Jerry Thiel and Sairam Ravi
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As liquid metal solidifies, it contracts first in volume and then physical size.  Accurately predicting the final dimensions has been accomplished with a set of simple rules along with significant tribal knowledge.  Although the age of creating master patterns with wood are mostly behind us, the industry still uses trial and error when producing patterns to meet specific casting dimensions.

This method was aided by the use of “shrink rules,” and more recently, CAD geometry volume compensation, neither of which accurately predict final casting dimensions. This method of producing patterns is very costly, often requiring as much as 40% of the original pattern cost for dimensional adjustments. Previous researchers have studied the effects of various geometry and areas constrained by cores. Previous research in sand expansion has identified several mechanisms whereby changes in the mold and core dimensions render current single volume percentage decreases inaccurate in determining final casting dimensions.

By understanding the dimensional changes sand undergoes during rapid heating and the rigidity of the molding media, accurate predictions can be made to the final casting dimensions given a specific pattern size.

Question: Can computer process modeling be used to determine casting dimensions from room temperature pattern dimensions?

1: Background

As the ability to create castings true to designs improves, reductions in machine stock can be made to decrease cost, improve reliability and speed production.

A conservative estimate is that a majority of all castings produced require some sort of machining operation.  As much as half of the machine stock added is commonly required to account for variations in the final dimensions.  These final casting dimensions are affected by several issues.  Conventional molding methods rely on forming casting cavities by forming sand around pattern shapes.  CNC machining has much improved the dimensional accuracy from manual pattern making methods allowing tooling tolerances in the thousandths of an inch from nominal.  The molding process itself imparts a large degree of variation in transferring pattern geometry to molds and cores.  These production methods inherently add as much as +/- 0.02 – 0.03 in. variation to the mold’s surface dimensions.  All of these considerations fail to account for the variation of pattern dimensions to final casting dimensions.

Accurately measuring the high temperature dimensional changes in molding materials has shed new light on additional sources of dimensional variation in final casting dimensions.  Dimensional changes of 1–1.5% result from the phase transformation of silica from alpha to beta quartz.  Changes over 4% are seen as a result of either tridymite or cristobalite transformations.  

These changes in dimensions cause changes in the volume of the casting cavity as well as the individual features.  The amount of dimensional change is directly proportional to the amount of heat transferred from the liquid metal to the mold and the length of time before solidification occurs.  The final dimensions of the casting also are affected by issues such as mold wall movement or casting swell in both green sand and chemically bonded molds. 

Computer modeling of the casting process has given us tools to understand and predict not only the internal soundness of the castings to optimize feeding systems, but also to understand thermal events at a higher level.  Although at this time this method only considers one variable in a group of many, it provides a valuable and at times extremely accurate prediction of final casting dimensions.

2: Procedure

The step cone casting test was originally developed to detect gas in the newly developed phenolic urethane binder system (Fig. 1-2).  Since then, its use has expanded to include the testing aggregates and binders for their susceptibility to penetration and veining defects. 

This test is conducted by pouring metal against a step cone core. The step cone core consists of six different sections with internal diameters from 1.5-4 in. (3.81 - 10.16 cm) in 0.5 in. (1.27 cm) increments. The different steps represent different section thicknesses of the metal casting and give a good understanding of the role of different cooling rates of the metal in casting quality and defects.

The flaskless mold is produced using a similar binder system, but it does not affect the veining, penetration or dimensional accuracy tendencies of the test casting. The test castings can be poured from a variety of metals including gray iron, steel and copper-based alloys. Pouring times for the molds are 10-12 seconds. Once the castings cool to room temperature, they are removed and the gates are sectioned off with loose sand. The castings are wire-brushed and sand blasted to remove any loose sand on the surface and then are tested for dimensional accuracy. Following this, they are sectioned and evaluated for veining and penetration defects.

A coordinate measuring machine (CMM) was used to measure the dimensions of cores and castings. Step cone cores were first measured 24 hours after being made.

The cores were then coated with a high solid zircon refractory coating, as per industry practice, and dried at 212F (100C). in an oven before being measured again to determine coating thickness. Once the castings were poured, they were sand blasted to remove adhering sand and measured along the six different steps. From the core and casting data, dimensional deviation of the casting from the core was calculated and plotted.

3: Results and Conclusions

The difference between the actual casting dimension and the theoretical casting dimension calculated from the shrink rule is apparent. The actual casting dimension depends on the section thickness of the casting. At the thinner casting sections, that is at the 4 in. (10.16 cm) step to the 3 in. (7.62 cm) step on the core, the casting is smaller than the original core size. However, at the thicker casting sections, the casting is larger than the original section size. The thicker metal sections take longer to solidify and the temperature of the core is higher than at the other sections.

Silica with 10% zircon displays a similar trend as silica in the thinner metal sections. At the 2 (5.08 cm) and 2.5 inch (6.32 cm) steps, a marked difference between the two samples appears. At the 1-in. (2.54 cm) step, however, both silica and silica with 10% zircon display a dimensional change of plus-0.03 in. (0.076 cm) in the casting.

