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Eliminating Modeling 'Trial & Error' with Casting Process Optimization.

Multivariable optimization optimization

Field of applied mathematics whose principles and methods are used to solve quantitative problems in disciplines including physics, biology, engineering, and economics.
 moves one step beyond solidification so·lid·i·fy  
v. so·lid·i·fied, so·lid·i·fy·ing, so·lid·i·fies
1. To make solid, compact, or hard.

2. To make strong or united.

 modeling, enabling the computer to automatically search for optimum casting gating, risering and design.

Casting process simulation is being used by foundries to model the production process before tooling is built and castings are made. The primary objectives of using simulation include:

* improving the quality of the casting produced, both in the first castings made and during the production life of the part;

* reducing the lead time needed for new components to enter production;

* reducing costs such as melting and handling by improving yield and reducing cleaning operations;

* optimizing the gating and risering system of a casting.

The traditional method of designing a casting relies on experience and a set of rules to arrive at an initial design for gating and feeding. Pattern or mold mold, name for certain multicellular organisms of the various classes of the kingdom Fungi, characteristically having bodies composed of a cottony mycelium. The colors of molds are caused by the spores, which are borne on the mycelium.  equipment then is produced according to according to
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

 this initial design, and test castings are made. If the test castings exhibit some unacceptable defect, then the pattern equipment is modified and new test castings are poured. This sequence may be repeated several times until suitable castings are made.

Computer modeling offers the potential to evaluate alternative process designs at a reduced time and cost compared to building equipment and producing sample castings. Casting process simulation software Simulation software is based on the process of imitating a real phenomenon with a set of mathematical formulas. It is, essentially, a program that allows the user to observe an operation through simulation without actually running the program.  accepts a user's design for a casting production system and then analyzes the design to predict the likelihood of defects. The user provides both the geometric data (the shape of the casting, risers and gating system) and the material property data for the model to be analyzed an·a·lyze  
tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es
1. To examine methodically by separating into parts and studying their interrelations.

2. Chemistry To make a chemical analysis of.

. Once an analysis has been completed, the user views the results of the analysis, typically by examining various graphic images and interpreting them. If an area of potential defect is found within the casting (such as internal shrinkage Shrinkage

The amount by which inventory on hand is shorter than the amount of inventory recorded.

The missing inventory could be due to theft, damage, or book keeping errors.
 porosity porosity /po·ros·i·ty/ (por-os´it-e) the condition of being porous; a pore.

1. The state or property of being porous.

), then the user must check the data and determine why the defect formed in the area shown. After isolating the problem, the user must decide what changes in the process or design might improve the situation and then alter the model. Running a new analysis will verify whether the change had the intended effect. If not, then the process must be repeated until the desired result is obtained.

The effect of this process is that the design must be modified through a trial-and-error sequence until the analysis shows that the desired result has been achieved. Trial and error on the foundry floor has been replaced with trial and error on the computer.

Applying Process Optimization Process optimization is the practice of making changes or adjustments to a process, to get results.

Optimization is the use of specific techniques to determine the most cost effective and efficient solution to a problem or design for a process.

In an effort to advance beyond the trial-and-error stage, a technique was developed to apply optimization methodology to the casting simulation process. Optimization technology uses various techniques to identify the input variables and constraints CONSTRAINTS - A language for solving constraints using value inference.

["CONSTRAINTS: A Language for Expressing Almost-Hierarchical Descriptions", G.J. Sussman et al, Artif Intell 14(1):1-39 (Aug 1980)].
 of the problem, to specify an objective or goal and to search for an optimum solution using an optimization algorithm (set of rules). One technique, multi-variable response surface optimization, considers the amount of change that results from modifying one or more design variables and determines whether this brings the casting closer to or farther from the desired objective. Basically, the user describes the casting requirements and details (size, shape, type of metal, etc.) and the desired goal (lowest porosity, highest yield, etc.) to the system, which then calculates the best designed casting to reach that goal. This technique can automatically modify the design of a given casting and its gating system and risers so that it produces an optimum condition.

