cost effective casting design

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Cost-Effective Casting Design:

What Every Component DesignerShould KnowViewing these six key factors as a system—while sketching geometries—provides a

workable methodology forconsistently good casting designs.

Michael A. Gwyn

Pelton Casteel, Inc., Milwaukee

Overall g eometry should be explo red—with structural, casting

and downstream manufactur ing needs in mind—before

lock ing in to a sol id mo del.

Structural design engineers who work successfully with castings commonly design in a narrow group of

casting types poured from familiar alloys (like the family of irons or the 300 series of aluminum) andmolded from familiar foundry processes (like green sand or nobake). Rules of thumb have beendevelo ed over the ears for common desi n situations.



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Close inspection of these rules reveals that they sometimes recommend conflicting geometry. Forexample, the use of gusseting instead of mass for stiffness might be labeled "recommended" in one set ofdesign rules and "poor" in another.

Further, when a design engineer leaves a familiar casting design realm for an unfamiliar one, unexpected

trouble may result. For example, let’s say we are moving from ductile iron to aluminum bronze while

staying in a familiar foundry process, nobake molding. No alarms are sounded among the "rules ofthumb," but there’s likely trouble in the usual "ductile iron-style" geometry. Good aluminum bronze

geometry is different than typical ductile iron geometry, and the molding process may need to supplementthe different geometry with heat transfer techniques. Not suspecting this, the design engineer’s newcasting design may suffer from "no-quotes," higher-than-expected prices and foundry requests for designchanges.

How are design engineers supposed to know that successfully casting geometry for aluminium bronzeshould somehow be different? And if a design engineer did know that, what would be the proper course ofdesign action?

The answer lies in a better understanding of the relationship among geometry, various foundry alloys and

structure. As shown in Fig. 1, there are six parameters (based on physics) that underlie cost-effective

casting design.

Casting Properties

1. Fluid Life

2. Solidification Shrinkage Type(eutectic, directional and

equiaxed) Volume (small,medium and large)

3.Slag/Dross Formation

Tendency

4. Pouring Temperature

Structural Properties

5. Section Modulus (stiffness ofcasting geometry)

6. Modulus of Elasticity (stiffness

of alloy itself)

Fig. 1. When co nsidered as a comp lete

system, these six parameters drive

cost-effective casting desig n.

All six, applied as a system, drive the geometry of casting design. Geometry is not only the result ofcasting design but is also the most powerful weapon in creating successful casting design.

This six-faceted system is capable of optimizing geometry for castability, structure, downstream



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processing (machining and assembly) and process geometry (risering, gating, venting and heat transferpatterns) in the mold. The process geometry forms the casting geometry.

Quickly sorting through possible casting and process geometries by marking up blueprints or by makingengineering sketches is the way to find optimal "system" geometry. An elegant result of good sketched

brainstorming can be a solid model of the casting and its process geometry, the basis of rapid prototyping

and/or computerized testing.

Applying the System

Optimizing casting geometry using the six-parameter system is not difficult. The six casting and structuralcharacteristics in Fig. 1 influence important variables in designing, producing and using metal castings.

These variables include:

• casting method;

• design of casting sections;

• design of junctions between casting sections;

• surface integrity;

•

internal integrity;• dimensional capability;• cosmetic appearance.

Both the designer and metalcaster possess a vital ally to streamline any casting design. Castinggeometry is the most powerful tool available to improve castability of the alloy and mechanical stiffness ofthe casting.

Carefully planned geometry can offset alloy problems in fluid life, solidification shrinkage, pouringtemperature and slag/dross forming tendency. Section modulus, an attribute of structural geometry, hasthe capability to increase stiffness and/or reduce stress—a capability that can be very important when

applied to alloys with lower strength and stiffness. Modulus of elasticity, an alloy’s inherent stiffness, canbe combined with section modulus and section length to limit or allow deflection in a casting design.To preview geometry’s ability to influence the four characteristics of "castability," consider the simple steel

fabrication in Fig. 2a that was converted into carbon steel and gray iron casting designs, Figs. 2b and 2c,respectively.

Fig. 2. Shown here is the original steel fabrication (2a), a

carbon steel casting design featuring geometry that suits its

four casting characteristics (2b), and a gray iron castingfeaturing an entirely different geometry that is also still based

on its fo ur casting alloy c haracteristics (2c).

