Applying PCs to 3-D solidification modeling.

Rapid advancement in computer technology has brought a powerful, new tool to the desks of foundry engineers.

Over the past decade, new technologies have opened many new doors for foundrymen. The pace of technological development seems to be continually increasing. Today, just keeping up with these advances is a demanding task.

One of the new developments that is gaining significant acceptance actually has its roots deep in the ancient traditions of foundry practice and knowledge; this is solidification modeling. This technology allows us to create an image of a casting (with its gates, risers, and the mold) on the computer screen and watch what happens as that casting cools and solidifies. With the computer's help, we can predict whether the risers are feeding properly, whether a particular section of a casting will freeze before or after another section, whether porosity will occur anyplace in the casting, and even what the microstructural characteristics of a given area might be.

In prior years, this knowledge was available only after much trial-and-error practice on the foundry floor; foundry engineers built up a body of knowledge about casting practice after many years of observation of successes and failures. There is still a tremendous need for engineers to be involved in, and understand, foundry practices. The new technology of modeling, however, can bring about process understanding more rapidly than before, as well as shortening the development time for new casting and rigging designs.

Today, the capability to perform sophisticated modeling on personal computers stems from two parallel developments over the last decade. The first is the phenomenal growth in the power available with personal computers. From our vantage point, PCs of the early 1980s were slow, with crude displays and limited memory. At the time, however, these machines represented a fantastic liberation from the large and expensive computers of the '60s and '70s.

For the first time, computer power was available to individuals on a modest budget. These machines were perfectly suited for simple approaches to modeling, such as calculating the "section modulus" (the ratio of volume to surface area) of various chunks of the casting so that Chvorinov's rule (those areas with the highest section modulus values freeze last) could be applied.

With the advancement in available memory capacity, and with special processors to speed up mathematical calculations, it became possible to perform some simple two-dimensional analyses of casting solidification using basic engineering principles. This was the beginning of solidification modeling on PCs. The advancement of computer power available to individuals is one of the phenomenal success stories of this century.

The second development that has been instrumental in delivering modeling power to the foundry has been the increase in sophistication of the software that is available to build and run casting models on personal computers. This software has developed in stages, from the early versions mentioned previously, through more complex two-dimensional models, to full three-dimensional models that have only recently become available. This article describes one such system, the AFS Solidification System (3-D).

3-D Modeling

The basis of this system is a simple engineering calculation for heat flow through materials. While this calculation is simple, its application to castings of complex shape is not. The approach taken, therefore, is to break a complex casting down into many small, regular shapes, similar to stacking many small cubes together to produce an approximation of the casting shape. Heat flow calculations can be applied to each of these small shapes in a simple manner. The entire casting can then be simulated by applying these calculations in a series of "waves" through the casting model. This allows us to predict in detail the order of solidification of various parts of the casting, as well as cooling rates and temperature gradients that can assist us in judging the soundness of the cast material.

In order to run a solidification model of a casting, a series of logical steps must be followed. The first step is to specify the properties of the materials that will be used in the casting process. This includes the cast material, as well as the molding medium and other materials (such as chills, facing sands or exothermic materials) that will appear in the mold/casting system. Cooling channels may also be of consideration in such processes as permanent mold casting.

In searching for data on various materials, one finds that this is an area in which much development work needs to be done for the industry, as the properties of many materials through various temperature ranges are not documented. In order to improve the useability of the system, simplifying assumptions about "average" material properties through the range of use are made. To further assist the user, a built-in database of material properties for a variety of materials is delivered with the system, with the ability for the user to add materials to customize the database as time goes on.

The next step is the creation of a geometric model of the casting, with its rigging system and the mold around it. In the AFS Solidification System, this phase is accomplished through use of a portion of the system called the "Model Builder." This, in essence, is a program that allows the user to construct a three-dimensional model by assembling pieces together in a variety of ways. Certain basic shapes, such as rectangular blocks, cylinders and spheres, can be created by entering a few variables that describe those shapes. Parts of models or complete castings that have already been created on computer-aided design (CAD) systems can be "imported" into the model builder.

One routine allows the user to trace a part print on a digitizer, which is a sort of electronic drawing board, to bring cross-sectional views into a model that can then be "swept" through space to create solid components. Other shapes can be drawn directly on the screen in the model builder by using a mouse, and then used to create solids.

Using any of a combination of these techniques, the casting, risers, gates, mold and chills can all be created in the three-dimensional virtual world inside the computer. We can only view this world through the two-dimensional display screen of the computer, however, by furnishing the user the ability to rotate the model and view it from any angle, as well as the ability to "zoom in" to see detailed features, we can begin to approach the patternmaker's feel for creation of complex three-dimensional objects.

Model Building

Building a model in this way presents some interesting situations that do not normally occur in the real world. For example, it is possible to create two different solids that "overlap." Within the overlapping volume, the computer can become confused as to which type of material actually occupies that volume of space. Fortunately, the system has the ability to indicate, through the use of a priority system, which material is actually present within that region. This feature is especially useful for creating cored areas within castings.

