cutting parameter combinations with relatively
higher cutting speeds in ME2 is much larger than 0.3 μm.
The signal to noise (S/N) ratio used in the Taguchi
method reflects both the average and the variation of the

quality characteristics. Therefore, in the present study,
instead of the average value, the S/N ratio is used so as to
convert the trial result data into a value for the evaluation
characteristics in the optimum setting analysis. The S/N
ratio ηi for region Ri can be expressed in decibel units, and
it is defined by a logarithmic function based on the mean
square deviation around the target:
"

1
hi ¼ À10log
n

n
X

!#
yij

2

ð11Þ

j¼1

where all the symbols have the same meaning as they did in
Eq. 4. It can be seen from Eq. 11 that the larger is the S/N
ratio, the smaller is the variance of surface roughness Ra
around the desired value.

Fig. 8 The mean S/N graph for
surface roughness in different
regions (ME1). a The mean S/N
graph for Ra in R1. b The mean
S/N graph for Ra in R2. c The
mean S/N graph for Ra in R3. d
The mean S/N graph for Ra in
R4. e The mean S/N graph for
Ra in R5

(a) The mean S/N graph for Ra in R1

(c) The mean S/N graph for Ra in R3

(e) The mean S/N graph for Ra in R5

(b) The mean S/N graph for Ra in R2

(d) The mean S/N graph for Ra in R4


8

Int J Adv Manuf Technol (2012) 61:1–13

Fig. 9 The mean S/N graph for
surface roughness in different
regions (ME2). a The mean S/N
graph for Ra in R1. b The mean
S/N graph for Ra in R2. c The

mean S/N graph for Ra in R3. d
The mean S/N graph for Ra in
R4. e The mean S/N graph for
Ra in R5

(a) The mean S/N graph for Ra in R1

(b) The mean S/N graph for Ra in R2

(c) The mean S/N graph for Ra in R3

(d) The mean S/N graph for Ra in R4

(e) The mean S/N graph for Ra in R5

Table 5 The cutting parameters and corresponding S/N ratios for Ra
in R5 (ME1)

Table 6 The cutting parameters and corresponding S/N ratios for Ra
in R5 (ME2)

Exp. no.

Exp. no.

1
2
3
4
5

6
7
8
9

v1 (m/min)

fz (mm/tooth)

ap (mm)

S/N ratio

350
350
350
700
700
700
1,050
1,050
1,050

0.02
0.04
0.06
0.02
0.04
0.06
0.02

0.04
0.06

0.1
0.2
0.3
0.2
0.3
0.1
0.3
0.1
0.2

26.97
23.80
22.97
22.04
23.85
29.03
18.52
25.24
21.61

10
11
12
13
14
15
16

17
18

v2 (m/min)

fz (mm/tooth)

ap (mm)

S/N ratio

1,400
1,400
1,400
1,750
1,750
1,750
2,100
2,100
2,100

0.02
0.04
0.06
0.02
0.04
0.06
0.02
0.04
0.06

0.1
0.2
0.3
0.2
0.3
0.1
0.3
0.1
0.2

12.88
23.85
21.18
12.00
17.39
9.78
7.85
8.12
7.98


Int J Adv Manuf Technol (2012) 61:1–13
Table 7 Results of the ANOVA
for Ra in the total machined
surface R5 (ME1)

9

Source

df

Sum of squares

Variance

F value

Contribution (%)

A
C

2
2

18.08
7.34

9.04
3.67

22.60
9.18

22.76
8.62

D

2

49.77

24.89

62.23

64.46

Error
Total

2
8

0.79
75.98

0.40

Figures 8 and 9 show the mean S/N response graphs for
surface roughness Ra in different regions. It can be seen
that, generally all the mean S/N ratios in Fig. 8 are much
higher than those in Fig. 9, indicating that if the cutting
speed surpasses 1,400 m/min, the surface quality will
deteriorate badly. From Fig. 8 which shows the mean S/N
graph for ME1, it can be seen that the feed rate fz has little
effect on the surface roughness in the five regions. As for

region R1, the effect of cutting speed v on surface
roughness is little. However, for all the other four regions,
as the cutting speed increases, the surface roughness
decrease firstly and then increase. In region R1, as the
depth of cut ap increases, the surface roughness increase
firstly and then decrease, while in the other regions the
surface roughness increase with the depth of cut. It can be
seen from the mean S/N graph for ME2 in Fig. 9 that the
surface roughness in the five regions all increases with the
cutting speed v. As the feed rate fz increases, the surface
roughness in all the regions decreases firstly and then
increases. The surface roughness in all the five regions
except for region R3 decrease with the depth of cut ap. In
region R3, as the depth of cut increases, the surface
roughness decreases firstly and then increases. It can be
concluded that within different speed ranges, the effects of
the cutting parameters on surface roughness in the five
regions change greatly.
For the experimental layout ME1, the optimum combinations of the cutting parameter levels are A1C2D1, A2C3D1,
A2C1D1, A2C1D1, and A2C3D1 for surface roughness in
regions R1, R2, R3, R4, and R5, respectively. As for the
experimental layout ME2, the optimum combinations of the
cutting parameter levels are B1C2D2, B1C2D3, B1C2D2,
B1C2D2, and B1C2D3. The optimum combinations of the

Table 8 Results of the ANOVA
for Ra in the total machined
surface R5 (ME2)

