4 CONCLUSIONS
In this study, a finite-element model was developed
to see the effect of a serrated-chip formation in the ma-
chining of the AISI304 stainless steel using finite-ele-
ment simulations. A computer-aided numerical simula-
tion of the turning process was also performed using
DEFORM – 2D software. It can be said that the 2D FEM
model gives reasonable results compared to the experi-
mental results in view of cutting forces, thrust force and
shear angles. This proves the accuracy of the developed
2D FEM model, which can be used for this type of
turning simulations.
5 REFERENCES
1 S. Coromant, Modern metal cutting: a practical handbook, Sandvik
Coromant Press, 1st ed., 1994
2 M. P. Groover, Fundamentals of Modern Manufacturing: Materials,
Processes, and Systems, Prentice Hall, Wiley, 1996
3 E. M. Trent, Metal Cutting, Elsevier Science, Butterworth-Heine-
mann, 2016
4 J. Paro, H. Hänninen, V. Kauppinen, Tool wear and machinability of
X5 CrMnN 18 18 stainless steels, Journal of Materials Processing
Technology, 119 (2001), 14–20, doi:10.1016/S0924-0136(01)
00877-9
5 D. O’Sullivan, M. Cotterell, Machinability of austenitic stainless
steel SS303, Journal of Materials Processing Technology, 124
(2002), 153–159, doi: 10.1016/S0924-0136(02)00197-8
6 L. Jiang, Å. Roos, P. Liu, The influence of austenite grain size and its
distribution on chip deformation and tool life during machining of
AISI 304L, Metallurgical and Materials Transactions A, 28 (1997),
2415–2422, doi: 10.1007/s11661-997-0198-z
7 T. H. C. Childs, Material Property Needs in Modeling Metal
Machining, Machining Science and Technology, 2 (1998), 303–316,
doi:10.1080/10940349808945673
8 M. C. Shaw, Metal Cutting Principles, Oxford University Press, 2005
9 K. Maekawa, T. Obikawa, Y. Yamane, T. H. C. Childs, Metal Ma-
chining: Theory and Applications, Elsevier Science, 2013
10 V. P. Astakhov, Metal Cutting Mechanics, Taylor & Francis, 1998
11 M. Bäker, The influence of plastic properties on chip formation,
Computational Materials Science, 28 (2003), 556–562, doi:10.1016/
j.commatsci.2003.08.013
12 T. Ozel, M. Sima, A. Srivastava, Finite element simulation of high
speed machining Ti-6Al-4V alloy using modified material models,
Transactions of the NAMRI/SME, 38 (2010), 49–56,
13 M. Sima, T. Özel, Modified material constitutive models for serrated
chip formation simulations and experimental validation in machining
of titanium alloy Ti–6Al–4V, International Journal of Machine Tools
and Manufacture, 50 (2010), 943–960, doi:10.1016/j.ijmachtools.
2010.08.004
14 R. Alvarez, R. Domingo, M. A. Sebastian, The formation of saw
toothed chip in a titanium alloy: influence of constitutive models,
Journal of Mechanical Engineering, 57 (2011), 739–749,
doi:10.5545/sv-jme.2011.106
15 G. Chen, C. Ren, X. Yang, X. Jin, T. Guo, Finite element simulation
of high-speed machining of titanium alloy (Ti–6Al–4V) based on
ductile failure model, The International Journal of Advanced Manu-
facturing Technology, 56 (2011), 1027–1038, doi:10.1007/s00170-
011-3233-6
16 D. Umbrello, Finite element simulation of conventional and high
speed machining of Ti6Al4V alloy, Journal of Materials Processing
Technology, 196 (2008), 79–87, doi:10.1016/j.jmatprotec.2007.
05.007
17 J. Q. Xie, A. E. Bayoumi, H. M. Zbib, Analytical and experimental
study of shear localization in chip formation in orthogonal machin-
ing, Journal of Materials Engineering and Performance, 4 (1995),
32–39, doi: 10.1007/bf02682702
18 P. J. Arrazola, T. Özel, Investigations on the effects of friction mo-
deling in finite element simulation of machining, International
Journal of Mechanical Sciences, 52 (2010), 31–42, doi:10.1016/
j.ijmecsci.2009.10.001
19 DEFORM-3D Material Library, http://home.zcu.cz/~sbenesov/
Deform2Dlabs.pdf, 12.04.2017
A. GÖK: 2D NUMERIC SIMULATION OF SERRATED-CHIP FORMATION IN ORTHOGONAL CUTTING OF AISI316H ...
956 Materiali in tehnologije / Materials and technology 51 (2017) 6, 953–956
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 6: a) Cutting and b) thrust force for MWDC
Table 3: Comparison of NM and MWDC
Cutting speed
(m/min)
Undeformed chip
thickness, t (mm)
Deformed chip
thickness, tc (mm)
Chip ratio, rc Shear angle, (with Eg. 17)
Shear angle, 
(FEM)
NM 100 0.5 1.85 0.268 15 17
MWDC 100 0.5 0.76 0.657 33.304 37
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
957–965
EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH
STRATEGIES ON TOOL ACCELERATION IN BALL-END
MILLING
U^INKI REZALNIH PARAMETROV IN STRATEGIJA ZA POSPE[EK ORODJA
PRI MEHANSKI OBDELAVI S KROGLI^NIM FREZALOM
Arif Gök1, Kadir Gök2, Mehmet Burak Bilgin1, Mehmet Ali Alkan3
1Amasya University, Faculty of Technology, Department of Mechnical Engineering, 05100 Amasya, Turkey
2Celal Bayar University, Favulty of Technology, Department of Mechanical and Manufacturing Engineering, 45100 Manisa, Turkey
3Mu

gla Sitki Kocman University, Ula Vocational High School, Department of Energy, 48000 Mu

gla, Turkey
arif.gok@amasya.edu.tr
Prejem rokopisa – received: 2017-04-08; sprejem za objavo – accepted for publication: 2017-06-22
doi:10.17222/mit.2017.039
The determination of the cutting-parameter values that cause increases in vibration values is important to minimize the errors
that can occur. Thus, the first aim of this study was to investigate the optimum cutting-parameter values and tool-path strategies
in ball-end milling of the EN X40CrMoV5-1 tool steel with three coated cutters using the Taguchi method. The parameters
taken into consideration are the cutting speed, feed rate, step over and tool-path strategies. The second aim of the study, a model
for the tool acceleration as a function of the cutting parameters, was obtained using the response-surface methodology (RSM).
As a result, the most effective parameter within the selected cutting parameters and cutting strategies for both inclined surfaces
and different coatings was the step over. In terms of tool coatings, the most deteriorating coating for the tool acceleration on
both inclined surfaces was the TiC coating. In addition, the response-surface methodology is employed to predict the
tool-vibration values depending on the cutting parameters and tool-path strategy. The model generated gives highly accurate
results.
Keywords: inclined surfaces, ball-end milling, tool acceleration, Taguchi method, response-surface methodology, response
optimization
Neoptimalni rezalni parametri med mehansko obdelavo lahko povzro~ijo ne`elene vibracije in posledi~no napake. Prvi cilj
avtorjev te {tudije je bil dolo~iti optimalne vrednosti rezalnih parametrov in strategije potovanja orodja med mehansko obdelavo
orodnega jekla EN X40CrMoV5-1 s krogli~nim frezalom s tremi rezili z razli~no prevleko (TiC, TiN in TiAlN). Za to so upora-
bili Taguchi-jevo metodo. Parametri, ki so jih avtorji zajeli v {tudiji so bili: hitrost rezanja, velikost odvzema, korak odvzema
(preskok) in strategija poti orodja. Drugi cilj avtorjev te {tudije je bil izdelati model pospe{evanja orodja v odvisnosti od
rezalnih parametrov, z uporabo metodologije odziva povr{ine (angl. RSM). Ugotovili so, da je korak odvzema (angl.: step over)
naju~inkovitej{i parameter med izbranimi rezalnimi parametri in rezalnimi strategijami, tako za oba izbrana nagiba
(ukrivljenosti) povr{ine, kot tudi izbrane trde prevleke. Med izbranimi trdimi prevlekami se je v vseh pogojih frezanja kot
najslab{a izkazala TiC prevleka. RSM metodologija dodatno omogo~a napoved vibracij orodja v odvisnosti od rezalnih
parametrov in izbrane strategije poti orodja. Izdelani model daje zelo to~ne rezultate.