In the thinner sections, the metal solidifies at a faster rate and is solid enough not to move with the core expansion. Due to similar alpha-beta peak expansion between the two samples, the thinner sections are similar to each other. However, a steeper contraction is seen in the zircon blend sample after the alpha-beta transition when compared to baseline silica. This will affect the thicker sections more as the metal solidifies at a slower rate and is mobile to move with the core which reaches higher temperatures when compared to the thinner sections. This will lead to a low expansion or contraction of the core at that particular step, leading to better dimensional accuracy.

At the thickest section of the casting, the metal will remain in a liquid state longer and is mobile when the core surface undergoes the cristobalite phase transition leading to a large secondary expansion.

Silica with 20% zircon displays a trend similar to the 10% zircon sample with slightly lower expansion at the thinner sections of the casting. This is due to the slightly lower peak expansion seen in the 20% zircon sample at the alpha-beta phase transition.

Better dimensional accuracy can be seen in the thicker sections of the casting.

Silica with 30% zircon displays lower expansion of the casting through the 1.5–3.5-in. (3.81 - 8.89 cm) core step when compared to baseline silica sand.

Silica with 40% zircon displays similar results in the 4- and 3.5-in. (8.89 cm) core section as 30% zircon. However, in the 3-in. (7.62 cm) and 2.5-in. (6.35 cm) section, the casting contracts more in the 40% zircon sample due to the sample having the lowest alpha-beta peak expansion, and subsequently, a lower contraction after the alpha-beta transition.

Prediction of Final Casting Dimensions

The high temperature properties of molding materials have a large effect on the quality of the finished casting. It also has been shown that the thermal expansion of molding aggregates is one such property that needs to be addressed.  This can cause changes in the dimensions of the cores and molds and thus finished castings. 

The versatility of the casting process is demonstrated by the ability of the metal in its liquid state to conform to the volume of its container. By understanding the heat transfer of the molding aggregate and its effect on the temperature of the cores and mold, we can estimate the dimensional changes that take place during the casting process. 

The temperature of the core already increased above 2,372F (1,300C) on the surfaces of the 1–2.5 in. step dimensions.  The temperature of the adjacent metal is above the liquidus temperature of the steel used in the experiment.  The thermal expansion of the sand increased the dimension of the core to 0.005 in. at the 2.5 in. step while the metal is still in its liquid state. 

Once the liquid metal solidifies, it contracts in its solid state according to the coefficient of thermal expansion (CTE) of the respective metal.  This solid state contraction for the ASTM A128 WCB steel was measured at 7.229 X 10-6 in/in. F.  The austenite transformation is visible at around 1,250F (676C).

The dimensions of the core at each diameter step were determined using the simulation core displacement results at the liquidus temperature of the adjacent metal (Fig. 6-7).  This event occurred at multiple time steps during the cooling of the casting relative to the core and casting section size.  This was the first attempt at determining the critical temperature (temperature at which solid state contraction following the published CTE occurs). 

The published shrink rule of 0.250 in./ft. of dimension fails to accurately predict the final casting dimension.  The predicted dimension of +0.008 in. at the 2.5-in. step shows a similar trend to the actual casting dimensions but underestimates the effect of the expansion of the core. 

As the casting cools past the liquidus temperature, the core temperature continues to increase.  This increase of core temperature continues to affect the dimensions of the expanding sand, resulting in increases in the core’s diameter.  The accurate prediction of final casting dimension must determine at which point the metal obtains its final form and at that point contracts as is predicted by the CTE of the solid metal.  By moving the core measurement further down the cooling of the metal to the solidus temperature, the predicted dimensions of 0.025 in. at the 2.5 in. step of the internal sections of the casting closely follow the actual measurements obtained by the CMM. 

This leads us to believe the final casting dimensions depend on the core dimensions related to the molding aggregates thermal expansion at the time of solidification (Fig. 5).

Zircon sand, which exhibits low expansion, was used to modify the expansion profile of the molding aggregate and therefore change the core dimensions at the critical or solidus temperature of the adjacent metal. 

The peak expansion for silica with 10% zircon is similar to baseline silica sand.  However, from 20% zircon onwards, a reduction in the alpha-beta phase transition peak expansion can be seen with silica with 40% zircon having the lowest peak of 0.005 in./in., which is lower than baseline silica by 56%.

The 100% silica sand has the greatest amount of expansion at the alpha/beta quartz, A/B transformation and a distinct transformation point to cristobalite.  The various blends of silica sand with zircon sands show a reduced amount of A/B peak transformation that reduce the core dimensions at the adjacent metal’s critical temperature reducing the predicted diameter of the casting section.  

Although the cases in this research are restrictive, it provides solid insight into more accurate predictions of final casting dimensions based on molding aggregates. Further studies will be undertaken to address large core mass and low metal mass situations where the core retains more strength and may restrict metal contraction.  

This article is based on a paper (16-076) that was presented at the 2016 CastExpo in Minneapolis.