Simulation and experiment study on cutting force of coated tool milling natural marble.
Guangyu, Yan ; Yuhou, Wu ; Dehong, Zhao 等
1. Introduction
Natural marble is a typical brittle material that is easy to
generate incontrollable brittle fracture in practical machining; it
intensifies the tool wear and decreases processing efficiency [1]. The
milling of natural marble is a complicated brittle deformation process
and the whole process refers to thermodynamics, physics and so on. The
flow stress characteristic of machining process is affected by a lot of
factors. As a result, the research of natural marble requires a
comprehensive research on the whole cutting process. With the rapid
development of manufacturing industry, the traditional experimental
method based on a large number of cutting experiment data can not
satisfy the need in the field of difficult-to-machine materials [2].
Therefore, the primary work of studying characteristics of material
cutting is designing a precise and reliable flow stress cutting mode.
The modern highly developed computer technology ensures wide use of the
finite element simulation software in the field of metal cutting. The
finite element simulation has become a very effective method in the
research of cutting characteristics and optimization process [3].
However, the simulation study on natural marble cutting characteristic
has attracted little attention. There is few study on cutting force
simulation in the present domestic stone processing field of our
country. Yuan Juntang took the simulation of aluminum alloy cutting
process by Deform-3D and study change rule of the milling force [4].
Cong Ming carried out the simulation research of drilling process of
engine cylinder block through Deform-3D and optimized the cutting
parameters.
Cutting force is a main reason of tool wear and workpiece brittle
fracture during the high speed milling process of natural marble.
Meanwhile, cutting force is an important composition of natural
marble's cutting characteristics [5]; it is mainly affected by the
machining parameters, which can be optimized by accurate prediction and
thus help increase processing efficiency and save the processing cost.
Natural marble milling process was simulated based on Deform-3D in this
paper; the milling force data obtained by simulation and experiment were
compared. The cutting parameters were optimized when coated tools
milling natural marble and an effective analysis on mechanism of milling
force was established.
2. Establishment of milling finite element model
2.1. Establishment of material properties
White marble is a kind of natural marble; it is mainly composed of
calcium carbonate (CaCO3). The white marble has a close texture and high
compressive strength. Secondary development of Deform Material Library
was carried out based on basic material properties due to Deform-3D does
not include the stone material whereas it includes stress, strain rate
and temperature. This paper found out the elastic modulus, Poisson
ratio, thermal conductivity and specific heat capacity of materials and
coated tools. The basic attributes [6], [7] of workpiece and tool
material are shown in Table 1.
Natural marble milling process is a complicated brittle fracture
process including little plastic cutting process. The flow stress is the
nonlinear function of temperature, strain and strain rate. Equation (1)
shows the stress and strain mechanical model in Deform Material Library
which is commonly used material constitutive relation model.
[bar.[sigma]] represents equivalent stress of work piece,
[bar.[epsilon]] represents equivalent strain, [??] represents strain
rate and T represents temperature.
[bar.[sigma]] = [bar.[sigma]] ([bar.[epsilon]], [??], T), (1)
where [bar.[sigma]]--equivalent stress of work piece, MPa;
[bar.[epsilon]]--equivalent strain; [??]--strain rate; T--temperature,
[degrees]C.
The stress-strain curve7 (as shown in Fig. 1) of natural marble was
drawn. According to the corresponding stress under different temperature
and strain values filled in the material defined module in Deform. The
ball endmill material is tungsten carbide (WC) and coating material is
titanium carbonitride (TiCN) from tool material library of Deform. The
parameters of two kinds of materials in the material property module are
added and then finish the definition of material.