4.16

100

cutting parameter levels for surface roughness in regions R3
and R4 are the same. And it seems that low feed rate and low
depth of cut is beneficial especially for surface roughness in
these two regions. It can be concluded that because of the
varying characteristics of the mechanical and thermal loads,
for different regions, there definitely exist differences in the
formation of surface profiles.
Tables 5 and 6 show the cutting parameters and
corresponding S/N ratios for the total machined surface R5
obtained by means of Eqs. 4 and 5. Based on the results
listed in Tables 5 and 6, the results of analysis of variance
(ANOVA) for surface roughness in the total machined
surface can be obtained as shown in Tables 7 and 8. For the
experimental layout ME1, the contribution order of the
cutting parameters for surface roughness Ra is axial depth
of cut, cutting speed, and feed rate, and the contribution of
feed rate is very small. As for ME2, the order is cutting
speed, feed rate and axial depth of cut, and the contributions of feed rate and axial depth of cut are approximately
the same. It can be concluded that as the cutting speed
surpasses 1,400 m/min, the degree of influences of cutting
speed and feed rate on surface roughness Ra increases
substantially especially for cutting speed, while that of axial
depth of cut decreases substantially.
The surface roughness Ra in the total machined surface
R5 is focused on in the regression analysis. The form of the
Taylor’s tool life equation in metal cutting is used, and a
functional relationship between the average value of surface
roughness in region R5 and the cutting parameters could be

postulated by:
Ra ¼ avb fzc adp ðmmÞ

ð12Þ

Source

df

Sum of squares

Variance

F value

Contribution (%)

B
C
D
Error
Total

2
2
2
2
8

192.90

47.08
46.85
2.20
289.03

96.45
23.54
23.43
1.10

87.68
21.40
21.30

65.98
15.53
15.45
3.04
100


10

Int J Adv Manuf Technol (2012) 61:1–13

By means of a logarithmic transformation, the nonlinear
form of Eq. 12 can be converted into the following linear
form:
lnRa ¼ lna þ b ln v þ c ln fz þ d ln ap

ð13Þ

where a, b, c, and d are the corresponding parameters. After
regression analysis, the regression equations for the surface
roughness are obtained as follows:

(a)

Deviation of the fitted surface
roughness Ra (ME1).

(b)

Deviation of the fitted surface
roughness Ra (ME2).

RaðME1 Þ ¼ 0:0176 Â v0:2582 Â fzÀ0:1896
 a0:5757
ðmmÞ
p

ð14Þ

RaðME2 Þ ¼ 3:9432 Â 10À13 Â v3:3612 Â fzÀ0:3223
 apÀ0:5207 ðmmÞ

ð15Þ

where Ra(ME1) and Ra(ME2) represent the surface roughness in experimental layouts ME1 and ME2, respectively.
Figure 10 compares the fitted values of surface roughness and the observed values for ME1 and ME2. Figure 11

shows the relative percentage error between the fitted and
the observed values. The average value of the relative error
for Ra(ME1) and Ra(ME2) are 4.6921% and 4.8906%,
respectively. It can be concluded that Eqs. 14 and 15 can
describe the behavior of the data well.

(a)

The fitted and observed surface
roughness in ME1.

(b)

The fitted and observed surface
roughness in ME2.

Fig. 10 The fitted values of surface roughness vs. the observed
values. a The fitted and observed surface roughness in ME1. b The
fitted and observed surface roughness in ME2

Fig. 11 Deviation of the fitted surface roughness from the observed
values. a Deviation of the fitted surface roughness Ra (ME1). b
Deviation of the fitted surface roughness Ra (ME2)

3.3 Chip formation
Figure 12 shows the chip formation under different cutting
speeds with axial depth of cut ap and feed rate fz fixed as
0.2 mm and 0.04 mm/tooth, respectively. As the cutting speed
increases, both the shape and the color of the chip change
gradually. When the cutting speed increases, the shape of the

chip changes in the following order: washer-shaped chip
(v=200 m/min), wave-shaped chip (v=400 m/min), arcshaped chip (v=600 m/min), long strip of chip (v=800–
1,400 m/min), short strip of chip (v=1,600–2,200 m/min), and
powder-shaped chip (v=2,400 m/min). It is found that the
color of the chip is blue when the cutting velocity is relatively
low (v=200–600 m/min). At higher cutting speed (v=800–
1,200 m/min), the color turns into purple. When the cutting
speed is no less than 1,400 m/min, the chip color is yellow.
At the cutting speed of 800 m/min, the chip color turns
from blue into purple and the shape of the chip changes
from arc-shaped chip to long strip of chip. As has been
discussed, at this cutting speed, optimum surface quality
can be obtained as shown in Fig. 6. When the cutting speed
surpasses 1,400 m/min, short strip of chip is about to form
and the chip color changes into yellow. This cutting speed
can be seen as a transition cutting speed for surface
roughness as has been mentioned. It seems that the
correspondence between the chip formation and the surface
roughness is obvious, indicating that the evolution of the


Int J Adv Manuf Technol (2012) 61:1–13
Fig. 12 Chip formation under
different cutting speeds
(fz =0.04 mm/tooth, ap =0.2 mm).
a v=200 m/min. b v=400 m/min.
c v=600 m/min. d v=800 m/min.
e v=1,000 m/min. f v=1,200
m/min. g v=1,400 m/min. h v=
1,600 m/min. i v=1,800 m/min. j

v=2,000 m/min. k v=2,200 m/
min. l v=2,400 m/min

11

(a) v = 200 m/min

(d) v = 800 m/min

(b) v = 400 m/min

(c) v = 600 m/min

(e) v = 1000 m/min

(f) v = 1200 m/min

(g) v = 1400 m/min

(h) v = 1600 m/min

(i) v = 1800 m/min

(j) v = 2000 m/min

(k) v = 2200 m/min

(l) v = 2400 m/min

surface quality can be estimated by means of observing the

variation of the chip shape and color.
It is also found that the serrated chip begins to arise when
the cutting speed is about 400 m/min as shown in Fig. 13b. As
the cutting speed increases, the serrated chip becomes more
and more obvious. As shown in Fig. 13e at the cutting speed
of 2,400 m/min, the serrated chip is about to be separated.

able variations of surface roughness, back cutting was
avoided, and the milled surface was divided and investigated separately and integratedly. The following conclusions can be obtained:
&

4 Conclusions
The effects of cutting speed on cutting forces, surface
roughness, and chip formation in high and ultra high-speed
face milling of AISI H13 steel were focused on in the
present study. Taking the critical cutting speed 1,400 m/min
into consideration, the effects of cutting parameters on
surface roughness within two cutting speed ranges (<1,400
and ≥1,400 m/min) were investigated experimentally by
means of Taguchi method. In order to reduce the undesir-

&

When the cutting speed increases from 200 to 2,400 m/
min with feed rate fz and axial depth of cut ap fixed,
both the static and dynamic cutting forces reach a valley
value at a cutting speed of 1,400 m/min. It can be
concluded that relatively stable cutting condition which
is beneficial to the surface finish of the workpiece can
still be obtained at a high cutting speed of 1,400 m/min.

