On different FE-based models to simulate cutting operation of titanium alloy (Ti-6Al-4V)/Skirtingu baigtiniu elementu modeliu taikymas titano lydinio Ti-6Al-4V pjovimo operacijoms.
Zhang, Y. ; Umbrello, D. ; Mabrouki, T. 等
1. Introduction
As it is known, finite element (FE) method provides precise
information concerning variables like plastic strain, strain rate or
stress evolutions during toolworkpiece interaction, which are difficult
to measure experimentally. After the early FE model [1], many research
works about metal cutting process have been performed. Wherein, Mabrouki
et al. [2] studied the chip formation and cutting force for dry cutting
with thermal physical coupled damage model, they also considered the
grain microstructure in the cutting model [3]. Filice et al. [4]
developed a wear model for the orthogonal cutting using uncoated carbide
tools. Outeiro et al. [5] predicted the residual stresses in the cutting
process, in particular. Finally, Umbrello et al. [6] incorporated the
microstructure transformation for predicting residual stresses.
With these numerical methods, a general understanding of chip
formation process can be improved. However, the effectiveness of these
models depends, to a large extent, on how accurate are the models used
to describe the metal cutting process and also the quality of the input
data used in such models, especially when different commercial codes are
used to develop the cutting model.
In recent years, researchers tried to find adequate FE-models and
simulation parameters for different FE software and metal materials.
Deshayes et al. [7] have carried out, based on a FE method comparison, a
study dealing with the cutting of AISI4340 steel alloy with ADVANTEDGE
and ABAQUS/EXPLICIT. Similar cutting simulations, with the two cited
software, were also performed by Arrazola et al. [8] in the case of
AISI4140. Soriano et al. [9] have also presented a comparison of 3D
machining models developed under commercially available FE software
ABAQUS/EXPLICIT, ADVANTEDGE and DEFORM3D for the machined material
Inconel 718.
Considering all above, it is necessary to conduct a comparison
study to evaluate the effectiveness of current predictive models not
only regarding forces, temperature distribution, chip compression and
morphology, but also parameters related with the integrity/quality of
the machined surface, such as residual stress, etc.
2. Aim of study
Benchmark studies are commonly carried out in a manner that all
conditions are kept equal for all the models of interest. Nevertheless,
it has been proved [10] that for machining process it not possible to
conduct a benchmark as usually done for the other manufacturing
processes. In fact, it was shown that each model results to be properly
predictive only if calibrated in the own simulation strategy. A specific
combination of material and damage models furnishes good numerical
results when these models are implemented in the same FE-code used for
calibrating material constants [10]. This happens since mechanical
theories, especially for damage models, implemented in FE-codes are
different as well as are different the thermal models applied for
describing the temperature and its evolution.
In this context, the aim of the study is to develop and calibrate
two different simulation models and apply them to predict the most
significant cutting parameters, comparing the different predictive
capabilities. Thus, for each FE model the most appropriated combination
of flow stress model, damage criterion and thermal model has been
utilized. Obviously, it is worth pointing out that the proposed flow
stress models, although dissimilar in their structure and for material
constants, describe equivalent material behaviour. In such
circumstances, the study is performed in the optimum conditions for the
two different simulation models. In addition, it also permits to
highlight the main problems related to current simulations supporting
metal cutting researchers for understanding the cutting process and its
influence on the material.
This paper is composed of three main parts: after a brief
description concerning the material properties of Ti alloy, the
numerical model setups in ABAQUS/EXPLICIT (v6.7) and DEFORM/IMPLICIT-2D
(v10.1) are described. Finally, the numerical and experimental results
are detailed, discussed and overall conclusions are pointed out.
3. Material properties
The workpiece material selected for this study is the Titanium
alloy Ti-6Al-4V, which has good specific strength, toughness and
corrosion resistance making it attractive for aerospace applications,
surgical implants, etc. Consequently, mechanical structure components
for these applications have precise requirements in terms of physical,
chemical properties [11] (Table 1), and thermo properties [12] (Fig. 1).
[FIGURE 1 OMITTED]
4. Finite element modelling
In order to build a common FE-model for chip formation process
during orthogonal cutting process, ABAQUS/EXPLICIT-2D and
DEFORM/IMPLICIT-2D software have been adopted.
