Question

A disk‑shaped part is to be cast out of aluminum. the diameter of the disk = 444 mm and its thickness = 21 mm. if the mold constant = 1.7 sec/mm2 in chvorinov's rule, how long will it take the casting to solidify (in the unit of seconds)?

Answer 1

To calculate the solidification time of the casting, we can use Chvorinov's Rule. First, we calculate the total surface area of the disk. Next, we calculate the solidification volume of the disk. Finally, we use Chvorinov's Rule to calculate the solidification time.

Step-by-step explanation:

To calculate the time it will take for the casting to solidify, we can use Chvorinov's Rule. Chvorinov's Rule states that the solidification time (t) is equal to the mold constant (n) divided by the product of the total surface area (A) and the solidification volume (V).

First, we need to calculate the total surface area of the disk. The disk is disk-shaped, so it is essentially a cylinder. The total surface area of a cylinder is given by the formula A = 2πrh + πr^2, where r is the radius and h is the height. In this case, the radius is half the diameter, so r = 444 mm / 2 = 222 mm. The height of the cylinder is the thickness of the disk, which is 21 mm. Substituting these values into the formula, we get A = 2π(222 mm)(21 mm) + π(222 mm)^2.

Next, we need to calculate the solidification volume of the disk. The solidification volume of a cylinder is given by the formula V = πr^2h. Substituting the values, we get V = π(222 mm)^2(21 mm).

Now we can calculate the solidification time using Chvorinov's Rule. The mold constant is given as 1.7 sec/mm^2. Substituting all the values into the formula, we get t = (1.7 sec/mm^2) / [2π(222 mm)(21 mm) + π(222 mm)^2] * π(222 mm)^2(21 mm).