Page 269 - Manufacturing Engineering and Technology - Kalpakjian, Serope : Schmid, Steven R.

248 Chapter 10 Fundamentals of Metal Casting

EXAMPLE l0.l Solidification Times for Various Shapes
Three metal pieces being cast have the same volume, Cube:
but different shapes: Gne is a sphere, one a cube, and 3 2
the other a cylinder with its height equal to its diame- V : ‘1 i ‘I 2 1> and A Z 6” 2 6°
ter. Which piece will solidify the fastest, and which C 1. d _
one the slowest? Assume that n = 2. Y In er'

Solution The volume of the piece is taken as unity. V I mlb Z 277,73 1, Z <_l_>1/3
Thus from Eq. (10.7), ’ 271' ’
Solidification time -*TT. A = 21712 + 2111*/1 = 61112 = 61r(*-> 2/3 = 5.54.
1
1
CX
(Surface area); tsphere Z tcube Z tcylinder I
ZW
The respective Surface areas are as follows: The respective solidification times are therefore

Sphere. 1/3
_
V-<3)1rr,r-(477)
_
_3_
4
3
Hence, the cube-shaped piece will solidify the fastest,
_
3 2/g, and the spherical piece will solidify the slowest.
A = 47772 = 4'n'<Z;T-> = 4.84.
l0.5.2 Shrinkage
Because of their thermal expansion characteristics, metals usually shrink (contract)
during solidification and while cooling to roorn temperature. S/Orin/cage, which
causes dimensional changes and sometimes warping and cracking, is the result of the
following three sequential events:
l. Contraction of the molten metal as it cools prior to its solidification.
2. Contraction of the metal during phase change from liquid to solid (latent heat
of fusion).
3. Contraction of the solidified metal (the casting) as its temperature drops to
ambient temperature.
The largest potential amount of shrinkage occurs during the cooling of the
casting to ambient temperature. The amount of contraction during the solidification
of various metals is shown in Table 10.1. Note that some metals (such as gray cast

TABLE l0.l
Volumetric Solidification Contractiun or
Expansion for Various Cast Metals
Contraction (%) Expansion (%)
Aluminum 7.1 Bismuth 3.3
Zinc 6.5 Silicon 2.9
Al-4.5% Cu 6.3 Gray iron 2.5
Gold 5.5
White iron 4-5 .5
Copper 4.9
Brass (70-30) 4.5
Magnesium 4.2
90% Cu-10% Al 4
Carbon steels 2.5-4
Al-12% Si 3.8
Lead 3.2