cutting force model
TRANSCRIPT
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Modeling of Cutting Forces for High-speed
Milling of Titanium Alloys
Dept of Mechanical Engineering
Prof. M. Rahman and Wang Zhigang
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Overview
Introduction
Literature review
Modeling of milling process
Modeling of cutting forces for high-speed milling of Ti-6Al-4V
Verification of the cutting force model Conclusions
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Cutting temperature as a result of cutting speed
Introduction
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Definition of high-speed machining (HSM)
Introduction
fibre-reinforced
plastics
bronze,brass
cast iron
steel
titaniumalloys
convent
ional
range
aluminum
alloys
cutting speed vc [m/min]
10 100 1000 10000
HSC-ran
ge
transitio
nrange
nickel basedalloys
Cutting Speed Area Depends on Material
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Higher productivity
Generate high-quality surfaces, burr-free
edges and stress-free components.
Cutting forces are lower
Minimize the heat effect on machined parts;eliminate the usage of cutting fluids
Significant advantages of HSM
Introduction (contd.)
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Aircraft & aerospace production, tool and die mold
manufacturing (high productivity)
Optical industry, fine mechanical parts (high surface
quality)
Precision mechanics, magnesium alloys (Cutting
heat taken away by chips)
Automotive industry, household equipments (low
cutting forces)
Applications of HSM
Introduction (contd.)
HSM is a strategic part of making F/A-18E/F tactical fighters
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their good strength-to-weight ratio
superior corrosion resistance.
Introduction (contd.)
Titanium alloys have been widely
used in the aerospace, biomedical,
automotive and petroleum industriesbecause of
Among all titanium alloys, Ti-6Al-4V
is most widely used.
Their machinability is very poor.
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Introduction (contd.)
The performance of conventional tools is poor
Advanced tool materials, such as cubic boronnitride (CBN), polycrystalline diamond (PCD)
Binderless CBN used in this study
High-speed machining of Ti-6Al-4V
Experiments are costly and time-consuming
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15 topics related to modeling of machining
operations
Six major operational groups: single straight edge
orthogonal, single straight edge oblique, turning,
milling, drilling and form-tool machining
Survey of recent research on modeling by CIRP
working group
Literature review
Over 55 major research group are currently active in
modeling efforts
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Experimental/empirical modeling (43% of
research groups)
Analytical modeling (32% of research group)
Numerical modeling (18% of research group)
Three categories of cutting force modeling
Literature review (contd.)
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Taylor, the father of metal cutting science,
firstly used empirical approach to propose
the well-known Taylors equation
The power-law form of Taylor equation
extended to predict cutting forces
Empirical model
Literature review (contd.)
vfCaF=
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Only valid for particular cutter geometry and
workpiece combination;
Large numbers of empirical experiments are
required;
Empirical model
Literature review (contd.)
This method is not suitable for cutting tool
design purpose
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Mechanistic model
Shear plane model
Shear zone model
Predictive machining theory
Analytical model
Literature review (contd.)
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Based on the assumption that the magnitude of
cutting forces depend on the uncut area
Tangential force in milling is given as:
Mechanistic model
Literature review (contd.)
AKF tt =
whereKtis the specific cutting pressure,
A is the uncut chip area;
Limits: Ktdepend on specific combination of tool/workpiece
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Initiated by Merchants shear plane theory
Use the minimum energy principle to
determine the shear angle
Shear plane model
Literature review (contd.)
Shear plane theory assumes that thin shear
zone is a plane, and that work material
deforms at constant flow stress
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Strain hardening properties of the work
material had a profound effect on the
hydrostatic stress distribution in the chip
formation zone.
Oxley and Welsh (1963) introduced the
parallel-sided shear zone model of chipformation.
Shear zone model
Literature review (contd.)
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Shear zone model
Literature review (contd.)
VC
Chip
Tool
A
BD
F
E
C
Between the boundary of CD and EF
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Based on the parallel-sided shear zone
model
The flow stress of a metal is influenced by:
Oxleys predictive machining theory
Literature review (contd.)
properties of work material
effective strain
effective rate of deformation or strain rate
cutting temperature
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Mostly use the finite element method (FEM)
More accurate than the analytical model
Predict cutting forces, strain, strain rate and
temperature, etc.
Numerical modeling
Literature review (contd.)
FEM requires much more computation time,
especially for 3-D simulation
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Relative motion between the cutting tool and
workpiece for face milling:
Modeling of milling process
Rotation of the spindle
Translational motion of
feed
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Traditional trochoid curve
The motion of the cutter is like the trace of a point fixed on a
circle that rolls along a line
Modeling of milling process (contd.)
