Alloy parts were cast with a sand mold that took 160 secs for a cube-shaped casting to solidify. The cube was 50 mm on a side. (a) Determine the value of the Chvorinov's mold constant. (b) If the same alloy and mold type were used, find the total solidification time for a cylindrical casting in which the diameter = 25 mm and length = 50 mm.

a) k = 6.4 s/cm²

b) Te = 160 s

Explanation:

a) Given

Solidification time in s: Te = 160 s

L = 50 mm = 5 cm

We use the formula

Te = k * (V/A) ⁿ

k = Te * (A/V) ⁿ

where

k is the Chvorinov's mold constant

V is casting volume in cm³ = V = L³ = (5 cm) ³ = 125 cm³

A is the surface area of the casting in cm² = A = L² = (5 cm) ² = 25 cm²

n = 2 (assumed)

⇒ k = 160 s * (25 cm²/125 cm³) ²

⇒ k = 6.4 s/cm²

b) Given

D = 25 mm = 2.5 cm ⇒ R = D/2 = 2.5 cm/2 = 1.25 cm

h = 50 mm = 5 cm

k = 6.4 s/cm²

n = 2

We find the volume as follows

V = π*R²*h ⇒ V = π * (1.25 cm) ² * (5 cm) = 24.5436 cm³

and the surface area

A = π*R² = π * (1.25 cm) ² = 4.9087 cm²

We apply the equation

Te = k * (V/A) ⁿ

⇒ Te = (6.4 s/cm²) * (24.5436 cm³/4.9087 cm²) ²

⇒ Te = 160 s