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Forces and Mechanics of Cutting
Why should we know?
Power requirement for the machine tool can be
calculated
Design of stiffness, etc. for the machine
tolerances
Whether workpiece can withstand the cuttingforce
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Ernst and Merchant (1941) did the first
scientific analysis
Normal = N
Along the tool = F
FC and FT along and normal to cutting along
the direction of tool movement with
velocity, v.
=N
F
sincos NSC FFF +=
sincos SNT FFF =
(1)
(2)
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( )
( )
( )
=
=
+
=
+=
=
=
+=
sin
cos
cos
cossin
sincos
sincos
cossin
RF
RF
FR
FFF
FFF
FFN
FFF
T
C
S
TCN
TCS
TC
TC(3)
(4)
(5)
(6)
(7)
(8)
(9)
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We can measure FC and FT using force
dynamometer. FS, FN, F, and N can be found.
FS and FN from equations 5 & 6.
F and N from 3 & 4
tan==
N
F( friction angle)=
sincos
cossin
TC
TC
FFFF
+
= Eq. 10
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Cutting Force FC depends on
FC increases as t0 increasesFC decreases as rake angle increases and as
speed increases
Why FC is affected by speed:As speed goes up, shear angle goes up, and
friction reduces.
Forces can also be affected by the noseradius. Large nose radius increases force.
(Blunt tool)
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Large nose radius can create positive rakeangle and cause rubbing and create plastic
deformation.
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Coefficient of friction in metal cutting range
from 0.5 to 2.0
Shows how high friction can rise on the
chip-tool interface
Forces on the tool tip are very high because
of small contact area.
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Stresses
Average shear stress
Average normal stress
The area where the stress acts (area of shear plane)
AS can be increased by increasing t0. is independent of rake angle
decreases with increase in rake angle.
S
S
A
F=
S
N
A
F=
sin0
wtAS =
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Consequently, normal stress in the shear
plane has no effect on the magnitude of
shear stress. Problems in finding stresses on the rake
face:
Hard to find the contact on the rake face.Stresses in practice is not uniformly distributed
on the rake face.
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Shear-angle relationship
Lets take friction angle as
Assume is independent of .Differentiate with respect to and equate to 0 (zero).
( )
( )
( ) ( )
0
0
sincossec
sin
cos
cos
t
F
A
F
wtA
RF
RF
C
S
S
S
S
C
+==
=
+=
=
In the previous slides we
called this
)(
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The equation (A) shows that
If decreases and/or increases then decreases.
In practice this analysis is corrupted because ofseveral reasons like:
Shear stress is effected by normal stresses.
is effected by etc.
(see graph 8.19)
( ) ( )
22
45
90tancottan
+=
==+
o (A)
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Specific Energy
Total power = FC
V
If width of unit = W
Total energy/unit volume of material
removal.
Frictional specific energy:00t
F
Vt
VFu CCt
==
( )
000
cossin
t
FFr
t
Fr
Vt
FVu
tCCf
+
===
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Power required to shear along the plane
As uf increases, shear angle decreases, andhence us goes up directly.
Thus friction plays an important part in
metal cutting.
sft
SSs
uuu
Vt
VFu
+=
=
0
( ) ( )
=
cos
sin
cos
sin
t
f
u
u
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P bl
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Problem t0=0.005 in, V=400 ft/min, =10
o, =0.25, tc=0.009,
Fc=125 lb, Ft=50 lb.
What % of total energy is consumed in friction?
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Summary Velocity triangle
Merchants circle
Compute Forces and obtain Fs, Fn etc based on
measuring Fc and Ft (Equations 1 to 10 of this slideset)
Calculate Shear stress and normal Stress
Specific energy
Shear angle relationships
Relationships between rake angle, velocity, shearangle and cutting force
Effect on Ft due to ve and +ve rake angle