Klju~ne besede: nagib (ukrivljenost) povr{ine, mehanska obdelava s krogli~nim frezalom, pospe{ek orodja, Taguchi metoda,
metodologija odgovora povr{ine, optimizacija odgovora
1 INTRODUCTION
Nowadays, machining is one of the most important
methods for manufacturing technologies and it remains
up-to-date.1 In the machining of inclined surfaces, tight
machining tolerances are generally requested for the
processes of finishing and semi-finishing, which are
accomplished using indexable insert ball-end mills.2,3
The forces that occur at high cutting speeds, especially
during hard machining, and at high rates of metal
removing, cause excessive, irregular vibrations of cutting
tools during the machining. These vibrations cause the
cutting tools to break, disrupting the process stability and
the quality. Therefore, generating the optimum cutting
parameters is crucial to obtain high productivity in the
manufacturing process of complex geometries and to
reach the desired tolerance values.4,5 The studies carried
out in the field commonly focus on:
1) the effect of cutting parameters and cutting strategies
of plain-surface milling,
2) analytical tool-acceleration calculations and measure-
ments for end-milling and turning operations.
W. H. Yang and Y. S. Tarng6 worked on the optimi-
zation of the cutting parameters for turning operations so
that both optimum cutting parameters were demonstrated
and the basic cutting parameters affecting the cutting
performance in turning were defined.
M. Kurt et al.7 worked on the optimization of the
cutting parameters for the finish surface and the accuracy
of the hole diameter during dry drilling. In this way,
optimum cutting conditions were obtained with the
process optimization.
C. Gologlu and N. Sakarya8 investigated the effects
of tool-path strategies on the surface roughness for
pocket-milling operations using cutting parameters with
Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965 957
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
UDK 621.927:621.9.07:621.926.5 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 51(6)957(2017)
different values. It was found that the most influential
parameter for one-way and spiral tool-path strategies was
the feed rate, and the depth of cut was the most im-
portant parameter for back-and-forth tool-path strategies.
S. Neseli et al.9 worked on the optimization of the
tool-geometry parameters for turning operations based
on the response-surface methodology. In parallel to this
study, Asilturk and Neseli10 worked on the multi-res-
ponse optimization of CNC turning parameters via a
Taguchi-method-based response-surface analysis. M. M.
De Aguiar et al.11 investigated the correlating surface
roughness, tool wear and tool vibration in the milling
process of hardened steel using long slender tools. In this
study, a good workpiece-surface roughness together with
a long tool life of long tools with small diameters was
achieved. H. Wang et al.12 worked on an investigation of
the influence of the tool-tip vibration on the surface
roughness and its representative measurement in ultra-
precision diamond turning. This paper is dedicated to a
study of the influence of the tool-tip vibration on the
surface roughness. A. O. Abouelatta and J. Madl13
worked on the surface-roughness prediction based on the
cutting parameters and tool vibrations in turning
operations. S. Orhan et al.14 worked on the relationship
between the vibration and the tool wear during end
milling.
The studies given above were concentrated on the
determination of the most appropriate parameters for the
machining processes involving flat and inclined surfaces.
However, the studies confirm that an aggregated effect of
the cutting parameters and tool-path styles on the tool
acceleration in inclined geometries (convex and concave)
were not widely investigated. This study examines the
effects of the cutting parameters and tool-path styles on
the tool acceleration in the machining of convex and
concave surfaces using ball-end mills. By doing so, it
aims to keep the tool-acceleration values at a minimum,
and to control the unwanted machining results such as
poor surface quality and machining errors.
1.1 Tool-path strategies and cutting parameters
In the experimental studies, contouring and ramping
tool-path styles are used to produce inclined surfaces.
These tool-path styles can be established based on
up-milling and down-milling strategies by making the
movements of ramping and contouring. Ramping and
contouring are inevitable choices of the tool-path styles
for the implementation of the up-milling and down-
milling strategies.5 In the ramping tool-path styles, the
cutter scans an inclined surface following the lines in
parallel to the surface radius. On the other hand, in the
contouring tool-path styles, the cutter scans an inclined
surface following the lines perpendicular to the surface
radius.15–17 In this study, the step-over values are kept
constant in both tool-path styles. After each step of the
machining, the cutter moves one step sideways to the
position, in which it returns back to the staring level of
that step and then makes the next step.15 In the study
under these conditions, four tool-path styles were gene-
rated: contouring up milling (CUM), contouring down
milling (CDM), ramping up milling (RUM) and ramping
down milling (RDM). The form radius of workpiece,
milling position angle, nominal depth of cut, step over
and spindle speed are indicated by R, , ap, fp, and S,
respectively (Figure 1).
In addition to the cutter path styles defined, three
different variable parameters were used for semi-finish-
ing operations. These were the cutting velocity (Vc), feed
rate (Vf) and cutting step over (fp). The cutting-velocity
and feed-rate values were taken from the reference cata-
logues of the tool manufacturer (Sandvik Company). In
order to determine the right cutting-tool values (Tab-
le 1), a number of experiments for each tool coating was
conducted based on the reference values.5 The cutting-
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
958 Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 1: Inclined surfaces and related cutter path styles: CUM-1
(upward step over), CDM-1 (upward step over), CUM-2 (downward
step over), CDM-2 (downward step over), RUM-1 (left step over),
RDM-1 (left step over), RUM-2 (right step over), RDM-2 (right step
over)
Table 1: Assignment of the levels to factors
Factors Level 1 Level 2 Level 3 Level 4
Cutting
velocity,
Vc (m/min) –
A
TiC
TiN
TiAlN
70
100
110
80
110
120
90
120
130
100
130
140
Feed rate,
Vf (mm/rev) –
B
TiC
TiN
TiAlN
223
318
350
255
350
382
286
382
414
318
414
445
Step over, fp
(mm) – C 0.8 1 1.5 2
Cutting path
styles – D
Contour-
ing up
milling
(CUM)
Contour-
ing down
milling
(CDM)
Ramping
up
milling
(RUM)
Ramping
down
milling
(RDM)
tool step-over values directly affect the tracks on the
surface made by the cutter, the load on the cutter and
processing time.8 The step-over value was chosen to be
5 % of the tool diameter and this value was set as the
lower level of fp. The depth of cut was taken as 0.3 mm
and fixed as a constant. An orthogonal array of L’16 was
chosen for the experimental design and four different
levels were defined for each cutting parameter (Table 1).
2 EXPERIMENTAL PART
The EN X40CrMoV5-1 hot-work tool steel was
selected for the study. The material is commonly used in
tool-making processes due to the quality characteristics
including high durability, high thermal conductivity, high
machinability and high cracking resistance.5 First,
experimental samples of (40 × 30) mm islands on a (220
× 135 × 50) mm block were machined. In the experi-
ments, an indexable cutter body of an Ø16 mm cylindri-
cal shank (CoroMill, R216-16A20-045) with a two-
fluted 30°-helix-angle end mill was used. The ball-end
inserts of TiC, TiN and TiAlN coated with 3-μm
R216-16 03 M-M H13A were used. Semi-finishing
operations were employed and no coolant was used in
the machining. The experiments were carried out on a
vertical machining center of a John Ford VMC 550, with
12000 min–1 and a 12-kW engine. The experimental
set-up is shown in Figure 2. The acceleration of the
vibration signals generated during the cutting was
measured using a piezoelectric accelerometer (VibroTest
60) based on the ISO 2954 standard. The accelerometer
was mounted on the workpiece via a magnetization
feature.
2.1 Tool acceleration
Tool acceleration occurs in machining operations due
to the interaction between the tool and workpiece struc-
ture. Each tooth pass leaves a modulated surface on the
workpiece due to the vibrations of the tool and work-
piece, causing a variation in the expected chip thickness.
Under certain cutting conditions (i.e., feed rate, depth of
cut and cutting velocity), significant chip-thickness
variations, and hence force and displacement variations,
occur and a vibration is present.18 Vibrations result in a
poor surface finish, excessive tool wear, reduced dimen-
sional accuracy and tool damage. For a milling process,
conservative cutting conditions are usually selected to
avoid vibrations that decrease productivity.19
The values of the tool acceleration were experimen-
tally measured during the machining of inclined surfaces
(Table 2).
Table 2: Measured values of tool acceleration
Convex inclined surface Concave inclined surface
Exp.
No.