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Traditional undeformed chip thickness
h
f
f
O
O
A
R
For high speed milling or micro-milling, there is a great need
for higher accuracy, so the circular tooth-pass could not meet
the requirement
Modeling of milling process (contd.)
)sin()( fh =
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The true tool trajectory during slot milling
Modeling of milling process (contd.)
O O DA
B
C
0
Tool tip
Workpiece
Chip
thickness
True tooltrajectory
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Analytical solution to undeformed chip thickness
where
Modeling of milling process (contd.)
02)sin(2 = aa
)2
sin(
=R
fa
RCDRBCh
)cos(
)cos()cos()(
===
)(24
83
12
23
2
1 543
23
2
22 aOaaaa +
++
+++=
where
and = 0 -
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Effects of nose radius
Modeling of milling process (contd.)
dFt
2
1
dFr
r-a
r
d
d
OO0
B
A
C
0
DII
E
I F
h() h()
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Non-uniform chip area
Modeling of milling process (contd.)
+
=+= 1
0
2
1
1
0
)sin
)((
2
1)(
2
1)(
2
12
22
22
22
d
arrdAOrdOBrS
+2
1 ]cos)(sin)(cos)(2sin)([2
1 2222222
dhhrhh
It needs to establish a model about 3-D milling
process to simulate the cutting process around
the tool tip
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Equivalent element representation
Modeling of milling process (contd.)
Represent the uneven uncut chip area with
the equivalent rectangular contact area
Represent the uneven intersection surfacewith the equivalent one which is suitable for
axisymmetric deformation simulation (Ozel,
1998)
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Equivalent element representation
Equivalent element representation with a parallelogram
Modeling of milling process (contd.)
Ft
er-a
r
OO0
B
A
C
Fr
he
3
FZ
D
Fr
h() h()
When chip thickness is less
than 0.05mm, the size effect is
very obvious.
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Overview of this section
Modeling of cutting force
Brief review of Oxleys theory
Deformation behavior of Ti-6Al-4V
Hybrid cutting force between Oxleys
theory and FEM simulation
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His model has been widely used by many researchers
Modeling of cutting force (contd.)
Two assumptions: cutting edge is perfectlysharp; uniform normal stress distributes at
the tool/chip interface
His work was mainly focused on the carbon
steel work material
Oxleys predictive cutting force theory
Two limitations:
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Cutting force diagram based on shear zone model
Modeling of cutting force (contd.)
VC
ChipTool
Fc
FSFN
A
B
G
l
lc
t2
Fn
FR
FR FT
Ff
t1
D
F
E
C
Based on the parallel-sided shear zone model
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Geometric and cutting forces relations:
Modeling of cutting force (contd.)
+=
=
=
=
sin/)cos()cos(
cos
)cos(sin
12 tt
VV
VV
CS
Cchip
cossin
)sin()sin(
cossin
)cos()cos(
cos
1
1
==
==
=
wtkFF
wtkFF
FF
ABRT
ABRC
SR
kAB, , n and C ?????
Cn+= )4/(21tan
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Oxleys predictive cutting forces theory:
Modeling of cutting force (contd.)
3/1n
ABABk =
Shear flow stresskAB along the shear plane
where 1 is initial stress constant, and n is strain-hardening
index, AB is effective strain along the shear plane. 1 and nvary with strain rate and temperature
3/ABAB =
Effective strain and strain-rate are calculated as
3/ABAB && =
where AB and are maximum strain and strain rate along
ABAB&
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Oxleys predictive cutting forces theory:
Modeling of cutting force (contd.)
Maximum strain and strain rate alongAB
where lis the length ofAB, and Cis strain-rate constant.
Velocity modified temperature
)cos(sin
cos
2
1
=AB
l
VC SAB =&
)]/lg(1[ 0mod &&vTT AB =
the constants v and 0& are taken as 0.09 and 1/sec
where TAB is the cutting temperature at shear planeAB,
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Oxleys predictive cutting forces theory:
Modeling of cutting force (contd.)
Temperature at shear plane AB
where TW is the initial workpiece temperature and TSZcanbe calculated from the equation:
SZWAB TTT +=
)cos(
cos1
1
=S
SZ
F
wStT
TAB depends on cutting forces and thermal properties of
workpiece material.
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Computation about the cutting temperature in
the shear zone
Modeling of cutting force (contd.)