[FIGURE 1 OMITTED]
2.2. Establishment of milling model and meshing
Milling force prediction has important significance on the research
of natural marble milling characteristics. The change characteristic of
coated tool high speed under different cutting parameters was mainly
studied in the simulation. The mechanism of the milling force was set up
then. First, establishment of milling model and meshing of milling
process [8] of coated tool should be carried on by Deform pretreatment
module. Fx is the cutting force of feed direction, Fy is the cutting
force of tangential direction, Fz is the cutting force of axial
direction. The geometric parameter of cutting tools: helix angle
([beta]) is 45[degrees], first clearance angle ([[alpha].sub.1]) is
10[degrees], second clearance angle ([[alpha].sub.2]) is 15[degrees],
inclination angle ([lambda]) is 14[degrees] and diameter (d) is 6 mm.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
The four nodes tetrahedron element was used in the meshing of
natural marble and coated tool in this paper. The four nodes element has
the characteristics of simple collection features and it is one of the
most basic elements in the finite element analysis. As Fig. 2 shows: the
milling force curve of normal size of four nodes tetrahedron element is
not accurate, it can not illustrate the relation between stress and
stain precisely, the difference of value is big and it has few numerical
points, so the element division of processing area needs a proper
encryption [9] (as Fig. 3 shows). There are 45406 elements and 8042
polyhedrons in worpiece. The ratio of normal part and encryption part is
5:1. Fig. 3 shows the geometric model of ball endmill and natural marble
created by Solidworks 3D modeling software.
The boundary conditions of milling process were concise; all the
surfaces of workpiece were set to a fixed form. Figure 4 shows the
detailed settings of motion parameters of cutting tool and boundary
conditions in the module of pretreatment. Spindle speed, feed speed and
cutting depth as three main influencing factors on cutting parameters
and it also restrict dynamic change of milling force in natural marble
milling.
3. Analysis on the results of the simulation and experiment
3.1. Experiment arrangement
The milling equipment in the experiment was the irregularity stone
turn-milling machining center (HTM50200). Dry cutting was used in the
test. Kistler dynamometer system (as shown in Fig. 5) was used for
acquiring and analyzing on milling force of natural marble. The
principle of measurement is shown in Fig. 6. The Kistler dynamometer can
measure three-component cutting force Fx, Fy and Fz.
3.2. Analysis on the experiment and simulation curve
In order to verify the accuracy of Deform-3D simulation on cutting
force of natural marble, comparative analysis of force curve by
practical machining and simulation was carried out. The experiment and
simulation were conducted under the same machining parameters, which is
the same cutting length, 75 mm and the same cut step distance between
two cutting path, 2 mm. Fig. 7 and Fig. 8 illustrate the cutting force
curve obtained by experiment and the cutting simulation after smooth
dealing respectively. The numerical cutting force obtained from the
experiment and simulation was the average cutting force calculated from
the steady part of the cutting force curve [10].
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
According to the cutting curve in Fig. 7 and Fig. 8, the cutting
force values of coated tools fluctuate within a certain range. The
images show the cyclical fluctuations of cutting force between the
minimum and maximum values and a gradual decline appears because of the
phenomenon of milling blade cut in and out during the machining process.
In terms of cutting mechanism, cutting force reaches to the yield limit
of the workpiece materials due to the impact and friction [11], the
surface material is stripped under the effect of brittle fracture. On
one hand, the load on the natural marble is dispersed into many micro
fields. Because of the actual contact area is less than theory contact
area, each micro-bulge will bear more loads and then abrupt change
occurs to cutting force. On the other hand, due to natural marble
belongs to hard-brittle materials, most of chips are powder under the
joint effect of friction and impact during milling process, the material
removal rate is fast, so the change of force is fast-varying.
Furthermore, there are a small number of maximum points and catastrophe
points in the simulation force curve. This is because that in the
pretreatment process, although using grid partition method partly, its
main principle still belongs to adaptive partition and some grid
division precision is lower, leading to calculation error, during the
process of calculating cutting force by Deform-3D. Therefore, in the
process of calculating the average force, the extreme point and cutting
force catastrophe points should be removed. Orthogonal simulation scheme
and results are shown in Table 2.
[FIGURE 8 OMITTED]
Cutting force values obtained from simulation and experiment are
compared in Table 2. It can be seen that a small number of force values
obtained from the experiment and simulation have shown big difference.
