Materials Selection and Design (2010) Part 15 docx

Various tools that can be used to estimate cost at different stages of the development process are described later in this section.. The second method of cost estimation is empirically b

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unique parts, the domains of cost estimation expand dramatically So, although domain limitation is necessary for estimates accuracy, it is not a panacea

cost-Database Commonality. Estimating the costs of a complex product through various phases of development and production requires organization of large amounts of data If the data for design, manufacturing, and cost are linked, there

is database commonality It has been found (Ref 3) that having database commonality results in dramatic reductions in

cost and schedule overruns in military programs In the same study, domain limitation was found to be essential in achieving database commonality

Having database commonality with domain limitation implies that the links between the design and specific manufacturing processes, with their associated costs, are understood and delineated Focusing on specific manufacturing processes allows one to collect and organize data on where and how costs arise in specific processes With this focus, the accuracy of cost estimates can be determined, provided that uniform methods of estimation are used, and provided that, over time, the cost estimates are compared with the actual costs as they arise in production In this manner, the accuracy

of complex cost estimates may be established and improved

In present engineering and design practice, many organizations do not have adequate database commonality, and the accuracy of cost estimates is not well known Database commonality requires an enterprise-wide description of cost-dominant manufacturing processes, a way of tracking actual costs for each part, and a way of giving this information in

an appropriate format to designers and cost estimators Most "empirical methods" of cost estimation, which are based on industrywide studies of statistical correlation of cost, may or may not apply to the experience of a specific firm (see the discussion in the sections that follow)

Costs are "rolled up" for a product when all elements of the cost of a product are accounted for Criteria for cost estimation using database commonality is simple: speed (how long does it take to roll up a cost estimate on a new design), accuracy (what is the standard deviation of the estimate, based on comparison with actual costs) and risk (what is the probability distribution of the cost estimate; what fraction of the time will the estimate be more than 30% too low, for example) One excellent indicator of database commonality is the roll-up time criteria World-class cost-estimation roll-

up times are minutes to fractions of days Organizations that have such rapid roll-up times have significantly less cost and schedule overruns on military projects (Ref 3)

Cost allocation is another general issue Cost allocation refers to the process by which the components of a design are assigned target costs The need for cost allocation is clear: how else would an engineer, working on a large project, know how much the part being designed should cost? And, if the cost is unknown and the target cost is not met, there will be time delays, and hence costs incurred due to unnecessary design iteration It is generally recognized that having integrated product teams (IPTs) is a good industrial practice Integrated product teams should allocate costs at the earliest stages of a development program Cost estimates should be performed concurrently with the design effort throughout the development process Clearly, estimating costs at early stages in a development program, for example, when the concept

of the product is being assessed, requires quite different tools than when most or all the details of the design are specified Various tools that can be used to estimate cost at different stages of the development process are described later in this section

Elements of Cost. There are many elements of cost The simplest to understand is the cost of material For example, if

a part is made of aluminum and is fabricated from 10 lb of the material, if the grade of aluminum costs $2/lb, the material cost is $20 The estimate gets only a bit more complex if, as in the case of some aerospace components, some 90% of the materials will be machined away; then the sale on scrap material is deducted from the material cost

Tooling and fixtures are the next easiest items to understand If tools are used for only one product, and the lifetime of the tool is known or can be estimated, then only the design and fabrication cost of the tool is needed Estimates of the fabrication costs for tooling are of the same form as those for the fabricated parts The design cost estimate raises a difficult and general problem: cost capture (Ref 4) For example, tooling design costs are often classified as overhead, even though the cost of tools relates to design features In many accounting systems, manufacturing costs are assigned

"standard values," and variances from the standard values are tabulated This accounting methodology does not, in general, allow the cost engineer to determine the actual costs of various design features of a part In the ledger entries of many accounting systems, there is no allocation of costs to specific activities or no activity-based accounting (ABC) (Ref 5) In such cases there are no data to support design cost estimates

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Direct labor for products or parts that have a high yield in manufacturing normally have straightforward cost estimates, based on statistical correlation to direct labor for past parts of a similar kind However, for parts that have a large amount

of rework the consideration is more complex, and the issues of cost capture and the lack of ABC arise again Rework may

be an indication of uncontrolled variation of the manufacturing process The problem is that rework and its supervision may be classified all, or in part, as manufacturing overhead For these reasons, the true cost of rework may not be well known, and so the data to support cost estimates for rework may be lacking

The cost estimates of those parts of overheads that are associated with the design and production of a product are particularly difficult to estimate, due to the lack of ABC and the problem of cost capture For products built in large volumes, of simple or moderate complexity, cost estimates of overheads are commonly done in the simplest possible way: the duration of the project and the level of effort are used to estimate the overhead This practice does not lead to major errors because the overhead is a small fraction of the unit cost of the product

For highly engineered, complex products built in low volume, cost estimation is very difficult In such cases the problem

of cost capture is also very serious (Ref 4)

Machining costs are normally related to the machine time required and a capital asset model for the machine, including depreciation, training, and maintenance With a capital asset model, the focus of the cost estimate is the time to manufacture A similar discussion holds for assembly costs: with a suitable capital asset model, the focus of the cost estimate is the time to assemble the product (Ref 1)

Methods of Cost Estimations. There are three methods of cost estimation discussed in the following sections of this article The first is parametric cost estimation Starting from the simplest description of the product, an estimate of its overall cost is developed One might think that such estimates would be hopelessly inaccurate because so little is specified

about the product, but this is not the case The key to this method is a careful limitation of the domain of the estimate (see

the previous section) This example deals with the estimate of the weight of an aircraft The cost of the aircraft would then

be calculated using dollars/pound typical of the aircraft type Parametric cost estimation is the generally accepted method

of cost estimation in the concept assessment phases of a development program The accuracy is surprisingly good about 30% (provided that recent product-design evolution has not been extensive)

The second method of cost estimation is empirically based: one identifies specific design features and then uses statistical correlation of costs of past designs to estimate the cost of the new design This empirical method is by far the most common in use For the empirical method to work well, the features of the product for which the estimate is made should

be unambiguously related to features of prior designs, and the costs of prior designs unambiguously related to design features Common practice is to account for only the major features of a design and to ignore details Empirical methods are very useful in generating a rough ranking of the costs of different designs and are commonly used for that purpose (Ref 1, 6, 7) However, there are deficiencies inherent in the empirical methods commonly used

The mapping of design features to manufacturing processes to costs is not one-to-one Rather, the same design feature may be made in many different ways This difficulty, the feature mapping problem, discussed in Ref 4, limits the accuracy of empirical methods and makes the assessment of risk very difficult The problem is implicit in all empirical methods The problem is that the data upon which the cost correlation is based may assume the use of manufacturing methods to generate the features of the design that do not apply to the new design It is extraordinarily difficult to determine the implicit assumptions made about manufacturing processes used in a prior empirical correlation A commonly stated accuracy goal of empirical cost estimates is 15 to 25%, but there is very little data published on the actual accuracy of the cost estimate when it is applied to new data

The final method discussed in this article is based on the recent development called complexity theory A mathematically rigorous definition of complexity in design has been formulated (Ref 8) In brief, complexity theory offers some improvement over traditional empirical methods: there is a rational way to assess the risk in a design, and there are ways

of making the feature mapping explicit rather than implicit Perhaps the most significant improvement is the capability to capture the cost impact of essentially all the design detail in a cost estimate This allows designers and cost estimators to explore, in a new way, methods to achieve cost savings in complex parts and assemblies

References cited in this section

1 G Boothroyd, P Dewhurst, and W Knight, Product Design for Manufacture and Assembly, Marcel Dekker,

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5 H.T Johnson and R.S Kaplan, Relevance Lost, the Rise and Fall of Management Accounting, Harvard

Business School Press, 1991

6 G Boothroyd, Assembly Automation and Product Design, Marcel Dekker, 1992

7 P.F Ostwald, "American Machinist Cost Estimator," Penton Educational Division, Penton Publishing, 1988

8 D.P Hoult and C.L Meador, "Predicting Product Manufacturing Costs from Design Attributes: A Complexity Theory Approach," No 960003, Society of Automotive Engineers, 1996

Manufacturing Cost Estimating

David P Hoult and C Lawrence Meador, Massachusetts Institute of Technology

Parametric Methods

An example for illustrating parametric cost estimation is that of aircraft In Ref 9, Roskam a widely recognized researcher in this field describes a method to determine the size (weight) of an aircraft Such a calculation is typical of parametric methods To determine cost from weight, one would typically correlate costs (inflation adjusted) of past aircraft of similar complexity with their weight Thus weight is surrogate for cost for a given level of complexity

Most parametric methods are based on such surrogates For another simple example, consider that large coal-fired power plants, based on a steam cycle, cost about $1500/kW to be built So, if the year the plant is to be built (for inflation adjustment) and its kW output is known, parametric cost estimate can be readily obtained