Assume TAB=Tw
Calculate for planeAB, thermal properties SandK;
Tmod, kAB;FS= kABlw;RTand ; TSZand TAB
Compare new TAB and old TAB
Calculate ; ;R=FS/cos,F,NandFC
TAB = new TAB
a small given value
a small given value
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Mean chip temperature calculation:
Modeling of cutting force (contd.)
Assume mean chip temperature TC=Tw + TSZ
Calculate the chip thermal properties S and K from
appropriate equations; TC; TC=Tw + TSZ+ TC
Compare new TCand old TC
Calculate for the toolchip interface shear flow stress kchip = 1/3
TC= new TC
a small given value
a small given value
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Oxleys predictive cutting forces theory:
Modeling of cutting force (contd.)
Shear flow stress at the tool-chip interface
where 1 corresponds to the value ofTmod. This equation
neglects the influence of strain on the flow stress above astrain of one.
Average shear stress at the tool-chip interface
3
1=chipk
wl
F
c
f=int
++=
])4/(21[31
sincos
sin1
Cn
Cntlc
where contact length
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Solution to shear angle Modeling of cutting force (contd.)
The solution to is taken at the intersection of the two curves.
Shear angle (deg)
kchip
int
0 45
600
Shears
tress(MPa)
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Determination of strain-rate constant
Modeling of cutting force (contd.)
Based on the assumption of uniform normal stress
along the tool-chip interface, the normal stress N atB
is also given by
CnkAB
N 222
1'
+=
c
NNwl
F
=
The tool-chip interface is assumed to be a direction of
maximum shear stress, the normal stress N at B isgiven by
Ccan be found by fulfilling the condition N = N
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Summary of the machining calculations
Modeling of cutting force (contd.)
For a given and C, the equilibrium values of
are found (when int is equal to the value ofkchip).
Then, the required value of C is determinedfrom the stress boundary condition.
The above procedure is iterated for a given range
ofand C until all the equilibrium conditions are
fulfilled.
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Modeling of cutting force (contd.)Given: cutting conditions: , U, t1, w, Tw and material properties; Assign values for 1, 2, , final
Assume the initial value ofC(say C= 5)
Calculate l= t1/sin; VS, AB andAB;
Calculate the flow stress int at tool/chip interface
Calculate ; ;R=FS/cos,F,NandFC
Calculate the tool/chip interface shear flow stress kchip
=45o?
Plot int and kchip versus and selectsolution point where int=kchip
Print the final results, such as , forces etc
Compare Nand N
=min?
PlotFc versus
and determine =min for minimumFc
= i
Assume (say = 5o)
=final?No
Yes
No
Yes
Yes
No
a small given value
a small given value
Calculation of temperature at shear plane
Calculate the mean temperature at the chips
= + 0.1oEstimate new C
=min
M d li f i f
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Summary of the machining calculations
Modeling of cutting force (contd.)
Five iterative procedures involved in the
computation: determination of temperature at
AB, and at tool-chip interface, possible ranges
of C, and . These three parameters are veryimportant for its accuracy.
Such a procedure is extremely time-consuming.
M d li f i f
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Modeling of flow stress properties of Ti-6Al-4V
Modeling of cutting force (contd.)
Johnson-Cook (JC) strength model representsthe flow stress of a material as the product of
strain, strain-rate and temperature:
])(1)][ln(1][)([0
m
rm
rn
TTTTCBA
++= &
&
ABn
AB
n
ABm
rm
rn
ABBA
nB
TT
TTCnB
d
d
])([
)(])(1)][ln(1[)(
1
0
1
+=
+=
&
&
Then, differentiate with respect to :
M d li f tti f
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20oC
Modeling of cutting force (contd.)
700oC
M d li f tti f
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Modeling of cutting forces
Modeling of cutting force (contd.)
In Oxleys model (1989), flow stress in the shear plane zone,
kAB can be calculated according to:
This is replaced by:
3/1n
ABABk =
3/=ABk
where is the effective flow stress alongAB, which can be
calculated using the constitutive equation.
M d li f tti f
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Modeling of cutting forces
Modeling of cutting force (contd.)
The change rate of flow stress (dk/ds2) normal toAB can be
assumed to be only related to the actual strain-rate
222 ds
dt
dt
d
d
dk
ds
d
d
dk
ds
dk
==
Then, the first term on the right-hand side of above equation
can be obtained as:
ABn
AB
n
AB kBA
nBd
dddk
])([3)(
33/
1
+==
(1)
(2)
M d li f tti f
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Modeling of cutting forces
Modeling of cutting force (contd.)
The second term on the R.H.S of Eq. (1) is the strain-rate
)cos(
cos
=
l
VC
dt
d C
The last term is the reciprocal of the cutting speed normal
toAB, which can be presented as
)sin(
1
2 CVds
dt=
Modeling of cutting force
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Modeling of cutting forces
Modeling of cutting force (contd.)