As the cutting speed increases from 200 to 2,400 m/min
with feed rate fz and axial depth of cut ap fixed as
0.04 mm/tooth and 0.2 mm, the surface roughness in
different regions all decreases firstly and then increases.
The cutting speed of 1,400 m/min is considered as a
critical value above which the surface roughness will
deteriorate badly. When the cutting speed is between 600


12

Int J Adv Manuf Technol (2012) 61:1–13

Fig. 13 Magnified chip formation under different cutting
speeds (fz =0.04 mm/tooth,
ap =0.2 mm) a v=200 m/min.
b v=400 m/min. c v=800
m/min. d v=1,400 m/min.
e v=2,400 m/min

(a) v = 200 m/min

(b) v = 400 m/min

(c) v = 800 m/min

(d) v = 1400 m/min

(e) v = 2400 m/min

&

and 900 m/min, low surface roughness is expected to be
obtained. When the cutting speed surpasses 1,400 m/min,
the higher tool wear rate has great effect on the increase
of the surface roughness with the cutting speed. One
thousand four hundred meters per minute is considered
to be a critical cutting speed for both the cutting forces
and surface roughness. At the cutting speed of 1,400 m/
min good surface quality, relatively low mechanical load
and high machining efficiency are expected to arise at the
same time for the cutting parameters under consideration.
Due to the variations of the characteristics of the
mechanical and thermal loads, the surface roughness
Ra in different regions of the machined surface respond
in varying ways to the changes of cutting parameters.
For the experimental layouts ME1 and ME2, the
optimum combinations of the cutting parameter levels
for surface roughness in the whole machined surface R5
are A2C3D1 (v=700 m/min, fz =0.06 mm/tooth, ap =
0.1 mm) and B1C2D3 (v=1,400 m/min, fz =0.04 mm/
tooth, ap =0.3 mm). The results of ANOVA for surface

&

roughness of the total machined surface show that for
the experimental layout ME1, the contribution order of
the cutting parameters is axial depth of cut, cutting
speed, and feed rate, and the contribution of feed rate is
very little; while for ME2, the order is cutting speed,

feed rate, and axial depth of cut, and the contributions
of feed rate and axial depth of cut are roughly the same.
When the cutting speed surpasses 1,400 m/min, the
cutting speed and feed rate become much more
influential to the surface roughness especially for
cutting speed, while the effect of axial depth of cut
declines greatly. It is found that when the cutting speed
is below 1,400 m/min, low surface roughness Ra below
0.3 μm can be obtained. By means of regression
analysis, two equations for the surface roughness of
the total machined surface R5 in experimental layouts
ME1 and ME2 are fitted. It is found that those equations
can describe the behavior of the data well.
As the cutting speed changes from 200 to 2,400 m/min
with invariable feed rate fz 0.04 mm/tooth and axial


Int J Adv Manuf Technol (2012) 61:1–13

depth of cut ap 0.2 mm, both the shape and color of the
chip change gradually. There exists obvious correspondence between the shape, color of the chip, and the
surface roughness obtained at different cutting speeds.
When the cutting speed surpasses 1,400 m/min which is
considered as a transition speed below which good
surface finish can still be obtained, short strip of chip is
about to form and the color of the chip turns into
yellow. It seems that the evolution of the surface quality
with cutting speed can be estimated by means of
observing the variation of the chip formation.
Acknowledgments This research is supported by the National Basic

Research Program of China (2009CB724402), the National Natural
Science Foundation of China (51175310), and the Graduate Independent
Innovation Foundation of Shandong University, GIIFSDU (yzc10119).

References
1. Liu ZQ, Ai X, Zhang H, Wang ZT, Wan Y (2002) Wear patterns
and mechanisms of cutting tools in high-speed face milling. J
Mater Process Technol 129:222–226
2. Nelson S, Schueller JK, Tlusty J (1998) Tool wear in milling
hardened die steel. J Manuf Sci Eng 120(4):669–673
3. Iqbal A, He N, Li L, Dar NU (2007) A fuzzy expert system for
optimizing parameters and predicting performance measures in
hard-milling process. Expert Syst Appl 32(4):1020–1027

13
4. Ghani JA, Choudhury IA, Hassan HH (2004) Application of
Taguchi method in the optimization of end milling parameters. J
Mater Process Technol 145(1):84–92
5. Vivancos J, Luis CJ, Costa L (2004) Optimal machining
parameters selection in high speed milling of hardened steels for
injection moulds. J Mater Process Technol 155–156:1505–1512
6. Vivancos J, Luis CJ, Ortiz JA (2005) Analysis of factors affecting
the high-speed side milling of hardened die steels. J Mater Process
Technol 162–163:696–701
7. Toh CK (2006) Cutter path orientations when high-speed finish
milling inclined hardened steel. Int J Adv Manuf Technol 27:473–480
8. Ding TC, Zhang S, Wang YW, Zhu XL (2010) Empirical models
and optimal cutting parameters for cutting forces and surface
roughness in hard milling of AISI H13 steel. Int J Adv Manuf
Technol 51:45–55