Parametric cost estimates have the advantage that little needs to be known about the product to produce the estimate Thus, parametric methods are often the only ones available in the initial (concept assessment) stages of product development

The first step in a parametric cost estimation is to limit the domain of application Roskam correlates statistical data for a dozen types of aircraft and fifteen sub types The example he uses to explain the method is that of a twin-engine, propeller-driven airplane The mission profile of this machine is given in Fig 1 (Ref 9)

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Fig 1 Mission profile

Inspection of the mission specifications and Fig 1 shows that only a modest amount of information about the airplane is given In particular, nothing is specified about the detailed design of the machine! The task is to estimate the total weight,

WTO or the empty weight, WE, of the airplane Roskam argues that the total weight is equal to the sum of the empty

weight, fuel weight, WF, payload and crew weight, WPL + Wcrew, and the trapped fuel and oil, which is modeled as a

fraction, Mtfo, to the total weight Mtfo is to be a small (constant) number, typically 0.001 to 0.005 Thus the fundamental equation for aircraft weight is:

WTO = WE + WF + WPL + Wcrew + MtfoWTO (Eq 1)

The basic idea of Roskam is that there is an empirical relationship between aircraft empty and total weights, which he finds to be:

The coefficients, A and B, depend on which of the dozen types and fifteen subtypes of aircraft fit the description in Table

1 and Fig 1 It is at this point that the principle of domain limitation first enters For the example used by Roskam, the

correlation used to determine A = 0.0966 and B = 1.0298 for the twin-engine, propeller-driven aircraft spans a range of

empty weights from 1000 to 7000 lb

Table 1 Mission specification for a twin-engine, propeller-driven airplane

1 Payload Six passengers at 175 lb each (including the pilot) and 200 lb total baggage

2 Range 1000 statute miles with maximum payload

3 Reserves 25% of mission fuel

4 Cruise speed 250 knots at 75% power at 10,000 ft and at takeoff weight

5 Climb 10 min to 10,000 ft at takeoff weight

6 Takeoff and landing 1500 ft ground fun at sea level, standard day Landing at 0.95 of takeoff weight

7 Powerplants Piston/propeller

8 Certification base FAR23

The method proceeds as follows to determine the weight of fuel required in the following way The mission fuel, WF, can

be broken down into the weight of the fuel used and the reserve fuel:

WF = WFres + WFused (Eq 3)

Roskam models the reserve fuel as a fraction of the fuel used (see Table 1) The fuel used is modeled as a fraction of the total weight, and depends on the phase of the mission, as described in Fig 1 For mission phases that are not fuel intensive, a fixed ratio of the weight at the end of the phase to that at the beginning of the phase is given Again, these ratios are specific to the type of aircraft For fuel-intensive phases, in this example the cruise phase, there is a relationship between the lift/drag ratio of the aircraft, the engine fuel efficiency, and the propeller efficiency Again, these three parameters are specific to the type of aircraft

When the fuel fraction of the total weight is determined by either a cruise calculation, or by the ratio of weight at the end

of a mission phase to the beginning of a mission phase, the empty weight can be written in terms of the total weight Then

Eq 2 is used to find the total weight of the aircraft

For the problem posed, Roskam obtains an estimated total weight of 7900 lb The accuracy can be estimated from the

scatter in the correlation used to determine the coefficients A and B, and is about 30% For details of the method Roskam

uses for obtaining the solution, refer to Ref 9

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Some limitations of the parametric estimating method are of general interest For example, if the proposed aircraft does not fit any of the domains of the estimating model, the approach is of little use Such an example might be the V-22, a tilt wing aircraft (Ref 10), which flies like a fixed-wing machine, but tilts its wings and propellers, allowing the craft to hover like a helicopter during take-off and landing Such a machine might be considered outside the domain of Roskam's estimating model The point is not that the model is inadequate (the V-22 is more recent than Roskam's 1986 article), but the limited product knowledge in the early stages of development makes it difficult to determine if a cost estimate for the V-22 fits in a well-established domain

Conversely, even complex machines, such as aircraft, are amenable to parametric cost estimates with fairly good accuracy, provided they are within the domain of the cost model In the same article, Roskam presents data for transport jets, such as those used by airlines It should be emphasized that the weight (and hence cost) of such machines, with more than one million unique parts, can be roughly estimated by parametric methods

Of course, cost is not the same as weight or, for that matter, any other engineering parameter The details of the manufacturing process, inventory control, design change management, and so forth, all play a role in the relationship between weight and cost The more complex the machine, the more difficult it is to understand if the domain of the parametric cost-estimating model is the same as that of the product being estimated

9 J Roskam, Rapid Sizing Method for Airplanes, J Aircraft, Vol 23 (No.7), July 1986, p 554-560

10 The Bell-Boeing V-22 Osprey entered Low Rate Initial Production with the MV-22 contract signed June 7,

1996, Tiltrotor Times, Vol 1 (No 5), Aug 1996

Empirical Methods of Cost Estimation

Almost all the cost-estimating methods published in the literature are based on correlation of some feature or property of the part to be manufactured Two examples are presented The first is from the book by Boothroyd, Dewhurst, and Knight (Ref 1), hereafter referred to as BDK Chapter 9 of this book is devoted to "Design for Sheet Metalworking." The first part of this chapter is devoted to estimates of the costs of the dies used for sheet metal fabrication This example was chosen because the work of these authors is well recognized (Boothroyd and Dewhurst Inc sells widely used software for design for manufacture and design assembly.) In this chapter of the book, the concept of "complexity" of stamped sheet metal parts arises The complexity of mechanical parts is discussed in the section "Complexity Theory" in this article

Example 1: Cost Estimates for Sheet Metal Parts

Sheet metal comes in some 15 standard gages, ranging in thickness from 0.38 to 5.08 mm It is commonly available in steel, aluminum, copper, and titanium Typical prices for these materials are 0.80-0.90$/lb for low-carbon steel, $6.00-

$7.00/lb for stainless steel, $3.00/lb for aluminum, $10.00/lb for copper, and $20.00/lb for titanium It is typically shipped

in large coils or large sheets

Automobiles and appliances use large amounts of steel sheet metal Aluminum sheet metal is used in commercial aircraft manufacture, but in lesser amounts due to the smaller number of units produced

Sheet metal is fabricated by shearing and forming operations, carried out by dies mounted in presses Presses have beds, which range in size from 50 by 30 cm to 210 by 140 cm (20 by 12 in to 82 by 55 in.) The press force ranges from 200 to

4500 kN (45 to 1000 lbf) The speed ranges from 100 strokes/min to 15 strokes/min in larger sizes

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Dies typically have four components: a basic die set; a punch, held by the die set, which shears or forms the metal; a die plate through which or on which the punch acts; and a stripper plate, which removes the scrap at the end of the fabrication process

BDK estimate the basic die set cost (Cds, in U.S dollars) as basically scaling with usable area (Au, in cm2):

The assessment of how part complexity affects cost arises repeatedly in cost estimating The subject is discussed at length

in the next section "Complexity Theory" From the data of BDK, the basic time to manufacture the die set (M, in hours) can be estimated by the following steps: Define the basic manufacturing points (Mpo) as

Note that the manufacturing time increases a bit less than linearly with part complexity This is consistent with the section

"Complexity Theory" BDK goes on to add two correction factors to Mpo The first is a correction factor due to plate size

and part complexity, fLW From BDK data it is found:

The second correction factor is to account for the die plate thickness BDK cites Nordquist (Ref 11), who gives a

recommended die thickness, hd, as:

where U is the ultimate tensile stress of the sheet metal, Ums is the ultimate stress of mild steel, a reference value, V, is the required production volume, and h is the thickness (in mm) of the metal to be stamped BDK recommends the second

correction factor to be:

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The die cost risk (i.e., uncertainty of the resulting estimate of die cost) is unknown, because it is not known how the model equations would change with different manufacturing processes or different die design methods

It is worth noting carefully that only some features of the design of the part enter the cost estimate: the length and width

of the punch area, the perimeter of the part to be made, the material, and the production volume Thus, the product and die designers do not need to be complete in all details to make a cost estimate Hence, the estimate can be made earlier in the product-development process Cost trades between different designs can be made at an early stage in the product-development cycle with empirical methods

Example 2: Assembly Estimate for Riveted Parts

The American Machinist Cost Estimator (Ref 7) is a very widely used tool for empirical cost estimation It contains data

on 126 different manufacturing processes A spreadsheet format is used throughout for the cost analysis One example is

an assembly process It is proposed to rivet the aluminum frame used on a powerboat The members of the frame are made from 16-gage aluminum The buttonhead rivets, which are sized according to recommendations in Ref 12, are

in in diameter and conform to ANSI standards Figure 2 shows the part

Fig 2 Powerboat frame assembly

There are 20 rivets in the assembly, five large members of the frame, and five small brackets Chapter 21 in Ref 7 includes six tables for setup, handling, pressing in the rivets, and riveting A simple spreadsheet (for the first unit) might look like Table 2 The pieces are placed in a frame, the rivets are inserted, and riveted The total cycle time for the first unit is 18.6 min There are several points to mention here First, the thickness of the material and the size of the rivets play

no direct part in this simple calculation The methods of Ref 7 do not include such details