])([
)(2
sin
1
)cos(
cos
])([3
)( 1
2
n
AB
n
ABAB
C
C
n
AB
n
ABAB
BAl
CnBk
Vl
CV
BA
nBk
ds
dk
+=
+=
Eq. (1) can be simplified as:
1
2
dsdsdkdp =
According to the stress equilibrium equation alongAB
from Oxley (1989), the following relation exists
(3)
Modeling of cutting force ( d )
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Modeling of cutting forces
Modeling of cutting force (contd.)
n
ABAB
n
ABBA
nBk
BAppC
)(2
])()[(
+=
Finally the unknown parameter Cis given by
By applying the equation alongAB, substituting for
dk/ds2 from Eq. (3), the next equation is given
])([
)(2n
AB
n
ABABBA
BA
CnBkpp
+=
wherepA andpB are the hydrostatic stresses at pointsA andB
Modeling of cutting force ( d )
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Modeling of cutting forces
Modeling of cutting force (contd.)
In Oxleys theory, the angle made by theresultant forceR withAB is expressed as
22
)
4
(21tan
s
l
k
k
AB
+=
The following equation is obtained
n
AB
n
AB
BABCn
++=)
4(21tan
Modeling of cutting force ( td )
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Based on above description, for given values of toolrake angle , the cutting speed VC, the thickness t1 and width of cut w of the undeformed chip,
together with the thermal and flow stress properties
of the workpiece material and the initial
temperature of the work Tw (say, 20oC in all
calculations), FEM can be employed to simulate
the metal deformation process .
Modeling of cutting force (contd.)
Modeling of cutting forces
Verification of the model
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Experimental setup
Verification of the model
workpiece
dynamometer
Work table
Cutter
Verification of the model (contd )
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Cutting tools: binderless cubic boron nitride
Cutting conditions
Experimental design and cutting conditions
Cutting speed: 300, 350 and 400 (m/min)
Feed rate: 0.075, 0.100 and 0.125 (mm/r)
Depth of cut: 0.075, 0.010 and 0.125 (mm)
Verification of the model (contd.)
Verification of the model (contd )
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Deformation zone of FEM simulation
Verification of the model (contd.)
Effects of cutting
edge radius has
been considered
Verification of the model (contd )
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Temperature distribution on the tip of the tool
Verification of the model (contd.)
Verification of the model (contd )
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Temperature simulation
Verification of the model (contd.)
Verification of the model (contd )
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(a) Estimated cutting forces
at a = 0.075mm,f= 0.075mm/r and v = 350m/min
-20
-10
0
10
20
30
40
0 45 90 135 180
Angular position (deg)
Cuttingf
orces(N)
Fx (N)
Fy (N)
Fz (N)
-20
-10
0
10
20
30
40
50
0 45 90 135 180
Angular position (deg)
Cuttingforces(N)
Fx (N)
Fy (N)
Fz (N)
(b) Experimental cutting forces
Verification of the model (contd.)
Verification of the model (contd.)
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at a = 0.10mm,f= 0.1mm/r and v = 350m/min
-20
-10
0
10
20
30
40
50
60
70
80
0 45 90 135 180
Angular position (deg)
Cutting
forces(N)
Fx (N)
Fy (N)
Fz (N)
-40
-20
0
20
40
60
80
100
0 45 90 135 180
Angular position (deg)
Cutting
forces(N)
Fx (N)
Fy (N)
Fz (N)
Verification of the model (contd.)
(a) Estimated cutting forces (b) Experimental cutting forces
Verification of the model (contd.)
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a = 0.10mm,f= 0.1mm/r and v = 400m/min
-30
-20
-10
0
10
20
30
40
50
60
70
0 45 90 135 180
Angular position (deg)
Cutting
forces(N)
Fx (N)
Fy (N)
Fz (N)
-20
-10
0
10
20
30
40
50
60
70
80
0 45 90 135 180
Angular position (deg)
Cutting
forces(N)
Fx (N)
Fy (N)
Fz (N)
Verification of the model (contd.)
(a) Estimated cutting forces (b) Experimental cutting forces
Conclusions
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Analytical solution to undeformed chip thickness
is derived; JC model is used to describe the deformation
behavior of the workpiece material;
After FEM simulation, a new cutting force model
for high-speed milling of Ti-6Al-4V is proposed;
The cutting forces can be predicted withreasonable accuracy for all three directions.
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Thank you for your attention!!!