9. Siller HR, Vila C, Rodríguez CA, Abellán JV (2009) Study of
face milling of hardened AISI D3 steel with a special design of
carbide tools. Int J Adv Manuf Technol 40:12–25
10. Wilkinson P, Reuben RL, Jones JDC, Barton JS, Hand DP,
Carolan TA, Kidd SR (1997) Surface finish parameters as
diagnostics of tool wear in face milling. Wear 205:47–54
11. Yang WH, Tarng TS (1998) Design optimization of cutting
parameters for turning operations based on the Taguchi method.
J Mater Process Technol 84:122–129
12. Dimla DE, Lister PM (2000) On-line metal cutting tool condition
monitoring. I: force and vibration analysis. Int J Mach Tools
Manuf 40(5):739–768
13. Toh CK (2004) Static and dynamic cutting force analysis when
high speed rough milling hardened steel. Mater Des 25:41–50
14. Childs T, Maekawa K, Obikawa T, Yamane Y (2000) Metal
machining: theory and applications. Wiley, New York
15. Boothroyd G, Knight WA (2005) Fundamentals of machining and
machine tools, 3rd edn. CRC, New York


Int J Adv Manuf Technol (2012) 61:15–24
DOI 10.1007/s00170-011-3687-6

ORIGINAL ARTICLE

A study on helical surface generated by the primary
peripheral surfaces of ring tool
S. Berbinschi & V. Teodor & N. Oancea

Received: 1 June 2011 / Accepted: 3 October 2011 / Published online: 22 October 2011

# Springer-Verlag London Limited 2011

Abstract Often in the engineering practice, cutting tools
bounded by primary peripheral surfaces of revolution are used
because of their effectiveness. Among these, ring and
tangential tools can be used for the generation of constant
pitch cylindrical helical surfaces. In this paper, we present an
algorithm for the profiling of these types of tools. The
algorithm is based on the topological representation of the
tool’s primary peripheral surface. The main goal is to devise a
methodology for the profiling of tools whose surfaces are
reciprocally enveloping with cylindrical helical surfaces. We
present a numerical example for the numerical determination
of the axial section form for this type of tools. The application
method for this algorithm was developed in the CATIA
graphical design environment within which the procedure is
developed as a vertical application. In addition, we present a
solution for the shape correction of the tool’s axial crosssection by considering the existence of singular points on the
profile of the helical surface to be generated where multiple
normals to the surface exist.

tools designated for the generation of the cylindrical helical
surfaces with constant pitch (threads) on specialized
machine tools or using specialized technological equipments for longitudinal turning machines.
The ring tool is frequently made as an enwrapping
milling tool. The advantage of this technological solution is
the increased productivity of this process. Although the
tools of this type generate in the cutting motion a revolving
surface, the issue of profiling the primary peripheral surface
of this surfaces reciprocally enveloping with cylindrical

helical surfaces with constant pitch, is a problem different
from the profiling of the side mill [1–4].
The profiling method of this type of tool uses the
fundamental theorems of the surfaces generation [1, 5] or
the complementary methods as “the minimum distance
method” [1], “the in-plane generating trajectories method”
[6]. Also, the development of the graphical design environment allows solving these problems using 3D design
environment [7–10] or using solid modeling [11, 12].

Keywords Ring tool . Helical surfaces generation .
Topological representation

2 Ring tool’s profiling algorithm

1 Introduction
The ring and tangential tools are tools bounded by a
revolution primary peripheral surface. The ring tools are
S. Berbinschi : V. Teodor (*) : N. Oancea
Manufacturing Science and Engineering Department,
“Dunărea de Jos” University of Galaţi,
Galaţi, Romania
e-mail:

The basic idea behind the proposed algorithm is that a
~ axis and p helical parameter, can
helical movement, with V
be decomposed in two rotations conjugated with this
relative motion as shown in Fig. 1.
The three movements, as shown in Fig. 1, are:
I

is the translation movement correlated with the
rotation movement II, in order to produce a helical
motion with the same helical parameter p as of the
surface to be generated. In most cases, this motion is
executed by the workpiece;


16

Int J Adv Manuf Technol (2012) 61:15–24

Fig. 1 The decomposition of the helical motion into two rotation
motions
Fig. 2 Ring surface reciprocally enveloping with helical surface

II

III

the rotation movement of blank around its own axis,
B. In the most practical cases, this motion is uniform;
and
the rotation motion of tool around its own axis, the
axis ~
A. This axis is positioned regarding the axis B at a
distance and inclined with angle α regarding the Z
axis.

One can represent these relative motions as

 À
Á
À
Á 
~; p % ~
B; wB
V
A; wA þ ~

ð1Þ

where
p ¼ a Á tanðbÞ ¼ b Á tanðaÞ

ð2Þ

with p is the helical parameter.
In this way, it is possible to choose as revolution
surface’s axis, the B axis, which may be established as the
axis of the ring surface. Also, it is possible to arbitrarily
choose the values b and β according to the dimension of
the helical surface and the diameter of the ring tool (see
Eqs. 1 and 2).
The Nikolaev’s theorem [5] for the determination of the
characteristic curve between the Σ helical surface, Fig. 2,
and the primary peripheral surface of ring tool allows to
determine the geometrical locus of points which belongs to
the Σ surface where the condition is accomplished:
À
Á

~
~ Σ ;~
r2 ¼ 0
ð3Þ
B; N
where, ~
B is the vector that overlapped the ring tool’s axis;
~
r2 is the
NΣ is the normal to the helical surface; and ~
position vector of the current point that belongs to the
helical surface, regarding the O2 origin of the reference
system joined with the axis X2.