The fabrication is a guide block to constrain low velocity/low load sliding motion, and it was welded fromrectangular bar stock, subsequently milled, drilled and tapped. The geometries in 2b and 2c are

considerably different as a consequence of differences among fluid life, solidification shrinkage type andamount, pouring temperature and tendency to form nonmetallic inclusions (See Junctions, Fig. 6).



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CASTING PROPERTIES

1. Fluid Life

Fluid life more accurately defines the alloy’s liquid characteristics than does the traditional term "fluidity."Molten metal’s fluidity is a dynamic property, changing as the alloy is delivered from a pouring ladle, die

casting chamber, etc. into a gating system and finally into the mold or die cavity. Heat transfer reducesthe metal’s temperature, and oxide films form on the metal front as this occurs. Fluidity decreases mostrapidly with temperature loss, and it can decrease significantly from the surface tension of oxide films.The absolute value of temperature is not the test of fluidity at a given moment. For example, some

aluminum alloys at 1200-1400F (650-750C) have excellent fluid life. However, some molten steels at3000F (1650C) have much shorter fluid life. In other words, a molten alloy’s fluid life also depends onchemical, metallurgical and surface tension factors.

Fluid life affects the design characteristics of a casting, such as the minimum section thickness that canbe cast reliably, the maximum length of a thin section, the fineness of cosmetic detail (like lettering andlogos) and the accuracy with which the alloy fills the mold extremities.

It is essential to understand that moderate or even poor fluid life does not limit the cost-effectiveness ofdesign. Knowing that an alloy has limited fluid life tells the designer that the part should feature:

• softer shapes and larger lettering;• finer detail in the bottom portion of the mold, where metal arrives first, fastest and generally

hottest;

• coarser detail in the upper portions of the mold where the metal is slower to arrive and moreaffected by oxide films and solidification "skin" formation. Even an alloy with good fluidity, whenoverexposed to oxygen, may form a high surface tension oxide film that makes the fluidity die,

"rounding off" of the leading metal front as it flows.• more taper toward thin sections.

Some alloys, like 356 aluminum, have been specifically designed metallurgically to enhance fluid life. Inthe case of 356, the high heat capacity of silicon atoms "revive" aluminum atoms as their fluid life beginsto wane.

2. Solidification Shrinkage

There are three distinct stages of shrinkage as molten metals solidify: liquid shrinkage, liquid-to-solid

shrinkage and patternmaker’s contraction.1. Liquid shr inkage is the contraction of the liquid before solidification begins. It is not an importantdesign consideration.

2. Liquid-to-solid shrinkage is the shrinkage of the metal mass as it transforms from the liquid’sdisconnected atoms and molecules into the structured building blocks of solid metal. The amount ofsolidification shrinkage varies greatly from alloy to alloy. Table 1 provides a guide to the liquid-to-solid

shrinkage of common alloys. As shown, shrinkage can vary from low to high shrinkage volumes. Alloys are further classified based on their solidification type: directional, eutectic-type and equiaxed (seedefinitions in Table 1). The type of solidification shrinkage in a casting is just as important as the amount

of shrinkage. Specific types of geometry can be chosen to control internal integrity when solidificationamount or types are a problem.



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Figures 3-5 illustrate what is implied by the three solidification shrinkage types defined in Table 1. In eachcase, a simple plate casting is shown with attached risering (a "riser" is a reservoir of liquid metalattached to a casting section to feed solidification shrinkage). Cross sections of the plate and riser(s)

show conceptually how solidification takes place; metallurgical reality is similar, but microscopic.Figure 3 shows solidification on and perpendicular to the casting surfaces, known as "progressive"solidification. At the same time, solidification moves at a faster rate from the ends of the section(s) toward

the source of feed metal (risers)—this is known as directional solidification. Directional solidificationmoves faster from the ends of the sections because of the greater amount of surface area through whichthe solidifying metal can lose its heat. The objective is for directional solidification to beat out progressive

solidification before it can "close the door" to the source of the feed metal. As shown, directionallysolidifying alloys require extensive risering and tapering, but they also have the capability for excellentinternal soundness when solidification patterns are designed properly.