Table 2 Spreadsheet example for assembly of frame (Fig 2)

Source(a) Process

21.2-1 Get 5 frame members from skid 1.05

21.2-1 Get 5 brackets from bench 0.21

21.2-2 Press in hardware (20 rivets) 1.41

21.2-3 Set 20 rivets 0.93

Total cycle time (minutes) 3.60 15

(a) Tables in Ref 7, Chapter 21

Yet common sense suggests that some of the details must count For example, if the rivet holes are sized to have a very small clearance, then the "press-in-hardware" task, where the rivets are placed in the rivet holes, would increase In a like manner, if the rivets fit looser in the rivet holes, the cycle time for this task might decrease The point of this elementary discussion is that there is some implied tolerance with each of the steps in the assembly process

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In fact, one can deduce the tolerance from the standard specification of the rivets From Ref 12, in the tolerance on in diameter buttonhead rivets is 0.010 in So the tolerance of the hole would be about the same size

The second point is that there are 30 parts in this assembly How the parts are stored and how they are placed in the riveting jig or fixture determines how fast the process is done With experience, the process gets faster There is a well-understood empirical model for process learning The observation, often repeated in many different industries, is that

inputs decrease by a fixed percentage each time the number of units produced doubles So, for example, L i is the labor in

minutes of the ith unit produced, and L0 is the labor of the first unit, then:

The parameter measures the slope of the learning curve The learning curve effects were first observed and documented

in the aircraft industry, where a typical rate of improvement might be 20% between doubled quantities This establishes

an 80% learning function, that is, = 0.80 Because this example is fabricated from aluminum, with rivets typical of aircraft construction, it is easy to work out that the 32nd unit will require 32.7% of the time (6.1 min) compared to the first unit (18.6 min)

Learning occurs in any well-managed manual assembly process With automated assembly, "learning" occurs only when improvements are made to the robot used In either case, there is evidence that, over substantial production runs and considerable periods of time, the improvement is a fixed percentage between doubled quantities That is, if there is a 20% improvement between the tenth and twentieth unit, there will likewise be a 20% improvement between the hundredth and two hundredth unit

The cost engineer should remember that, according to this rule, the percentage improvement from one unit to the next is a steeply falling function After all, at the hundredth unit, it takes another hundred units to achieve the same improvement

as arose between the 10th and 20th units (Ref 13)

1 G Boothroyd, P Dewhurst, and W Knight, Product Design for Manufacture and Assembly, Marcel

Dekker, 1994, Chapt 1

11 W.N Nordquist, Die Designing and Estimating, 4th ed., Huebner Publishing, 1955

12 E Oberg, F.D Jones, and H.L Horton, Machinery's Handbook, 22nd ed., Industrial Press, 1987, p

1188-1205

13 G.J Thuesen, and W.J Fabrycky, Engineering Economy, Prentice Hall, 1989, p 472-474

Complexity Theory

Up to now this article has dealt with the cost-estimation tools that do not require a complete description of the part or assembly to make the desired estimates What can be said if the design is fully detailed? Of course, one could build a prototype to get an idea of the costs, and this is often done, particularly if there is little experience with the manufacturing methods to be used For example, suppose there is a complex wave feed guide to be fabricated out of aluminum for a modern radar system The part has some 600 dimensions One could get a cost estimate by programming a numerically controlled milling machine to make the part, but is there a simpler way to get a statistically meaningful estimate of cost, while incorporating all of the design details? The method that fulfills this task is complexity theory

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There has been a long search for the "best" metric to measure how complex a given part or assembly is The idea of using dimensions and tolerances as a metric comes from Wilson (Ref 14) The idea presented here is that the metric is a sum of

log (d i /t i ), where d i is the ith dimension and t i is its associated tolerance (i ranges over all the dimensions needed to describe the part) According to complexity theory, how complex a part is, I, is measured by:

(Eq 12)

Originally, the log function was chosen from an imperfect analogy with information theory It is now understood that the log function arises from a limit process in which tolerance goes to zero while a given dimension remains fixed In this limit, if good engineering practice is followed, that is, if the accuracy of the machine making the part is not greatly different than the accuracy required of the part, and if the "machine" can be modeled like a first-order damped system, then it can be shown that the log function is the correct metric Because of historical reasons, the log is taken to the base

2, and I is measured in bits Thus Eq 12a is written:

(Eq 12a)

There are two main attractions of the complexity theory First, I will include all of the dimensions required to describe the

part Hence, the metric captures all of the information of the original design For assemblies, the dimensions and tolerances refer to the placement of each part in the assembly, and second, the capability of making rigorous statements of

how I effects costs In Ref 8 it is proven that if the part is made by a single manufacturing process, the average time (T) to

fabricate the part is:

Again, in many cases, the coefficient A must be determined empirically from past manufacturing data The same formula

applies to assemblies made with a single process, such as manual labor The extension to multiple processes is given in Ref 8

A final aspect of complexity theory worth mentioning is risk Suppose a part with hundreds of dimensions is to be made

on a milling machine The exact sequence in which each feature of the part is cut out will determine the manufacturing

time But there are a large number of such sequences, each corresponding to some value of A Hence there is a collection

of As, which have a mean that corresponds to the average time to fabricate the part That is the meaning of Eq 13

It can be shown that the standard deviation of manufacturing time is:

where T is the standard deviation of the manufacturing time, and A is the standard deviation of the coefficient A A

can be determined from past data These results have a simple interpretation: Parts or assemblies with tighter (smaller)

tolerances take longer to make or assemble because with dimensions fixed, the log functions increase as the tolerances decrease More complex parts, larger I, take longer to make (Eq 13), and more complex parts have more cost risk (Eq 14)

These trends are well known to experienced engineers

In Eq 8, a large number of parts from three types of manufacturing processes were correlated according to Eq 13 The results of the following manual lathe process are typical of all the processes studied in Eq 8 Figure 3 shows the

correlation of time with I, the dimension information, measured in bits An interesting fact, shown in Fig 4 is that the

accuracy of the estimate is no different than that of an experienced estimator

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Fig 3 Manufacturing time and dimension information for the lathe process (batch size 3 to 6 units)

Fig 4 Accuracy comparison for the lathe process

In Eq 13, the coefficient, A, is shown to depend on the machine properties such as speed, operation range, and time to

reach steady-state speed Can one estimate their value from first principals? It turns out that for manual processes one can make rough estimates of the coefficient

The idea is based on the basic properties of human performance, known as Fitts' law Fitts and Posner reported the maximum human information capacity for discrete, one-dimensional positioning tasks at about 12 bits/s (Ref 15) Other experiments have reported from 8 to 15 bits/s for assembly tasks (Ref 16)

The rivet insertion process discussed previously in this article is an example The tolerance of the holes for the rivets is estimated to be 0.010 in., that is, the same as the handbook value of the tolerance of the barrel of the rivet (Ref 12) Then

it is found that d/t 0.312/0.010 = 31.2 and log2 = 4.815 bits for each insertion The initial rate of insertion (Ref 7) was

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20 units in 1.41 min That corresponds to A = 1.14 bits/s Clearly, there is some considerable improvement available if the

maximum values quoted (Ref 15, 16) can be achieved for rivet insertion

Example 3: Manual Assembly of a Pneumatic Piston

In Ref 1 there is an extensive and helpful section on manual assembly The method BDK used categorizes the difficulty of assembling parts by a number of parameters, such as the need to use one or two hands, the need to use mechanical tools, part symmetry, and so on Figure 5 (reproduced from an example in Ref 17) shows the assembly of a small pneumatic piston Table 3 lists assembly times

Table 3 Assembly times for piston example (Fig 5)

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Fig 5 Assembly of pneumatic piston Dimensions in millimeters

Consider the entries for the two screws The handling code, 68, describes a part with 360° symmetry that can be handled with standard tools The insertion code, 39, describes a part not easy to align or position The time for assembly of the screws is nominally 32 s, less an allowance of 31 s for repetitive operations

Now consider a simplified design (Fig 6 and Table 4) The same tables from Chapter 21 in Ref 7 are used as in Table 2 Software is available to automate the table look-up process For the same problem using complexity theory, there is only

one coefficient, A = 1.5 bits/s for the small manual assembly This value is found by calculating the bits of information in the initial design and using the time found in Ref 17 to determine A

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Table 4 Assembly times for simplified piston design (Fig 6)

Fig 6 Simplified assembly of pneumatic piston Dimensions in millimeters

The tolerances were obtained in the following way For the screws, the size was chosen to be M3X0.5 a coarse thread metric size consistent with insertion into molded nylon As reported in Ref 12, the tolerance is ANSI B1.13M-1979

