A numerical approach on parametric sensitivity analysis for an aeronautic aluminium alloy turning process.
Ijaz, H. ; Zain-ul-abdein, M. ; Saleem, W. 等
1. Introduction
The usage of aluminum alloys like A2024-T351 as structural parts in
aeronautic and avionic industry is very common these days due to its
good strength to weight ratio properties. These types of materials
undergo numerous dry cutting machining processes before taking final
shape [1-2]. These materials experience severe cutting forces during the
machining processes in the manufacturing industry that may affect the
chip formation and work piece distortions [3]. In industry, different
machining processes are used based on machinist models and empirical
studies. High costs of experiments in terms of time, price and
availability of expensive materials demand an alternative strategy in
the form of finite element analysis to estimate them. Hence optimization
of different machining parameters (like cutting speed, feed rate, tool
geometry etc) with the help of finite element analysis attains a value
of prime importance [4-5].
The cutting process in metals may be described as a crack like
entity between the two surfaces i.e. chip and work piece. Two
established theories, damage mechanics and fracture mechanics, may be
employed to study the crack growth behavior in materials. Fracture
mechanics theory established on the basis that a crack like entity
already exists in material and it deals with the propagation of crack
[6]. On the other hand damage mechanics theory not only predicts the
propagation of crack but also simulate the process of crack initiation
[7]. In the present work, Johson-Cook plasticity material model coupled
with damage evolution law is adopted to simulate the crack growth
behaviour between the two surfaces [8]. Johnson-Cook model provides
description of metal material behavior by considering large strains,
high strain-rates and temperature dependent viscoplasticity.
In the present study 2D finite element analysis of turning process
of aluminum alloy A2024-T351 is performed to study the process of chip
formation and different parameters affecting the aforementioned process
using commercially available FE software, Abaqus/Explicit [9]. This
particular finite element simulation study will help to understand the
turning process of aluminum alloy and to optimize the machining
parameters required for the turning process. The authenticity of finite
element analysis is verified by comparing the simulation results with
the available experimental data [10].
This article is organized as follows: in section 2, mathematical
details of employed material model of Johnson-Cook are discussed.
Section 3 contains the details of FE model and simulation results. Then
a comprehensive parametric study is presented and discussed in section
4. Finally some concluding remarks are given in section 5.
2. Material model
The Johnson-Cook material model is adopted in the present study for
the cutting simulation and chip formation phenomenon. If [bar.q] is the
equivalent plastic flow stress then following expression can be written
[8]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)
where A, B and n are material constants for strain hardening; C is
the material constant for strain hardening rate, m is material constant
for thermal softening effect, [T.sub.room] is the reference ambient
temperature and [T.sub.melt] is the melting temperature of the material.
Similarly in the above equation, [bar.[epsilon]] is the equivalent
plastic strain, [??] is the plastic strain rate, [??] is the reference
strain rate. If [??] is the plastic strain at damage initiation then it
can be expressed by following criteria [8]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)
constants that can be found from experiments and P is the pressure
stress [8]. During the analysis, the damage is initiated when a scalar
damage parameter m exceeds 1 and this parameter can be expressed as
[11]:
[omega] = [summation][DELTA][bar.[epsilon]]/[[bar.[epsilon]].sub.0i] (3)
Based on Hillerborg's fracture energy proposal, the energy
[G.sub.f] required to open a unit area of crack may be written as [12]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)
In the above equation L is the characteristic length of element and
[[bar.u].sub.f] is the equivalent plastic displacement at failure and
can be computed by the following equation [13]:
[[bar.u].sub.f] = 2[G.sub.f]/[[sigma].sub.f]. (5)
If E is the modulus of elasticity of material and [upsilon] is the
Poisson ratio then fracture energy Gf for mode I and mode II crack
growth can identified from experiments by the following relation [10]:
[([G.sub.f]).sub.I,II] = (1 - [[upsilon].sup.2]/E)
[([K.sup.2.sub.c]).sub.I,II]. (6)
In the above equation [K.sub.IC] and [K.sub.IIC] are material
constants for mode I and mode II crack growth respectively and termed as
fracture toughness of the material. For A2024-T351, the fracture
toughness values are: [K.sub.IC] = 26 (MPa [square root of m]) and
[K.sub.IIC] = 37 (MPa [square root of m]) [14]. A linear or exponential
damage evolution law can be considered for degradation of material under
applied force. If D is damage variable, following two equations
represent the linear and exponential type of damage evolution law
respectively [14]:
Ls u
D = L[bar.[epsilon]]/[[bar.u].sub.f] = [bar.u]/[[bar.u].sub.f]; (7)
D = 1-exp(-[[integral].sup.[bar.u].sub.0] [bar.Q]/[G.sub.f]
d[bar.u]). (8)
[FIGURE 1 OMITTED]
3. Finite element analysis
2D finite element analysis of turning process is performed using
Abaqus/Explicit [9]. Johnson-Cook material model along with damage
evolution law is available in Abaqus/Explicit. Four node quadrilateral
continuum elements with plane strain assumption (CPE4RT) are used for
coupled temperature-displacement analysis [15].