Optimization requires the identification of three basic factors:

Design Variables--These are features of a particular design that are allowed to vary while the system searches for an optimum condition. Design variables usually are geometric features, such as the diameter and height of a riser or a riser/sleeve combination. They also can be process specifications, such as the pouring temperature of the casting alloy alloy (ăl`oi, əloi`) [O. Fr.,=combine], substance with metallic properties that consists of a metal fused with one or more metals or nonmetals. .

Constraints--Constraints are the parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind.  values of process data. Constraints may be specified as a minimum condition, in which case the result value must be at or above the given constraint Constraint

A restriction on the natural degrees of freedom of a system. If n and m are the numbers of the natural and actual degrees of freedom, the difference n - m is the number of constraints.
 value, or as a maximum condition, where the result value must he at or below the given constraint value. One or more constraints may be specified for each optimization run. An example of a constraint is a maximum allowable porosity level.

Objective Function--The objective function specifies what the given process design is trying to achieve. An objective function tells the optimization system what process result should be used to judge whether or not the optimum condition has been achieved. The system user selects an objective function and specifies whether the value of that function is to be minimized or maximized. For example, one might select predicted shrinkage porosity as an objective function and minimize its value. Only one objective function can be specified for each optimization run.

The sequence of events for optimizing a design contains specific steps and allows for backtracking (algorithm) backtracking - A scheme for solving a series of sub-problems each of which may have multiple possible solutions and where the solution chosen for one sub-problem may affect the possible solutions of later sub-problems.  to make adjustments (Fig. 1). The user creates an initial process design--a 3D model of the casting with gating, risers and all relevant material data--like any casting simulation. The user then selects the design variables, constraints and objective function and launches an optimization run. Optimization is achieved by running a series of simulations automatically: varying the values of the design variables, checking to make sure that constraints are not violated vi·o·late  
tr.v. vi·o·lat·ed, vi·o·lat·ing, vi·o·lates
1. To break or disregard (a law or promise, for example).

2. To assault (a person) sexually.

 and searching for a maximum or minimum value for the selected objective function.

Refining refining, any of various processes for separating impurities from crude or semifinished materials. It includes the finer processes of metallurgy, the fractional distillation of petroleum into its commercial products, and the purifying of cane, beet, and maple sugar  Parameters

In order to develop a procedure for optimization, the desired goals must be understood. Many casting simulations are run to predict shrinkage in castings (either in the form of macroporosity or microporosity), with the goal of producing a sound casting. Others are run to determine the best size, shape and position for the gating and risers on a new casting.

Macroporosity and microporosity form under specific, and sometimes different, circumstances. Macroporosity can be predicted by simulating the volumetric volumetric /vol·u·met·ric/ (vol?u-met´rik) pertaining to or accompanied by measurement in volumes.

Of or relating to measurement by volume.
 changes occurring in solidifying so·lid·i·fy  
v. so·lid·i·fied, so·lid·i·fy·ing, so·lid·i·fies
1. To make solid, compact, or hard.

2. To make strong or united.

 metals, and then simulating the flow of liquid feed metal in response to these volumetric changes. Microporosity seems to form in areas of poor directional solidification Directional solidification is a series of measures applied to control the feeding of castings. As most metals and alloys solidify, changing from the liquid state to the solid state they will undergo an appreciable volume contraction. , which can be measured by looking at temperature gradients temperature gradient
The rate of change of temperature with displacement in a given direction from a given reference point.

temperature gradient 
, local solidification times and the velocity of the solidification wavefront Noun 1. wavefront - (physics) an imaginary surface joining all points in space that are reached at the same instant by a wave propagating through a medium
wave front
 through various parts of the casting. When dealing with porosity, the proper data for constraints and the objective function must be selected to achieve a sound casting in the most efficient way possible.

Foundry engineers also are concerned with the cost of producing a casting. A major cost is the energy involved in melting the metal to make a casting; the less metal required to be poured, the lower the melt cost. Therefore, when dealing with the concept of optimizing a casting design, one must take into account the total amount of metal required vs. the net metal in the casting. It may be that several alternate riser designs could result in a sound casting, and the optimization system should be capable of identifying which of these designs is preferable from a cost standpoint.

The following optimization case studies illustrate how original designs can be improved to eliminate porosity and improve yields.


