The starting length of a shaft is 25.00 mm. This shaft is to be inserted into a hole in an expansion fit assembly operation. To be readily inserted, the shaft must be reduced in length by cooling. Determine the temperature to which the shaft must be reduced from room temperature (20° C) in order to reduce its length to 24.98 mm. Refer to the Table below.

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Chapter1: Basic Modes Of Heat Transfer
Section: Chapter Questions
Problem 1.68P
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3. The starting length of a shaft is 25.00 mm. This shaft is to be inserted into a hole in an
expansion fit assembly operation. To be readily inserted, the shaft must be reduced in length
by cooling. Determine the temperature to which the shaft must be reduced from room
temperature (20° C) in order to reduce its length to 24.98 mm. Refer to the Table below.
Volumetric properties in U.S. customary units for selected engineering materials.
Coefficient of Thermal
Density, p
Expansion, a
Melting Point, T
Material
g/cm
Ib/in
c'x 10
x 10
°C
'F
Metals
Aluminum
2.70
0.098
24
13.3
660
1220
Copper
Iron
0.324
0.284
0.410
8.97
17
9.4
1083
1981
2802
7.87
12.1
6.7
1539
Lead
11.35
29
16.1
327
621
Magnesium
Nickel
1.74
0.063
0.322
0.284
26
14.4
7.4
650
1202
8.92
13.3
1455
2651
7.87
7.31
19.30
7.15
Steel
Tin
12
23
6.7
0.264
12.7
232
449
Tungsten
Zinc
0.697
4.0
2.2
3410
6170
0.258
40
22.2
420
787
Ceramics
b.
Glass
2.5
0,090
1.8-9.0
1.0-5.0
Alumina
3.8
0.137
9.0
5.0
NA
NA
b.
Silica
2.66
0,096
NA
NA
Polymers
Phenol resins
Nylon
Teflon
Natural rubber
1.3
0.047
60
33
b
1.16
0.042
100
55
2.2
0.079
100
55
1.2
0.043
80
45
Polyethylene (low density)
Polystyrene
0.033
0.038
0.92
180
100
1.05
60
33
Transcribed Image Text:3. The starting length of a shaft is 25.00 mm. This shaft is to be inserted into a hole in an expansion fit assembly operation. To be readily inserted, the shaft must be reduced in length by cooling. Determine the temperature to which the shaft must be reduced from room temperature (20° C) in order to reduce its length to 24.98 mm. Refer to the Table below. Volumetric properties in U.S. customary units for selected engineering materials. Coefficient of Thermal Density, p Expansion, a Melting Point, T Material g/cm Ib/in c'x 10 x 10 °C 'F Metals Aluminum 2.70 0.098 24 13.3 660 1220 Copper Iron 0.324 0.284 0.410 8.97 17 9.4 1083 1981 2802 7.87 12.1 6.7 1539 Lead 11.35 29 16.1 327 621 Magnesium Nickel 1.74 0.063 0.322 0.284 26 14.4 7.4 650 1202 8.92 13.3 1455 2651 7.87 7.31 19.30 7.15 Steel Tin 12 23 6.7 0.264 12.7 232 449 Tungsten Zinc 0.697 4.0 2.2 3410 6170 0.258 40 22.2 420 787 Ceramics b. Glass 2.5 0,090 1.8-9.0 1.0-5.0 Alumina 3.8 0.137 9.0 5.0 NA NA b. Silica 2.66 0,096 NA NA Polymers Phenol resins Nylon Teflon Natural rubber 1.3 0.047 60 33 b 1.16 0.042 100 55 2.2 0.079 100 55 1.2 0.043 80 45 Polyethylene (low density) Polystyrene 0.033 0.038 0.92 180 100 1.05 60 33
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