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Fig. 3. Direct ional solidif icat ion o n a p late casting is il lus trated

here. Extensive riser ing and tapering (bottom) allows for

excellent internal casting soundness.

Figure 4 illustrates the eutectic-type alloy, the most forgiving of the three. Such alloys typically have lesssolidification shrinkage volume. Risers are much smaller, and in special cases can be eliminated bystrategically placed gates. The key feature with these alloys is the extended time that the metal feed

avenue stays open. The plate solidifies more uniformly all over and all at once, similar to eutecticsolidification. Eutectic-type alloys are less sensitive to shrinkage problems from abrupt geometrychanges.

Fig. 4. Eutectic-type solid if ication is the most forg iving o f the alloyshr ink age types. Risers may be mu ch sm aller with these al loys, as

the avenue of l iquid feed metal remains open through sol idi f ication.



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Alloys that exhibit equiaxed solidification respond the most dramatically to differences in geometry (Fig.5). Shrinkage in these alloys tends to be widely distributed as micropores, typically along the center planeof a casting section. The reason is that solidification occurs not only progressively from casting surfaces

inward and directionally from high surface area extremities toward lower surface area sections, but alsoequiaxially via "islands" in the middle of the liquid. These islands of solidification interrupt the liquidpathway of directional solidification. Gradually, the pathways freeze off, leaving micropores of shrinkage

around and behind the islands that grew in the middle of the pathway. Larger risers, thicker sections andtapering (shown at center of Fig. 5) are counterproductive, causing micropores to coalesce into largerpores across more of the casting cross section. As illustrated at the bottom of Fig. 5, microporosity is kept

small and confined to a narrow mid-plane in the casting section by more "thermally neutral" geometry withsmaller, further-spaced risers.

Fig. 5. Designs for equ iaxed solidify in g alloys are shown here.

The large riser design (second from bottom) il lustrates how

not to feed a section. While such a taper and large riser

worked with direct ional solidif icat ion, using this approach

here adds more heat to an area that needs to cool more

uniformly, and results in larger, coalesced shrinkage. The

proper casting and process geometry (smaller risers and a

thermally neutral shape) is il lustrated at b ottom.

As illustrated in Fig. 3-5, there is a significant bilateral and reciprocal relationship between solidificationshrinkage and geometry. Most simply, eutectic-type solidification is tolerant of a wide variety of

geometries; the least reciprocity is required. Most complex, equiaxed solidification requires the mostengineering foresight in the choice of geometry and may require supplemental heat transfer techniques inthe mold process. In the middle lies directional solidification, while capable of the worst shrinkage

cavities, it is the most capable of very high internal integrity when the geometry is properly designed.Well-planned geometry in a directionally solidifying alloy can eliminate not only shrinkage but the need forany supplemental heat transfer techniques in the mold.In fact, the real mechanism behind the bilateral and reciprocal relationship between solidification

shrinkage and geometry is heat transfer. All three modes of heat transfer, radiation, conduction and



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efficiency. Convection and conduction, are very important in casting solidification, and transfer rates arehighly affected by geometry.3. Patternmaker’s Contraction is the contraction that occurs after the metal has completely solidified

and is cooling to ambient temperature. This contraction changes the dimensions of the casting from thoseof liquid in the mold to those dictated by the alloy’s rate of contraction. So, as the solid casting shrinksaway from the mold walls, it assumes final dimensions that must be predicted by the pattern- or diemaker.

This variability of contraction is another important casting design consideration, and it is critical todimensional accuracy. Tooling design and construction must compensate for it. Achieving dimensions that are "just like the blueprint" require the foundry’s pattern- and/or diemaker to be

included. The unpredictable nature of patternmaker’s contraction makes tooling adjustments inevitable.For example, a highly recommended practice for critical dimensions and tolerances is to build thepatterns/dies/coreboxes with extra material on critical surfaces so that the dimensions can be fine-tuned

by removing small amounts of tooling stock after capability castings have been made and measured.