The condition 3 has the geometrical significance, the fact
that the three vectors are in the same plane. Moreover, the
contact points (the tangency points) between the Σ helical
surface and the primary peripheral surface of the ring tool
defines the characteristic of Σ surface, in the rotation
movement of this around the ~
B axis. The characteristic
curve represents the geometric locus of intersection points
between the normal draws from the points belongs to the ~
B
axis to the surface to be generated (so, the projection of the
~
B axis to the Σ surface).
In this way, for the Σ surface known in the X2Y2Z2
reference system by equations form:



Σ ~
r2 ¼ X2 ðu; vÞ~i þ Y2 ðu; vÞ~j þ Z2 ðu; vÞ~
k;
ð4Þ
with u and v as independent variable parameters. In the
X2Y2Z2 reference system, it is defined the normal to the
surface,


~i
~
~j
k 



~Σ ¼  XÁ 2u YÁ 2u ZÁ 2u :
ð5Þ
N


 Á

Á
Á
 X 2v Y 2v Z 2v 
The axis of the future ring tool has directrix parameters
~
B ¼ ~i:

After developing, the condition 3 will be,


 X2 ðu; vÞ Y2 ðu; vÞ Z2 ðu; vÞ 




NY 2
NZ2
 NX 2
¼0


1

0
0

ð6Þ

ð7Þ

equivalent with a link between the variable parameters,
v ¼ vðuÞ

ð8Þ


Int J Adv Manuf Technol (2012) 61:15–24

17

In this way, the characteristic curve on the Σ surface is
given by the 4 and 9 equations assembly:

Table 1 Input parameters of the trapezoidal thread
Symbol

Description

Z (mm)

X (mm)

CΣ jX2 ¼ X2 ðuÞ; Y2 ¼ Y2 ðuÞ; Z2 ¼ Z2 ðuÞ:

ð9Þ

A
B

Initial point on thread crest
Initial point on thread flank

50
50

20
0

By revolving the characteristic curve 10 around the X2
axis, the axis overlapped to ~
B is generated the primary
peripheral surface of the ring tool—SB. The axial section of
the primary peripheral surface of the ring tool, ðCΣ ÞX2 Y Z2 is

C

Initial point on thread bottom

40

−10

D
E

Final point on thread bottom
Final point on thread flank
Flute sense
Helix pitch

40
50
Right
50

−20
−30

Distance between tool’s axis
and thread axis

100

2

determined as:

 H ¼ X2 ðuÞ;

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðSB ÞX2 Y2 Z2 
 R ¼ Y22 ðuÞ þ Z22 ðuÞ:

ð10Þ

2.1 Profiling of tool in CATIA design environment
An application of the presented algorithm for the profiling
of the ring tool for the generation of a trapezoidal thread
was presented (see Fig. 2). The 3D method to profile the
ring tool—HSGT (helical surface generating tool)—is
grounded on the generative shape design environment
facilities. The worked piece (in fact, the generated surface)
is 3D modeled, as it can be observed in Fig. 3. The worked
piece reference system, XYZ, and the ring tool reference
system, X2Y2Z2, the last one as Euler system, are created
(see Fig. 2).
By giving the “projection” command, the ring tool

axis projection onto the Σ surface is realized; thus, the
characteristic curve is determined. By subsequently using
the “revolve” command, the tool primary peripheral
surface (S) results after rotating the characteristic curve
around Z2 axis.
The ring tool axial section is then obtained as an
intersection between the surface S and a plain which
includes the Z2 (~
A) axis—by applying the “intersection”
command. The coordinates of points that defined the
generating profile of the thread and the distance between
axes are given in Table 1. In Fig. 3, the 3D model of the

Fig. 3 Generating profile of the trapezoidal thread

Se
Pe
b

thread axial profile was shown. In Fig. 4, the HSGT–visual
basic application (VBA) was presented, where the profile’s
elements and the tool’s type are given. Figure 5 presented
the relative position of the primary peripheral surface for
the ring tool, its axis, the characteristic curve, and the axial
section of the surface. Because the axial section of the
helical surface has singular points, the points C and D will
result in discontinuity points on the surfaces in enveloping
(see Fig. 5).
2.2 Numerical results—ring tool for trapezoidal thread
In Table 2 and Fig. 6, we present the coordinates of the

characteristic curves and of the axial cross-section of ring
tool. The existence of the singular points (see Fig. 5, the
points C′ and D′) leads to intersection points for the
characteristic curves on adjacent flanks, which impose to
take a decision regarding the form of the axial section. The
simplest solution is to eliminate the portions from the
characteristic curve, in points C′ and D′, if there are
acceptable modifications of the generated surfaces at the
thread bottom. In Fig. 6, the intersection zone of the
profiles that forms the axial section and eliminates further
in the profile board construction for the ring tool was
shown.

zA

zB

zC

xA

xB

xC

zD

zE

xE

xD

b

Fig. 4 The HGST-VBA application

100


18

Int J Adv Manuf Technol (2012) 61:15–24
R [mm]

H [mm]

o
-12
-16
-20

Removed Areas

-24

C'

-28
C

Gauge Profile

Caxial

-32
-36
-40

Fig. 5 The primary peripheral surface for the ring tool, the axis, the
characteristic curve, and the axial section of the surface

138 142 146 150

Fig. 6 The axial section of the primary peripheral surface for ring tool

3 Tangential tool
2.3 Ring tool for ball thread
Figure 7 showed the model of the ball thread and its axial
section (an assembly of circle’s arc, filleted), as so as the
following reference systems:
Xyz
X1Y1Z1
x0y0z0 and x0′y0′z0′

is the reference system associated
with the ball thread;
reference system associated with
the ring tangential tool’s primary
peripheral surface; and

additional reference systems.

The generation movement assembly, the movements I,
II, and III, has the significances given in Fig. 1. In Table 3,
the input parameters correlated with the HGST-VBA
application. Figures 7 and 8 present the forms and the
coordinates of the characteristic curve and the axial section
for the helical surfaces assembly that composes the ball
thread flute. Obviously, in this case, singular points on the
profile do not exist.