[FIGURE 2 OMITTED]
4.1. ABAQUS/EXPLICIT(tm): Model features
The software ABAQUS/EXPLICIT (V6.7) has been used to set up a
FE-model in two-dimensions (2D) as presented in Fig. 2. To control the
contact between tool and workpiece during cutting simulation, four parts
are participated for the cutting model (Fig. 2) [13]. The work-piece is
allowed to move with the cutting speed, while the tool is fixed on its
top and right sides.
4.1.1. Material constitutive model
Concerning the material behavior of Ti-6Al-4V, the Johnson-Cook
(J-C) constitutive model [14] is implemented in ABAQUS and is expressed
by the following equation of the equivalent stress:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
The values of coefficients A, B, C, n and m for the Ti-6Al-4V alloy
are reported in Table 2 from the work of [13].
4.1.2. Chip formation criterion
In the present model, the adopted numerical methodology is based on
the fracture energy as an intrinsic material parameter for controlling
damage evolution criterion after damage initiation.
Damage initiation
The strain cumulative damage law is employed for the damage
initiation:
[omega] = [SIGMA] [DELTA][bar.[epsilon]]/ [[bar.[epsilon]].sub.0i],
(2)
where [DELTA][bar.[epsilon]] is the equivalent plastic strain
increment in one loading increment and [[bar.[epsilon]].sub.0i] is the
equivalent plastic strain is used for determining the damage initiation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
The constant parameters for Eq. (3) are from [13]. Damage
initiation is assumed to be activated when [omega] = 1.
Damage evolution
The evolution of damage is based on the concept of the
Hillerborg's fracture energy [15, 16], which is presented as a
stress-displacement response after damage initiation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where L is the characteristic length presented by the square root
of the integration point element area. The linear and exponential damage
evolutions are adopted part 3 and part 2 respectively [13]. For plane
strain condition, the adopted Gf can be deduced by:
[G.sub.f] = [K.sup.2.sub.C] (1 -[v.sup.2])/E, (5)
where [K.sub.C] is the fracture toughness [11].
Moreover, the classic Zorev's [17] stick-slip friction model
is implemented to simulate frictional contact between chip and tool with
a constant friction coefficient [13]. Finally, the thermo-physical
properties of both cutting tool and workpiece are given in Table 2. The
contact and damage data can be obtained from [13].
4.2. DEFORM/IMPLICIT: Model features
Parallel to the cutting simulations performed with ABAQUS, other FE
based simulations were carried out using DEFORM2D, which makes use of an
implicit Lagrange formulation. A plane strain coupled thermomechanical
analysis is performed in orthogonal cutting conditions. The workpiece is
meshed with isoparametric quadrilateral elements and modelled as
elastic-viscoplastic, while the tool is modelled as rigid.
The material behaviour for Ti-6Al-4V is modelled with the flow
stress developed by Scientific Forming Technologies Corporation (SFTC)
based on the works in [18, 19]. It is important to highlight that such
flow stress exhibit similar behaviour for Ti-6Al-4V alloy of the J-C
model implemented in ABAQUS.
4.2.1. Constitutive equation
An elastic-visco-plastic material model with Von Mises yield
criterion and associated flow rule is used. In the deformation zone, the
following equation is given:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where: [[??].sub.ij] strain rate components; [[sigma]'.sub.ij]
is the deviatoric stress and [bar.[sigma]] and [??] are effective stress
and strain rate.
4.2.2. Chip formation criterion
The chip segmentation is a consequence of the fracture process that
takes place during chip formation. In this research, Cockroft and
Latham's fracture criterion (CLFC) [20] (Eq. (7)) were adopted to
present the effect of the stress on the chip segmentation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
Where: [[epsilon].sub.f] is the effective strain; a1 principal
stress and C the material constant representing resistance to failure
(sometimes called "damage value"). CLFC means that when the
integral of the left term (applied state) in Eq. (7) reaches the value
of C (material state), the fracture occurs and the chip segmentation
starts. Usually, the adequate C value is determined by numerical
calibration on available experimental data. In this work, C is set equal
to 240 MPa as found by SFTC through the above mentioned calibration.
