Question

A disk-shaped part is to be cast out of aluminum. The diameter 500 mm and thickness = 20 mm. If the mold constant = 3.0 s/mm2 in Chvorinov's Rule, how long will it take the casting to solidify, in minutes?

Answer 1

Chvorinov's Rule with Askeland Method: t = 4.286694102 minutes

Chvorinov's Rule with Degarmo Method:

1. Minimum time required at constant n = 1.5 : t = 1.408751434 minutes
2. Maximum time required at constant n = 2.0 : t = 4.286694102 minutes

Step-by-step explanation:

Data:

Aluminum disc

Diameter (D) = 500 mm

Thickness = Height (h) = 20 mm

Mold Constant (C) = 3.0 sec /
`mm^(2)`

Required:

Solidification time (t) in minutes = ?

Formula:

The solidification time can be found by using the Chvorinov's Rule:

`t = C (\frac {V}{A})^(n)`

Where;

t = solidification time

C = mold constant

V = Volume of disc

A = Surface area of disc

n = constant

Note: According to Askeland n = 2.0 and According to Degarmo n varies 1.5 to 2.0 therefore , we will do for both method and by Degarmo method we can predict maximum and minimum solidification time.

Solution:

First, we will find the volume of the disc

disc = cylinder

therefore, Volume of cylinder is given by:

`V = (\pi )/(4) * D^(2) * H`

Where:

V = Volume of Cylinder

H = Height of disc

D = Diameter of disc

Now, putting dimensional values in above equation

`V = (\pi )/(4) * 500^(2)  *20`

V = 3926990.817
`mm^(3)`

Second, we will find the surface area of the disc

Therefore, surface area of cylinder is given by:

`A = (\pi * D * H) + (2 * (\pi )/(4) * D^(2) )`

Where:

A = Surface area of disc

D = Diameter of disc

H = Height of disc

Now, putting dimensional values in above equation

`A = (\pi * 500 * 20) + (2 * (\pi )/(4) * 500^(2) )`

A = 424115.0082
`mm^(2)`

Finally, Moving towards the final solution

• Chvorinov's Rule with Askeland Method n = 2:

Rewriting the equation:

`t = C (\frac {V}{A})^(2)`

Putting the dimensional and constants values in the equation

`t = 3.0 (\frac {3926990.817}{424115.0082})^(2)`

t = 257.2016461 seconds

Converting to minutes

t = 4.286694102 minutes

• Chvorinov's Rule with Degarmo Method n = 1.5 (Minimum Solidification Time)

Rewriting the equation:

`t = C (\frac {V}{A})^(2)`

Putting the dimensional and constants values in the equation

`t = 3.0 (\frac {3926990.817}{424115.0082})^(1.5)`

t = 84.52508604 seconds

Converting to minutes

t = 1.408751434 minutes

• Chvorinov's Rule with Degarmo Method n = 2.0 (Maximum Solidification Time)

Rewriting the equation:

`t = C (\frac {V}{A})^(2)`

Putting the dimensional and constants values in the equation

`t = 3.0 (\frac {3926990.817}{424115.0082})^(2)`

t = 257.2016461 seconds

Converting to minutes

t = 4.286694102 minutes

Answer 2

t =253.8s

Step-by-step explanation:

Chvorinov's Rule can be written as:

`t=B((V)/(A) )^(n)`

where t is the solidification time,

V is the volume of the casting,

A is the surface area of the casting that contacts the mold,

n is a constant

B is the mold constant

The S.I. units of the mold constant B are s/m2.

According to Askeland, the constant n is usually 2.

`V=(\pi D^(2)h )/(4) = 3.9*10^6`mm3

`As=\pi D h+2(\pi )/(4) D^(2) =0.424*10^6` mm2

`V/A=9.198`mm

`t = 3.0*9.198^2` =253.8s