(m/s2
peak)
(TiC)
(m/s2
peak)
(TiN)
(m/s2
peak)
(TiAlN)
(m/s2
peak)
(TiC)
(m/s2
peak)
(TiN)
(m/s2
peak)
(TiAlN)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0.125
0.197
0.205
0.292
0.137
0.145
0.261
0.253
0.210
0.249
0.174
0.181
0.191
0.131
0.138
0.129
0.117
0.189
0.216
0.239
0.154
0.167
0.217
0.206
0.196
0.247
0.162
0.187
0.175
0.186
0.135
0.127
0.103
0.214
0.235
0.286
0.149
0.195
0.277
0.218
0.174
0.219
0.189
0.228
0.182
0.197
0.130
0.128
0.287
0.428
0.501
0.637
0.356
0.311
0.556
0.477
0.389
0.461
0.292
0.481
0.447
0.345
0.308
0.297
0.254
0.277
0.411
0.471
0.346
0.265
0.456
0.461
0.379
0.381
0.260
0.398
0.417
0.357
0.293
0.259
0.241
0.358
0.383
0.465
0.326
0.275
0.411
0.437
0.325
0.375
0.317
0.263
0.445
0.281
0.279
0.254
The orthogonal array chosen was L16 (44), with 16
rows corresponding to the number of experiments (4 fac-
tors with 4 levels each). To obtain the optimum cutting
performance, the smaller-the-better quality characteristic
for the tool acceleration was adopted. The S/N ratio was
defined as follows in Equation (1):
S
N N
Yi
i
n
= −
=
∑10 1 2
1
lg (1)
where Yi is the observed data at the ith experiment and n
is the number of experiments.
2.2 Response-surface methodology
The response surface methodology (RSM) is a
well-known up-to-date approach to the optimization of
input-parameter models based on either physical or
simulation experiments and experimental observations.
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965 959
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 2: Experimental set-up
different values. It was found that the most influential
parameter for one-way and spiral tool-path strategies was
the feed rate, and the depth of cut was the most im-
portant parameter for back-and-forth tool-path strategies.
S. Neseli et al.9 worked on the optimization of the
tool-geometry parameters for turning operations based
on the response-surface methodology. In parallel to this
study, Asilturk and Neseli10 worked on the multi-res-
ponse optimization of CNC turning parameters via a
Taguchi-method-based response-surface analysis. M. M.
De Aguiar et al.11 investigated the correlating surface
roughness, tool wear and tool vibration in the milling
process of hardened steel using long slender tools. In this
study, a good workpiece-surface roughness together with
a long tool life of long tools with small diameters was
achieved. H. Wang et al.12 worked on an investigation of
the influence of the tool-tip vibration on the surface
roughness and its representative measurement in ultra-
precision diamond turning. This paper is dedicated to a
study of the influence of the tool-tip vibration on the
surface roughness. A. O. Abouelatta and J. Madl13
worked on the surface-roughness prediction based on the
cutting parameters and tool vibrations in turning
operations. S. Orhan et al.14 worked on the relationship
between the vibration and the tool wear during end
milling.
The studies given above were concentrated on the
determination of the most appropriate parameters for the
machining processes involving flat and inclined surfaces.
However, the studies confirm that an aggregated effect of
the cutting parameters and tool-path styles on the tool
acceleration in inclined geometries (convex and concave)
were not widely investigated. This study examines the
effects of the cutting parameters and tool-path styles on
the tool acceleration in the machining of convex and
concave surfaces using ball-end mills. By doing so, it
aims to keep the tool-acceleration values at a minimum,
and to control the unwanted machining results such as
poor surface quality and machining errors.
1.1 Tool-path strategies and cutting parameters
In the experimental studies, contouring and ramping
tool-path styles are used to produce inclined surfaces.
These tool-path styles can be established based on
up-milling and down-milling strategies by making the
movements of ramping and contouring. Ramping and
contouring are inevitable choices of the tool-path styles
for the implementation of the up-milling and down-
milling strategies.5 In the ramping tool-path styles, the
cutter scans an inclined surface following the lines in
parallel to the surface radius. On the other hand, in the
contouring tool-path styles, the cutter scans an inclined
surface following the lines perpendicular to the surface
radius.15–17 In this study, the step-over values are kept
constant in both tool-path styles. After each step of the
machining, the cutter moves one step sideways to the
position, in which it returns back to the staring level of
that step and then makes the next step.15 In the study
under these conditions, four tool-path styles were gene-
rated: contouring up milling (CUM), contouring down
milling (CDM), ramping up milling (RUM) and ramping
down milling (RDM). The form radius of workpiece,
milling position angle, nominal depth of cut, step over
and spindle speed are indicated by R, , ap, fp, and S,
respectively (Figure 1).
In addition to the cutter path styles defined, three
different variable parameters were used for semi-finish-
ing operations. These were the cutting velocity (Vc), feed
rate (Vf) and cutting step over (fp). The cutting-velocity
and feed-rate values were taken from the reference cata-
logues of the tool manufacturer (Sandvik Company). In
order to determine the right cutting-tool values (Tab-
le 1), a number of experiments for each tool coating was
conducted based on the reference values.5 The cutting-
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
958 Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 1: Inclined surfaces and related cutter path styles: CUM-1
(upward step over), CDM-1 (upward step over), CUM-2 (downward
step over), CDM-2 (downward step over), RUM-1 (left step over),
RDM-1 (left step over), RUM-2 (right step over), RDM-2 (right step
over)
Table 1: Assignment of the levels to factors
Factors Level 1 Level 2 Level 3 Level 4
Cutting
velocity,
Vc (m/min) –
A
TiC
TiN
TiAlN
70
100
110
80
110
120
90
120
130
100
130
140
Feed rate,
Vf (mm/rev) –
B
TiC
TiN
TiAlN
223
318
350
255
350
382
286
382
414
318
414
445
Step over, fp
(mm) – C 0.8 1 1.5 2
Cutting path
styles – D
Contour-
ing up
milling
(CUM)
Contour-
ing down
milling
(CDM)
Ramping
up
milling
(RUM)
Ramping
down
milling
(RDM)
tool step-over values directly affect the tracks on the
surface made by the cutter, the load on the cutter and
processing time.8 The step-over value was chosen to be
5 % of the tool diameter and this value was set as the
lower level of fp. The depth of cut was taken as 0.3 mm
and fixed as a constant. An orthogonal array of L’16 was
chosen for the experimental design and four different
levels were defined for each cutting parameter (Table 1).
2 EXPERIMENTAL PART
The EN X40CrMoV5-1 hot-work tool steel was
selected for the study. The material is commonly used in
tool-making processes due to the quality characteristics
including high durability, high thermal conductivity, high
machinability and high cracking resistance.5 First,
experimental samples of (40 × 30) mm islands on a (220
× 135 × 50) mm block were machined. In the experi-
ments, an indexable cutter body of an Ø16 mm cylindri-
cal shank (CoroMill, R216-16A20-045) with a two-
fluted 30°-helix-angle end mill was used. The ball-end
inserts of TiC, TiN and TiAlN coated with 3-μm
R216-16 03 M-M H13A were used. Semi-finishing
operations were employed and no coolant was used in
the machining. The experiments were carried out on a
vertical machining center of a John Ford VMC 550, with
12000 min–1 and a 12-kW engine. The experimental
set-up is shown in Figure 2. The acceleration of the
vibration signals generated during the cutting was
measured using a piezoelectric accelerometer (VibroTest
60) based on the ISO 2954 standard. The accelerometer
was mounted on the workpiece via a magnetization
feature.
2.1 Tool acceleration
Tool acceleration occurs in machining operations due
to the interaction between the tool and workpiece struc-
ture. Each tooth pass leaves a modulated surface on the
workpiece due to the vibrations of the tool and work-
piece, causing a variation in the expected chip thickness.
Under certain cutting conditions (i.e., feed rate, depth of
cut and cutting velocity), significant chip-thickness
variations, and hence force and displacement variations,
occur and a vibration is present.18 Vibrations result in a
poor surface finish, excessive tool wear, reduced dimen-
sional accuracy and tool damage. For a milling process,
conservative cutting conditions are usually selected to
avoid vibrations that decrease productivity.19
The values of the tool acceleration were experimen-
tally measured during the machining of inclined surfaces
(Table 2).
Table 2: Measured values of tool acceleration
Convex inclined surface Concave inclined surface
Exp.
No.
(m/s2
peak)
(TiC)
(m/s2
peak)
(TiN)
(m/s2
peak)
(TiAlN)
(m/s2
peak)
(TiC)
(m/s2
peak)
(TiN)
(m/s2
peak)
(TiAlN)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0.125
0.197
0.205
0.292
0.137
0.145
0.261
0.253
0.210
0.249
0.174
0.181
0.191
0.131
0.138
0.129
0.117
0.189
0.216
0.239
0.154
0.167
0.217
0.206
0.196
0.247
0.162
0.187
0.175
0.186
0.135
0.127
0.103
0.214
0.235
0.286
0.149
0.195
0.277
0.218
0.174
0.219
0.189
0.228
0.182
0.197
0.130
0.128
0.287
0.428
0.501
0.637
0.356
0.311
0.556
0.477
0.389
0.461
0.292
0.481
0.447
0.345
0.308
0.297
0.254
0.277
0.411
0.471
0.346
0.265
0.456
0.461
0.379
0.381
0.260
0.398
0.417
0.357
0.293
0.259
0.241
0.358
0.383
0.465
0.326
0.275
0.411
0.437
0.325
0.375
0.317
0.263
0.445
0.281
0.279
0.254
The orthogonal array chosen was L16 (44), with 16
rows corresponding to the number of experiments (4 fac-
tors with 4 levels each). To obtain the optimum cutting
performance, the smaller-the-better quality characteristic
for the tool acceleration was adopted. The S/N ratio was
defined as follows in Equation (1):
S
N N
Yi
i
n
= −
=
∑10 1 2
1
lg (1)
where Yi is the observed data at the ith experiment and n
is the number of experiments.