[FIGURE 3 OMITTED]
In Fig. 3, the mechanical and thermal boundary conditions of the 2D
FE model are schematically shown. As far as friction modeling is
concerned, a simple model based on the constant shear hypothesis is
implemented with the shear factor kept at m = 0.6, considering as
dominant the phenomena appearing in the sticking zone, in which this
model is effective.
This value is chosen on the basis of an iterative procedure aimed
at reducing the errors on the predictions of cutting forces, chip
morphology parameters and temperature distribution as well as thermal
steady-state along primary and secondary shear zones.
5. Experimental design
To evaluate the robustness of the two simulation models, several
numerical tests are taken into account. In particular, the numerical
values obtained by means of FE simulation, in terms of cutting force
([F.sub.c]), thrust force ([F.sub.t]), cheap peak ([h.sub.1]), chip
valley ([h.sub.2]), chip pitch ([L.sub.1]), chip compression ratio
(CCR), maximum temperature on workpiece ([T.sub.W]) and maximum
temperature over the tool rake surface ([T.sub.T]), are considered and
compared with those experimentally available in literature [10, 18, 21,
22]. Furthermore, numerical residual stress profiles in circumferential
direction are numerically extracted from the machined surface and
sub-surface and compared with those experimentally measured by X-Ray
Diffraction (XRD) technique [10]. Schematically speaking, the available
experimental data are divided into four groups.
The first group is mainly focused on studying the physical
phenomenon accompanying cutting process with positive rake angle of the
cutting tool [18]. The second group concerns the cutting with negative
rake angle [21], and the third group aims to investigate the effect of
the tool wear on the residual stress distribution after machining [22].
Finally, the fourth group focuses on studying the influence of the
[V.sub.C] variation on the residual stress evolution considering a
constant tool flank wear [10]. The cutting conditions are summarized in
Table 3.
6. Results and discussions
6.1. Cutting force evolution, chip morphology and temperature
Table 4 shows the computed results based on both ABAQUS and DEFORM
simulations as far as cutting forces, chip morphology and temperature
are regarded. Results concerning principal cutting force allow
establishing that the two codes allow a good prediction regarding
experimental ones although lowest errors can be obtained by using
ABAQUS. In contrast, DEFORM allows to better describe the evolution of
thrust forces, even if it is possible to compare the numerical values
with only one experimental evidence (Group IV). Furthermore, DEFORM
permits to better describe the evolution of both [F.sub.c] and [F.sub.t]
instead of ABAQUS, since with increasing of the [V.sub.C], both the
cutting forces decrease (Groups I and II). It is worth pointing out that
this well-known behaviour is not observed neither from DEFORM as well as
from ABAQUS when Group 4 is considered. In fact, both the FE codes
exhibit higher cutting forces when [V.sub.C] rises.
Chip morphology is analysed in terms of chip segment shape (valley,
pick and pitch), as shown in Fig. 4. Numerical results are compared with
experimental ones for groups I, II and IV ([V.sub.C] = 90 m/min), while
the simulation results from group III and the other case of Group IV can
be used for qualitative comparison. Analyzing the errors obtained in the
predictions of the chip morphology (Table 4), it is possible to state
that from a numerical point of view, ABAQUS provided the lowest errors
in most of the cases.
[FIGURE 4 OMITTED]
Regarding the chip formation process, it is worth underlining that
in ABAQUS the chip segmentation is the result of a thermal softening
state coupled with damage degradation. Moreover, the element deletion is
available only in the sacrificial zone, while the other part, which is
not deleted, becomes part of the chip. In DEFORM software, the chip
formation is obtained by implementing Cockroft and Latham's
criterion, thus allowing to describe the effect of tensile stress on the
chip segmentation during orthogonal cutting. In addition, in DEFORM, the
element deletion feature is also applied in these numerical simula-
tions to better describe the chip fracture instead of the remeshing
methodology. Finally, for all the investigated cases, both the maximum
temperature range on both tool and workpiece are collected. As it can be
observed, the results are almost similar although those found in DEFORM
exhibits always higher values of about 50 - 100[degrees]C compared to
those revealed in ABAQUS. Such discrepancy is related to the thermal
models used in the cited FE codes as better illustrate in the next
paragraph on which the influence of tool wear on thermal field and
temperature distribution is investigated.
