7.2 The ``common'' diagram

In the diagram, the solution is determined by
finding the intersecting point of the runner/mold characteristic line
with the pump (die casting machine) characteristic line.
The intersecting point sometime refereed to as the operational point.
The machine characteristic line is assumed to be understood to some degree
and it requires finding experimentally two coefficients.
The runner/mold characteristic line requires knowledge on the
efficiency/discharge coefficient, , thus
it is an essential parameter in the calculations.
Until now, has been evaluated either experimentally, to be assigned to
specific runner, or by
the liquid metal properties (
) [#!poro:dcrf!#]
which is de facto the method used today and refereed herein as the ``common''
diagram^{2}.
Furthermore, is assumed constant regardless to any change in any of the
machine/operation parameters during the calculation.
The experimental approach is arduous and expensive,
requiring the building of the actual mold for each attempt with average cost of
$5,000-$10,000 and is rarely used in the industry^{3}. A short discussion about this
issue is presented in the Appendix comments to referee 2.

Herein the ``common'' model (constant ) is constructed. The assumptions made in the construction of the model as following

- assumed to be constant and depends only the metal.
For example, NADCA recommend different values for aluminum, zinc and magnesium
alloys.
- Many terms in Bernoulli's equation can be neglected.
- The liquid metal is reached to gate.
- No air/gas is present in the liquid metal.
- No solidification occurs during the filling.
- The main resistance to the metal flow is in the runner.
- A linear relationship between the pressure, and flow rate (squared),
.

According to the last assumption, the liquid metal pressure at the plunger
tip, , can be written as

Where:

the pressure at the plunger tip

the flow rate

maximum pressure which can be attained by the die casting machine

in the shot sleeve

maximum flow rate which can be attained in the shot sleeve

The and values to be determined for
every set of the die casting machine and the shot sleeve.
The value can be calculated using a static force balance.
The determination of value is done by measuring the velocity
of the plunger when the shot sleeve is empty.
The maximum velocity combined with the shot sleeve
cross-sectional area yield the maximum flow rate,

where represent any possible subscription e.g.

Thus, the first line can be drawn on diagram as it shown by the
line denoted as *1* in Figure .
The line starts from a higher pressure () to a maximum flow rate (squared).
A new combination of the same die casting machine and
a different plunger diameter creates a different line.
A smaller plunger diameter has a larger maximum pressure () and
different maximum flow rate as shown by the line denoted as *2*.

The maximum flow rate is a function of the maximum plunger velocity and the
plunger diameter (area).
The plunger area is a obvious function of the plunger diameter,
.
However, the maximum plunger velocity is a far-more complex function.
The force that can be extracted from a die casting machine is essentially
the same for different plunger diameters.
The change in the resistance as results of changing the plunger (diameter)
depends on the conditions of the plunger.
The ``dry'' friction will be same what
different due to change plunger weight,
even if the plunger conditions where the same.
Yet, some researchers claim that plunger velocity is almost invariant in regard
to the plunger diameter^{4}.
Nevertheless, this piece of information has no bearing on the derivation
in this model or reformed one, since we do not use it.

= 90 true mm

= 90 true mm

A simplified force balance on the rode yields (see more details in section page )where subscript denotes the actuator.

In the ``common'' diagram is defined as

Note, therefore is also defined as a constant for every metal

The flow rate at the gate can be expressed as

The flow rate in different locations is a function of the temperature. However, Eckert poro:ecksimilarity

Hence, we have two equations () and () with two unknowns ( and ) for which the solution is

insert a discussion in regards to the trends insert the calculation with respect to and

copyright Dec , 2006

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