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The spring tolerance is derived using a standard wire size, 0.076 in (0.193 mm), which gives a spring index D/d = 12.95, (D = spring diameter, d = wire diameter) well within the Spring Manufacturers Institute recommended range The

tolerance quoted is the standard tolerance for this wire diameter and spring index

The plastic parts are presumed to be injection molded, with a typical tolerance of 0.1 mm The screws are assumed to tighten to a tolerance of = th of a turn

These data, which can be easily verified in practice, give essentially the same results as the other empirical methods Calculations for the original design (Fig 5) and the simplified design (Fig 6) are compared in Tables 5 and 6, respectively This compares well with the results of Ref 17 (73% reduction) versus 76% reduction here

Table 5 Original manual assembly design

Feature (No.) Dimensions, mm Tolerance Bits Notes

1 31 0.1 8.276124 Horizontal location of plate

There are two comments to make:

• This method requires only one coefficient for hand assembly of small parts A 1.6 bits/s and no

In the simplified manufacturing process, the coefficient A = 1.6 bits/s is substantially less than the Fitts' law (discussed

earlier in this section on complexity theory) value of 8 bits/s The discrepancy may lie in the time it takes an assembler to pick up and orient each part before the part is assembled Jigs and trays, and so forth, that reduce this pick-and-place orientation effort would save assembly time As before, there is some considerable improvement available if the

maximum values quoted (Ref 15, 16) can be achieved for manual assembly The value obtained here (A = 1.16) is close to

that deduced from Ref 7 for the hand insertion of rivets

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Using complexity theory and a single assembly process, the ratio of the assembly times can be calculated with out any

knowledge of the coefficient, A Thus complexity theory offers advantages when a single process is used, even if little or

nothing is known about the performance of the process

1 G Boothroyd, P Dewhurst, and W Knight, Product Design for Manufacture and Assembly, Marcel

Dekker, 1994, Chapt 1

16 J Annett, C.W Golby, and H Kay, The Measurement of Elements in an Assembly Task The Information

Output of the Human Motor System, Quart J Experimental Psychology, Vol 10, 1958

17 G Boothroyd and P Dewhurst, Product Design for Assembly, Boothroyd Dewhurst, 1989

Cost Estimation Recommendations

Which type of cost estimate one uses depends on how much is know about the design In the early stages of concept assessment of a new part or product, parametric methods, based upon past experience, are preferred Risk is hard to quantify for these methods, because it can be very difficult to determine whether the new product really is similar to those used to establish the parametric cost model

If there is some detailed information about the part or product, and the method of manufacturing is well known, then the empirical methods should be used They can indicate the relative cost between different designs and give estimates of actual costs

If detailed designs are specified, and a single manufacturing process is to be used, complexity theory should be used to compare the relative costs and cost risks of the different designs, even if the manufacturing process is poorly understood

If there are detailed designs available, and well-known manufacturing methods are used, either complexity theory or empirical methods can be used to generate cost estimates If a rigorous risk assessment is needed, complexity theory should be used

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5 H.T Johnson and R.S Kaplan, Relevance Lost, the Rise and Fall of Management Accounting, Harvard

Business School Press, 1991

9 J Roskam, Rapid Sizing Method for Airplanes, J Aircraft, Vol 23 (No.7), July 1986, p 554-560

10 The Bell-Boeing V-22 Osprey entered Low Rate Initial Production with the MV-22 contract signed June 7,

1996, Tiltrotor Times, Vol 1 (No 5), Aug 1996

11 W.N Nordquist, Die Designing and Estimating, 4th ed., Huebner Publishing, 1955

1188-1205

13 G.J Thuesen, and W.J Fabrycky, Engineering Economy, Prentice Hall, 1989, p 472-474

14 D.R Wilson, "An Exploratory Study of Complexity in Axiomatic Design," Doctoral Thesis, Massachusetts Institute of Technology, 1980

15 P.M Fitts, and M.I Posner, Human Performance, Brooks/Cole Publishing, Basic Concepts in Psychology Series, 1967

16 J Annett, C.W Golby, and H Kay, The Measurement of Elements in an Assembly Task The Information

Output of the Human Motor System, Quart J Experimental Psychology, Vol 10, 1958

17 G Boothroyd and P Dewhurst, Product Design for Assembly, Boothroyd Dewhurst, 1989

Design for Casting

Thomas S Piwonka, The University of Alabama

Introduction

CASTING offers the designer cost advantages over other manufacturing methods for most components, especially those having complex geometries Casting properties are usually isotropic, and castings may be designed for function rather than for ease of assembly, like built-up structures Fillet radii are usually generous, decreasing stress concentration factors Converting a built-up assembly to a casting is usually accompanied by a decrease in part count, assembly time,

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and inventory, and a savings in weight With the development of rapid prototyping, expensive tooling is not necessary, and parts can be delivered within days after the order is placed The casting process is well understood, and high integrity castings are as reliable as forgings Indeed, castings prove their quality everyday in applications as demanding as prostheses, automotive chassis components, primary aircraft structures, and rotating hardware in gas turbine engines

Designers face a number of challenges in the design of castings To begin with, there are a wide variety of casting alloys Complete mechanical property data, especially for dynamic properties, are sometimes lacking for these alloys Static property data, though often found in handbooks, may consist of "typical values," which are of little help in creating an efficient design These typical values obscure a crucial fact: casting properties are determined during solidification and subsequent heat treatment This means that properties will vary depending on how quickly the casting solidifies and how the casting is heat treated

Thus, to create effective designs, designers should be acquainted with fundamental information about how casting design influences casting solidification and how casting solidification influences casting properties This article approaches design by reviewing the aspects of castings with which designers should be familiar It also reviews methods used by foundries to produce high-integrity castings Specification of casting quality levels should be based on solid knowledge of the effect of casting discontinuities and on component testing Procurement of high-quality castings requires the involvement of the designer, the purchasing agent, and the foundry in a cooperative effort

Design Considerations

Casting design begins with the determination of the stresses that must be supported by the cast component and the geometrical constraints on that component The designer then arranges the cast material to support the stresses in the most efficient way However, in designing a part that will be cast, the designer will optimize the design by taking into account characteristics of the casting process Because the properties of the casting determine its performance, those features of the casting process that affect the casting properties are reviewed here This discussion emphasizes those concepts that designers and foundries can use to obtain maximum performance from cast parts

Designers must begin the design process with a thorough understanding of what properties the component must have in addition to strength and ductility Fundamental properties such as Young's modulus, Poisson's ratio, density, thermal conductivity, and coefficient of thermal expansion vary between alloy families and within alloy families Cast alloy selection should begin by taking these differences into account

How the Casting Process Affects Casting Properties. The properties of a component depend on the way it is made because the microstructure of the component depends on the manufacturing method, and the properties depend in turn on the microstructure Thus the choice of making a part by casting, by forging, or by machining will affect the performance of the part Once the decision is made on how the part is to be manufactured, the details of the processing parameters employed also affect component properties

Component design is usually approached with the assumption that the material is uniform and isotropic and that there is

an inherent small and random scatter in properties Exceptions are made for fiber-reinforced composite materials and for components where directionality of properties is beneficial (directionally solidified gas turbine blades, for example) In castings, properties will be uniform in specific casting sections from casting to casting provided that the casting variables are constant for each casting However, they may vary in a predictable manner from point to point within the casting

Casting microstructure is determined by cooling rate, that is, how fast each part of the casting freezes The cooling rate is roughly proportional to the ratio of the square of the surface area of the casting to the square of its volume (a consequence

of what metal casters know as Chvorinov's law) In other words, bulky castings freeze much slower than thin castings a sphere of a given volume will freeze more slowly than a thin plate of the same volume because the plate has much more surface area to transfer the same quantity of heat into the mold Because the sphere solidifies more slowly, its microstructure will be coarser than that of the plate even if both are poured from the same melt at the same temperature Because microstructure determines casting properties, the properties of the sphere and the plate will be different

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Casting is the solidification of liquid confined in a mold, which shapes the final component A cavity is made in a mold, which may be a reusable aggregate, such as sand, or a metal mold, used in permanent mold and die casting The metal is

delivered to the mold cavity through channels in the mold or die, which are called runners The passages between the runner and the mold cavity, where the metal enters the mold, are called gates

Castings are frequently complex shapes made up of some bulky sections and some thin sections Obviously, the thin sections will solidify faster than the thick sections; therefore, their properties will differ from those of the thick sections Certain other geometric features will also influence solidification rate For instance, concave sections, or reentrant angles, solidify more slowly than fins or protrusions, again affecting the resultant local structure and the properties In other words, property variation within a casting, which is caused by local differences in cooling rate, is natural, expected, and entirely reproducible it is not "random" scatter It can be predicted and should be taken into account during component design to enhance the component performance