The tangential tool is a tool bounded by a revolution
primary peripheral surface. The tangential tools are tools
designated for the generation of the cylindrical helical
surfaces with constant pitch (threads) on specialized
machine tools or using specialized technological equipments for longitudinal lather machines. The tangential tool
may used on a grinder machine.
3.1 Ring tangential tool: algorithm
The problem of profiling the ring tangential tool, Fig. 9, is, in
principle, similar with the known problem of the side mill
tool’s profiling. In principle, the Nikolaev [5] condition for
the determination of the characteristic curve—the tangency
curve between a cylindrical helical surface with constant
pitch, Σ, and a revolution surface with ~
A axis, with position
known in the reference system of the Σ surface—is:


~
~Σ ;~

A; N
r1 ¼ 0;

ð11Þ

Table 2 Coordinates of points on the characteristic curves and the axial section of ring tool
Profile

Crt. no.

X (mm)

Y (mm)

Z (mm)

Crt. no.

X (mm)

Y (mm)

Z (mm)

Characteristic curve

1
2
3
4

..
.

−3.7081
−3.4432
−3.1696
−2.5961
..
.

39.8280
40.9627
42.0962
44.3593
..
.

−23.2389
−22.0605
−20.8829
−18.5303
..
.

26
27
28
29
30

44.4147
43.3140
42.2112
41.1065
39.9999

1
2
3
4
..
.

R (mm)
150.0197
148.9044
147.7900
146.6766
..
.

H (mm)
12.3447
13.4541
14.5646
15.6760
..
.

26

27
28
29
30

−1.3370
−0.9506
−0.5724
−0.2025
0.1589
R (mm)
145.7095
146.8372
147.9658
149.0955
150.2260

−37.1742
−35.9989
−34.8229
−33.6461
−32.4685
H (mm)
37.5908
38.6877
39.7835
40.8784
41.9723

Profile

Axial section


Int J Adv Manuf Technol (2012) 61:15–24
Characteristic
Curves

19

Ring Tool's Axial
Section

Fig. 7 Characteristic curve and axial section of the ring tool

where ~
A is the versor of the rotation axis of the tool bounded
by a revolution surface;
~Σ
N
~
r1

is the normal at the helical surface; and
is the vector which link the current point onto the Σ
surface with a point of the ~
A axis (frequently, the
origin of the reference system joined with this axis,
here X1Y1Z1).

Condition 11 is equivalent with the statement: the

characteristic curve of a cylindrical helical surface with
constant pitch, Σ, in the rotation motion around a fixed axis,
~
A, is composed by all the points belongs to the Σ surface,
which represent the projection of the ~
A axis to the Σ surface.
The specific problem is that the tool’s axis position is deferent
regarding the position of the side mill, regarding the blank.
The generation process kinematics presumes the following motions:
I
II

is the rotation motion of the blank,
translation motion of the blank correlated with the
motion I, and

Fig. 8 Axial section of ring tool

III

the rotation movements of the ring tangential tool (the
cutting motion).

The assembly of motions I and II defines a helical
motion with axis and helical parameter identical with the
axis and the helical parameter of the surface to be
generated.
They are defined the reference systems:
xyz

X1Y1Z1

is the reference system where is defined the
helical surface (the Z axis is the axis of the helical
surface).
reference system joined with the ring tangential
tool (the X1 axis is the axis of the ring tangential
tool).

If, in the XYZ reference system, it is defined the Σ
helical surface:
!
!
!
Σ:!
r ¼ xðu; vÞ Á i þ yðu; vÞ Á j þ zðu; vÞ Á k

ð12Þ

Table 3 Input parameters of the ball thread
Symbol

Description

Value

p
r
e

Helical parameter
Flank radius
Half distance between the centers
of circles with radius r
Diameter of centers cylinder of the
axial profile
Distance between the Dj diameter
and the center of circle with radius r
External diameter of thread
Fillet radius
Helix sense
Distance between axis
Tool’s angle in plane XZ
Tool’s angle in plane ZX

2.5464 mm
5.4 mm
0.155 mm

Dj
h
D
r0
Se
Daxis
β
α

49 mm

with u and v variable parameters, then, by the coordinates
transformation, see Fig. 9,
  
 X1   cos b
  
  
 Y1  ¼  0
  
 Z1   sin b

 



0 Àsin b 
 x þ a
 

1 0
 Á y þ b
 

0 cos b   z À c 

ð13Þ

0.17 mm

the helical surface Σ refers to the reference system X1Y1Z1,
by equations:

48 mm
1 mm
Right
150 mm
10°
6.0566°


 X1 ¼ ½xðu;vÞ À aŠcos b À ½zðu;vÞ À cŠsin b;


Σ  Y1 ¼ yðu;vÞ À b;

 Z1 ¼ ½xðu;vÞ À aŠsin b þ ½zðu;vÞ À cŠcos b;
with a, b, and c technological constants.

ð14Þ


20

Int J Adv Manuf Technol (2012) 61:15–24

Rs

Tool's frontal
circle (Rs)

Re

M

Tool's frontal
circle
Projection

θ

Rs
Helix (Re)
Re
x

o
T

y

b
z

V,p

c

Pe

Helix
Projection (Re)

Rs cos

Fig. 10 The ring tangential tool’s axis position
Fig. 9 The generation process kinematics with the ring tangential tool

In the condition for the determination of the characteristic curve 11 defining:
~
A ¼ ~i the versor of the ring tool;
~Σ
N
the normal to the Σ surface, in the reference system
X1Y1Z1
~
k;
r1 ¼ X1 ðu;vÞ Á~i þ Y1 ðu;vÞ Á~j þ Z1 ðu;vÞ Á ~

ð15Þ

the current vector on the Σ surface, in the reference system
X1Y1Z1, Eq. 14.
The Eqs. 11 and 14 assembly represents the characteristic curve, in principle, in form:

 X1 ¼ X1 ðuÞ;


ðCΣ ÞX1 Y1 Z1  Y1 ¼ Y1 ðuÞ;

 Z1 ¼ Z1 ðuÞ:

ð16Þ

By revolving, the characteristic curve around the X1 axis
is determined the primary peripheral surface of the ring
tangential tool. The constants a, b, c, and β are determined
from the condition that the trajectory of the S point,
corresponding to the external diameter of the Σ surface,
to be tangent at the helix (see Figs. 9 and 10).
Also, the projection of the helix corresponding to the Re
blank radius, in the same plane yz, is a curve with form:

 y ¼ R sin 8 ;
e

ð17Þ
LE 
 z ¼ p Á 8;
with 8 variable and p helical parameter, p ¼

pe
2p .