This is because that certain difference exists between actual machining
environment and ideal conditions in the simulation and a few errors
arise from data transmission. The average error between experimental
value and simulation value is within 10%, the overall distribution of
simulation tallies with the actual value [12], indicating that the
predict method of cutting force of natural marble based on Deform-3D is
reliable in terms of the curve shape and the values of the cutting
force.
3.3. Analysis on the effect of parameters on milling force
In order to study the characteristics of milling force further, the
influence mechanism of different cutting parameters on cutting force
should be analyzed in this paper. Figure 9 shows the influence curves of
cutting parameters on cutting force.
As shown in Fig. 9, the simulative cutting force of natural marble
has a tendency to decrease along with the increase of spindle speed,
where the Fx and Fy change are obvious. It is because that the cutting
speed increases along with the increases of spindle speed. The contact
time of cutting edge and workpiece decreases in unit time. Due to the
lower thermal conductivity of natural marble, the heat quantity
generated from the increased cutting speed can not spill out in time and
lead to partly high temperature of natural marble surface and reduces
the friction coefficient, softening materials and then reduces the
cutting force [13].
In the initial changing stages of spindle speed, the cutting force
has an obvious downward trend that indicates the softening effect of
material at high temperature is stronger than other factors. When the
spindle speed changes from 3000 r [min.sup.-1] to 5000 r [min.sup.-1],
the downward trend slows down and gradually stays almost unchanged. It
is the work hardening phenomenon appears and increases the surface
hardness [14] of natural marble. However, its decrease trend is gentle
compared with initial change of spindle speed that causes the trend of
cutting force changes. The work hardening phenomenon recedes when the
spindle speed reaches to 5000-7000 r [min.sup.-1].
The curve of cutting force changing with cutting depth is shown in
Fig. 10. It can be seen from the curve that cutting force of three
directions has an obvious linear increasing trend. The reason of
increasing trend of cutting force is that: the cutting area on the axial
profile increased with the increase of cutting depth, and the cutting
force increased with the cutting volume of cutting blade increased in
unit time.
The curvilinear relationship between feed speed and simulate
cutting force is shown in Fig. 11.
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
The curve illustrated that cutting force increases along with the
increase of feed speed but the range of change is not big and the X
direction cutting force is obvious. The increasing trend is more obvious
when the feed speed changes within the range of 1500 to 3000 mm
[min.sup.-1]. Nevertheless, when the feed speed reaches to the range of
3000 to 3500 mm [min.sup.-1], the brittle-ductile transition appears and
cutting force have a gentle decrease trend. Fig. 12 shows the surface
texture of natural marble. The plasticity of marble increases with the
increases of temperature [15], the Area A of SEM picture has the uneven
surface and ravines, which is a typical brittleness removal and the
surface of Area B is flat and smooth that indicates ductile cutting
occurs on the marble milling process. Part of the surface grain of stone
is removed and the rest of the surface has tensile stress, deformation
layer of stone has a trend of reinstatement [16] with the effect of
plastic extension and the material below the surface has to prevent this
kind of change, and then the surface stress has redistribution that
leads to decreases of real cutting force.
According to the results of experiment, three parameters restrict
the change of milling force. A mathematical formula needs to be figured
out using the force data by MATLAB. Eq. (2) shows the mathematic
relation between machining parameters and milling force. [X.sub.1]
represents spindle speed, [X.sub.2] represents feed speed, [X.sub.3]
represents the cutting depth and Y represents the cutting force. The
R-square statistics is 0.9537, the p value is 0.0001 and p < 0.05,
indicating the empirical equation is reliable.