3. Slag/Dross Formation

Among foundrymen, the terms slag and dross have slightly different meanings. Slag typically refers tohigh-temperature fluxing of refractory linings of furnaces/ladles and oxidation products from alloying.Dross typically refers to oxidation or reoxidation products in liquid metal from reaction with air during

melting or pouring, and can be associated with either high or low pouring temperature alloys.Some molten metal alloys generate more slag/dross than others and are more prone to contain small,round-shaped nonmetallic inclusions trapped in the casting. Unless a specific application is exceedingly

critical, a few small rounded inclusions will not affect casting structure significantly. In most commercialapplications, nonmetallic inclusions are only a problem if they are encountered during machining orappear in a functional as-cast cosmetic surface.

The best defense against nonmetallic inclusions is to inhibit their formation through good melting, ladling,pouring and gating practices. Ceramic filters, which can be used with alloys that have good fluid life, haveadvanced the foundry’s ability to eliminate nonmetallics. Vacuum melting and pouring are applied inextremely dross-prone alloys, like titanium.

4. Pouring Temperature

Even though molds must withstand extremely high temperatures of liquid metals, interestingly, there arenot many choices of materials with refractory characteristics. When pouring temperature approaches amold material refractory limit, the heat transfer patterns of the casting geometry become important.Sand and ceramic materials with refractory limits of 3000-3300F (1650-1820C) are the most common

mold materials. Metal molds, such as those used in diecasting and permanent molding, have temperaturelimitations. Except for special thin designs, all alloys that have pouring temperatures above 2150F(1180C) are beyond the refractory capability of metal molds.

It’s also important to recognize the difference between heat and temperature; temperature is the measureof heat concentration. Lower temperature alloys also can pose problems if heat is too concentrated in asmall area—better geometry choices allow heat to disperse into the mold.

Design of Junctions

A junction is a region in which different section shapes come together within an overall casting geometry.Simply stated, junctions are the intersection of two or more casting sections. Figure 6 illustrates both "L"and "T" junctions among the four junction types, which also include "X" and "Y" designs.



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Fig. 6. Junction geometry is important to alloys with

considerable shrinkage and/or pouring temperature. The

casting geometry at left shows "L" and "T" junctions. The

il lustrat ions at r ight show the consequences of junction

design and geometry increasingly dif f icult combinations of

shr inkage amount and/or temperature. In reviewing Fig. 2, the

gray iron ju nctio ns (2c) are similar to type 1 above, and steel

(2b) are similar to type 3.

Designing junctions is the first step to finding castable geometry via the six-faceted system for casting

design. Figure 6 illustrates that there are major differences in allowable junction geometry, depending onalloy shrinkage amount and pouring temperature. Alloy 1 allows abrupt section changes and tight

geometry, while alloy 3 requires considerable adjustment of junction geometry, such as radiusing,spacing, dimpling and feeding. Figure 7 illustrates a very high form of the foregoing principles in a criticalautomotive application.

Fig. 7. This premium A356 aluminum casting for a crit ical

structural applicat ion on a minivan saved 14 lb over its

stamped steel weldment predecessor and offered nine

addit ional mounting locations. Close inspection shows extra

geometry at junctions and surfaces where heat transfer mustbe enhanced for high stru ctural integr ity. The permanent mold

process features additional geometry and heat transfer

techniques to augment the casting’s geometry for structural

integr ity.



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Considerations of Secondary Operations in Design

System-wide thinking also must include the secondary operations, such as machining, welding and joining, heat treating, painting and plating.One aspect that affects geometry is the use of fixturing to hold the casting during machining. Frequently,

the engineers who design machining fixtures for castings are not consulted by either the design engineer

or the foundry engineer as a new casting geometry is being developed. Failure to do so can be asignificant oversight that adds machining costs. If the casting geometry has been based on the four

casting characteristics of the alloy, then the designer knows the likely surfaces for riser contacts and mayhave some idea of likely parting lines and core match lines. These surfaces and lines will be irregularitieson the casting geometry and will cause problems if they contact fixturing targets.

It is best to define the casting dimensional datums as the significant installation surfaces, in order offunction priority, based on how the casting is actually used. Targets for machining fixtures should beconsistent with these datum principles.

There is nothing more significant in successful CNC and transfer line machining of castings than thereligious application of these datum fixture and targeting principles.

