Casting is a very important topic in GATE Mechanical Engineering exam. It covers a major portion of the syllabus in the subject of manufacturing engineering. In this article, we are sharing some important formulas to remember for the chapter of casting process. 

Chvorinov's rule:

Solidification time = C. [Volume of casting / Surface area of casting]2

If multiple castings are being compared, then assuming the castings have same volume, solidification time, t = C. [1/surface area]2

Cubic casting:

Volume, V = a= 1, a = 1

Surface area = 6a2 = 6 units

 

Cylindrical casting:

Let 'r' be the radius and 'h' be the height of the cylinder. 

 , 

Surface area = 

Spherical casting:

Let 'r' be the radius of the sphere. 

, therefore 

Surface area = 

From the above analysis, it is clear that spherical casting has the maximum solidification time (i.e. it will solidify the slowest) and the cubic casting casting has the least solidifcation time (i.e. it will solidify fastest).

Calculation of optimum pouring time:

Steel castings:

, where m = mass of the casting in kg and K = constant which varies from 1.95 for 45 kg castings to 0.65 for 45,000 kg castings. An alternate relation can be 

Gray Iron castings:

 for m upto 450 kg

 for m > 450 kg

where T = average section thickness in mm and K = (Fluidity index of iron in inches)/40. 

Fluidity indes is the length of the solidified metal in the spiral passing. The greater the length of the solidified metal, the greater its fluidity. 

Light metal alloys:

, where K = 0.1 for T < 6 mm, 1.19 for 6 mm < T < 12 mm and 2.13 for T > 12 mm.

Copper base and ferrous alloys:

 where p = 0.5 for m upto 500 kg, 0.67 for 500 kg < m < 5000 kg and 0.70 for m > 5000 kg.

Expression to calculate choke area (CA):

  where

m = mass of the casting in kg

 = mass density of the metal

t = pouring time

c = efficiency factor and is a function of the gating system used and

H = effective head of liquid metal

H = h for top gate

H =  for bottom gate, hm = total height of mould cavity

H =  for parting line gate, hc = height of mould cavity in cope

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