One way to take account of this during the design phase is to apply a "section size" effect, a factor by which the local casting properties are adjusted based on local dimensions While this technique is often effective, the designer should remember that casting properties depend on cooling rate, not section size Cooling rate depends not only on section size but also on pouring temperature, mold material, gating system, the presence or absence of chills in the mold, mold coatings, and insulation Thus, within limits (some very broad), the properties can be controlled by the metal caster to produce those which the designer desires

Cast iron provides the most dramatic example of the differences in properties caused by differences in structure resulting from cooling rate differences When cast iron (which is essentially a solution of carbon and silicon in iron) solidifies, the carbon can take different forms, depending on its composition and solidification rate and the way the metal has been treated during melting Chill cast iron (white iron) has properties completely different from gray iron of the same composition, caused solely by the accelerated cooling rate in the "chilled" iron White iron freezes so quickly that the carbon combines with the iron to solidify as the compound Fe3C, known as cementite because it is hard and brittle In

gray iron, which solidifies more slowly, the carbon appears as graphite flakes; this iron is easy to machine

Ductile iron also has properties significantly different from gray iron; in this case the carbon solidifies as tiny spheres in a steel matrix Since the spheres of graphite are less effective as stress raisers, compared to the flakes of carbon in gray iron, ductile iron has significant ductility, whereas gray iron does not, even though they both may have nearly identical compositions In this case, the difference in structure, which produces the property difference, is caused not by cooling rate, but by chemical treatment of the melt, which alters the undercooling at the beginning of solidification, which in turn affects the way the carbon solidifies It is important here to realize that in castings, similar compositions, in similar geometries, can have very different properties, depending on the way the castings are made

Designers frequently use handbook data in designing components Very often, these data are developed using Gaussian statistics As noted above, such data can be misleading if not corrected to reflect differences in cooling rate from section

to section within a casting Gaussian statistics are appropriate for those materials that are truly ductile, meaning those that have a tensile elongation over 8 to 10% Many casting alloys, however, when completely free of discontinuities, have elongations of only 5 to 10% Indeed, this is often the reason that these alloys are commonly cast: their low ductilities make them hard to form by forging or machining Use of Gaussian statistics to determine design allowables in these alloys is incorrect, leads to "casting factors," and causes significant overdesign, waste of material, and weight penalties Casting factors are arbitrary increases in casting section thickness applied to compensate for perceived lack of reproducibility of casting properties Such factors are unnecessary and wasteful (Ref 1) For this reason, it is important that designers recognize that designing with low ductility (not brittle) materials requires a different approach than designing with ductile materials Also, casting versions of wrought alloys may have different compositions than the wrought alloys to aid in solidification

Reproducibility of properties produced by a process is most important for the designer because the components that are designed must behave according to the design Reliability is often evaluated using Weibull statistics (Ref 2), which consider the probability of the existence of a discontinuity that would cause failure This is particularly appropriate for the design of low ductility materials In analyzing data using Weibull statistics, one evaluates the value of the Weibull modulus The higher the Weibull modulus is, the more reliable the material will be (that is, the higher the Weibull modulus, the less the variation in property within a given section of the component)

For tensile properties, ceramics typically have Weibull moduli of approximately 10 Aluminum alloy forgings typically have Weibull moduli of approximately 50 Conventionally cast aluminum castings have Weibull moduli of approximately 30; using techniques for "premium quality castings," castings with Weibull moduli of 50 are routinely produced for use as

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primary structures for commercial aircraft (Ref 3, 4) For carefully made thin sections, the Weibull modulus can be above

80 (Ref 5), well above that expected for forgings

Ductile iron, most cast steel alloys, and copper-base alloys commonly have high ductilities, and the use of Gaussian statistics to determine design allowables is appropriate However, gray and compacted graphite iron, superalloys, some tool steels, and many aluminum alloys are low ductility alloys and should be approached using Weibull statistics

Basic Features of Solidification. Solid and liquid alloys usually have different densities, which means when solidification is complete, the solid will occupy less space than the liquid (in most alloys) In other words, the solid

"shrinks." Because solid metal is more dense than liquid metal, the metal shrinks when it solidifies, and the final casting

will not fill the mold unless this shrinkage is compensated To do this, the foundry adds a riser to the casting This riser is

a reservoir of molten metal, which supplies liquid metal to the solidifying casting and compensates for the shrinkage that occurs If the riser is to function properly, the liquid metal that it contains must be able to flow through the solidifying casting to reach the areas in the casting where solidification and hence shrinkage is occurring

In alloy solidification, the picture is complicated by the fact that alloys freeze over a range of temperatures This means

that small nuclei of solid grains form at the beginning of solidification and grow (forming dendrites, the term for

solidifying grains) as the temperature in the casting falls and solidification progresses As these grains grow, they form a

"mush" of liquid and solid, which becomes progressively more solid until solidification is complete Because each small dendrite that forms is a site where shrinkage occurs during solidification, feeding the shrinkage means finding a way to cause metal to flow between the dendrites to the location where solidification (and shrinkage) is taking place As the dendrites grow, the paths that deliver liquid metal from the riser to the areas where solidification is taking place become smaller until they are at last too narrow to allow metal to pass (There is one exception to this rule In cast iron, both gray and ductile, the graphite that solidifies expands on solidification Because graphite forms at the end of solidification, its expansion often (but not always) compensates for the shrinkage of the iron For this reason, cast iron often needs very little in the way of risers.)

Liquid metal can dissolve much more gas in solution than solid metal Therefore, when metal solidifies, gas that is present

in the liquid is rejected and forms bubbles A commonly encountered example is that of hydrogen in aluminum If these bubbles are trapped in the casting when it freezes, the result is a pore Pores that result from gas may be spherical, indicating that they formed early in solidification when the metal was mostly liquid, or they may be interdendritic in shape, showing that they formed late in solidification, when the liquid that remained was present between dendrites

As the solidification rate increases, the microstructure of the casting is refined That is, the grains are smaller, and the spacing between the arms of the dendrites that make up grains is finer Mechanical properties usually improve as the microstructure becomes finer Because the properties depend on the microstructure, which depends on the solidification rate, which in turn depends on the processing variables used by the foundry and the casting design, designers have a major influence on the final properties of the casting

Using solidification simulation programs, foundries predict how fast each section of each casting will solidify and, therefore, what will be the properties of each section The use of these programs combined with the application of statistical process control techniques has transformed casting into a high technology manufacturing process capable of reliably producing critical components for the most demanding applications

General Design Considerations for Castings. Casting design influences the way the casting solidifies because the geometry of the casting influences how fast each section solidifies; therefore, it is a major factor in determining how castings will perform The overarching principle of good casting design is that casting sections should freeze progressively, allowing the risers to supply liquid metal to feed shrinkage that occurs during solidification There are a number of excellent summaries of principles of good casting design (Ref 6, 7, 8), and a comprehensive booklet was published on design of premium quality aluminum alloy castings (Ref 9) This latter publication also includes general information on the specification and process of approving foundry sources, which is applicable to castings made from any metal

Designing for progressive solidification requires tapering walls so that they freeze from one end to the other, as shown in Fig 1, and avoiding situations where two heavy sections are separated by a thin section (This is a poor design because metal must feed one heavy section through the thin section; when the thin section freezes before the heavy section, the flow path will be cut off and shrinkage may form in the heavy section.)

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Fig 1 Redesign of castings to provide progressive solidification through the use of tapered walls (a) Elbow

design (b) Valve fitting design Source: Ref 10

Junctions also concentrate heat, leading to areas in the casting where heat is retained These areas solidify more slowly than others, thus having a coarser structure and different properties from other sections, and solidify after the rest of the casting has solidified, so that shrinkage cannot be fed Minimizing the concentration of heat in junctions, therefore, aids in improving casting properties Examples of this are shown in Fig 2

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Fig 2 Redesign of a casting to minimize heat concentration (a) Design has numerous hot spots (X junctions)

that will cause the casting to distort (b) Improved design using Y junctions Source: Ref 6

Concave corners concentrate heat, so they freeze later and more slowly than straight sections, while convex corners lose heat faster, and freeze sooner and more quickly than straight sections In designing a casting, the designer should use properties from test bars that have solidified at the actual cooling rate in that section of the casting This cooling rate can

be determined by instrumenting a casting and measuring the cooling rate in various sections or by simulating its solidification using a commercial solidification simulation program

The hollow spaces in castings are formed by cores, refractory shapes placed in the molds and around which the casting

freezes These cores are later removed from the casting, usually by thermal or mechanical means However, each core requires tooling to form it and time to place it in the mold Casting designs that minimize cores are preferable to minimize costs Some examples are given in Fig 3

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Fig 3 Redesign of castings to eliminate cores (a) Casting redesigned to eliminate outside cores (b)

Simplification of a base plate design to eliminate a core (c) Redesign of a bracket to eliminate a core and to decrease stress problems Source: Ref 10

The designer must provide surfaces for the attachment of gates and risers The casting must solidify toward the riser in order to be sound, and gates must be located so that the mold fills from the bottom to the top so that oxide films that form are swept to the top surface of the casting or into risers where they will not affect casting properties Gate and riser locations must be accessible for easy removal to minimize processing costs The position of gate and riser contacts may also add costs if they are placed where subsequent machining will be required to remove gate stubs or riser pads in the finished component