The geometry of the model and different boundary conditions are
shown in Fig. 1. To optimize the contact conditions between the work
piece and tool, the work piece component is divided into three
partitions. Different partitions of work piece are: 1) chip 2) tool-tip
passage zone and 3) work piece support. To facilitate the chip
formation, the thickness of the tool-tip passage zone should be of the
order of tool edge radius [16]. These three partitions of work piece are
joined together using the tie constraint option available in
Abaqus/Explicit. During the cutting operation tool comes in contact with
the work piece and chip, furthermore chip also makes self contact during
the machining process. A coulomb friction model is employed for
tool-chip-work piece interaction [17-18]. The finite element simulation
requires the identification of different damage parameters [19-21], The
identified Johnson-Cook material parameters used for damage initiation
and damage evolution for A2024-T351 are given in Table 1 [14]. The
different material properties of A2024-T351 are given in Table 2 [14].
In order to authenticate the simulation process, finite element
analysis results will be compared with available experimental data on
turning machining of A2024-T351. The experimental results of cutting
forces against different cutting feeds and velocities are given in Table
3 [10].
In order to authenticate the simulation process, finite element
analysis results will be compared with available experimental data on
turning machining of A2024-T351. The experimental results of cutting
forces against different cutting feeds and velocities are given in Table
3 [10].
In this section 2D finite element analysis of cutting process of
A2024-T351 is performed for a feed rate f = 0.4 mm and friction
coefficient [mu] = 0.15 against velocity Vc = 800 m/min. Fig. 2
represents the reaction force (Fc) obtained from numerical analysis for
cutting speed of 800 m/min. The average cutting force obtained from
numerical results is 943.4 N and is in good agreement with experimental
results. Since the deviation of numerical results from experimental
results is of the order of 3.4% which shows the authenticity of
simulation work. Fig. 3 shows the resultant Von misses stress profile
during the chip formation process.
4. Parameters affecting the cutting process
In the previous section finite element analysis has been performed
on turning simulation for A2024-T351 aluminium alloy and results are
successfully compared with experimental results. After verifying the
simulation results a comprehensive parametric sensitivity analysis
considering different cutting parameters is performed in this section.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
4.1. Effect of cutting speed
The effect of different cutting speeds on the reaction force is
studied in the present section. The values of feed rate f= 0.4 mm and
friction coefficient [mu] = 0.15 are employed to study the effect of
different values of cutting speed. Fig. 4 presents the variation of
cutting force with cutting speed. Although from Fig. 4 a slight
increasing trend is observed but there is not an appreciable difference
in values of cutting force as the cutting speed increases from 200 m/min
to 800 mm/min. Similarly temperature profile at different velocities is
shown in Fig. 5. From Fig. 5, one can note that by increasing the
cutting speed, maximum temperature at the tool-chip interface also
increases. In the present case, maximum temperature increases
approximately from 231[degrees]C for Vc = 200 m/min to 336[degrees]C for
Vc = 800 m/min. Hence selection of cutting speed can be attributed to
total time required to complete a job, machine capability &
accuracy, required surface finish and maximum affordable temperature of
the work piece.
4.2. Effect of feed rate
The effect of feed rate (f) on cutting force is considered in this
section. Fig. 6 shows the results of cutting force vs cutting speed for
two different feed rate values i.e. f = 0.3 & 0.4 and [mu] = 0.15.
The reaction forces obtained from numerical results are also in good
agreement with experimental results, see Table 3 for comparison.
From Fig. 6, it is clear that reaction force decreases considerably
as the feed rate (f) decreases. Similarly, temperature profile at
different feed rate (f is shown in Fig. 7. From Fig. 7, one can note
that maximum nodal temperature increases with the increase in feed rate.
