Page 265 - Manufacturing Engineering and Technology - Kalpakjian, Serope : Schmid, Steven R.

2 Chapter 10 Fundamentals of Metal Casting

where Q is the volume rate of flow (such as m3/s), A is the cross sectional area of
the liquid stream, and 1/ is the average velocity of the liquid in that cross section.
The subscripts 1 and 2 refer to two different locations in the system. According to
this law, the flow rate must be maintained everywhere in the system. The wall
permeability is important, because otherwise some liquid will escape through the
walls (as occurs in sand molds). Thus, the flow rate will decrease as the liquid
moves through the system. Coatings often are used to inhibit such behavior in sand
molds.
Sprue Design. An application of the two principles just stated is the traditional
tapered design of sprues (shown in Fig. 10.8). Note that in a free-falling liquid
(such as water from a faucet), the cross sectional area of the stream decreases as the
liquid gains velocity downward. Thus, if we design a sprue with a constant cross
sectional area and pour the molten metal into it, regions can develop where the liq-
uid loses contact with the sprue walls. As a result, aspiration (a process whereby air
is sucked in or entrapped in the liquid) may take place. One of two basic alterna-
tives is used to prevent aspiration: A tapered sprue is used to prevent molten metal
separation from the sprue wall, or straight-sided sprues are supplied with a choking
mechanism at the bottom, consisting of either a choke core or a runner choke, as
shown in Fig. 11.3. The choke slows the flow sufficiently to prevent aspiration in
the sprue.
The specific shape of a tapered sprue that prevents aspiration can be deter-
mined from Eqs. (10.3) and (10.4). Assuming that the pressure at the top of the
sprue is equal to the pressure at the bottom, and that there are no frictional losses,
the relationship between height and cross sectional area at any point in the sprue is
given by the parabolic relationship
A1_ lv;
AZ- bl, (10.5)

where, for example, the subscript 1 denotes the top of the sprue and 2 denotes the
bottom. Moving downward from the top, the cross sectional area of the sprue must
therefore decrease. Depending on the assumptions made, expressions other than
Eq. (10.5) can also be obtained. For example, we may assume a certain molten-
metal velocity, V1, at the top of the sprue. Then, using Eqs. (10.3) and (10.4), an
expression can be obtained for the ratio A1/A2 as a function of lvl, loz, and VI.

Modeling. Another application of the foregoing equations is in the modeling of
mold Elling. For example, consider the situation shown in Fig. 10.7 where molten
metal is poured into a pouring basin; it flows through a sprue to a runner and a gate
and fills the mold cavity. If the pouring basin has a much larger cross sectional area
than the sprue bottom, then the velocity of the molten metal at the top of the pouring
basin is very low and can be taken to be zero. If frictional losses are due to a viscous
dissipation of energy, then fin Eq. (10.3) can be taken to be a function of the vertical
distance and is often approximated as a linear function. Therefore, the velocity of the
molten metal leaving the gate is obtained from Eq. (10.3) as
1/ = c\/Zgh,

where lv is the distance from the sprue base to the liquid metal height and c is a fric-
tion factor. For frictionless flow, c equals unity and for flows with friction, c is
always between 0 and 1. The magnitude of c varies with mold material, runner
layout, and channel size and can include energy losses due to turbulence, as well as
viscous effects.