1 J Gruner, "Structural Aluminum Aircraft Casting with No Casting Factor," presented at Aeromat '96 (Dayton, OH), ASM International, June 1996

2 W Weibull, A Statistical Distribution Function of Wide Applicability, J Appl Mech., Vol 18, 1951, p 293

3 J Campbell, J Runyoro, and S.M.A Boutorabi, Critical Gate Velocities for Film-Forming Alloys, AFS Trans., Vol 100, 1992, p 225

4 N.R Green and J Campbell, Proc Spring 1993 Meeting (Strasbourg, France), European Division Materials

Research Society, 4-7 May, 1993

5 N.R Green and J Campbell, The Influence of Oxide Film Filling Defects on the Strength of Al-7Si-Mg

Alloy Castings, AFS Trans., Vol 102, 1994, p 341

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6 Manufacturing Considerations in Design, Steel Castings Handbook, 5th ed., P.F Wieser, Ed., Steel

Founders' Society of America, 1980, p 5-6

7 Materials Handbook, Vol 15, Casting, ASM International, 1988, p 598

8 Investment Casting, P.R Beeley and R.F Smart, Ed., The Institute of Materials, 1995, p 334

9 Design and Procurement of High-Strength Structural Aluminum Castings, S.P Thomas, Ed., American

Foundrymen's Society, 1995

10 Manufacturing Design Considerations, Chap 7, Steel Castings Handbook, 6th ed., M Blair and T.L

Stevens, Ed., Steel Founders' Society of America and ASM International, 1995

The Effect of Casting Discontinuities on Properties

Poor casting design can interfere with the ability of the foundry to use the best techniques to produce reliable castings The designer also specifies the quality requirements that ensure that the cast component will perform as desired Over specification causes needless expense and can be avoided by understanding the effect of discontinuities on casting performance and the effect of casting design on the tendency for discontinuities to form during the casting process Important types of casting discontinuities include porosity, inclusions, oxide films, second phases, hot tears, metal penetration, and surface defects

Porosity is a common defect in castings and takes many forms Pores may be connected to the surface, where they can

be detected by dye penetrant techniques, or they may be wholly internal, where they require radiographic techniques to

discover Macroporosity refers to pores that are large enough to see with the unaided eye on radiographic inspection, while microporosity refers to pores that are not visible without magnification

Both macroporosity and microporosity are caused by the combined action of metal shrinkage and gas evolution during solidification It has been shown (Ref 11, 12) that nucleation of pores is difficult in the absence of some sort of substrate, such as a nonmetallic inclusion, a grain refiner, or a second phase particle This is why numerous investigations have shown that clean castings, those castings that are free from inclusions, have fewer pores than castings that contain inclusions Microporosity is found not only in castings, but also in heavy section forgings that have not been worked sufficiently to close it up

When the shrinkage and the gas combine to form macroporosity, properties are deleteriously affected Static properties are reduced at least by the portion of the cross-sectional area that is taken up with the pores (since there is no metal in the pores, there is no metal to support the load there, and the section acts as though its area was reduced) Because the pores may also cause a stress concentration in the remaining material (Ref 13, 14), static properties may be reduced by more than the percentage of cross-sectional area that is caused by the macroporosity

Dynamic properties are also affected A study of aluminum alloys showed that fatigue properties in some were reduced 11% when specimens having x-ray quality equivalent to ASTM E 155 level 4 were tested, and that they were reduced 17% when specimens having quality of ASTM E 155 level 8 were tested (Ref 15)

Static properties are mostly unaffected by microporosity Microporosity is found between dendrites and, like macroporosity, is caused by the inability of feed metal to reach the interdendritic areas of the casting where shrinkage is occurring and where gas is being evolved However, because this type of porosity occurs late in solidification, particularly

in long-range freezing (mushy-freezing) alloys, it is particularly difficult to eliminate The most effective method is to increase the thermal gradient (often accomplished by increasing the solidification rate), which decreases the length of the mushy zone This technique may be limited by alloy and mold thermal properties, and by casting geometry, that is, the design of the casting

As long as the micropores are less than 0.2 mm in length, there is no effect on dynamic properties; fatigue properties of castings with pores that size or smaller are in the same range as those of castings where no micropores were found (Ref

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16, 17, 18) The shape of the micropore is as important as its size, with elongated pores having a greater effect than round pores (Ref 19) Areas where microporosity is expected can be predicted by solidification modeling, similar to the prediction of macroporosity (see below) Microporosity can be healed by hot isostatic pressing (HIP) In one study comparing HIP and non-HIP samples, no difference was found in fatigue lives of HIP and non-HIP samples (Ref 20) However, the HIP samples showed a lower crack growth rate than non-HIP samples In another study (Ref 21), HIP improved fatigue crack growth resistance only close to threshold levels (Additional information about HIP is provided in the section "Hot Isostatic Pressing" in this article.) As noted above, the design of the casting directly affects its tendency

to solidify in a progressive manner, thereby affecting both the quality and the price of the cast component

Porosity and casting costs are minimized in casting designs that emphasize progressive solidification toward a gate or riser, tapered walls, and the avoidance of hot spots

Inclusions are nonmetallic particles that are found in the casting They may form during solidification as some elements (notably manganese and sulfur in steel) precipitate from solution in the liquid More frequently, they are formed before

solidification begins The former are sometimes called indigenous inclusions, and the latter are called exogenous

inclusions Inclusions are ceramic phases; they have little ductility A crack may form in the inclusion and propagate from the inclusion into the metal, or a crack may form at the interface between the metal and the inclusion In addition, because the inclusion and the metal have different coefficients of thermal expansion, thermally induced stresses may appear in the metal surrounding the inclusion during solidification (Ref 22) As a result, the inclusion acts as a stress concentration point and reduces dynamic properties As in the case of microporosity, the size of the inclusion and its location determine its effect (Ref 23, 24) Small inclusions that are located well within the center of the cross section of the casting have little effect, whereas larger inclusions and those located near the surface of the casting may be particularly detrimental to properties Inclusions may also be a problem when machining surfaces, causing excessive tool wear and tool breakage

Exogenous inclusions are mostly oxides or mixtures of oxides and are primarily slag or dross particles, which are the oxides that result when the metal reacts with oxygen in the air during melting These are removed from the melt before pouring by filtration Most inclusions found in steel castings arise from the oxidation of metal during the pouring

operation (Ref 25) This is known as reoxidation, and takes place when the turbulent flow of the metal in the gating

system causes the metal to break up into small droplets, which then react with the oxygen in the air in the gating system

or casting cavity to form oxides Metal casters use computer analysis of gating systems to indicate when reoxidation can

be expected in a gating system and to eliminate them However, casting designs that require molten metal to "jet" through

a section of the casting to fill other sections will recreate these inclusions and should be avoided

Oxide films are similar to inclusions and have been found to reduce casting properties (Ref 3, 4, 5) These form on the surface of the molten metal as it fills the mold If this surface film is trapped within the casting instead of being carried into a riser, it is a linear discontinuity and an obvious site for crack initiation It has been shown (Ref 26, 27) that elimination of oxide films, in addition to substantially improving static properties, results in a five-fold improvement of fatigue life in axial tension-tension tests

Oxide films are of particular concern in nonferrous castings, although they also must be controlled in steel and stainless steel castings (because of the high carbon content of cast iron, oxide films do not form on that metal) If the film folds over on itself as a result of turbulent flow or "waterfalling" (when molten metal falls to a lower level in the casting during mold filling), the effects are particularly damaging Casting design influences how the metal fills the mold, and features of the design that require the metal to fall from one level to another while the mold is filling should be avoided so that waterfalls are eliminated Oxide films are avoided by filling the casting from the bottom, in a controlled manner, by pumping the metal into the mold using pneumatic or electromagnetic pumps If the casting is poorly designed, waterfalling will result An example is given in Fig 4

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Fig 4 Redesign of a casting to avoid waterfalling (a) In this design, waterfalling results when casting is filled

from the bottom (b) Improved design provides a path for the metal to follow as it fills the mold

Second phases, which form during solidification, may also nucleate cracks if they have the proper size and morphology (Ref 28) An example is aluminum silicon alloys, where the silicon eutectic is present as large platelets, which nucleate cracks, and along which cracks propagate (Ref 29, 30) The size of these platelets may be significantly reduced by modifying the alloy with additions of sodium or strontium However, such additions increase the size of micropores (Ref 31), and for this reason, many foundrymen rely on accelerated solidification of the casting to refine the silicon As noted above, solidification rates normally increase, and the structure is thus refined, in thin sections Heavy sections are to be avoided if a fine structure is desired Generally speaking, however, secondary phases in the structure of castings become important in limiting mechanical behavior of castings only in the absence of nonmetallic inclusions and microporosity (Ref 32)