6.2. Temperature distribution due to tool wear
Two numerical comparisons were done in order to highlight the
evolution of different outputs computed by ABAQUS and DEFORM software:
(i) temperatures comparison on machined surface and subsurface near the
tool tip for different flank wear; (ii) Temperatures distribution along
the primary and secondary shear zones and their maximum values.
To analyze the influence of tool wear on temperature distribution
beneath the machined surface, the flank wear size of cutting tool is
considered as an initial state and kept constant during the cutting
simulation. The tools' geometry shapes with flank wear are
illustrated in Fig. 5.
[FIGURE 5 OMITTED]
Fig. 5 shows that both DEFORM and ABAQUS predict similar
temperature values on the machined surface. Furthermore, for a given
code numerical results present a temperature gradient about 90[degrees]C
for the two flank wear lengths at the generated surface. Therefore, both
DEFORM and ABAQUS take into account the heat generated along the flank
face/workpiece interface due to modelled flank wear. In contrast, there
is some discrepancy in temperature prediction below the machined surface
(Fig. 5) since for both modelled tool flank wears, DEFORM shows higher
temperature than ABAQUS. The reason is related to the different heat
global coefficient and interface thermal model adopted and implemented
in the two used software. Moreover, the difference is also due to the
different description of the movements.
[FIGURE 6 OMITTED]
In addition, the temperature distribution in the whole cutting
model is presented in Fig. 6. It can be noted that there is a
disagreement between ABAQUS and DEFORM. Also, it is underlined that a
non-concordance in the chip morphologies. Indeed, the chip segmentation
morphology obtained by ABAQUS is the result of a thermal softening state
coupled with damage degradation. The temperature given by DEFORM
modelling is higher at the secondary shear zone and this is due to the
fact that the contact is considered as perfect at tool-chip interface.
Besides both DEFORM and ABAQUS show a
maximum temperature increase when tool with higher flank wear is
used. Except these similarities between the two software, DEFORM shows
higher maximum temperatures in both tool and chip. The reason is once
again related to the different formulation, interface thermal model and
heat global exchange coefficient at the tool/chip interface (the low
value of heat exchange coefficient at the tool/chip interface directly
leads to the temperature discontinuity at the rake face for ABAQUS,
which is assumed that the non-perfect contact condition is considered
between tool chip interface under simulation test).
6.3. Residual stress distribution considering tool wear
To consider the effect of successive cutting sequences on residual
stress distribution, the physical state from the first cut is saved and
used as initial condition for the second one. Other cutting conditions
of the second cut are the same as those of the first one. In order to
predict residual stress based on ABAQUS software, three unloading steps
were implemented at the end of each cut in this study:
1. release of the cutting forces;
2. release of the clamping forces;
3. release of the workpiece to the room temperature.
After external force release and cooling down to room temperature,
the final residual stress distribution on the workpiece is shown in Fig.
7.
[FIGURE 7 OMITTED]
The stresses in Region II are selected to evaluate the residual
stresses, and the predicted residual stresses should be also averaged
over the same volume and the mean value should be taken. The oscillated
residual stresses caused by the segmented chip are observed on the
machined surface, which present the microstructure of the machined
surface. It should be mentioned that the residual stress is extracted
from element integration point. Consequently, the stress on the machined
surface is located at the centre of the first layer element (4 Lim below
the machined surface), and the stresses are averaged along 2-3 mm in the
circumferential direction after their calculation in element integration
points. Vice versa, as far as DEFORM procedure since an automatic method
for residual stress collection is not yet implemented in SFTC-DEFORM-2D
V.10, the following procedure was employed:
1. for several time steps, the tool was released from the machined
surface (unloading phase) and the workpiece was cooled down to the room
temperature;
2. residual stress profiles at several locations (coincident to
Region II, Fig. 7.) of the machined surface were collected and the
average values were calculated, as described in the work of Liu and Guo
[23].