From the condition that the two curves 16 and 17 to be
tangents in the M point, is determined the equations assembly:
–

the condition of common point:

RS cos q þ b ¼ Re sin 8 ;

ð18Þ

RS cos b sin q þ c ¼ p Á 8 ;

ð19Þ

–

the condition of common tangent:

ÀRS sin q ¼ Re cos 8 ;

ð20Þ

RS cos b cos q ¼ p;

ð21Þ

The 18, 19, 20, and 21 equations assembly determine
the values b, c, 8, and θ (the linear value a and the angle
β have to be accepted from a constructive point of view,
a = Re).
3.2 Applications
3.2.1 Ring tangential tool for trapezoidal thread
In the following, an application of the proposed algorithm
for the determination of the primary peripheral surface of
the ring tangential tool, for generation of a trapezoidal
thread, with generatrix of helical surface presented in Fig. 3

Int J Adv Manuf Technol (2012) 61:15–24

21
Table 4 Input parameters of the trapezoidal thread (straight lined
segments)
Symbol

Description

Y (mm)

Z (mm)

A

Initial point of thread head

50

20

B

Initial point of thread flank

50

0

C

D

Initial point of thread bottom
Final point of thread bottom

40
40

−10
−20

E

Final point of thread flank
Helix sense
Helix pitch

50
Right
50 mm

−30

x coordinate of tool’s origin
y coordinate of tool’s origin

−50 mm
−32 mm

z coordinate of tool’s origin

Tool’s rotation around Y1 axis

150 mm
−18°

Se
pe
a
b
c
Ue

deformation of the thread bottom, according to a required
target.
3.2.2 Ring tangential tool for ball thread
Figure 14 presented the model of the ball thread and its
axial section, an assembly of circle’s arc, filleted, as so as
the reference systems:
Fig. 11 HSGT application—ring tangential tool, trapezoidal thread

Xyz
is presented. The method is the same with those described
in paragraph 2.1.
The input data for the profile of the thread, the helix pitch,
and the distance between the tool’s axis and the thread’s axis
are inserted in the HSGT application, presented in Fig. 11,
according to Table 4. Figure 12 represented the surfaces of
the trapezoidal thread’s flank, characteristic curves on the
thread’s flanks, primary peripheral surfaces of the ring
tangential tool, and the axial section.

The form of the axial section of the ring tangential
tool (the plane X1Y1) is represented in Fig. 13. We have
to notice that the axial tool’s profile is asymmetric.
Obviously, in the points B and C (see Fig. 12) on the
composed profile of the tool, emerged discontinuities that
may be solved by link this zones and accepting a

  
 X1   1
0
  
  
 Y1  ¼  0 cos b
  
 Z1   0 Àsin b

 2
  cos a 0
 
 6
1
 Á 4 0
 


cos b
sin a 0

0
sin b

X1Y1Z1
x0y0z0 and x0′y0′z0′

is the reference system associated
with the ball thread;
reference system associated with
the ring tangential tool’s primary
peripheral surface; and
additional reference systems (see
Fig. 15).

The generation movement assembly, the movements I,
II, and III, has the significances given in Fig. 9.
In this way, the helix belongs to the ball thread flute and
situated onto the cylinder with radius Re:
x ¼ Re cos 8 ;
y ¼ Re sin 8 ;
z ¼ Àp 8 ;

ð22Þ

is transferred, by coordinates transformation:

 
  3 


  
0 

Àsin a 
  Re cos 8   0 


  7 

 
0  Á  Re sin 8  À  Re 5 À  0 
 
  


 0 
 ÀRS 
cos a   p 8

ð23Þ


22

Int J Adv Manuf Technol (2012) 61:15–24
Axial section

Composed
Peripheral Surface
of the Tangential
Ring Tool

Characteristic

Curves

A
D
C

B

Flanks of the
worm hole
x
V,p

y

z

o

Fig. 14 Ball thread; axial profile, and reference systems

Fig. 12 3D model of the helical surface; 3D model of the ring
tangential tool’s primary peripheral surface

The helix, in the reference system X1Y1Z1, associated
with the ring tangential tool with the circle:
X1 ¼ RS cos q;
Y1 ¼ 0;

ð24Þ

Z1 ¼ RS sin q;
of the ring tangential tool’s primary peripheral surface,
allow to determine the parameters: α, β, θ, and 8.
Other solution may be obtained by knowing the angle of
helix for the cylinder with radius Re,
a ¼ arctg

p
Re

ð25Þ

and the normal plane to the helix in the point O0 (see
Fig. 15).
The plane of the circle RS is revolved around the axis x0
(x0′), with the angle β determined from constructive point

of view from the condition to avoid the interference
between the tool and the opposite flank, see Fig. 14. The
x axis is symmetrical with the arcs with radius r. In Table 5,
the input parameters correlated with the application HSGT.
In Figs. 16 and 17, we present the forms and the
coordinates of the characteristic curve and the axial section
for the helical surfaces assembly that composes the ball
thread flute. Obviously, in this case, it is not possible to
define singular points on the profile.

