A cylindrical riser is to be designed for a sand casting mold. The length of the cylinder is to be 1.5 times its diameter. The casting is a square plate, each side = 12 in and thickness = 1.1 in. If the metal is cast iron, and the mold constant = 13.0 min/in2 in Chvorinov's rule, determine the length of the riser in inches so that it will take 35% longer for the riser to solidify.

Answer :

Answer:

d = 2.711

H = 4.06 inch

Explanation:

Given Data:

length = 1.5 times of diameter of cylinder

square plate side = 12 inch, thickness = 1.1 inch

mold constant = 13.0 min/in^2

Casting volume

[tex]V= tl^2[/tex]

t is thickness and L is length

substitute t = 1.1 inch, L =12 inch

[tex]v = 1.1\times 12^2 = 158.4 inc^3[/tex]

casting area

[tex]A = 2L^2 + 4Lt[/tex]

[tex]A = 2\times 12^2 + 4\times 12\times 1.1[/tex]

A = 340.8 in^2

Ratio between casting volume and area

[tex]\frac{v}{A} = {158.4}{340.8} = 0.464[/tex]

Total solidification time TST using chvorinov rule

[tex]TST = Cm [\frac{V}{A}]^2[/tex]

Cm is mold constant

[tex]TST = 13\times 0.464^2[/tex][/tex]

TST = 2.798 min

TST for riser

riser [tex]TST = 1.30\times2.798 = 3.63[/tex]

Riser volume [tex]v = \frac{\piD^2 H}{4}[/tex]

[tex]v = 0.25\pi\times D^2(1.5D)[/tex]

[tex]v = 0.375\pi D^3[/tex]

Riser area

[tex]A =\frac{2\pi D^2}{4} + \pi DH[/tex]

[tex]A = 0.5\pi D^2 +1.5\pi D^2[/tex]

[tex]A = 2\pi D^2[/tex]

RATIO of riser volume and area

[tex]\frac{v}{A} = \frac{0.375\piD^3}{2.0\pi D^2} = 0.1875 D[/tex]

TST for riser

[tex]TST = Cm [\frac{v}{A}]^2

[tex]TST= 13 \times (0.1875 D)^2 [/tex]

[tex]3.36 =13\times (0.1875 D)^2[/tex]

d = 2.711

[tex]H = 1.5 \times 2.711  =4.06 inc[/tex]

H = 4.06 inch

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