2.2 Response-surface methodology
The response surface methodology (RSM) is a
well-known up-to-date approach to the optimization of
input-parameter models based on either physical or
simulation experiments and experimental observations.
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
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MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 2: Experimental set-up
These approximated models need to be assessed statis-
tically for their adequacy, and then they can be utilized
for an optimization of the initial model.10 Response-sur-
face-methodology problems follow a functional relation
between responses and independent variables, and this
relation can be explained using the second-order polyno-
mial model in Equation (2):20
 
 
 
 
 = + + + +
= =
∑ ∑ ∑∑0
1
1
1
2
i
i
k
ii
i
k
i ii i j
ji
X X X X (2)
where  is the estimated response (the tool accelera-
tion); 
0 is the constant; 
i, 
ii and 
ij represent the
coefficients of linear, quadratic and cross-product terms,
respectively. X reveals the coded variables.
3 RESULTS
The S/N ratios of the four factors from Equation (1)
were calculated for each of the tool coatings, and convex
and concave inclined surface types (Figures 3 to 8). The
largest S/N ratios always yield the optimum quality with
the minimum variance.5 Therefore, the level with the
largest value determines the optimum level of each
factor. From Figures 3 and 4, relating to the milling of
the TiC-coated convex and concave inclined surfaces, the
optimum levels in terms of the tool acceleration can be
observed at A4 for Vc (100 m/min), B1 for Vf (223 min–1)
and C1 for fp (0.8 mm). For the tool-path styles, the opti-
mum levels can be observed at D4 (UMC) for the convex
inclined surface and D1 (DMR) for the concave inclined
surface. From Figures 5 and 6, relating to the milling of
the TiN-coated convex and concave inclined surfaces, the
optimum levels in terms of the tool acceleration can be
observed at A4 for Vc (130 m/min), B1 for Vf
(318 min–1), C1 for fp (0.8 mm) and D1 (DMR) for the
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
960 Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 7: S/N ratios for milling convex inclined surfaces with a
TiAlN-coated cutterFigure 4: S/N ratios for milling a TiC-coated concave inclined surface
Figure 3: S/N ratios for milling a TiC-coated convex inclined surface
Figure 6: S/N ratios for milling a TiN-coated concave inclined surface
Figure 5: S/N ratios for milling a TiN-coated convex inclined surface
tool-path style. Likewise, from Figures 7 and 8, relating
to the milling of the TiAlN-coated convex and concave
inclined surfaces, the optimum levels in terms of the tool
acceleration can be observed at A4 for Vc (140 m/min),
B1 for Vf (358 mm/rev), C1 for fp (0.8 mm) and D1
(DMR) for the tool-path style.
In the machining of inclined surfaces, as seen in Fig-
ures 3 to 8, the tool-acceleration values decreased
slightly with an increase of Vc, in line with the data from
references4,18,21. The literature emphasizes that a slight
increase in Vc is caused by the following reasons: defor-
mations of the main cutting edge of the cutting tool
increase with a decrease in Vc, and this causes an in-
crease in the contact length between the cutting tool and
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965 961
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 8: S/N ratios for milling a TiAlN-coated concave inclined
surface
Table 3: ANOVA of the tool acceleration for inclined surface types
Source of variance DOF, v SS Variance, V F ratio (=5 %) p PCR (%)
Convex inclined surface (TiC)
Cutting velocity, Vc (m/min) 3 0.0050203 0.0016734 5.92 0.049 11.70
Feed rate, Vf (m/rev) 3 0.0092032 0.0030677 10.85 0.041 21.50
Step over, fp (mm) 3 0.0255268 0.0085089 30.09 0.010 59.60
Tool-path style 3 0.0022432 0.0007477 2.64 0.223 5.20
Error, e 3 0.0008483 0.0002828 2.00
Total 15 0.0428417 100.00
Concave inclined surface (TiC)
Cutting velocity, Vc (m/min) 3 26.015 8.672 1.84 0.050 13.63
Feed rate, Vf (m/rev) 3 21.613 7.204 1.53 0.048 11.32
Step over, fp (mm) 3 120.608 40.203 8.52 0.036 63.19
Tool-path style 3 8.455 2.818 0.6 0.659 4.43
Error, e 3 14.148 4.716 7.41
Total 15 190.839 100.00
Convex inclined surface (TiN)
Cutting velocity, Vc (m/min) 3 0.002192 0.0007307 3.54 0.490 10.99
Feed rate, Vf (m/rev) 3 0.002838 0.0009461 4.58 0.042 14.23
Step over, fp (mm) 3 0.014166 0.0047221 22.88 0.014 71.03
Tool-path style 3 0.000126 0.0000419 0.2 0.888 0.63
Error, e 3 0.000619 0.0002064 3.1
Total 15 0.019941 100.00
Concave inclined surface (TiN)
Cutting velocity, Vc (m/min) 3 0.006494 0.002165 0.44 0.048 3.22
Feed rate, Vf (m/rev) 3 0.04115 0.013717 2.81 0.040 20.42
Step over, fp (mm) 3 0.133717 0.044572 9.14 0.021 66.37
Tool-path style 3 0.005465 0.001822 0.37 0.780 2.71
Error, e 3 0.014633 0.004878 7.26
Total 15 0.20146 100.00
Convex inclined surface (TiAlN)
Cutting velocity, Vc (m/min) 3 0.005747 0.001916 1.42 0.050 15.07
Feed rate, Vf (m/rev) 3 0.009267 0.003089 2.29 0.045 24.3
Step over, fp (mm) 3 0.017734 0.005911 4.37 0.028 46.51
Tool-path style 3 0.00132 0.00044 0.33 0.809 3.46
Error, e 3 0.004055 0.001352 10.63
Total 15 0.038123 100.00
Concave inclined surface (TiAlN)
Cutting velocity, Vc (m/min) 3 0.005838 0.001946 5.53 0.047 6.37
Feed rate, Vf (m/rev) 3 0.020738 0.006913 19.63 0.018 22.63
Step over, fp (mm) 3 0.059669 0.01989 56.49 0.004 65.12
Tool-path style 3 0.004318 0.001439 4.09 0.139 4.71
Error, e 3 0.001056 0.000352 1.15
Total 15 0.091619 100.00
These approximated models need to be assessed statis-
tically for their adequacy, and then they can be utilized
for an optimization of the initial model.10 Response-sur-
face-methodology problems follow a functional relation
between responses and independent variables, and this
relation can be explained using the second-order polyno-
mial model in Equation (2):20
 
 
 
 
 = + + + +
= =
∑ ∑ ∑∑0
1
1
1
2
i
i
k
ii
i
k
i ii i j
ji
X X X X (2)
where  is the estimated response (the tool accelera-
tion); 
0 is the constant; 
i, 
ii and 
ij represent the
coefficients of linear, quadratic and cross-product terms,
respectively. X reveals the coded variables.
3 RESULTS
The S/N ratios of the four factors from Equation (1)
were calculated for each of the tool coatings, and convex
and concave inclined surface types (Figures 3 to 8). The
largest S/N ratios always yield the optimum quality with
the minimum variance.5 Therefore, the level with the
largest value determines the optimum level of each
factor. From Figures 3 and 4, relating to the milling of
the TiC-coated convex and concave inclined surfaces, the
optimum levels in terms of the tool acceleration can be
observed at A4 for Vc (100 m/min), B1 for Vf (223 min–1)
and C1 for fp (0.8 mm). For the tool-path styles, the opti-
mum levels can be observed at D4 (UMC) for the convex
inclined surface and D1 (DMR) for the concave inclined
surface. From Figures 5 and 6, relating to the milling of
the TiN-coated convex and concave inclined surfaces, the
optimum levels in terms of the tool acceleration can be
observed at A4 for Vc (130 m/min), B1 for Vf
(318 min–1), C1 for fp (0.8 mm) and D1 (DMR) for the
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
960 Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 7: S/N ratios for milling convex inclined surfaces with a
TiAlN-coated cutterFigure 4: S/N ratios for milling a TiC-coated concave inclined surface
Figure 3: S/N ratios for milling a TiC-coated convex inclined surface
Figure 6: S/N ratios for milling a TiN-coated concave inclined surface
Figure 5: S/N ratios for milling a TiN-coated convex inclined surface
tool-path style. Likewise, from Figures 7 and 8, relating
to the milling of the TiAlN-coated convex and concave
inclined surfaces, the optimum levels in terms of the tool
acceleration can be observed at A4 for Vc (140 m/min),
B1 for Vf (358 mm/rev), C1 for fp (0.8 mm) and D1
(DMR) for the tool-path style.