4 Conclusions
This paper presents algorithms and numerical applications

for the profiling of ring tools for the generation of
cylindrical helical surfaces with constant pitch, based on
the topological representation of the tool’s primary peripheral surface. The proposed method uses the capabilities of
the CATIA graphical design environment. This method

Y1

Rs
y0
Helix
Projection in xy
plane

'

o1

Z1

y0

X1
z0

Re

o0

x0

z 0'

x 0'

Rs

y

o
z

Fig. 13 Axial section of the ring tangential tool’s primary peripheral
surface

x

Re

Fig. 15 Ball thread; axial profile, and reference systems


Int J Adv Manuf Technol (2012) 61:15–24

23

Table 5 Input parameters of the ball thread
Symbol

Description

Value

p
r

Helical parameter
Flank radius

2.5464 mm
5.4 mm

e

Half distance between the centers
of circles with radius r
Diameter of centers cylinder of the
axial profile
Distance between the Dj diameter
and the center of circle with radius r
External diameter of thread
Fillet radius
Helix sense
Distance between axis

0.155 mm

48 mm
1 mm
Right
150 mm

Tool’s angle in plane zy
Tool’s angle in plane xz

10°
6.0566°

Dj
h
D
r0
Se
Daxis
β
α

49 mm
0.17 mm

allows to determine the composed characteristic curves of
the helical surfaces (the case of the helical flutes of the
motion threads) as so as, the highlighting of the singular
points on the tool’s profile, including modalities for the
solving of the inherent discontinuities by the method of
virtual extending of the profiles.
The results obtained in graphical and numerical form
confirm the method quality. Based on this method, an
original software, in VBA, was created.
The profiling of the ring tangential tool is similar to the
profiling of the side mill tool. The particular position of

tool’s axis may limit the length of the machined thread.
The specific application HSGT allows the determination
of the characteristic curve (in particular for composed
characteristic curves for complex surfaces) and allows the
solving of problems due of the singular points. The profile,
in the tool’s axial section, is rigorously determined in the
specifically HSGT application.
The proposed method, developed in the CATIA
graphical design environment, for the profiling of the
ring tangential tool’s primary peripheral surfaces allows
determining the characteristic curves and the axial

Fig. 16 Characteristic curve and axial section of ring tangential tool

Fig. 17 Axial section of ring tangential tool

section. The HSGT application is based on the decomposition of the helical movement—the self-generating
movement of the surface to be generated—a cylindrical
helical surface with constant pitch. They are presented
with analytical and graphical solutions for the determination of the constructive parameters of the generating
tool. Also, four numerical applications for cylindrical
helical surface with constant pitch used in machine
part’s construction were presented.
Acknowledgments The authors gratefully acknowledge the financial support of the Romanian Ministry of Education, Research and
Innovation through grant PN_II_ID_791/2008.

References
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Int J Adv Manuf Technol (2012) 61:25–33
DOI 10.1007/s00170-011-3691-x

ORIGINAL ARTICLE

Tool wear and surface quality in milling
of a gamma-TiAl intermetallic
Paolo Claudio Priarone & Stefania Rizzuti &
Giovanna Rotella & Luca Settineri

Received: 24 July 2011 / Accepted: 6 October 2011 / Published online: 30 October 2011
# Springer-Verlag London Limited 2011

Abstract Advanced structural materials for high-temperature
applications are often required in aerospace and automotive
fields. Gamma titanium aluminides, intermetallic alloys that
contain less than 60 wt.% of Ti, around 30–35 wt.% of
aluminum, and other alloy elements, can be used as an
alternative to more traditional materials for thermally and
mechanically stressed components in aerospace and automotive engines, since they show an attractive combination of
favorable strength-to-weight ratio, refractoriness, oxidation
resistance, high elastic modulus, and strength retention at

elevated temperatures, together with good creep resistance
properties. Unfortunately such properties, along with high
hardness and brittleness at room temperature, surface damage,
and short and unpredictable tool life, undermine their
machinability, so that gamma-TiAl are regarded as difficult
to cut materials. A deeper knowledge of their machinability is
therefore still required. In this context the paper presents the
results of an experimental campaign aimed at investigating the
machinability of a gamma titanium aluminide, of aeronautic
interest, fabricated via electron beam melting and then
thermally treated. Milling experiments have been conducted
with varying cutting speed, feed, and lubrication conditions
(dry, wet, and minimum quantity lubrication). The results are
presented in terms of correlation between cutting parameters
and lubrication condition with tool wear, surface hardness and
roughness, and chip morphology. Tool life, surface roughness,
and chirp morphology showed dependence on the cutting

P. C. Priarone : S. Rizzuti (*) : G. Rotella : L. Settineri
Department of Production Systems and Business Economics,
Politecnico di Torino,
Corso Duca degli Abruzzi,
10129 Turin, Italy
e-mail:

parameters. Lubrication conditions were observed to heavily
affect tool wear, and minimum quantity lubrication was
shown to be by far the method that allows to extend tool life.
Keywords Intermetallic alloy . Machinability . Tool wear .
Lubrication

1 Introduction
Gamma titanium aluminides (γ-TiAl) are intermetallic
alloys that contain 44–48 atomic percent Al (32–35 in
weight percent), with element additions of Cr, or Mn to
increase ductility, and Nb to improve strength and oxidation
resistance; γ-TiAl alloys can be used as an alternative to
Ni-based superalloys for thermally and mechanically
stressed components in aerospace and automotive engines
[1, 2]. Gamma-TiAl alloys show approximately half the
density of Ni superalloys, high strength/weight ratio, high
stiffness, high refractoriness, and high temperature strength.
Furthermore, they show fatigue resistance values close to
100% of yield strength [2].
In spite of these advantages, γ-TiAl alloys show some
drawbacks: low ductility at room temperature, which
typically ranges between 0.3% and 4% in terms of
elongation at rupture (depending on composition and
microstructure), together with low fracture toughness.
Furthermore, these characteristics, along with low thermal
conductivity and chemical reactivity with many tool
materials, make γ-TiAl difficult to cut materials. Other
features impairing machinability are the sensitivity to strain
rate, with a strong tendency to hardening, the saw tooth
chip shape, the built-up edge and the presence of abrasives
in the alloy microstructure that contribute to accelerated
wear of the cutting edge, and the formation of large crater