Moreover the difference in rise in temperature at higher velocities is
much higher in comparison of lower velocities. At Vc = 200 m/min, the
maximum temperature varies from 231[degrees]C to 237[degrees]C for f =
0.3 and 0.4 respectively. But on the other hand as the cutting speed
increases from 200 to 800 m/min, the maximum temperature varies from
301[degrees]C to 336[degrees]C for f = 0.3 and 0.4 respectively. Now
selection of final cutting feed depends upon the total time to finish
the work piece since small feed values will take more time to achieve
final dimensions of finished parts. Moreover small feed values also
carry the advantage of less cutting force and temperature values.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
4.3. Effect of friction coefficient
The friction coefficient between tool-chip interface also plays its
role on the resultant cutting force values. The effect of friction
coefficient p on the reaction force is depicted in Fig. 8. In this
figure, results for two feed rates, f = 0.3 & 0.4, are shown. The
results show that the effect of friction coefficient on cutting reaction
force is not that great as its value increased from 0.1 to 0.15 for both
f = 0.3 & 0.4. On the other hand the friction coefficient value
affects the temperature profile appreciably. From Fig. 9, one can
observe that the maximum temperature increases from 258[degrees]C to
289[degrees]C for friction coefficient [mu] values of 0.1 and 0.15
respectively at cutting speed of 400 m/min. similarly this increase in
temperature is from 293[degrees]C to 336[degrees]C for friction
coefficient [mu] values of 0.1 and 0.15 respectively at cutting speed of
800 m/min. Moreover the friction coefficient value depends on the two
cutting surfaces quality i.e. tool and work piece surfaces and direct
control on this cutting parameter it is difficult to attain.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
5. Conclusions
In this article a comprehensive study is conducted on different
parameters that influence the turning process of aluminium alloy using
the finite element analysis. The authenticity of finite element work is
verified by comparing the results with available experimental data. The
effect of four different parameters like cutting speed, feed rate,
friction coefficient and rake angle on resultant reaction force is
studied. The effect of cutting speed and friction coefficient on the
reaction force is not much significant but they appreciably affect the
maximum temperature at the tool-chip interface. On the other hand both
feed rate and rake angle have strong influence not only on cutting
reaction force but also on maximum tool-chip interface temperature. From
the conducted study one can say that these parameters may influence the
total time required to complete the job and the net resultant force
experienced by the tool and work piece. Hence the selection of good
parameters for a particular turning process of aluminium alloy may
depend on the required total time to finish the job and net resultant
forces that work piece and tool can withstand during turning operation.
Finally one can also conclude that finite element analysis may replace
the critical experimental work and help to save precious time and money.
In the present work, a 2D finite element analysis is performed and good
numerical results that are comparable with the experimental results are
obtained. But the same effort will be made in future on 3D finite
element analysis for better and real time analysis of turning process in
metals.
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H. Ijaz, Mechanical Engineering Department, University of Jeddah,
Jeddah, Saudi Arabia, E-mail:
[email protected]
M. Zain-ul-abdein, Mechanical Engineering Department, University of
Jeddah, Jeddah, Saudi Arabia, E-mail:
[email protected]
W. Saleem, Mechanical Engineering Department, University of Jeddah,
Jeddah, Saudi Arabia, E-mail:
[email protected]
M. Asad, Mechanical Engineering Department, University of
Management & Technology, 54770 Lahore, Pakistan,
E-mail:
[email protected]
T. Mabrouki, Ecole Nationale d'Ingenieurs de Tunis (ENIT),
Tunis, E-mail:
[email protected] crossref
http://dx.doi.org/10.5755/j01.mech.22.2.12825
Received July 31, 2015
Accepted March 15, 2016
Table 1
Johnson-Cook material parameters for A2024-T351 [14]
A, MPa B, MPa n C m D1 D2 D3 D4 D5
352 440 0.42 0.0083 1 0.13 0.13 -1.5 0.011 0
Table 2
Work piece and tool properties [14]
Tool
(Tungsten
Physical parameter Work piece (A2024-T351) Carbide)
Density [rho], Kg/[m.sup.3] 2700 11900
Elastic modulus E, Gpa 73 534
Poisson ratio v 0.33 0.22
Specific heat [C.sub.p], [C.sub.p] = 0.557 T + 400
JK[g.sup.-1] [degrees] 877.6
[C.sup.-1]
Thermal conductivity 25 [less than or equal 50
[lambda], W[m.sup.-1] to] T [less than or equal
[C.sup.-1] to] 300: [lambda] = 0.247
T + 114.4 300 [less than
or equal to] T [less than
or equal to]
[T.sub.melt]: [lambda] =
-0.125 T + 226.0
Expansion [alpha], [alpha] + 8.9 x [10.sup.- X
[micro][mm.sup.-1] 3] T + 22.2
[degrees][C.sup.-1]
[T.sub.melt], [degrees]C 520 X
[T.sub.room], [degrees]C 25 25
Table 3
Experimental results [10]
Cutting force [F.sub.c], N
Cutting Speed
[V.sub.c], m/min
Feed f, mm 200 400 800
0.3 778 N 769 N 769 N
0.4 988 N 978 N 976 N