In the machining of inclined surfaces, as seen in Fig-
ures 3 to 8, the tool-acceleration values decreased
slightly with an increase of Vc, in line with the data from
references4,18,21. The literature emphasizes that a slight
increase in Vc is caused by the following reasons: defor-
mations of the main cutting edge of the cutting tool
increase with a decrease in Vc, and this causes an in-
crease in the contact length between the cutting tool and
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965 961
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Figure 8: S/N ratios for milling a TiAlN-coated concave inclined
surface
Table 3: ANOVA of the tool acceleration for inclined surface types
Source of variance DOF, v SS Variance, V F ratio (=5 %) p PCR (%)
Convex inclined surface (TiC)
Cutting velocity, Vc (m/min) 3 0.0050203 0.0016734 5.92 0.049 11.70
Feed rate, Vf (m/rev) 3 0.0092032 0.0030677 10.85 0.041 21.50
Step over, fp (mm) 3 0.0255268 0.0085089 30.09 0.010 59.60
Tool-path style 3 0.0022432 0.0007477 2.64 0.223 5.20
Error, e 3 0.0008483 0.0002828 2.00
Total 15 0.0428417 100.00
Concave inclined surface (TiC)
Cutting velocity, Vc (m/min) 3 26.015 8.672 1.84 0.050 13.63
Feed rate, Vf (m/rev) 3 21.613 7.204 1.53 0.048 11.32
Step over, fp (mm) 3 120.608 40.203 8.52 0.036 63.19
Tool-path style 3 8.455 2.818 0.6 0.659 4.43
Error, e 3 14.148 4.716 7.41
Total 15 190.839 100.00
Convex inclined surface (TiN)
Cutting velocity, Vc (m/min) 3 0.002192 0.0007307 3.54 0.490 10.99
Feed rate, Vf (m/rev) 3 0.002838 0.0009461 4.58 0.042 14.23
Step over, fp (mm) 3 0.014166 0.0047221 22.88 0.014 71.03
Tool-path style 3 0.000126 0.0000419 0.2 0.888 0.63
Error, e 3 0.000619 0.0002064 3.1
Total 15 0.019941 100.00
Concave inclined surface (TiN)
Cutting velocity, Vc (m/min) 3 0.006494 0.002165 0.44 0.048 3.22
Feed rate, Vf (m/rev) 3 0.04115 0.013717 2.81 0.040 20.42
Step over, fp (mm) 3 0.133717 0.044572 9.14 0.021 66.37
Tool-path style 3 0.005465 0.001822 0.37 0.780 2.71
Error, e 3 0.014633 0.004878 7.26
Total 15 0.20146 100.00
Convex inclined surface (TiAlN)
Cutting velocity, Vc (m/min) 3 0.005747 0.001916 1.42 0.050 15.07
Feed rate, Vf (m/rev) 3 0.009267 0.003089 2.29 0.045 24.3
Step over, fp (mm) 3 0.017734 0.005911 4.37 0.028 46.51
Tool-path style 3 0.00132 0.00044 0.33 0.809 3.46
Error, e 3 0.004055 0.001352 10.63
Total 15 0.038123 100.00
Concave inclined surface (TiAlN)
Cutting velocity, Vc (m/min) 3 0.005838 0.001946 5.53 0.047 6.37
Feed rate, Vf (m/rev) 3 0.020738 0.006913 19.63 0.018 22.63
Step over, fp (mm) 3 0.059669 0.01989 56.49 0.004 65.12
Tool-path style 3 0.004318 0.001439 4.09 0.139 4.71
Error, e 3 0.001056 0.000352 1.15
Total 15 0.091619 100.00
the workpiece. The longer contact length between the
cutting tool and the workpiece increases the friction
force on the cutting-tool rake face and this leads to an
increase in the tool acceleration depending on the cutting
forces.4,21 The chip cross-sectional area generated by fp
and Vf is the most influential factor in determining the
tool acceleration. As the fp and Vf values increase, the
tool acceleration increases as seen in Figures 3 to 8.
3.1 Analysis of variance
A statistical analysis of variance (ANOVA) was per-
formed to examine, which cutting parameters were
statistically significant for the tool acceleration. The p
values of ANOVA for all the cutting parameters and
tool-path styles are shown at a significance level of 95 %
(Table 3). Thus, it can be stated that the differences bet-
ween the measured values meaningfully result from the
differences between the levels.5
For the response value of the tool acceleration (Table 4)
of the TiC-coated cutter, the most significant parameters
were fp (p = 0.010), Vf (p = 0.041) and Vc (p = 0.049)
when machining the convex inclined surfaces. Similarly,
in the machining of the concave inclined surfaces, fp, Vf
and Vc were again the significant parameters with the p
values of 0.036, 0.048 and 0.05, respectively. For the
cutting-force values of the TiN-coated cutter, fp (p =
0.014), Vf (p = 0.042) and Vc (p = 0.049) were significant
parameters when machining the convex inclined sur-
faces. Likewise, fp, Vf and Vc were the most significant
control factors with the p values of 0.021, 0.04 and 0.048
when machining the concave inclined surfaces. Lastly,
for the cutting-force values of the TiAlN-coated cutter, fp
(p = 0.028), Vf (p = 0.045) and Vc (p = 0.05) were the
most significant control factors when machining the
convex inclined surfaces. Similarly, when machining the
concave inclined surfaces with the TiAlN-coated cutter,
fp, Vf and Vc were the most significant control factors
with the p values of 0.004, 0.018 and 0.047, respectively.
According to the response values of the tool acceleration
(Table 3), when machining both convex and concave
inclined surfaces with the TiC-, TiN- and TiAlN-coated
cutters, the most significant control factors were fp, Vf
and Vc. It is worth mentioning that fp was superior to Vf
in all the cases.
3.2 Determination of the optimum machining parame-
ters and confirmation experiments
The optimum parameters in machining convex in-
clined surfaces were A4B1C1D1 for the TiC-coated
cutter; A4B1C1D1 for the TiN-coated cutter; and
A4B1C1D3 for the TiAlN-coated cutter. On the other
hand, in terms of the tool acceleration, the optimum
parameters in machining concave inclined surfaces were
A4B1C1D4 for the TiC-coated cutter; A4B1C1D1 for the
TiN-coated cutter; and A4B1C1D1 for the TiAlN-coated
cutter. By making a prediction considering the para-
meters, the results can be calculated in advance using
Equations (3) to (4) (Table 4):8
   

cal m m m
m
Max Max
Max
= + −
⎛
⎝
⎜
⎞
⎠
⎟ + −
⎛
⎝
⎜
⎞
⎠
⎟ +
+ −
S
N
S
N
S
N
1 2
3
⎛
⎝
⎜
⎞
⎠
⎟ + −
⎛
⎝
⎜
⎞
⎠
⎟Max m
S
N 4

(3)
where cal is the calculated S/N ratio under the optimum
machining conditions; m is the arithmetic mean of the
S/N ration of the studied surface form.
Acccal
20
cal
=
−
10

(4)
Acccal is the calculated base quantity; cal is the calcu-
lated S/N ratio.
Table 4: Calculated values for convex and concave inclined surfaces
Coatings
Convex inclined
surface
Concave inclined
surface
cal(dB) Acccal(m/s2 peak) cal(dB)
Acccal
(m/s2 peak)
TiC 20.727 0.092 20.915 0.090
TiN 19,337 0.108 13.722 0.206
TiAlN 14.991 0.178 14.379 0.191
Two test trails for each coating type at the optimal-
control-factor settings were conducted as confirmation
experiments. The tests were carried out with new cutters,
one for each coating type in order to prevent undesirable
effects caused by worn cutting tools.5 The results of the
experiments are presented in Table 5, showing the
acceleration values (Accmea) and S/N ratios (mea).
Table 5: Comparison between confirmatory-test results and calculated
values for convex and concave inclined surfaces
Exp.
No.
Accele-
ration
(m/s2 peak)
Accele-
ration mea
(m/s2 peak)
Accele-
ration
(mea,dB)
Absolute
differences
(%)*
Convex inclined surface
TiC
1 0.086
0.090 20.906 0.2
2 0.094
TiN
1 0.091
0.101 19.871 0.7
2 0.111
TiAlN
1 0.153
0.172 15.236 0.6
2 0.191
Concave inclined surface
TiC
1 0.101
0.103 19.741 1.3
2 0.105
TiN
1 0.202
0.203 13.849 0.3
2 0.204
TiAlN
1 0.179
0.188 14.506 0.3
2 0.197
*
Acc Acc
Acc
cal mea
mea
−
× 100
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
962 Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
3.3 Confidence interval
Estimating the mean is only a point estimate based on
the average of the results obtained from the experiment.