[FIGURE 8 OMITTED]
Fig. 8 shows the effect of flank wear length on circumferential
residual stress distribution beneath the newly machined surface. As
general trends, both the software highlight that when the flank wear was
increased from 0.03 to 0.2 mm, the surface residual stress towards the
tensile region. This is due to the higher magnitude of temperature
generated along flank face/workpiece interface.
Moreover, both DEFORM and ABAQUS show that the maximum compressive
residual stress as well as the beneficial depth decreases with
increasing of flank wear. In addition, the distance where maximum
compressive residual stress is located seems to be not affected by flank
wear. However, both the software show some gap between experiments and
simulations when considering the influence of first cut. The reason of
such discrepancy should be related to firstly the material flow stresses
used in both ABAQUS and DEFORM which are not suitable for describing
pertinently material states. Secondly, It is worth pointing out that in
both computations, the residual stresses due to phase transformation
were neglected and, especially in the case of DEFORM (temperature near
to phase transformation effect), such assumption is not properly
corrected.
6.4. Cutting speed effect on residual stress distribution
considering a fixed tool wear
To study the influence on circumferential residual stress
distribution on the machined surface, different cutting speeds varying
from [V.sub.C] = 55 m/min to [V.sub.C] = 90 m/min with constant flank
wear are adopted in Fig. 9.
[FIGURE 9 OMITTED]
It can be noted that, the distribution of the compressive RS
computed by ABAQUS is still mainly localized within 60 Lim, while the
simulation result from DEFORM extends to 200 Lim, which shows an
acceptable numerical RS prediction compared to ABAQUS. However, both two
codes illustrate that the maximum compressive RS as well as the
beneficial depth increases with increasing of the cutting speed, which
is in contrast with the experimental facts. It implies that the contact
thermal properties between tool/machined surface still need to improve
for both codes mentioned above.
6.5. Effectiveness and Robustness of FE codes: comparison and
overall
Taking into account what it is discussed in the previous paragraphs
and in order to complete the assessment of the two described simulation
strategies, it is useful at this point to draw an overall comparison
between the two used codes for cutting modeling. In order to perform
detailed simulations and precise control for the mesh and the boundary
conditions, then the software package ABAQUS seems to be adequate.
However, if an efficient, easy to setup machining simulation is needed,
and then the software package DEFORM seems to be satisfactory. This
package allows quick setup of simulations and provides the built in
modules for material library, tool and workpiece geometries and process
parameters.
7. Conclusions
In this study, a comparison of four groups of simulations performed
with two different 2D FE models is presented in the case of Ti-6Al-4V
alloy cutting. The computed results were compared with experimental
ones. Some observations concerning the results obtained based on the
using of ABAQUS and DEFORM can be pointed following:
1. The serrated chip formation can be modelled using the mentioned
two codes with appropriate material and damage models.
2. The temperature distribution at the tool-chipworkpiece
interfaces displays that the segmentation is the result of a thermal
softening state or/and the coexisting fracture phenomenon, among other
phenomena.
3. The simulation results of temperature and residual stress show
the similar tendency for two kinds of models, even though there is some
gap between them due to the optimal conditions for each of them
(material laws, damage criteria, etc.
4. Potentially, these two simulated models can be exploited to
perform other numerical comparisons with both commercial and in-house
codes.
10.5755/j01.mech.19.3.4656
Received December 06, 2011 Accepted May 15, 2013
Acknowledgments
The authors of LaMCoS laboratory would like to acknowledge the
financial support of China Scholarship Council (CSC), and National
Natural Science Foundation of China (Microscale grinding and micro
milling-grinding compound machining process, support No. 52075064).
