Engineering, 11.07.2019 02:20 milak23

Adisk-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?

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Answer from: asharrogers17

t =253.8s

Explanation:

Chvorinov's Rule can be written as:

$t=B(\frac{V}{A} )^{n}$

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.

$V=\frac{\pi D^{2}h }{4} = 3.9*10^6$ mm3

$As=\pi D h+2\frac{\pi }{4} D^{2} =0.424*10^6$ mm2

V/A=9.198 mm

t = 3.0*9.198^2 =253.8s

Answer from: 163565

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

Chvorinov's Rule with Degarmo Method:

Minimum time required at constant n = 1.5 : t = 1.408751434 minutesMaximum time required at constant n = 2.0 : t = 4.286694102 minutes

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:

$V = \frac{\pi }{4} * D^{2} * H$

Where:

V = Volume of Cylinder

H = Height of disc

D = Diameter of disc

Now, putting dimensional values in above equation

$V = \frac{\pi }{4} * 500^{2} *20$

V = 3926990.817 $mm^{3}$

Second, we will find the surface area of the disc

Therefore, surface area of cylinder is given by:

$A = (\pi * D * H) + (2 * \frac{\pi }{4} * D^{2} )$

Where:

A = Surface area of disc

D = Diameter of disc

H = Height of disc

Now, putting dimensional values in above equation

$A = (\pi * 500 * 20) + (2 * \frac{\pi }{4} * 500^{2} )$

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

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Adisk-shaped part is to be cast out of aluminum. the diameter 500 mm and thickness = 20 mm. if the m...

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