It gives a 50 % chance of being greater or lower than the
mean.22 Therefore, confidence interval (CI) should be
calculated. A confidence interval includes the maximum
and minimum value between which the true average
should be at some stated percentage of confidence. Con-
fidence interval is used to verify the quality characte-
ristics of confirmation experiments. The following
formula is used to verify the predictions:23
CI F V
n re e
= +
⎛
⎝
⎜
⎞
⎠
⎟0 05 1
1 1
. ( , )
eff
(5)
Where F0.05(1,e) is the F ratio at a 95 % confidence24
against degree of freedom 1 and the error of e; Ve is the
error variance; neff is the effective number of replication
and is the number of test trials (r = 2).
n
N
Veff T
=
+1
(6)
where N is the total number of experiments; T is the
total main factor of degrees of freedom (VT = 12). The
confidence-interval (CI) values for the convex and
concave inclined surfaces obtained using Equations (5)
and (6) are provided in Table 6.
Table 6: CI values
Tool acceleration (m/s2 peak)
TiC TiN TiAlN
Convex inclined surface 0.047 0.023 0.062
Concave inclined surface 2.027 0.120 0.061
The S/N ratio differences between the estimated
values obtained using Equations (2) and (3), and the
results obtained with the confirmation experiments are
shown in Table 5. The differences appear to be the
smallest at a confidence-interval value of 5 % given in
Table 6. Therefore, both inclined surfaces and all the
coatings used are confirmed as safe, having the optimal
control-factor settings.
3.4 Prediction of the tool acceleration
A tool-acceleration prediction model based on the
cutting-parameter values was developed using the
response-surface methodology (RSM). The RSM is a
methodology that uses a combination of statistical and
mathematical techniques for the development and opti-
mization of processes. The RSM optimizes (maximizes,
minimizes or makes nominal) the response using a
polynomial model of the first order or second order.5 As
a result of the machinability experiments conducted, a
first-order model and a quadratic polynomial tool-acce-
leration model depending on the values of Vc, Vf and fp
were obtained as shown in Equation (7):
RMS k k V k V k f= + ⋅ + ⋅ + ⋅0 1 2 3C f p (7)
RMS k k V k V k f k V
k V k f k
= + ⋅ + ⋅ + ⋅ + ⋅ +
+ ⋅ + ⋅ + ⋅
0 1 2 3 4
5 6 7
C f p C
2
f
2
p
2 V V k V f k V fC f C p f p⋅ + ⋅ ⋅ + ⋅ ⋅8 9
(8)
The values of the polynomial and first-order model
regression coefficients and the correlation coefficient for
the mathematical model of Ra are given in Tables 7 and 8.
Table 7: First-order-model coefficients and correlation coefficients
Coeffi-
cient
Multi-
plier
Regression coefficients
Convex inclined
surface
Concave inclined
surface
TiC TiN TiAlN TiC TiN TiAlN
k0 Sabit 0.195 0.183 0.197 0.533 0.376 0.344
k1 Vc -0.025 -0.011 -0.020 -0.099 -0.025 -0.022
k2 Vf 0.023 0.013 0.029 0.095 0.059 0.021
k3 fp 0.051 0.037 0.042 0.183 0.116 0.078
%
Correlation coefficients
89.19 88.80 86.26 85.77 83.48 83.72
Table 8: Polynomial-regression coefficients and correlation coeffi-
cients
Coeffi-
cient
Multi-
plier
Regression coefficients
Convex inclined
surface
Concave inclined
surface
TiC TiN TiAlN TiC TiN TiAlN
k0 Sabit 0.205 0.206 0.217 0.534 0.322 0.333
k1 Vc -0.037 -0.015 -0.024 -0.166 -0.005 -0.043
k2 Vf 0.016 0.010 0.030 0.132 0.063 0.017
k3 Fp 0.045 0.030 0.025 0.181 0.060 0.037
k4 Vc × Vc -0.028 -0.020 -0.022 -0.010 0.012 -0.005
k5 Vf × Vf 0.002 -0.009 -0.018 0.023 0.055 0.000
k6 fp × fp 0.057 -0.012 0.000 -0.014 0.015 0.014
k7 Vc × Vf -0.010 -0.012 -0.029 -0.004 -0.096 -0.070
k8 Vc × fp -0.008 -0.004 0.002 0.082 0.000 -0.027
k9 Vf × fp -0.017 -0.006 -0.006 -0.125 0.031 0.000
%
Correlation coefficients
91.79 94.54 90.57 92.13 97.04 85.29
The correlation coefficients for the convex inclined
surface were 91.79, 94.54 and 90.57 % for the TiC, TiN,
and TiAlN coatings, respectively. On the other hand, the
related coefficients for the concave inclined surface were
92.13, 97.04 and 85.29 % for the coatings of TiC, TiN
and TiAlN, respectively. The values indicate that the
model generated is successful at predicting the tool-acce-
leration values for both inclined surfaces.
3.5 Optimization of the response
One of the most important aims of the experiments
related to manufacturing is to achieve the desired tool
acceleration of the optimal cutting parameters.9 To this
end, the response-surface optimization is the ideal tech-
nique for determining the tool acceleration in ball-end
milling. Here, the goal is to minimize the tool accele-
ration. The RSM-optimization result for the acceleration
parameter for the convex inclined surface and the TiC
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965 963
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
the workpiece. The longer contact length between the
cutting tool and the workpiece increases the friction
force on the cutting-tool rake face and this leads to an
increase in the tool acceleration depending on the cutting
forces.4,21 The chip cross-sectional area generated by fp
and Vf is the most influential factor in determining the
tool acceleration. As the fp and Vf values increase, the
tool acceleration increases as seen in Figures 3 to 8.
3.1 Analysis of variance
A statistical analysis of variance (ANOVA) was per-
formed to examine, which cutting parameters were
statistically significant for the tool acceleration. The p
values of ANOVA for all the cutting parameters and
tool-path styles are shown at a significance level of 95 %
(Table 3). Thus, it can be stated that the differences bet-
ween the measured values meaningfully result from the
differences between the levels.5
For the response value of the tool acceleration (Table 4)
of the TiC-coated cutter, the most significant parameters
were fp (p = 0.010), Vf (p = 0.041) and Vc (p = 0.049)
when machining the convex inclined surfaces. Similarly,
in the machining of the concave inclined surfaces, fp, Vf
and Vc were again the significant parameters with the p
values of 0.036, 0.048 and 0.05, respectively. For the
cutting-force values of the TiN-coated cutter, fp (p =
0.014), Vf (p = 0.042) and Vc (p = 0.049) were significant
parameters when machining the convex inclined sur-
faces. Likewise, fp, Vf and Vc were the most significant
control factors with the p values of 0.021, 0.04 and 0.048
when machining the concave inclined surfaces. Lastly,
for the cutting-force values of the TiAlN-coated cutter, fp
(p = 0.028), Vf (p = 0.045) and Vc (p = 0.05) were the
most significant control factors when machining the
convex inclined surfaces. Similarly, when machining the
concave inclined surfaces with the TiAlN-coated cutter,
fp, Vf and Vc were the most significant control factors
with the p values of 0.004, 0.018 and 0.047, respectively.
According to the response values of the tool acceleration
(Table 3), when machining both convex and concave
inclined surfaces with the TiC-, TiN- and TiAlN-coated
cutters, the most significant control factors were fp, Vf
and Vc. It is worth mentioning that fp was superior to Vf
in all the cases.
3.2 Determination of the optimum machining parame-
ters and confirmation experiments
The optimum parameters in machining convex in-
clined surfaces were A4B1C1D1 for the TiC-coated
cutter; A4B1C1D1 for the TiN-coated cutter; and
A4B1C1D3 for the TiAlN-coated cutter. On the other
hand, in terms of the tool acceleration, the optimum
parameters in machining concave inclined surfaces were
A4B1C1D4 for the TiC-coated cutter; A4B1C1D1 for the
TiN-coated cutter; and A4B1C1D1 for the TiAlN-coated
cutter. By making a prediction considering the para-
meters, the results can be calculated in advance using
Equations (3) to (4) (Table 4):8
   

cal m m m
m
Max Max
Max
= + −
⎛
⎝
⎜
⎞
⎠
⎟ + −
⎛
⎝
⎜
⎞
⎠
⎟ +
+ −
S
N
S
N
S
N
1 2
3
⎛
⎝
⎜
⎞
⎠
⎟ + −
⎛
⎝
⎜
⎞
⎠
⎟Max m
S
N 4

(3)
where cal is the calculated S/N ratio under the optimum
machining conditions; m is the arithmetic mean of the
S/N ration of the studied surface form.
