Solidification modeling of cast aluminum wheels.

Alloy wheel fabrication is one of the more exacting tasks facing the foundryman. This critical automobile part may be broken down into three sections (Fig. 1).

Hub-where the wheel bolts to the vehicle.

Rim-also called wheel bed, which must be checked for air tightness and curb impact resistance.

Spoke-which joins the hub to the rim. This highly stressed section must resist the forces transmitted from the road to the tire. Maximum solidification takes place in sharp curves, when the spoke section is subjected to rotary bending.

Fatigue tests must be performed on special machines that reproduce actual conditions and measure the number of cycles to wheel failure. These tests are systematic during the stage of prototype development, and performed on samples picked from production lots. Alloy wheels also undergo 100% x-ray inspection where cracks can be detected usually near the rim/spoke Y junction.

In fact, few castings combine such complexity in shape with such high requirements in terms of physical integrity, not to mention dimensional accuracy, surface finish and corrosion resistance. Directional Solidification 

Alloy wheels may be manufactured by the gravity, pressure or centrifugal casting processes. However, low pressure permanent mold (LPPM) is the most commonly used foundry process for this application.

A consistent high level of casting integrity can be achieved only if a sufficient degree of directional solidification is maintained throughout the freezing process.

A simple geometric approach, based on solidification modulus, is adequate to assess solidification directionality in sand or investment casting. However, this procedure presents some shortcomings when it comes to permanent mold casting because of the differences in thermal conditions at the mold/casting interface. This is because, in large part, neither mold temperature nor coating application are uniform. Actually, the foundryman can take advantage of this potential lack of uniformity to enhance directional solidification so as to produce quality castings.

Consequently, solidification modeling is the only scientific approach that may help establish "close-to-target" production parameters prior to the initiation of trial runs. Solidification Modeling

About a dozen commercial software packages(l,2) have emerged f rom the considerable amount of activity deployed in universities and research centers around the world. They range from the simpler AfSolid, which reproduces on a personal computer the solidification history of an extrusion" of any shape, to the most complex schemes, solving simultaneous fluid mechanics and heat transfer problems (i.e., Magma, Procast, Simulor).

The use of solidification modeling has encountered some skepticism and restraint with potential users because of the prevailing intricate shape of castings and the large number of parameters that have to be taken into account. Also, some of these packages are too complex for their general use by the "hands-on" foundryman. This is particularly true when it is clear that no mathematical analysis, however sophisticated, will give infallible answers. Some physical phenomena and many production parameters simply cannot accurately be "cast" into equations.

In order to avoid disillusionment when initiating a program it is suggested that one of the less complex software packages be used. AfSolid is a good example of the basic solidification modeling programs that are available; its merits and limitations have been we d mented.(3) However simplified the underlying assumptions may be, making decisions on the basis of an AfSolid analysis is a giant step toward consistency and repeatability as compared to the old way based on feel and intuition. In fact, scientific analysis does not preclude experience; it only builds on it because it allows us to document each new experiment so as to be in a position of using it on castings of different configurations and/or fabricated under a different set of conditions.

Modeling LPPM Alloy Wheel

The potential of modeling can be demonstrated by studying the solidification of a wheel cast in aluminum A356 at a temperature of 125OF (680C) in a mold preheated at a uniform 57OF (300C), dressed with a white insulating coating 180 him thick.

When wheel geometry and thermal properties of aluminum are known, along with the mold metal heat transfer coefficients,(4) the cooling solidification simulation can be performed via Afsolid.

Figure I indicates that 33 seconds into the cooling process, complete solidification (white area) has taken place at the upper edge of the rim. The rest of the casting is mainly in a mushy state, a consequence of the relatively large freezing range (1080-115OF/580-620C) of alloy A356. The situation would be quite different for the short-freezing range alloys of higher silicon content also used in wheel foundries. From the single shot of Fig. 1, it can be deduced that solidification will exhibit a high degree of directionality in the spoke and hub section, contrary to what takes place at the rim/spoke Y junction and possibly in the rim upper section. It may be safely concluded that for the present wheel geometry only these areas should be of interest as far as solidification shrinkage is concerned.