Drawings and Dimensions

The tool that has had the most dramatic positive impact on the manufacture of parts that reliably fittogether is geometric dimensioning and tolerancing (GD&T), as defined by ANSI Y14.5M—1994. When

compared to traditional (coordinate) methods, GD&T:

• considers tolerances, feature-by-feature;

• minimizes the use of the "title block" tolerances and maximizes the application of tolerancesspecific to the requirement of the feature and its function;

• is a contract for inspection, rather than a recipe for manufacture. In other words, GD&T specifies

the tolerances required feature-by-feature in a way that does not specify or suggest how thefeature should be manufactured. This allows casting processes to be applied more creatively,often reducing costs compared to other modes of manufacture, as well as finish machining costs.

GD&T encourages the manufacturer to be creative in complying with the drawing’s dimensional

specifications because the issue is compliance with tolerance, not necessarily compliance with amanufacturing method. By forcing the designer to consider tolerances feature-by-feature, GD&T oftenresults in broader tolerances in some features, which opens up consideration of lower cost manufacturing

methods, like castings. Figure 8 illustrates GD&T principles applied to a design made as a casting. Notethe use of installation surfaces as datums and the use of geometric zones of tolerance.



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Fig. 8. Shown h ere is an example of what a GD&T drawing

should look l ike, complete with datum def in i t ions and

geometric tolerance zones.

Factors that Control Casting Tolerances

How a cast feature is formed in a mold has a significant effect on the feature’s tolerance capability. The

following six parameters control the tolerance capability of castings. In order of preference, they are:Molding Process —The type of molding process (such as green sand, shell, investment, etc.) has thegreatest single influence on tolerance capability. How a given molding process is mechanized and the

sophistication of its pattern or die equipment can refine or coarsen its base tolerance capability.Casting Weight and Longest Dimension —Logically, heavier castings with longer overall dimensionsrequire more tolerance. These two parameters have been defined statistically in tolerance tables for some

alloy families.Mold Degrees of Freedom —This parameter is least understood. Just as some molding processes havemore mold components (mold halves, cores, loose pieces, chills, etc.) than others, some casting designs

require more mold components. Each mold component has its own tolerances, and tolerances arestacked as the mold is assembled. More mold components mean more degrees of freedom; hence moretolerance. Good design for tolerance capability minimizes degrees of freedom in the mold for features

with critical dimensions.Draft —It is common for casting designs to ignore the certainty of draft, including mold draft, draft on waxand/or styrofoam patterns made from dies, and core draft. Since 1° of draft angle generates 0.017 in. of

offset per in. of draw (about 0.5 mm/30 mm), draft can quickly use up all of a tolerance zone and more.

Patternmaker’s Contraction —The uncertainty of patternmaker’s contraction is why foundrymennormally recommend producing first article and production process verification castings (sometimes

called "sample" or "capability" castings) to establish what the dimensions really will be before going intoproduction. A common consequence of patternmaker’s contraction uncertainty is a casting dimension thatis out of tolerance, not because it varies too much, but because its average value is too far from nominal.In other words, the dimension contracted more or less than was expected.

Cleaning and Heat Treating —Many casting dimensions are touched by downstream processing. At theleast, most castings are touched by abrasive cutting wheels and grinding—even precision castings. Manycastings are heat-treated, which can affect straightness and flatness.



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When considering the breadth and depth of geometry’s importance in casting design, from its influenceon castability, the geometry of gating/risering, structural form, cosmetic appearances and downstreamfixturing, extensive brainstorming of geometry is highly recommended. The standard for "optimal" casting

geometry is high, but the possibilities for geometry are limitless. Find ways of exploring geometry quickly,such as engineering sketching, before committing to a print or solid model.

STRUCTURAL PROPERTIES

In the preceding section, it was stated that: 1) castability affects geometry but 2) well-chosen geometryaffects castability. In other words, a geometry can be chosen that offsets the metallurgical nature of the

more difficult-to-cast alloys. Knowing how to choose this "proactive" geometry is the key to consistentlygood casting designs—in any foundry alloy—that are economical to produce, machine and assemble intoa final product.

While the casting properties section was the foundry engineering spectrum of geometry for the benefit ofdesign engineers; the structural properties section is the design engineering spectrum of geometry for thebenefit of foundry engineers. Geometry found between these two spectrums offers boundless opportunity

for castings.