Acccal
20
cal
=
−
10

(4)
Acccal is the calculated base quantity; cal is the calcu-
lated S/N ratio.
Table 4: Calculated values for convex and concave inclined surfaces
Coatings
Convex inclined
surface
Concave inclined
surface
cal(dB) Acccal(m/s2 peak) cal(dB)
Acccal
(m/s2 peak)
TiC 20.727 0.092 20.915 0.090
TiN 19,337 0.108 13.722 0.206
TiAlN 14.991 0.178 14.379 0.191
Two test trails for each coating type at the optimal-
control-factor settings were conducted as confirmation
experiments. The tests were carried out with new cutters,
one for each coating type in order to prevent undesirable
effects caused by worn cutting tools.5 The results of the
experiments are presented in Table 5, showing the
acceleration values (Accmea) and S/N ratios (mea).
Table 5: Comparison between confirmatory-test results and calculated
values for convex and concave inclined surfaces
Exp.
No.
Accele-
ration
(m/s2 peak)
Accele-
ration mea
(m/s2 peak)
Accele-
ration
(mea,dB)
Absolute
differences
(%)*
Convex inclined surface
TiC
1 0.086
0.090 20.906 0.2
2 0.094
TiN
1 0.091
0.101 19.871 0.7
2 0.111
TiAlN
1 0.153
0.172 15.236 0.6
2 0.191
Concave inclined surface
TiC
1 0.101
0.103 19.741 1.3
2 0.105
TiN
1 0.202
0.203 13.849 0.3
2 0.204
TiAlN
1 0.179
0.188 14.506 0.3
2 0.197
*
Acc Acc
Acc
cal mea
mea
−
× 100
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
962 Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
3.3 Confidence interval
Estimating the mean is only a point estimate based on
the average of the results obtained from the experiment.
It gives a 50 % chance of being greater or lower than the
mean.22 Therefore, confidence interval (CI) should be
calculated. A confidence interval includes the maximum
and minimum value between which the true average
should be at some stated percentage of confidence. Con-
fidence interval is used to verify the quality characte-
ristics of confirmation experiments. The following
formula is used to verify the predictions:23
CI F V
n re e
= +
⎛
⎝
⎜
⎞
⎠
⎟0 05 1
1 1
. ( , )
eff
(5)
Where F0.05(1,e) is the F ratio at a 95 % confidence24
against degree of freedom 1 and the error of e; Ve is the
error variance; neff is the effective number of replication
and is the number of test trials (r = 2).
n
N
Veff T
=
+1
(6)
where N is the total number of experiments; T is the
total main factor of degrees of freedom (VT = 12). The
confidence-interval (CI) values for the convex and
concave inclined surfaces obtained using Equations (5)
and (6) are provided in Table 6.
Table 6: CI values
Tool acceleration (m/s2 peak)
TiC TiN TiAlN
Convex inclined surface 0.047 0.023 0.062
Concave inclined surface 2.027 0.120 0.061
The S/N ratio differences between the estimated
values obtained using Equations (2) and (3), and the
results obtained with the confirmation experiments are
shown in Table 5. The differences appear to be the
smallest at a confidence-interval value of 5 % given in
Table 6. Therefore, both inclined surfaces and all the
coatings used are confirmed as safe, having the optimal
control-factor settings.
3.4 Prediction of the tool acceleration
A tool-acceleration prediction model based on the
cutting-parameter values was developed using the
response-surface methodology (RSM). The RSM is a
methodology that uses a combination of statistical and
mathematical techniques for the development and opti-
mization of processes. The RSM optimizes (maximizes,
minimizes or makes nominal) the response using a
polynomial model of the first order or second order.5 As
a result of the machinability experiments conducted, a
first-order model and a quadratic polynomial tool-acce-
leration model depending on the values of Vc, Vf and fp
were obtained as shown in Equation (7):
RMS k k V k V k f= + ⋅ + ⋅ + ⋅0 1 2 3C f p (7)
RMS k k V k V k f k V
k V k f k
= + ⋅ + ⋅ + ⋅ + ⋅ +
+ ⋅ + ⋅ + ⋅
0 1 2 3 4
5 6 7
C f p C
2
f
2
p
2 V V k V f k V fC f C p f p⋅ + ⋅ ⋅ + ⋅ ⋅8 9
(8)
The values of the polynomial and first-order model
regression coefficients and the correlation coefficient for
the mathematical model of Ra are given in Tables 7 and 8.
Table 7: First-order-model coefficients and correlation coefficients
Coeffi-
cient
Multi-
plier
Regression coefficients
Convex inclined
surface
Concave inclined
surface
TiC TiN TiAlN TiC TiN TiAlN
k0 Sabit 0.195 0.183 0.197 0.533 0.376 0.344
k1 Vc -0.025 -0.011 -0.020 -0.099 -0.025 -0.022
k2 Vf 0.023 0.013 0.029 0.095 0.059 0.021
k3 fp 0.051 0.037 0.042 0.183 0.116 0.078
%
Correlation coefficients
89.19 88.80 86.26 85.77 83.48 83.72
Table 8: Polynomial-regression coefficients and correlation coeffi-
cients
Coeffi-
cient
Multi-
plier
Regression coefficients
Convex inclined
surface
Concave inclined
surface
TiC TiN TiAlN TiC TiN TiAlN
k0 Sabit 0.205 0.206 0.217 0.534 0.322 0.333
k1 Vc -0.037 -0.015 -0.024 -0.166 -0.005 -0.043
k2 Vf 0.016 0.010 0.030 0.132 0.063 0.017
k3 Fp 0.045 0.030 0.025 0.181 0.060 0.037
k4 Vc × Vc -0.028 -0.020 -0.022 -0.010 0.012 -0.005
k5 Vf × Vf 0.002 -0.009 -0.018 0.023 0.055 0.000
k6 fp × fp 0.057 -0.012 0.000 -0.014 0.015 0.014
k7 Vc × Vf -0.010 -0.012 -0.029 -0.004 -0.096 -0.070
k8 Vc × fp -0.008 -0.004 0.002 0.082 0.000 -0.027
k9 Vf × fp -0.017 -0.006 -0.006 -0.125 0.031 0.000
%
Correlation coefficients
91.79 94.54 90.57 92.13 97.04 85.29
The correlation coefficients for the convex inclined
surface were 91.79, 94.54 and 90.57 % for the TiC, TiN,
and TiAlN coatings, respectively. On the other hand, the
related coefficients for the concave inclined surface were
92.13, 97.04 and 85.29 % for the coatings of TiC, TiN
and TiAlN, respectively. The values indicate that the
model generated is successful at predicting the tool-acce-
leration values for both inclined surfaces.
3.5 Optimization of the response
One of the most important aims of the experiments
related to manufacturing is to achieve the desired tool
acceleration of the optimal cutting parameters.9 To this
end, the response-surface optimization is the ideal tech-
nique for determining the tool acceleration in ball-end
milling. Here, the goal is to minimize the tool accele-
ration. The RSM-optimization result for the acceleration
parameter for the convex inclined surface and the TiC
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965 963
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
coating is shown in Figure 9. The optimum cutting para-
meters obtained for all the surface types and all the coat-
ings are shown in Table 9.
4 CONCLUSIONS
The tool acceleration in a ball-end-milling process
with cutting parameters and different tool-path strategies
was measured, along with the orthogonal array, during
the experiments. The results obtained are as follows:
• Both the Taguchi and response-surface statistical
analyses indicated that the main effect of the step
over is the most significant factor for the tool accele-
ration.
• According to the confirmation experiments under the
optimal conditions, the measured tool-acceleration
values for the convex inclined surfaces were found to
be smaller than those of the calculated tool-accelera-
tion values. On the other hand, for the concave
inclined surfaces, the measured tool-acceleration
values were found to be larger than those of the
calculated tool-acceleration values. Nevertheless, the
absolute difference in the percentile of the measured
and calculated values was not more than 3.57 for
both inclined surface types.
• The tool-acceleration values obtained for the ma-
chining of the convex inclined surfaces were found to
be smaller in comparison to the values obtained for
the machining of the concave inclined surfaces
(Table 3). This is because the chip was comfortably
removed from the cutting zone of the convex inclined
surface. Besides, the cutting tool affects the inner
surface and the contacts with the workpiece, resulting
in a longer cutting edge during the tool acceleration.
• The tool-acceleration values for the contouring tool-
path style were found to be smaller than those for the
ramping tool-path style (Figures 3 to 8). This is
because the contouring tool-path style causes move-
ments parallel to the axis of the inclined surface.