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Y. Zhang, D. Umbrello, T. Mabrouki, S. Rizzuti, D. Nelias, Y. Gong
Y. Zhang *, D. Umbrello **, T. Mabrouki *, S. Rizzuti ***, D.
Nelias *, Y. Gong ****
* Universite de Lyon, CNRS, INSA-Lyon, LaMCoS, UMR5259, F69621,
France, E-mail:
[email protected]
** University of Calabria, Department of Mechanical Engineering,
87036 Rende (CS), Italy, E-mail:
[email protected]
*** Politecnico di Torino, DISPEA, 10129 Torino, Italy, E-mail:
[email protected]
**** Northeastern University, School of Mechanical Engineering
& Automation, Shenyang, 110819, China, E-mail:
[email protected]
Table 1
Physical and chemical properties of Ti-6Al-4V [11]
Al, % C, % H, % Fe, %
5.5 - 6.8 [less than or [less than or [less than or
equal to] 0.08 equal to] 0.015 equal to] 0.4
Al, % N, % O, % Ti, %
5.5 - 6.8 [less than or [less than or 87.7 - 91.0
equal to] 0.3 equal to] 0.2
E,
Al, % V, % S, % GPa V
5.5 - 6.8 3.5 - 4.5 < 0.05 110 0.3
[rho] [C.sub.p], k, W/m/
Al, % kg/[m.sup.3] J/kg/[degrees]C [degrees]C
5.5 - 6.8 4430 Fig. 1., a Fig. 1., b
Table 2
Thermo-physical parameters for the ABAQUS FE model
Parameters Value
A, MPa 1098
Plastic Johnson-Cook Law B, MPa 1092
n 0.93
C 0.014
m 1.1
Proprieties Workpiece Tool (P20)
Density [rho], kg [m.sup.-3] 4430 15700
Elasticity E, GPa 210 705
Poisson's ratio v 0.33 0.23
Material Inelastic heat fraction 0.9 X
[beta]
Conductivity k, W [m.sup.-1] See Fig. 1 24
[degrees][C.sup.-1]
Specific heat c, J See Fig. 1 178
[Kg.sup.-1] [degrees]
[C.sup.-1]
Expansion [a.sub.d], um 9 5
[m.sup.-1] [degrees]
[C.sup.-1]
[T.sub.melt,] [degrees]C 1630 X
[T.sub.room,] [degrees]C 20 20
Table 3
Process parameters employed in the study
Group Group
Cutting parameters I [18] II [21]
Cutting speed Vc, m/min 120 180
Uncut chip thickness, mm 0.127 0.1
Depth of cut, mm 2.54 2
Cutting edge radius, [micro]m 30 20
Rake angle, deg 15 -4
Clearance angle, deg 6 7
Flank wear, mm - -
Experimental Results
Force Cutting force 559 548
[F.sub.c], N
Thrust force - -
[F.sub.t], N
Chip peak [h.sub.1], 165 131
[micro]m
Chip mor- Chip valley [h.sub.2], 46 62
phology [micro]m
Chip pitch [L.sub.1], 140 100
[micro]m
Chip compression 1.30 1.31
ratio: CCR
Group III [22]
Cutting parameters III-1 III-2
Cutting speed Vc, m/min 320 320
Uncut chip thickness, mm 0.1 0.1
Depth of cut, mm 1 1
Cutting edge radius, [micro]m sharp sharp
Rake angle, deg 5 5
Clearance angle, deg 8 8
Flank wear, mm 0.03 0.2
Experimental Results
Force Cutting force - -
[F.sub.c], N
Thrust force - -
[F.sub.t], N
Chip peak [h.sub.1], - -
[micro]m
Chip mor- Chip valley [h.sub.2], - -
phology [micro]m
Chip pitch [L.sub.1], - -
[micro]m
Chip compression - -
ratio: CCR
Group IV [10]
Cutting parameters IV-1 IV-2
Cutting speed Vc, m/min 55 90
Uncut chip thickness, mm 0.15 0.15
Depth of cut, mm 4 4
Cutting edge radius, [micro]m 30 30
Rake angle, deg 6 6
Clearance angle, deg 7 7
Flank wear, mm 0.14 0.14
Experimental Results