Hot tears form when casting sections are constrained by the mold from shrinking as they cool near the end of solidification These discontinuities are fairly large and are most often weld repaired If not repaired, their effect is not readily predictable (Ref 17) While generally they are detrimental to casting properties, under some circumstances they do not affect them Hot tears are caused by a combination of factors, including alloy type, metal cleanliness, and mold and core hardness However, poor casting design is the primary cause Castings should be designed so that solidifying sections are not subjected to tensile forces caused by shrinkage during solidification, as the solidifying alloy has little strength before it solidifies An example is given in Fig 5, and an extensive discussion on how to prevent hot tears through casting design is provided in Ref 34

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Fig 5 Redesign of a casting to eliminate hot tears Mold restraint coupled with nonuniform freezing of the

various sections of this aluminum alloy 356 casting resulted in hot tears Moving the wall and increasing its thickness corrected the problem Part dimensions in inches Source: Ref 33

Metal Penetration. Molten metal may penetrate the surface of the mold, forming a rough surface or, in extreme cases, actually becoming intimately mixed with the sand in the mold In iron castings, this is normally the result of the combination of metallostatic head (the pressure exerted on the molten iron at the bottom of the mold by the weight of the metal on top of it) and the surface tension relationships between the liquid iron and molding materials (Ref 35) In cast iron, it is frequently also the result of the expansion of graphite at the end of solidification, forcing liquid metal into the mold if the casting is not properly designed with a tapered wall to promote directional solidification and avoid hot spots

Surface Defects. Surface finish is also an important specification Surface discontinuities affect fatigue life (Ref 36, 37), and obviously smoother surfaces are superior to rough surfaces Designers should be certain that fatigue data used in design calculations has been taken from as-cast surfaces rather than machined surfaces, as most surfaces on castings where stress concentrations might be expected are not machined Surface finish in castings is controlled by the application

of coatings to the mold as well as proper selection of mold materials Metal mold casting processes generally produce better surfaces than sand casting processes

Design and Service Considerations. The existence of casting discontinuities does not, in and of itself, indicate that casting performance in service will be affected Equally important are the size, location, and distribution of these discontinuities (Ref 18, 38, 39, 40) Those discontinuities that are small and located near the center of the casting have little effect, while those located at or near the surface of the casting are usually damaging Clustered discontinuities and those that occur in a regular array have a greater effect on properties than those that are isolated and randomly distributed

In specifying acceptable levels of discontinuities, such as microporosity and inclusion sizes and distribution, the designer should determine the critical flaw size that will deleteriously affect performance in service This permits the foundry to design a casting practice that will eliminate such discontinuities at minimum cost

3 J Campbell, J Runyoro, and S.M.A Boutorabi, Critical Gate Velocities for Film-Forming Alloys, AFS

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Trans., Vol 100, 1992, p 225

11 E.L Rooy, Hydrogen: The One-Third Solution, AFS Trans., Vol 101, 1993, p 961

12 N Roy, A.M Samuel, and F.H Samuel, Porosity Formation in Al-9 Wt Pct Mg - 3 Wt Pct Cu Alloy

Systems: Metallographic Observations, Met Mater Trans., Vol 27A, Feb 1996, p 415

13 M.K Surappa, E Blank, and J.C Jaquet, Effect of Macro-porosity on the Strength and Ductility of Cast

Al-7Si-0.3Mg Alloy, Scr Metall., Vol 20, 1986, p 1281

14 C.H Cáceres, On the Effect of Macroporosity on the Tensile Properties of the Al-7%Si-0.4%Mg Casting

Alloy, submitted to Scr Metall., 1994

15 C.M Sonsino and K Dietrich, Einflu der Porosität auf das Schwingfestigkeitverhalten von

Aluminium-Gu werkstoffen, Giessereiforschung, Vol 43 (No 3 and 4), 1992, p 119-140

16 B Skallerud, T Iveland, and G Härkegård, Fatigue Life Assessment of Aluminum Alloys with Casting

Defects, Eng Fract Mech., Vol 44 (No 6), 1993, p 857

17 M.J Couper, A.E Neeson, and J.R Griffiths, Casting Defects and the Fatigue Behaviour of an Aluminium

Casting Alloy, Fatigue Fract Eng Mater Struct., Vol 13 (No 3), 1990, p 213

18 J.C Ting and F.V Lawrence, Jr., Modeling the Long-Life Fatigue Behavior of a Cast Aluminum Alloy,

Fatigue Fract Eng Mater Struct., Vol 16 (No 6), 1993, p 631

19 J.T Berry, Linking Solidification Conditions and Mechanical Behavior in Al Castings A Quarter Century

of Evolving Evidence, AFS Trans., Vol 103, 1995, p 837

20 S Kennerknecht, "Design and Specification of Aluminum Airframe Structural Castings," presented at Aeromat '95 (Anaheim, CA), ASM International, May 1995

21 G.O Rading, J Li, and J.T Berry, Fatigue Crack Growth in Cast Al-Cu Alloy A206 with Different Levels

of Porosity, AFS Trans., Vol 102, 1994, p 57

22 I.P Volchok, Non-Metallic Inclusions and the Failure of Ferritic-Pearlitic Cast Steel, Cast Metals, Vol 6

(No 3), 1993, p 162

23 P Heuler, C Berger, and J Motz, Fatigue Behaviour of Steel Casting Containing Near-Surface Defects,

24 J Motz et al., Einfluss oberflächener Fehlstellen im Stahlgu auf die Ri einleitung bei

Schwingungsbeanspruchung, Geissereiforschung, Vol 43, 1991, p 37

25 C.E Bates and C Wanstall, Clean Steel Castings, in Metalcasting Competitiveness Research, Final Report,

DOE/ID/13163-1 (DE95016652), Department of Energy, Aug 1994, p 51

26 C Nyahumwa, N.R Green, and J Campbell, "The Effect of Oxide Film Filling Defects on the Fatigue Life Distributions of Al-7Si-Mg Alloy Castings," presented at the International Symposium on Solidification Science and Processing (Honolulu, HI), Japan Institute of Metals and TMS, Dec 1995

27 J Campbell, The Mechanical Strength of Non-Ferrous Castings, Proc 61st World Foundry Cong (Beijing),

1995, p 104; available from the American Foundrymen's Society, Des Plaines, IL

28 K.E Höner and J Gross, Bruch verhalten und mechanische Eigenschafter von Aluminium-Silicium-Gu

legierungen in unterschiedlichen Behandlungszuständen, Giessereiforschung, Vol 44 (No 4), 1992, p 146

29 F.T Lee, J.F Major, and F.H Samuel, Effect of Silicon Particles on the Fatigue Crack Growth

Characteristics of Al-12 Wt Pct - 0.35 Wt Pct Mg - (0 to 0.02) Wt Pct Sr Casting Alloys, Met Mater Trans., Vol 26A (No 6), June 1995, p 1553

30 J.F Major, F.T Lee, and F.H Samuel, Fatigue Crack Growth and Fracture Behavior of Al-12 wt% Si-0.35

wt% Mg (0-0.02) % Sr Casting Alloys, Paper 96-027, AFS Trans., Vol 104, 1996

31 D Argo and J.E Gruzleski, Porosity in Modified Aluminum Alloy Castings, AFS Trans., Vol 96, 1988, p

65

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32 T.L Reinhart, "The Influence of Microstructure on the Fatigue and Fracture Properties of Aluminum Alloy

Castings," presented at Aeromat '96 (Dayton, OH), ASM International, June 1996

33 Permanent Mold Casting, Forging and Casting, Vol 5, Metals Handbook, 8th ed., American Society for

Metals, 1970, p 279

34 A.L Kearney and J Raffin, Heat Tear Control Handbook for Aluminum Foundrymen and Casting Designers, American Foundrymen's Society, 1987

35 D.M Stefanescu et al., Cast Iron Penetration in Sand Molds: Part I: Physics of Penetration Defects and

Penetration Model, Paper 96-206, AFS Trans., Vol 104, 1996

36 R.L Naro and J.F Wallace, Effect of Mold-Steel Interface Reactions on Casting Surface and Properties,

AFS Trans., Vol 75, 1967, p 741

37 R.L Naro and J.F Wallace, Effect of Mold-Steel Interface Reactions on Casting Surfaces, AFS Trans., Vol

40 A Needleman and V Tvergaard, A Numerical Study of Void Distribution Effects on Dynamic, Ductile

Crack Growth, Eng Fracture Mech., Vol 38 (No 2/3), 1991, p 157

Casting Tolerances

Casting tolerances depend on the alloy being poured, the size of the casting, and the molding method used Generally speaking, casting dimensional accuracy increases as one moves to the right in Fig 6 and as the casting dimensions decrease However, there is significant overlap between processes, and new developments are continually being made so that even this general trend may not apply for a specific cast component In addition, evidence is mounting that most foundries produce castings that are more accurate dimensionally than called for in casting specifications For this reason, designers should consider more than one casting process during the design stage and select a process that offers the best combination of dimensions, properties, and cost Each casting process has its particular strengths, and designers should acquaint themselves with each (Ref 41) Table 1 lists factors that affect the selection of an appropriate casting process for aluminum alloy parts Additional information on the selection of casting processes is provided in the article