The next step in the process is a combined one of meshing the model and creating a mold. Meshing the model refers to the process, mentioned earlier, of breaking the model down into small regular shapes so that the cooling process can be simulated. This is an essentially automatic process, with the user being asked only to determine the number of elements into which the model should be broken. A small number of elements creates a coarse grid that only fairly approximates the casting, yet which will simulate quickly. A large number of nodes creates a fine grid and a better approximation of the casting, yet may take somewhat longer to simulate. An approach that generally works well is to create first-pass analyses with coarse grids, then refine the grid as the design finalizes and final verification runs are processed.

As part of the meshing process, the system has the ability to automatically create mold material around the casting. One option for mold creation is a shell mold that creates a shell of a certain specified thickness around the casting. This is especially useful for modeling such processes as investment casting. Another option creates a rectangular mold around the casting, as would normally be found in a sandcasting process. It is also possible to bypass the automatic mold creation process, as the user can create the mold material as part of the solid-model-building activity.

Another useful concept in model building deals with "planes of symmetry." If a casting is symmetrical about a center plane, or axi-symmetric about a center axis (such as a hub casting), then it is not necessary to model the entire casting. The casting model can be "cut" along a plane of symmetry; only a portion of the casting then needs to be modeled, with exactly the same results as if the entire casting were modeled. This reduces the number of elements necessary to run a casting simulation, with a corresponding reduction in the time required to process the simulation.

After creating a mesh that approximates the casting and mold, the system allows the user to set heat-transfer coefficients on various surfaces of the meshed model.

This is particularly useful in simulating such processes as permanent mold casting, where mold sprays of various types and thicknesses are used on the surfaces of the casting and the risers. The system actually simulates the "spraying" of mold spray onto the mold surfaces by showing a view of the mold or casting and allowing the spray to be applied to the desired surfaces with a mouse. The view can be rotated so that all required areas to be sprayed can be made visible and accessible. This technique also can be used to simulate the effect of an insulating riser sleeve in a sandcasting operation.

Once all of the preliminary steps described above are completed, the simulation itself actually takes place. This consists of a number of time steps during which the system calculates the heat flow occurring between all of the small elements which have been created. This allows the system to track the progressive temperature, through time, at all points within the casting, risers and mold and to predict the successively solidified areas.

Using Simulation

When solidification is complete, a number of useful items of information can be extracted from the simulation. This is actually the heart of the system because the whole purpose for doing solidification modeling is to predict where the casting is sound and where problem areas may occur. The most basic way of viewing the results of the simulation is to look at the progressively solidified shapes that occurred during cooling. This allows the user to view areas where isolated hot spots may have occurred, or where the feeding paths from the riser into the casting may have "pinched off" and the volumetric shrinkage of the cast material is likely to produce porosity.

The system also tracks other parameters, such as the temperature gradients and cooling rates that were occurring as the casting material solidified. This information has been shown to be correlated with casting quality in a number of ways, such as predicting the occurrence of porosity as well as being indicative of the formation of desirable or undesirable microstructures within the casting. Particular combinations of these parameters, such as the temperature gradient divided by the square root of the cooling rate, have been used extensively to predict porosity in cast materials. Studies of new parameters and their correlation with porosity in castings are ongoing within the industry, supported by AFS and its members as well as government agencies.

Once a simulation of a part has been run, and potential problem areas have been identified, it is possible to modify the model in an effort to eliminate the problems and rerun the simulation to see what effect the changes may have had. Just as in the case of pouring actual castings and varying the process to produce good castings, it is possible to vary many things in the setup of the simulation. The size, number or placement of risers can be modified. The part geometry itself may need to be modified for better directional solidification. The pouring temperature of the cast material may be altered. The mold design and material, placement, size and chill material, location and size of cooling channels or insulating sleeves, as well as many other things can be experimented with by modifying the model and its initial conditions.

Given the ability to experiment with all of these factors prior to actually pouring castings, it is reasonable to expect a higher probability of good parts early in the casting production phase, with a corresponding reduction in development time. Higher quality and reduced lead times are critical to a foundry's success in today's markets.

Some additional capabilities of the system include the ability to run a "batch" of simulations in an unattended mode, so that the user can create a variety of models and instruct the computer to run them sequentially without the need to start and stop each one independently. The system also has the ability to automatically simulate cycling of metal molds (such as permanent mold or diecasting applications). This involves the successive introduction of "shots" of metal into the mold (and mold cooling during the ejection cycle), with the mold temperature progressively building up to a steady-state condition by repeated cycling.

Other Uses

Other potential uses for the system remain to be explored. Since the heat-transfer calculations do not specifically require that a solidifying material be simulated, any situation involving conductive heat flow can potentially be analyzed. One process example that may be studied with the system is shell coremaking. In this case, heat penetration into the sand might be used to predict the thickness of the subsequent shell to be formed. It also could be used to study the internal temperature distributions in parts that are being heat treated, where there is a concern that massive areas are not receiving the same treatment as thinner areas due to time lags in transferring heat.

In summary, the technology of simulation of heat transfer offers opportunities to improve foundry processes in many ways:

* by improving the abilities and knowledge of foundry engineers;

* by reducing lead times and improving quality for new parts;

* by helping to solve problems in our existing processes;

* and by improving the ability to communicate our foundry knowledge to designers and users of castings.

As the past few years have shown, this technology will continue to improve and become more powerful. While the use of such tools must always be tempered with practical, experienced foundry managers and engineers, it is clear that solidification modeling will be an accepted and essential part of foundry practice in years to come.