Structural Geometry

Because castings can easily apply shape to structural requirements, most casting designs are used tostatically or dynamically control forces. In fact, castings find their way into the most sophisticatedapplications because they can be so efficient in shape, properties and cost. Examples are turbine blades

in jet engines, suspension components (in automobiles, trucks and railroad cars), engine blocks, airframecomponents, fluid power components, etc.When designing a component structurally, a design engineer is generally interested in safely controlling

forces through choice of allowable stress and deflection. Although choice of material affects allowablestress and defection, the most significant choice in the designer’s structural arsenal is geometry. As wewill see, geometry directly controls stiffness and stress in a structure.

The casting processes are limitless in their combined ability to allow variations in shape. Not many yearsago, efficient structural geometry was limited by the designer’s ability to visualize in 3-D. Now, computergenerated solid models and rapid prototypes are greatly enhancing the designer’s ability to visualize

structural shapes. This technology often leads to casting designs.Improved efficiency in solid modeling software has led to an interesting design dilemma. Solid models arereadily applicable to Finite Element Analysis (FEA) of stress. FEA enables the engineer to quicklyevaluate stress levels in the design, and solid models can be tweaked in shape via the software so

geometry can be optimized for allowable, uniform stress. Figure 9 depicts a meshed solid model and astress analysis via the mesh elements.

Fig. 9. The mesh (l) show s the size of th e finite elements th at

are used for the FEA stress analysis (right). The high-stress

areas (red) cou ld be reduced wit h a geometry ch ange.



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However, optimum geometry for allowable, uniform stress may not be acceptable geometry for castability.When a foundry engineer quotes a design that considered structural geometry only, requests forgeometry changes are likely. At this point, the geometry adjustments for castability may be more

substantial than the solid model software can "tweak." The result can be no-quotes, higher-than-expectedcasting prices, or starting over with a new solid model. A practical solution to this problem is to concurrently engineer geometry considering structural, foundry

and downstream manufacturing needs. The result can be optimal casting geometry. The most efficienttechnique is to make engineering sketches or marked sections and/or views on blueprints. The idea is toexplore overall geometry before locking in to a solid model too quickly. Engineering sketches or mark-ups

are easy and quick to change—even dramatically—in the concurrent brainstorming process; solid modelsare not. A solid model should be the elegant result, not the knee-jerk start.

The Objective

Our objective is to explore geometry possibilities, looking for an ideal shape that is both castable in thechosen foundry alloy and allowable in stress and deflection for that alloy. As noted, there is great variety

in the four metallurgical characteristics that govern alloy castability. Similarly, great variety exists amongmetals in their allowable stress and deflection. Therefore, an ideal casting shape for all six of the castingdesign factors in Fig. 1 is not necessarily a trivial exercise. For alloys that have good castability, choosing

geometry for allowable stress and deflection is the best place to start. For alloys with less than the bestcastability, it is better to first find geometry that assists castability, and then modify it for allowable stressand deflection.

Not all alloys are like ductile iron, which is both highly castable and relatively resistant to stress, andmoderately resilient against deflection. For ductile iron, many geometries may be equally acceptable.Martensitic high-alloy steel has fair-to-poor castability, but can have amazing resistance to stress and can

tolerate very large deflections without structural harm. Therefore, structural geometry is easy to develop,but a coincidental castable shape is more difficult to design. Premium A356 aluminum has goodcastability, but rather weak resistance to stress and low tolerance for deflection. Carefully chosenstructural geometry, however, combined with solidification enhancements in the molding process, has

resulted in extremely weight-effective A356 structural components for aircraft, cars and trucks.

5. Section Modulus

Playing with sketches before building a solid model means that we have to find another way to evaluatestress and deflection. This "other way" is the essence of efficient structural evaluation of geometry incasting design.