"Manufacturing Processes and Their Selection" in this Volume

Table 1 Factors affecting selection of casting process for aluminum alloys

Casting process Factor

Sand casting Permanent mold casting Die casting Cost of

equipment

Lowest cost if only a few items required

Less than die casting Highest

Casting rate Lowest rate 11 kg/h (25 lb/h) common; higher

rates possible

4.5 kg/h (10 lb/h) common; 45 kg/h (100 lb/h) possible

Size of casting Largest of any casting method Limited by size of machine Limited by size of machine

Cores must be able to be pulled because they are metal; undercuts can be formed only by collapsing cores or loose pieces

Minimum wall

thickness

3.0-5.0 mm (0.125-0.200 in.) required; 4.0 mm (0.150 in.) normal

3.0-5.0 mm (0.125-0.200 in.) required; 3.5 mm (0.140 in.) normal

1.0-2.5 mm (0.100-0.040 in.); depends on casting size

Type of cores Complex baked sand cores

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Best linear tolerance is 4 mm/m (4 mils/in.)

Surface finish 6.5-12.5 m (250-500 in.) 4.0-10 m (150-400 in.) 1.5 m (50 in.); best finish of the three

Porosity may be present

Cooling rate 0.1-0.5 °C/s (0.2-0.9 °F/s) 0.3-1.0 °C/s (0.5-1.8 °F/s) 50-500 °C/s (90-900 °F/s)

Strength Lowest Excellent Highest, usually used in the as-cast condition

Fatigue

properties

Overall quality Depends on foundry technique Highest quality Tolerance and repeatability very good

Remarks Very versatile as to size,

shape, internal configurations

Excellent for fast production rates

Source: Ref 42

Fig 6 General relationship between dimensional accuracy and casting process

Casting design also affects tolerances Critical dimensions should not cross parting lines in molds or injection or core dies The choice of pattern materials also can affect dimensional tolerances

Stresses that arise from unequal contraction of parts of the casting as it cools from solidification temperatures (Ref 43), as well as those that result from heat treating (Ref 44) can distort castings so that they no longer conform to design dimensions This also affects tolerances and may lead to extra costs to straighten castings Solidification stresses are caused by shrinkage during casting solidification when different sections of the casting solidify at different times and rates Because casting solidification rates depend on the casting design, the designer should consider the effect of the component design on casting distortion Some examples are given in Fig 7

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Fig 7 Designing castings to prevent distortion caused by mold restraint The original design, shown in top and

front views in (a), was altered to three possible preventative designs, as follows (b) Preferred method incorporating a tie bar (c) Less effective method than that shown in (b) (d) Open cavity created in the molding media to relieve restraint upon flanges during casting solidification by allowing solid sand mass to collapse during shrinkage and minimize restraint Dimensions given in inches Source: Ref 45

41 ASM Handbook, Vol 15, Casting, D.M Stefanescu, Ed., ASM International, 1988

42 A Kearny and E.L Rooy, Aluminum Foundry Products, ASM Handbook, Vol 2, Properties and Selection: Nonferrous Alloys and Special-Purpose Materials, ASM International, 1990, p 139

43 J Cech et al., Rationalizing Foundry Production and Assuring Quality of Castings with the Aid of

Computer Science, Paper 10, Proc 62nd World Foundry Congress (Philadelphia), 1996; available from the

American Foundrymen's Society, Des Plaines, IL

44 J Campbell, Review of Reliable Processes for Aluminum Aerospace Castings, Paper 96-158, AFS Trans.,

Vol 104, 1996

45 D.E Groteke, Dimensional Tolerances and Allowances, ASM Handbook, Vol 15, Casting, ASM

International, 1988, p 617

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Hot Isostatic Pressing

Occasionally, there are applications where designers require that casting soundness be 100% of theoretical density For those castings, HIP is recommended In HIP treatments, the castings are placed in a pressure vessel, and an inert gas is introduced, partially pressurized, and heated while it is confined to the pressure vessel The gas, unable to expand, increases in pressure and exerts this pressure on the surface of the casting As the casting is softened by the heat, internal voids collapse under the pressure

Hot isostatic pressing treatment is relatively inexpensive If the porosity to be healed is relatively large (macroporosity), HIP will form small dimples on the surface of the casting that may require weld repair Because HIP is a thermal as well

as a pressure treatment, it can alter the microstructure (and therefore the properties) of components if not carefully designed Hot isostatic pressing will not affect inclusions or oxide folds and, therefore, will not repair castings that have those types of discontinuities It also has no effect on pores that are connected to the surface Hot isostatic pressing has made possible the use of alloys that, because of their composition, do not solidify pore free and, without HIP, could not be used for high-integrity applications

Solidification Simulation and Its Use in Designing Castings

This article has emphasized the importance of the casting design in influencing the way the casting solidifies and, thus, the cast structure and the properties that are produced Since the cast structure controls the heat treated structure and the final structure controls the properties of the component, it is clear that successful design of castings means that the designer must be able to predict the effect of the design on the structure of the final part This is done today by using solidification simulation models Most progressive foundries today use simulation models in engineering the casting process Designers are encouraged to work with foundries and have them run solidification models on their designs in a concurrent design process to engineer castings that perform satisfactorily and are reasonably priced

Solidification simulation models have been extensively developed over the last twenty years, and today there are a large variety of them (Ref 46) The more elementary models are based on Chvorinov's law and operate by comparing surface area to volume ratios of adjoining casting sections to predict the order in which the sections solidify (that is, how progressive the solidification will be) Those models are satisfactory for predicting whether or not macroporosity will form on solidification; some models are also effective at predicting the location of microporosity

Advanced models use finite element or finite difference methods to predict how the casting fills and, from those results, are able to establish the temperature of each point in the mold and each point in the liquid metal at the start of solidification From this, a more accurate picture of the way the casting solidifies is possible These models are also capable of predicting the grain size and structure and are now being used to predict casting properties that result from a specific casting design and manufacturing process Solidification models today are capable of predicting the distortion that will occur during casting and heat treatment and can be used to minimize residual stresses Some of the commercial packages include expert systems to help orient the casting in the mold to minimize casting defects and to suggest gating and risering schemes

These models are a powerful tool for concurrent engineering of cast components The designer, working with the foundry, can see how the casting will solidify before the casting is poured If problem areas are found with the design, it can be altered, and the new design can be simulated This iteration can be repeated until a satisfactory design is developed When these simulations are combined with rapid prototyping methods, expedited delivery of cast components can be achieved

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The designer must begin the design of a casting with an understanding of what properties are desired and required throughout the cast component Flaw sizes must be kept below the critical level, and the designer should know what that level is Critical flaw sizes will vary according to location in the casting; that information should be reflected in specifications that also vary by location in order to minimize manufacturing costs

Casting design influences how the castings solidify and, hence, the properties that are obtained Many collections of casting data in handbooks overlook the effect of cooling rate on casting performance and, as a result, do not provide adequate information for designers Designers are therefore encouraged to work with foundries to develop data bases of reliable mechanical property data that reflect the effect of cooling rates of the alloy and the sections that the designer intends to use This is particularly important for areas of the casting where stress concentrations are likely; use of a solidification simulation program should ensure that these areas are not also areas of slow solidification

Designers should be aware that different casting alloys have different levels of "castability," meaning that development of reliable casting properties may be more difficult in some alloys than others Specification of a casting alloy solely on the results of test bar data (test bars are easy to cast and often do not reflect casting problems encountered in actual castings) without consulting the metal caster can lead to high casting costs as the foundry compensates for castability difficulties with the alloy

Reference cited in this section

46 Modeling of Casting, Welding and Advanced Solidification Processes VII, M Cross and J Campbell, Ed.,

TMS/AIME, 1995

Conclusions

The casting process offers the designer exceptional design flexibility at reasonable cost The designer is the key to successful application of the process Because casting design affects solidification rate, the design also affects the properties that can be obtained and the discontinuities that can arise from the process Close cooperation between designer and foundry is essential to realize the benefits of the process

Today's technology, both in component design and manufacturing process design, makes extensive use of computer simulation for optimization In the future, the combination of these technologies will enable designers and metal casters to produce highly engineered cast components

References

1 J Gruner, "Structural Aluminum Aircraft Casting with No Casting Factor," presented at Aeromat '96 (Dayton, OH), ASM International, June 1996

2 W Weibull, A Statistical Distribution Function of Wide Applicability, J Appl Mech., Vol 18, 1951, p 293

3 J Campbell, J Runyoro, and S.M.A Boutorabi, Critical Gate Velocities for Film-Forming Alloys, AFS Trans., Vol 100, 1992, p 225

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