Mathematically determined solidification for timing the...

Metal founding – Process – With measuring – testing – inspecting – or condition determination

Reexamination Certificate

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Reexamination Certificate

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06631752

ABSTRACT:

BACKGROUND OF THE INVENTION
“A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.”
The quest for a “solidification time” began in the early 1950's when Doehler-Jarvis Corporation constructed a 2000-ton machine demonstrating the capability to produce castings weighing more than 70 pounds. Previous die casting machines were limited to 800 tons of locking force, maximum and could only produce castings weighing up to approximately 2 pounds. The “solidification time” it was believed would indicate on the basis of the wall thickness, the alloy temperature and the die temperature time, the maximum time allowable to fill a casting of given weight (volume). The hypothesis was that the temperature of the solidifying metal in the thinnest wall of the casting could not fall below the solidus point of the alloy before the cavity was filled and a high static pressure applied to the molten metal.
Perhaps the first reference to the concept of “solidification time” in relation to “fill time” can be found in H. H. Doehler's 1951 book, “Die Casting”, McGraw-Hill Book Company, in two statements. “In the final analysis, the last portion of metal necessary to complete a casting must enter before the portion that entered first has solidified. It therefore follows that injection speed is one of the most important variables in die casting.” Doehler determined a relative injection speed for a number of zinc and aluminum alloys, stating which alloy should be injected faster than another does but gave no absolute values.
Subsequent researchers produced solidification times either based on empiricism or formulated equations based upon a rationale of classical metallurgy. In 1957 J. Lapin formulated a table for the “solidification times” of various wall thickness and metals in his “Analytical Approach to Gate Design”, This empiricism was one of the earliest attempts to quantify a number for the time in which a die cavity had to be filled. Following the postulate that to produce a high quality die casting the die caster should fill the die cavity before the alloy reaches the solidus or final freezing temperature, F. C Bennett, Dow Chemical Company, in “Designing Die Casting Dies to Work on Early Shots” presented an equation in November 1966 for the filling time. Bennett's equation assumed half of the thermal energy above the solidus was concentrated at the mid-plane of a given wall and calculated the time for this energy to drop through a gradient determined by the molten alloy-die surface temperature difference.
Bennett's equation is: &thgr;=
q*x
/(
k*S
(
tm−td
))
where: &thgr;=the maximum fill time in seconds, S=surface area (square inches),
tm=mid plane alloy temperature (°F.), td=die surface temperature (°F.)
x=midplane-to-die distance (inches), q=the heat flow during fill time &thgr;, (Btu)
In 1965, culminating three years of research sponsored by the American Foundrymen's Society, the American Die Cast Institute, and the International Lead, Zinc Research Organization, Wallace, J. F. and Stuhrke W. F., Case Institute of Technology “Gating of Die Castings”, developed the constant flux model for heat flow in a die casting die. A series of equations were formulated which permitted the prediction of temperature-time curves for the steel die surface to which the heat from the molten alloy was being transferred. The equations of the researchers were erroneously based on the linear flux model of Franz Neumann, “Die partiellen Differentialgleichungen der mathematischen Physic, Wallace, and Stuhrke placed a thermocouple in the surface of a die casting die which cast alternatively ⅛ inch or ¼ inch plates of zinc alloy, Zamak 3 or aluminum alloy 380. Relying on classical metallurgy, i.e. 1) that the superheat (heat above the liquidus) flowed out of alloys before the heat of solidification and 2) the alloys must fill the cavities while their temperature is above the classical solidus the Case researchers searched for an impediment to the heat transfer from alloy to die. This study produced considerable quantitative and supportive data, which has aided the die cast industry even to the present date but did not result in a scientific basis for the solidification of metals in a die casting die.
Also accepting the classical metallurgy hypothesis, which necessitated a “film coefficient”. was C. W. Nelson, Dow Chemical Company, “Nature of Heat Transfer at the Die Face”. To conduct his study with the goal of finding a “solidification time” Nelson mounted five thermocouples in a die casting die which produced a 3″×8″¼″ thick magnesium AZ91 alloy plate similar to the Wallace work and produced die temperature recordings. One of the thermocouples was exposed at the surface and measured the AZ91 boundary temperature as the casting die would sense it. Based on the die surface temperature recordings Nelson drew a magnesium boundary surface profile above the thermocouple die temperature curve for the time frame that he perceived. The assumption was made the magnesium curve commenced at the liquidus line and decayed from this point. Nelson then proceeded to calculate the “film coefficient” factor “h” for the superheat, the matrix, and finally the solidified cooling magnesium.
In spite of the inability to demonstrate a sound technical “solidification time” devices had been produced which could measure the hydraulic pressure in the cylinder used to inject the metal into the die. The generic name for such a device is hydrauliscope and in its simplest versions consists of a pressure transducer located in the inlet of the injection cylinder with the analog output of the transducer converted to digital then being fed to a computer. The computer display of the transducer output will have the pressure variable plotted on the vertical axis and time on the horizontal. Significant events in the injection cylinder displacement of molten alloy correlate with pressure changes. A pressure rise occurs when the injection cylinder and piston have traveled such that molten metal now must be displaced through the ingate orifice to the casting and the resistance to the cylinders movement increases. When the cavity has filled and further displacement of metal is not possible the kinetic energy of the moving injection mechanism and fluid in the cylinder is dissipated and its dissipation is revealed by a sharp rise in the pressure followed by a damped oscillation of the pressure. The “fill time” is therefore the difference between the readily detectable sharp rise signaling the die cavity is full and the earlier pressure rise, well recognized as the time when metal commences to flow into the cavity.
Without considerable precision in the determination of the “solidification time” the “fill time” must depend on the experience of the user. Following the Nelson work in 1970 the quest for the “solidification time” was largely abandoned until the inventor decided to readdress the problem. In 1961 the inventor attempted to solve the problem on the basis of the concept of a temperature gradient between the center of an alloy wall and the die surface but found due to the unavailability of elevated temperature properties for the die cast alloys and restricted computer capability it could at best be a crude approximation. By 1996, computers with state of the art hardware and software were available at the retail level for several thousand dollars, which were more powerful than those costing several millions in 1961.
Essential to the advancement of a science in the transient supercooling and solidification of metal in a die casting die was the formulation of a mathematical analysis that was not an empiricism and had its roots in trad

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