The equivalent of FEA for the design engineer’s structural analysis is computerized "mold filling" and"solidification analysis" for the foundry engineer; the basis for both is a solid model.The "other way" for the foundry engineer is the manual calculation of gating, solidification patterns and

riser sizes; these are established, relatively simple mathematical techniques used long before the adventof solid models. (See references.)This "other way" for the design engineer is not so simple. To take full advantage of engineering

sketching/print marking as a way to brainstorm geometry, we must be able to quickly evaluate stress anddeflection at important cross-sections in the sketches. As the design engineer well knows, the classicformulas for bending stress, torsional stress and deflection are relatively simple. Each, however, contains

the same parameter, Section Modulus, which is a function of shape and difficult to compute. Therefore, aquick, simple way to compute or estimate Section Modulus (more specifically, its foundational parameter, Area Moment of Inertia) is needed so that we can move from sketch to improved sketch in our casting

geometry brainstorming.Interestingly, the difficulty in computing Area Moment of Inertia for casting shapes is one of the hiddenreasons for the design and use of fabrications. Fabrications are made from building blocks of wrought

shapes, like I-beams, rectangular bars, angles, channels and tubes. These shapes, which are simple andconstant over their length, have Area Moments of Inertia that are easy to calculate or are available in



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however, are heavy and nonuniform in stress compared to a casting well-designed for the same purpose.

Quick Method for Estimating Area Moment of Inertia from Sketches

Although there are five kinds of stress (tension, compression, shear, bending and torsion), the interestingones for complex structures are bending and torsion, and their equations are shown in Fig. 10. (If more

than one type of stress is involved in the same section, the Principle of Superposition allows the individualstress types to be analyzed separately and then added together; once again, the larger of the stresses tobe combined are usually from bending or torsion.)



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Fig. 11. The three significant parameters in deflection arelength (L), Area Moment of Inert ia (I) and Modulus of

Elasticity (E). Simply, increasing L increases deflection,

whi le increasing E or I decreases deflection.

In all three cases, the relationships apply to a cross-section of the geometry. It is easy to draw a scalecross-section, whether it be from an engineering isometric sketch or from a marked-up view on a

blueprint.If we can find a way to quickly estimate Area Moment of Inertia, we can readily estimate stresses in ourbrainstormed sketches as well as estimate whether deflection will increase or decrease. Note that Area

Moment of Inertia is in the denominator in each relationship, meaning that increased Area Moment ofInertia reduces stress and deflection.Maximum tensile stress in bending is often most critical in structural design. Section Modulus is defined

as the Area Moment of Inertia divided by the maximum distance from the center of bending (centroid) to

the outermost edge of the casting cross-section. Section Modulus is similar to a "stiffness index" becauseit considers not only magnitude of Area Moment of Inertia, but also maximum section depth. If maximum

section depth increases faster than Area Moment of Inertia, a geometry change can actually increasemaximum tensile stress, rather than reduce it. This "index" termed Section Modulus accounts for thatpotential problem.

The estimation method recommended is based on three principles. One is intuitive and the other two arefrom the mathematics of engineering mechanics. The principles are:1. The design engineer ’s sense of load magnitudes and component size/shape —Engineers



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engineers can learn this "sense," and when they do, they become effective concurrent engineeringpartners in their customers’ casting designs.2. The equation for A rea Moment of Inert ia (Fig. 12) —Although the calculus for an interesting casting

cross-section can be very difficult, the relationship expressed between "depth of section" (Y) and "changein cross-sectional area" (dA) is very simple.

Fig. 12. Illustrated is the simple relationsh ip between depth of

section (Y) and change in cross section (dA). When dA

increases rapidly away from the center, stiffness increases

dramatically. The position and shape of the two rectangles in Fig. 12 (top) clearly demonstrates this simple yetpowerful relationship. The change in shape of the inside of the tube (at bottom of the Fig. 12) is an evenmore dramatic illustration. Calculations weren’t made in either case, but the qualitative impact of Y2dA on

stiffness and stress is unmistakable.3. Area Mom ent of Inert ia —Once the engineering sense of structural size and Y2dA have been appliedqualitatively to a sketched cross-section, the Parallel Axis Theorem can be applied to simple building

blocks in the cross-section to estimate Area Moment of Inertia quantitatively. A numerical value for AreaMoment of Inertia is required to calculate the stress level in the sketched cross-section.



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The Parallel Axis Theorem is illustrated in Fig. 13 (see Appendix for example equation).

Fig. 13. This relationship enables the quick estimation of Area

Moment of Iner t ia v ia bui ld ing blocks. The bui ld ing b locks

must be referenced to the centroid. The centroid can be

calculated, but it is easier and quicker to use a "paper doll" ofthe cross-section and simply find its balance point.

