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IE 215 Solutions for Problems due Sep 10, 2008 (Chs 21, 22)
21.31 Orthogonal cutting is performed on a metal whose mass specific heat = 1.0 J/gC, density = 2.9 g/cm
3
,
and thermal diffusivity = 0.8 cm
2
/s. The following cutting conditions are used: cutting speed is 4.5 m/s,
uncut chip thickness is 0.25 mm, and width of cut is 2.2 mm. The cutting force is measured at 1170 N.
Using Cook's equation, determine the cutting temperature if the ambient temperature = 22
°
C.
Solution
:
ρ
C
= (2.9 g/cm
3
)(1.0 J/g
°
C) = 2.90 J/cm
3

°
C = (2.90x10
3
) J/mm
3

°
C
K
= 0.8 cm
2
/s = 80 mm
2
/s
U
=
F
c
v
/
R
MR
= 1170 N x 4.5 m/s/(4500 mm/s x 0.25 mm x 2.2 mm) = 2.135 Nm/mm
3
T
= 0.4
U
/(
ρC
) x (
vt
o
/
K
)
0.333
T
= 22 + (0.4 x 2.135 Nm/mm
3
/(2.90x10
3
) J/mm
3
C) [4500 mm/s x 0.25 mm/80 mm
2
/s]
0.333
T
= 22 + (0.2945 x 10
3
C)(14.06)
.333
= 22 + 294.5(2.41) = 22
°
+ 710
°
=
732
°
C
21.34 It is desired to estimate the cutting temperature for a certain alloy steel whose hardness = 240 Brinell.
Use the appropriate value of specific energy from Table 21.3 and compute the cutting temperature by means
of the Cook equation for a turning operation in which the following cutting conditions are used: cutting
speed is 500 ft/min, feed is 0.005 in/rev, and depth of cut is 0.070 in. The work material has a volumetric
specific heat of 210 in lb/in
3
F and a thermal diffusivity of 0.16 in
2
/sec. Assume ambient temperature =
88
°
F.
Solution
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 Fall '08
 Groover

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