sand casting

1.0 Calculations

1.1 Sizing of component (including Shrinkage allowance)

When cooling from molten state, all metals decrease in volume. When cold, casting will be smaller than their pattern. In order for parts to be of correct size, patterns are made larger to allow shrinkage. The extra size is called Shrinkage Allowance.
Different metals have different Shrinkage Allowances.
For the purpose of our project, we have been using Brass having shrinkage allowance of 1.5%.

Length
Nominal Dimension/mm
Dimension for Shrinkage/mm
A
15
15.2
B
50
50.8
C
25
25.4
D
29
29.4
E
25
25.4

Dimension for shrinkage (mm) = (1.5/100) x Nominal Dimension + Nominal Dimension
Source:-
http://en.wikipedia.org/wiki/Casting_%28metalworking%29
Metal Casting a Sand Casting Manual for Small foundry volume 2.pdf

1.2 Height of the Sprue

Starting from principle of conservation of Energy (Bernoulli’s equation)

Since; we are working with absolute Pressure at pouring basin surface, therefore P1 = 0, we are considering datum about point as 3, therefore h3=0, we are assuming v1 (velocity of fluid in pouring basin) to be negligible as compared to v3, therefore v1=0,

Balancing equation at 1& 3

Equation 1
Now balancing equation at 1 & at h

Since; we are considering datum about point as 3, therefore h3=0,
We are assuming v (velocity at casting interface to be small), therefore v=0,
We are assuming v3=0 & P=0,
 Equation 2
We substitute Equation 2 in Equation 1.
We end up with;

We assume h=0,
∴  Equation 3
Source:- Manufacturing Notes - Dr.Ramasawmy
Where,
v3=Velocity of metal at sprue base (m/s) g= acceleration due to gravity (m/s2) ht= Height of sprue (m) h= height of metal in mould at any instant
P1,P3 & P pressure at points 1,3 & h respectively. ρ= Density of Brass (kg/m3) m=mass of brass in kg v1,v3 & v, velocity at position 1,3 and h respectively.
Now, Q=Av
Where Q=Volumetric discharge (m3/s)
A= Area (m2)