in order to improve the accuracy of the simulation, the wheel has been split into two parts, as shown in Fig. 2, along a plane across which very little heat is transferred. The rim and the spoke are thus analyzed separately, which is legitimate if the plane of separation is adiabatic.(1)

Mold Coating and Temperature

Critical zones of the wheel casting, which were located earlier for uniform mold temperature and coating conditions, are analyzed in a more detailed fashion in Fig. 3, showing solidification at 14 and 33 seconds after mold filling. The figure at left shows clearly that a negative gradient is established in the upper part of the rim early in the solidification process so that mass feeding will be interrupted long before complete solidification occurs. Shrinkage will result. Where and how much shrinkage will occur depends on the ability of the alloy to feed across a partially solidified zone and on the liquid metal pressure applied by the LPPM casting machine. The temperature map after 33 seconds (Fig. 3, rt) shows that a shrinkage cavity also will form at the Y junction. Process Mold Temperature

The widely varying sections of the casting at hand will generate temperature differences in the mold after a few production cycles. Typical mold temperature distribution measured during the established regime was recorded by Ohtsuka. (6)

Although AfSolid does not allow nonuniform external surface temperatures, it is still possible to take into account surface temperature variations by altering the value of the surface heat transfer coefficients at the casting/mold interface. The temperature maps in Fig. 5 show that, in spite of the favorable influence of mold temperature distribution, shrinkage problems will be encountered, although to a lesser degree.

The clear-cut result of this simulation is that a sound casting will not be obtained with a uniform mold coating even after running-in the mold with prescribed temperatures. Mold Coating Crucial

AfSolid allows for the assignment of individual heat transfer coefficients to each section of the wheel contour. This was done by combining the available heat transfer properties of mold coatings(4) to the typical process mold coating distribution of Fig. 4.(6)

Temperature maps of Fig. 6 were obtained by incorporating the difference of both mold temperature and coating thickness. They show clearly that no negative temperature gradients exist in both critical sections of the wheel. In this instance, the likelihood of solidification shrinkage can be appraised through objective numerical criteria such as Niyama's (contained in AfSolid) or the solid fraction gradient,(7) readily measurable on the casting temperature maps.

Calibration, however, must be performed by running statistically significant foundry experiments because local factors like origin of ingots, amount of returns, cleanliness and gas level in the melt as well as modification will affect the criterion numerical threshold separating good castings from rejects.

Modeling Delivers

Understanding the phenomena taking place during casting solidification is, in itself, paramount to the soundness of the technical decisions that must be made in a foundry, especially when starting a new production run. However, the major benefit of solidification modeling is to eliminate development delays and shorten trial run campaigns. The consequent reduction in the time span between design and finished product is a decisive marketing advantage today, especially in consumer goods industries.

Solidification modeling helps foundrymen get ready to face this increasing pressure while enabling them to convince their customers that, in spite of the unavoidable fluctuations in production parameters, their process is under control and capable of consistently producing castings within specifications.

Editors note: Since the time of this writing, an enhanced version of AFSolid is now available. The program includes automatic simulation of the complete permanent mold casting process, with thermal cycling of the mold. For more information on this software circle No. 342 on the Reader Action Card.

For a free copy of this article circle No. 343 on the Reader Action Card.

References

1 .T. Bex, "Solidification Modeling Reduces Casting Defects,' modern casting, pp 23-25 (Mar 1991).

2. G. Sciama, "Simulation de la Solidification et du Remplissage..." Fonderie-Fondeur d'aujourd'hui, pp 21-36 (Dec 1990).

3. L. Smiley, "Computer Solidification Modeling, modern casting, pp 35-37 ( Oct 1990).

4. F. Chiesa, "Thermal Conductance at the Mold/Metal Interface,"AFT Transactions, vol 98, pp 193-200 (1990).

5. F. Chiesa, "Heat Losses During Filling of Permanent Molds," AFS Transactions, vol. 97, p 17-26 (1989)

6. Y. Ohtsuka et al., Application of Computer Simulation to Aluminum Permanent Mold Casting," AFS Transactions, vol 89, p 638 (1982).

7. Z.H. Lee, "Prediction of Microshrinkage Porosity..." Proceedings of the 57th World Foundry Congress, CIATF, Osaka (Sep 23-28, 1990).