6. Modulus of Elasticity



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Fig. 14. As shown, alloy famil ies vary considerably in

stiffness. The steepness of the elastic slope is the Modulu s of

Elasticity. Heat treatment doesn ’t chang e the slope, but it can

raise the yield point.

One subtlety about Modulus of Elasticity is that it is not affected by heat treatment. However, heattreatment can affect the height of the elastic slope. This is very important because the height at which the

elastic slope begins to curve is called the metal’s "yield stress." This is the stress level at which plasticdeformation begins and the metal is permanently affected. Stresses should be designed below this levelso that deflections in the casting under load do not damage it.

For example, consider the family of steels in Fig. 14; heat treatment can considerably raise the point atwhich an alloy steel yields. Although the steel is no stiffer at higher stress levels, it can withstand theadditional stress without damage. The same is true for heat-treatable aluminum alloys, but the magnitude

of heat treatment effect on yield stress is considerably less than that for steels.

Summary

Figure 15 and the Appendix illustrate a hypothetical casting design using the recommended six factorsbehind good geometry selection. The first four factors describe the alloy’s "castability." The final twofactors are from engineering mechanics and are Modulus of Elasticity and Section Modulus, an aspect of

Area Moment of Inertia.



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Fig. 15. Shown here is a prelim inary engin eering sketch of a

structural casting designed to control torsion and bending

forces. Complet ion o f this design as a duc ti le iron casting is

descr ibed in the appendix. As a ductile iron casting design (see castability characteristics in Table 1), the following example isintended to illustrate structural geometry more than geometry for castability. As noted previously, for

alloys that are highly castable like ductile iron, it is convenient to focus first on geometry for structure andlet the alloy’s friendly foundry characteristics adapt to the structural needs.Briefly, as ductile iron, the casting could be made in a horizontally-parted sand mold with the center

cylindrical section pointed down. One core would form the "tongue and groove" tabs, bolt holes andhollowed center of the cylinder. A second core would form the top side of the I-beam feature and thecorresponding bottom side of the four-hole plate. Two risers would feed solidification shrinkage in the

center section from the tab sides of the four hole plate. A third riser would follow the side of the secondcore and feed the cylindrical end of the I-beam section.The appendix on page 21 illustrates the main point: This casting design is nothing more than an

engineering sketch with a sense of size and proportion. Using the "quick method" of sketching cross-

sectional areas, Area Moment of Inertia can be estimated with simple building blocks and minimalcalculation. Once a value is known, stress can be easily calculated for the chosen cross-section. A

relative measure for deflection can be easily calculated as well.Final design would be a solid model, based on at least two or three sketched iterations of combinedstructural and castable geometry. Detailed structural evaluation could then be done via FEA. Any

remaining stress problems could be easily solved by tweaking the solid model, which is already close tooptimal geometry. Finally, the solid model could be modified to add risers and a gating system so thatcomputer analysis of solidification and mold filling could verify the geometry chosen for castability.



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William F. Baker, Electric Steel Castings Co.; Leo Baran, formerly of the American Foundrymen’s Society;Malcolm Blair, Steel Founders’ Society of America; Richard Heine, Univ. of Wisconsin-Madison; JayJanowak, Grede Foundries, Inc.; John Jorstad, CMI International; Raymond Monroe, Steel Founders’

Society of America; Mark Morel, Morel Industries; Tom Prucha, CMI International; Fred Schleg, formerlyof the American Foundrymen’s Society; and Jack Wright, consultant.

References

"Basic Principles of Gating & Risering," AFS’ Cast Metals Institute • "Risering Steel Castings (1973),"Steel Founders’ Society of America • R.W. Heine, "Comparing the Functioning of Risers to Their Behavior

Predicted by Computer Programs," AFS Transactions, vol 1985 p. 481 • M.A. Gwyn, "Cost-EffectiveCasting Design," AFS • R.W. Heine, "Risering Principles Applied to Ductile Iron Castings Made in GreenSand," AFS Transactions 1979, vol. 87, p. 65 • R.W. Heine, "Design Method for Tapered Riser Feeding of

Ductile Irons," AFS Transactions 1982, vol 90, p. 147 • "AFS Risering System—Riser Sizer," Developedat U.W.-Madison • C.R. Loper, Jr., R.W. Heine and R.A. Roberts, AFS Transactions 1968, p. 373.

cost effective casting design

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