Force Cutting force 748
[F.sub.c], N
Thrust force 612
[F.sub.t], N
Chip peak [h.sub.1], 227
[micro]m
Chip mor- Chip valley [h.sub.2], 117
phology [micro]m
Chip pitch [L.sub.1], 161
[micro]m
Chip compression 1.51
ratio: CCR
Table 4
Numerical effects obtained after the sensitivity analysis with
two FE - Codes
Simulation Test Cutting force
[F.sub.c] [F.sub.t]
GI_Vc_120 541.3 39.0
Error with experiment, % -3.17 -
ABAQUS GII_Vc_180 580.0 164.5
Error with experiment, % 5.8 -
GIII_Vc Wear_0.03 166.5 21.0
_320 Wear_0.2 186.9 40.4
GIV [V.sub.B] Vc_55 947 208
_0.14 Error with 30 -66
experiment, %
Vc_ 90 1022 305
GI_Vc_120 508.9 305.4
Error with experiment, % -8.96 -
DEFORM GII_Vc_180 501.1 270.9
Error with experiment, % -8.56 -
GIII_Vc Wear_0.03 228 101
_320 Wear_0.2 267 111
GIV_[V.sub.B] Vc_55 844 380
_0.14 Error with 12.8 -37.9
experiment, %
Vc_ 90 876 392
Chip morphology
Simulation Test parameters
[h.sub.1] [h.sub.2]
GI_Vc_120 161.5 48.0
Error with experiment, % -2.12 4.35
ABAQUS GII_Vc_180 132.0 77.0
Error with experiment, % 0.76 24.19
GIII_Vc Wear_0.03 131.2 34.0
_320 Wear_0.2 131.7 31.2
GIV [V.sub.B] Vc_55 186.9 69
_0.14 Error with -17.6 -41.0
experiment, %
Vc_ 90 186.9 51.4
GI_Vc_120 152 42
Error with experiment, % -7.88 -8.70
DEFORM GII_Vc_180 155.5 47.8
Error with experiment, % 18.70 -22.90
GIII_Vc Wear_0.03 157 34.1
_320 Wear_0.2 190.5 54
GIV_[V.sub.B] Vc_55 213 55
_0.14 Error with -6 -50
experiment, %
Vc_ 90 189 69
Chip morphology
Simulation Test parameters
[L.sub.1] CCR
GI_Vc_120 133.0 1.27
Error with experiment, % -5 -2.12
ABAQUS GII_Vc_180 96 1.32
Error with experiment, % -4 0.76
GIII_Vc Wear_0.03 96.0 1.31
_320 Wear_0.2 96.0 1.32
GIV [V.sub.B] Vc_55 136.1 1.24
_0.14 Error with -15.5 -17.44
experiment, %
Vc_ 90 136.1 1.25
GI_Vc_120 133 1.20
Error with experiment, % -5.00 -7.69
DEFORM GII_Vc_180 121.0 1.55
Error with experiment, % 21 18.32
GIII_Vc Wear_0.03 214.5 1.57
_320 Wear_0.2 221.5 1.905
GIV_[V.sub.B] Vc_55 176 1.42
_0.14 Error with 9.3 -5.9
experiment, %
Vc_ 90 157 1.26
Work- Tool
Simulation Test
[[theta]. [[theta].
sub.WT] sub.TT]
GI_Vc_120 591-689 486-631
Error with experiment, % - -
ABAQUS GII_Vc_180 754-919 462-611
Error with experiment, % - -
GIII_Vc Wear_0.03 631-693 514-580
_320 Wear_0.2 629-699 541-603
GIV [V.sub.B] Vc_55 466-523 263-321
_0.14 Error with - -
experiment, %
Vc_ 90 546-585 294-379
GI_Vc_120 678-781 621-707
Error with experiment, % - -
DEFORM GII_Vc_180 820-934 672-766
Error with experiment, % - -
GIII_Vc Wear_0.03 805-918 793-903
_320 Wear_0.2 819-933 817-932
GIV_[V.sub.B] Vc_55 570-725 459-580
_0.14 Error with - -
experiment, %
Vc_ 90 584-750 504-595
[F.sub.c], N: Cutting torce.
[h.sub.1], [micro]m: Chip peak.
[[theta].sub.WT] [degrees]C: Maximum temperature on workpiece
[F.sub.t] N: Thrust force.
[h.sub.2], um: Chip valley.
CCR: Chip compression ratio.
[L.sub.1], [micro]m: chip pitch.
[[theta].sub.TT] [degrees]C: Maximum temperature over
tool rake surface.