Y = 24.6620[X.sub.1] - 0.0057[X.sub.1.sup.2] +
0.0001[X.sub.2.sup.2] + 25.7358[X.sub.3.sup.2] - 8.6425[X.sub.3.sup.3] +
1.2292. (2)
[FIGURE 12 OMITTED]
4. Conclusion
The milling process simulation of natural marble based on Deform-3D
was carried out in this paper. The error of cutting force between
simulation and experiment is within 10%, suggesting the simulation value
is reliable. According to the analysis, the cutting force decreases
along with the increase of spindle speed and the downtrend of cutting
force slows down due to the work-hardening of workpiece when spindle
speed changes around 3000-5000 r/min; the cutting force decreases along
with the increase of feed speed. The cutting force has a linear increase
due to the axial cutting quantity increases. The cutting force increases
as the increase of feed speed below 3000 mm/min. Once the feed speed
reaches to 3000 mm/min, the brittle-ductile transition appears through
the analysis on the SEM picture of natural marble, and then the surface
cutting force has a redistribution that decreases the real cutting
force. Empirical equation of cutting force was obtained by MATLAB
through experimental data. Therefore, large spindle speed and feed
speed, small cutting depth can reduce cutting force and the phenomenon
of brittle-ductile transition will increase the surface quality and
improve cutting performance of coated tool.
Acknowledgement
This work was financially supported by the Natural Science
Foundation of China (51375317), the Ministry of Education Innovation
Team Plans (IRT1160); Liaoning Province Natural Science Foundation
(2014020069).
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Received September 15, 2015
Accepted July 04, 2016
Yan Guangyu, Shenyang Jianzhu University, Shenyang 110168, China,
E-mail: 775083630@qq.com
Wu Yuhou, Shenyang Jianzhu University, Shenyang 110168, China,
E-mail: wuyh@sjzu.edu.cn
Zhao Dehong, Shenyang Jianzhu University, Shenyang 110168, China,
E-mail: 85755340@qq.com
Wang He, Shenyang Jianzhu University, Shenyang 110168, China,
E-mail: 4404992@qq.com
http://dx.doi.org/10.5755/j01.mech.22A16160
Table 1
Basic attributes of work piece and tool materials
Material Density [rho], Elasticity Poissn
kg [m.sup.-3] modulus E, ratio
GPa
Natural marble 2931 117.90 0.25
Ball endmill 1487 448.00 0.23
Material Thermal Thermal Specific
expansivity, conductivity, heat capacity
[10.sup.-6] W [m.sup.-1] C, J
[K.sup.-1] [kg.sup.-1]
[K.sup.-1]
Natural marble 1.4 3.57 793
Ball endmill 8.0 30.00 502
Table 2
Orthogonal experiment arrangement and results
Spindle Feed speed, Cutting Fx, N
speed, r mm depth,
[min.sup.-1] [min.sup.-1] mm
Test Simulate
value value
1 2000 1500 1.0 35.69 32.84
2 2000 2500 2.0 45.31 40.78
3 2000 3000 3.0 50.32 54.81
4 2000 3500 4.0 60.90 65.16
5 3000 1500 2.0 38.21 35.62
6 3000 2500 1.0 28.63 33.35
7 3000 3000 4.0 58.24 62.09
8 3000 3500 3.0 48.20 43.98
9 5000 1500 3.0 44.74 41.44
10 5000 2500 4.0 54.30 58.64
11 5000 3000 1.0 36.75 33.69
12 5000 3500 2.0 40.21 36.96
13 7000 1500 4.0 60.31 56.09
14 7000 2500 3.0 47.62 43.23
15 7000 3000 2.0 43.64 38.26
16 7000 3500 1.0 32.65 37.60
Average error (%) 9.1
Fy, N Fz, N
Test Simulate Test Simulate
value value value value
1 22.25 20.56 10.65 11.89
2 31.98 29.64 12.42 13.57
3 36.62 33.51 20.21 18.69
4 39.39 43.47 19.25 21.26
5 23.31 20.64 12.56 11.21
6 24.20 20.44 12.32 11.05
7 45.01 40.88 20.95 19.23.
8 32.45 29.62 14.26 15.32
9 27.32 25.99 12.80 13.50
10 43.31 39.89 18.62 17.09
11 22.38 20.10 14.10 12.23
12 27.57 21.96 13.90 13.21
13 43.34 39.25 21.05 18.10
14 32.87 28.32 16.00 15.30
15 32.65 21.80 13.32 12.69
16 22.39 20.37 12.18 11.47
Average error (%) 9.5 9.6