Previous studies support the finding that the move-
ments made in parallel to the surface axis are ideal to
move the chips away.
• The RSM was found to be effective for the identi-
fication and development of the significant relation-
ships between the cutting parameters.
• The highest correlation coefficients were obtained
with the tool-acceleration prediction model. The pre-
diction model can be employed in relative studies.
• The optimum combination of the cutting parameters
for the response optimization of all surface types
includes the values of the largest cutting velocity, the
smallest step over and the feed rate.
5 REFERENCES
1 A. Gok, A new approach to minimization of the surface roughness
and cutting force via fuzzy TOPSIS, multi-objective grey design and
RSA, Measurement,70 (2015), 100–109, doi:10.1016/j.measurement.
2015.03.037
2 A. Gok, C. Gologlu, H. I. Demirci, M. Kurt, Determination of Sur-
face Qualities on Inclined Surface Machining with Acoustic Sound
Pressure, Strojni{ki vestnik – Journal of Mechanical Engineering, 58
(2012) 10, 587–597, doi:10.5545/sv-jme.2012.352
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
964 Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Table 9: Response optimization for tool-acceleration-parameter components
Parameter Goal
Optimum combination Lower Target Upper Pre.response
Desira-
bility
Vc (mm/min) Vf (m/rev) fp (mm)
Convex surface, TiC
Acceleration (m/s2 peak) Min. 100 223 0.8 0.125 0.125 0,292 0.119 1
Convex surface, TiN
Acceleration (m/s2 peak) Min. 130 318 0.8 0.117 0.117 0.239 0.116 1
Convex surface, TiAlN
Acceleration (m/s2 peak) Min. 140 350 0.8 0.103 0.103 0.286 0.112 1
Concave surface, TiC
Acceleration (m/s2 peak) Min. 100 223 0.8 0.287 0.287 0.637 0.249 1
Concave surface, TiN
Acceleration (m/s2 peak) Min. 130 318 0.8 0.254 0.254 0.471 0.226 1
Concave surface, TiAlN
Acceleration (m/s2 peak) Min. 140 350 0.8 0.241 0.241 0.465 0.222 1
Figure 9: Response-optimization plot for the tool-acceleration-
parameter components for the convex surface and TiC coating
3 M. C. Shaw, Metal cutting principles, Oxford Oxford University
Press, 2nd Edition ed., 2005
4 E. M. Trent, Metal Cutting, Elsevier Science, Butterworth-Heine-
mann, 4th Edition ed., 2016
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style effects on cutting force and tool deflection in machining of
convex and concave inclined surfaces, Int J Adv Manuf Technol, 69
(2013) 5–8, 1063–1078, doi:10.1007/s00170-013-5075-x
6 W. H. Yang, Y. S. Tarng, Design optimization of cutting parameters
for turning operations based on the Taguchi method, Journal of
Materials Processing Technology, 84 (1998) 1–3, 122–129,
doi:10.1016/S0924-0136(98)00079-X
7 M. Kurt, E. Bagci, Y. Kaynak, Application of Taguchi methods in the
optimization of cutting parameters for surface finish and hole
diameter accuracy in dry drilling processes, Int Journal of Adv
Manuf Technol. 40 (2009) 5–6, 458–469, doi:10.1007/s00170-
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8 C. Gologlu, N. Sakarya, The effects of cutter path strategies on
surface roughness of pocket milling of 1.2738 steel based on Taguchi
method, Journal of Materials Processing Technology, 206 (2008)
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9 S. Neºeli, S. Yaldýz, E. Türkeº, Optimization of tool geometry para-
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parameters via Taguchi method-based response surface analysis,
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12 H. Wang, S. To, C. Y. Chan, Investigation on the influence of tool-tip
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vibration analysis during end milling of AISI D3 cold work tool steel
with 35 HRC hardness, NDT & E International, 40 (2007) 2,
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18 M. Günay, E. Yücel, Application of Taguchi method for determining
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20 M. C. Kathleen, Y. K. Natalia, R. Jeff, Response surface metho-
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21 M. Sarýkaya, A. Güllü, Taguchi design and response surface
methodology based analysis of machining parameters in CNC
turning under MQL, Journal of Cleaner Production, 65 (2014),
604–616, doi:10.1016/j.jclepro.2013.08.040
22 D. Montgomery, Design and analysis of experiments, New York:
Wiley, 2000
23 M. Nalbant, H. Gökkaya, G. Sur, Application of Taguchi method in
the optimization of cutting parameters for surface roughness in
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doi:10.1016/j.matdes.2006.01.008
24 T. Ding, S. Zhang, Y. Wang, X. Zhu, 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 (2010) 1–4,
45–55, doi: 10.1007/s00170-010-2598-2
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965 965
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
coating is shown in Figure 9. The optimum cutting para-
meters obtained for all the surface types and all the coat-
ings are shown in Table 9.
4 CONCLUSIONS
The tool acceleration in a ball-end-milling process
with cutting parameters and different tool-path strategies
was measured, along with the orthogonal array, during
the experiments. The results obtained are as follows:
• Both the Taguchi and response-surface statistical
analyses indicated that the main effect of the step
over is the most significant factor for the tool accele-
ration.
• According to the confirmation experiments under the
optimal conditions, the measured tool-acceleration
values for the convex inclined surfaces were found to
be smaller than those of the calculated tool-accelera-
tion values. On the other hand, for the concave
inclined surfaces, the measured tool-acceleration
values were found to be larger than those of the
calculated tool-acceleration values. Nevertheless, the
absolute difference in the percentile of the measured
and calculated values was not more than 3.57 for
both inclined surface types.
• The tool-acceleration values obtained for the ma-
chining of the convex inclined surfaces were found to
be smaller in comparison to the values obtained for
the machining of the concave inclined surfaces
(Table 3). This is because the chip was comfortably
removed from the cutting zone of the convex inclined
surface. Besides, the cutting tool affects the inner
surface and the contacts with the workpiece, resulting
in a longer cutting edge during the tool acceleration.
• The tool-acceleration values for the contouring tool-
path style were found to be smaller than those for the
ramping tool-path style (Figures 3 to 8). This is
because the contouring tool-path style causes move-
ments parallel to the axis of the inclined surface.
Previous studies support the finding that the move-
ments made in parallel to the surface axis are ideal to
move the chips away.
• The RSM was found to be effective for the identi-
fication and development of the significant relation-
ships between the cutting parameters.
• The highest correlation coefficients were obtained
with the tool-acceleration prediction model. The pre-
diction model can be employed in relative studies.
• The optimum combination of the cutting parameters
for the response optimization of all surface types
includes the values of the largest cutting velocity, the
smallest step over and the feed rate.
5 REFERENCES
1 A. Gok, A new approach to minimization of the surface roughness
and cutting force via fuzzy TOPSIS, multi-objective grey design and
RSA, Measurement,70 (2015), 100–109, doi:10.1016/j.measurement.
2015.03.037
2 A. Gok, C. Gologlu, H. I. Demirci, M. Kurt, Determination of Sur-
face Qualities on Inclined Surface Machining with Acoustic Sound
Pressure, Strojni{ki vestnik – Journal of Mechanical Engineering, 58
(2012) 10, 587–597, doi:10.5545/sv-jme.2012.352
A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
964 Materiali in tehnologije / Materials and technology 51 (2017) 6, 957–965
MATERIALI IN TEHNOLOGIJE/MATERIALS AND TECHNOLOGY (1967–2017) – 50 LET/50 YEARS
Table 9: Response optimization for tool-acceleration-parameter components
Parameter Goal
Optimum combination Lower Target Upper Pre.response
Desira-
bility
Vc (mm/min) Vf (m/rev) fp (mm)
Convex surface, TiC
Acceleration (m/s2 peak) Min. 100 223 0.8 0.125 0.125 0,292 0.119 1
Convex surface, TiN
Acceleration (m/s2 peak) Min. 130 318 0.8 0.117 0.117 0.239 0.116 1
Convex surface, TiAlN
Acceleration (m/s2 peak) Min. 140 350 0.8 0.103 0.103 0.286 0.112 1
Concave surface, TiC
Acceleration (m/s2 peak) Min. 100 223 0.8 0.287 0.287 0.637 0.249 1
Concave surface, TiN
Acceleration (m/s2 peak) Min. 130 318 0.8 0.254 0.254 0.471 0.226 1
Concave surface, TiAlN
Acceleration (m/s2 peak) Min. 140 350 0.8 0.241 0.241 0.465 0.222 1
Figure 9: Response-optimization plot for the tool-acceleration-
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A. GÖK et al.: EFFECTS OF CUTTING PARAMETERS AND TOOL-PATH STRATEGIES ON TOOL ACCELERATION ...
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