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21.1 In an orthogonal cutting operation, the tool has a rake angle = 15
°
. The chip thickness before the
cut = 0.30 mm and the cut yields a deformed chip thickness = 0.65 mm. Calculate (a) the shear plane
angle and (b) the shear strain for the operation.
Solution
:
(a)
r
=
t
o
/
t
c
= 0.30/0.65 = 0.4615
= tan
1
(0.4615 cos 15/(1  0.4615 sin 15)) = tan
1
(0.5062) =
26.85
°
(b) Shear strain
γ
= cot 26.85 + tan (26.85  15) = 1.975 + 0.210 =
2.185
21.4 In a turning operation, spindle speed is set to provide a cutting speed of 1.8 m/s. The feed and
depth of cut of cut are 0.30 mm and 2.6 mm, respectively. The tool rake angle is 8
°
. After the cut, the
deformed chip thickness is measured to be 0.49 mm. Determine (a) shear plane angle, (b) shear strain,
and (c) material removal rate. Use the orthogonal cutting model as an approximation of the turning
process.
Solution
: (a)
r
=
t
o
/
t
c
= 0.30/0.49 = 0.612
= tan
1
(0.612 cos 8/(1 – 0.612 sin 8)) = tan
1
(0.6628) =
33.6
°
(b)
= cot 33.6 + tan (33.6  8) = 1.509 + 0.478 =
1.987
(c)
R
MR
= (1.8 m/s x 10
3
mm/m)(0.3)(2.6) =
1404 mm
3
/s
21.10 The shear strength of a certain work material = 50,000 lb/in
2
. An orthogonal cutting operation is
performed using a tool with a rake angle = 20
°
at the following cutting conditions: cutting speed = 100
ft/min, chip thickness before the cut = 0.015 in, and width of cut = 0.150 in. The resulting chip thickness
ratio = 0.50. Determine (a) the shear plane angle, (b) shear force, (c) cutting force and thrust force, and
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 Fall '08
 Groover

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