VELOCITY
OF METAL FLOW IN A SPRUE
Green sand casting is one of the simplest and most
popular casting processes. The following figure shows the schematic diagram of
a simple green sand mold together with all the components of the gating system.
The gating system of a sand mold consists of pouring basin, sprue, sprue basin,
runner, gates, and runner extension. The design of the gating system mainly
involves considerations of fluid flow. To avoid formation of casting defects, it
is necessary to control the rate of mold filling. Too fast a metal flow causes
air entrapment, porosity and dross formation, and erosion of sand, whereas too
slow a flow causes the metal to solidify prematurely, yielding defects such as
misrun (an incomplete casting) and cold laps (inhomogeneous or layered casting surface).
A well-designed gating system evenly distributes the incoming metal to all
parts of the mold without causing turbulence or sand erosion.
A pouring basin is either rectangular or square in
cross-section, with a fiat base and a fillet at the base near the sprue
entrance. Spherical pouring basins with a curved base cause vortex flow and
casting defects. A sprue connects the pouring basin to the runner. A sprue is usually
tapered to allow for downward laminar flow, and the sprue basin provides space
for the metal to dissipate some energy before changing its direction as it
flows into the runners.
EXAMPLE
The figure shows a tapered sprue with the metal head
H1 in the pouring basin, and the total metal head, H2.
The cross-sectional areas at the top and the bottom of the sprue are A1
and A2. Determine the metal flow velocity at the top and bottom of
the sprue. Also derive a relation between heads H1, H2
and cross-sectional areas A1, A2 of the sprue.
SOLUTION
From the basic fluid mechanics, using Bernoulli’s
Principle, we have
The velocity of fluid
(v) at a cross-section with head ‘h’ is given by
Metal head at the top of sprue is H1 and
metal head at the bottom of sprue is H2.
Similarly, considering the metal flow in the gating
system,
The metal flow velocity at the top (vtop)
of the sprue is given by
The metal flow velocity at the bottom (vbottom)
of the sprue is given by
We know that the fluid mass crossing the areas A1
and A2 per unit time is constant i.e. the metal mass flow rate is
constant.
So, the mass flow rate (ṁ) at the top of
sprue is equal to that at the bottom of the sprue.
Mass flow rate (ṁ) = velocity × density ×
Area of cross-section
This yields the fundamental relationship A1√H1
= A2√H2 .
very good
ReplyDeleteplease tell how-to find taper angle?
ReplyDelete