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'' diagram2. 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 industry3. 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
According to the last assumption, the liquid metal pressure at the plunger
tip, , can be written as
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,
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 diameter4. 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
In the ``common'' diagram is defined as
insert a discussion in regards to the trends insert the calculation with respect to and