The first example is an automotive bracket In programming, brackets (the [ and ] characters) are used to enclose numbers and subscripts. For example, in the C statement int menustart [4] = ; the [4] indicates the number of elements in the array, and the contents are enclosed in curly braces.  casting made in aluminum using the permanent mold process (Fig. 2).The initial casting design indicated microporosity in the casting due to inadequate feeding, making a redesign re·de·sign  
tr.v. re·de·signed, re·de·sign·ing, re·de·signs
To make a revision in the appearance or function of.

 altering the risers and gating system necessary. Since metal dies are expensive to produce and even more expensive to alter, the risers and gating system must be designed for optimum performance before the first die is cut.

During the optimization process, the riser height and width were allowed to vary, and the objective function was to minimize the amount of microporosity in the casting [measured using the Franco Chiesa Criterion (FCC (1) (Federal Communications Commission, Washington, DC, The U.S. government agency that regulates interstate and international communications including wire, cable, radio, TV and satellite. The FCC was created under the U.S. ) Criterion]. The FCC Criterion combines the local solidification time with the speed in which solidification is moving through the casting to predict microporosity, including hydrogen gas in the melt. The optimization process required six simulation runs, each of which ran automatically under the control of the optimization module.

The optimized casting shows no indications of microporosity in the casting; it is confined con·fine  
v. con·fined, con·fin·ing, con·fines
1. To keep within bounds; restrict: Please confine your remarks to the issues at hand. See Synonyms at limit.
 to the riser (Fig. 2).

Microporosity levels changed during the optimization run--initially, porosity ran as high as 1.4% (Fig. 3). Through the optimization process, microporosity was reduced to 0.42% maximum and was restricted to the riser.

The riser height and width also varied during the optimization runs. The final riser design, which produced a porosity-free casting, had a height and width of about 1.14 and 1.5 times the original design sizes, respectively (Fig. 3). In this case, the riser size increased and yield decreased, but microporosity was limited to the risers.

The final result was a good casting; the initial design produced a scrap casting. While optimization cannot guarantee that good castings can be made from bad ones, many situations occur where this does happen when the design is close to meeting the specified goal (in this case, minimized porosity) and the design variables allow for that goal to be reached.

Improving Yield

The second example shows how optimization can be applied to new jobs to produce the highest yield possible.

This case study focuses on a plain carbon steel alloy support frame casting for heavy equipment made in green sand. The first step was to run a simulation of the part without the gating system and risers to see how the casting design influenced solidification behavior. The goal was to find hot spots hot spots

acute moist dermatitis.
 in the casting and help design an effective risering system.

The casting actually has five different feeding paths or sections of the casting that freeze off separately and must be fed. An initial risering design for the part is shown in Fig. 4. Four side risers and one top riser were used, each employing an insulating riser sleeve
Sleeve (O. Eng. slieve, or slyf, a word allied to slip, cf. Dutch sloof) is that part of a garment which covers the arm, or through which the arm passes or slips.

The optimization run was set up with 10 variables--the height and diameter of each riser. Each of these variables was allowed to vary independently. If riser height were to remain constant, or to vary in the same way with each riser, the number of variables could have been reduced and results reached more quickly. The constraint on the problem was a material density minimum value of 0.994, and the objective was to maximize yield.

Since this project had 10 variables, more simulations were required to reach a solution. However, since no operator involvement was needed, the full optimization was processed in 10 hr. The final gating system and riser design uses all five of the original risers (but at shorter heights), as well as the piping behavior expected of the optimized casting (Fig. 5).

Benefits of Reducing Trial and Error in Modeling

The application of optimization technology to casting process simulation offers the potential to add "intelligence" to the process by allowing the software system to make decisions about modifying an initial design until a given objective is achieved, all without human intervention. By reducing the amount of trial and error that is necessary in traditional modeling, the foundry engineer's time can be devoted to other critical aspects of the process.
COPYRIGHT 2001 American Foundry Society, Inc.
No portion of this article can be reproduced without the express written permission from the copyright holder.
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Comment:Eliminating Modeling 'Trial & Error' with Casting Process Optimization.
Author:Schmidt, David C.
Publication:Modern Casting
Geographic Code:1USA
Date:Aug 1, 2001
Previous Article:Simulation Case Histories: Solving Problems while Optimizing Processes.
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