1. Optimization of Casting Process Design with SOLIDCast® and HyperOpt®

2. What is OPTICast®? OPTICast® is a new software program from Finite Solutions, Inc., developers of the SOLIDCast® Solidification Modeling System (formerly sold as AFSolid 2000). OPTICast® works in combination with SOLIDCast® to automatically modify a casting process design until an optimum condition is reached. This allows the design engineer to develop and submit an initial process design, then let the computer find a final design which maximizes both quality and yield.

3. What makes OPTICast® work? OPTICast® uses the HyperOpt® system from Altair Engineering, Inc. to find the optimum design. HyperOpt® is a world-class optimization engine which is used by the major automobile companies, among many others. As an example, HyperOpt® was recently applied to a sheet metal stamping to reduce the initial blank size by 9% and saving the manufacturer over $40,000 in material savings. Now, for the first time, HyperOpt® has been applied to the casting process.

4. What is Optimization? Optimization is a mathematical method for finding the “best” solution to a given problem. Optimization allows us to automate the search for a design solution, freeing the engineer’s time to work on other issues, and providing a more thorough and repeatable design process.

5. So, how does Optimization work? Design Variables Constraints An Objective Function Optimization requires that you first develop an initial design. For example, this would typically be an initial design for gating and risering the casting. Based on this design, you then need to select three elements:

6. Design Variables These are things that are allowed to vary when the computer is searching for an optimum process design. A typical example would be the height and diameter of a riser. Other examples might be pouring temperature, pouring time or mold preheat temperature. A feature on the casting (such as a pad or rib) might also be designated as a design variable.

7. Constraints A constraint is some aspect of a design that determines whether that design is acceptable or not. For example, porosity level might be a constraint. Since SOLIDCast® can predict the level of porosity in a casting, you might specify a certain level as being the maximum allowable. Any designs which result in higher-level porosity will be rejected. Process yield might also be a constraint. If the foundry has a target level for yield, the system can be instructed to reject any designs which produce a yield below the target level.

8. The Objective Function The Objective Function is the single result which you are trying to either maximize or minimize. For example, one possible Objective Function might be minimization of porosity in the casting. Another might be maximization of yield. Still others might be minimization of total solidification time, maximization of cooling rate, or minimization of predicted microporosity.

9. The Optimization Process Once you have defined your Design Variables, Constraints and the Objective Function, then OPTICast® takes over. The system begins running a series of simulations, varying the design with each simulation, until it is satisfied that the desired objective has been achieved. At that point, the optimization is complete and OPTICast® reports to you the combination of design variables which best satisfies your objective.

10. A Simple Example Let’s look first at a very simple example – a casting with a single top riser.

11. In this example, we have imported a casting model from CAD, and then created an initial riser design as a cylindrical top riser within SOLIDCast®.

12. Having selected the casting alloy, the mold material and the type of riser sleeve, we next mesh this model. This is a typical step in SOLIDCast® prior to running any simulation.

13. Now, we tell the system that we want to optimize this casting by selecting Create New Optimization Project from the Mesh menu.

14. This creates a blank Optimization Project. All we have to do is fill in the blanks. First, we select the shapes which comprise the riser, and designate these as a Design Variable by clicking on the “Add Variable” button.

15. The Vertical Scale and the Horizontal Scale of the riser are now Design Variables. In this example, we are allowing these to vary up to 1.5 times or as low as 0.5 times our initial design.

16. Now we need to select a “Pin Point”. This is the attachment point of the riser to the casting. This point will remain at a constant position while the dimensions of the riser are scaled up or down. To select the Pin Point, we can “hide” the casting and click on the bottom center…

17. … of the riser. This establishes our attachment point for this geometric feature.

18. For this example, we have only one riser to design. This means that we have two design variables: the height and the diameter of the riser.

19. We could also select other items of process data such as the fill time or the initial temperature of the casting or mold materials as design variables. (In this simple case we won’t select these.)

20. Now we may want to specify a constraint. As you can see, there are numerous items that we could pick. Here, we have selected Material Density (a measure of shrinkage porosity) as a constraint, with a minimum value of 0.994. If we can achieve this, our casting will be substantially free from shrinkage.

21. Finally, we select an Objective Function. In this case, we have elected to maximize the yield. In effect, we’re telling the system to find the smallest riser which produces a sound casting (no shrinkage).

22. Now that we’ve set up our optimization run, all we have to do is select Start Optimization Run from the menu. OPTICast® will now begin running a series of simulations, varying the design variables until the smallest feasible riser is found.

23. Later, when the Optimization Run is complete…

24. … we can view the results. OPTICast® can display a series of graphs to show us how it arrived at the final result. To view the graphs, we select View Graphs from the menu.

25. The first graph shows the value of the Objective Function for each simulation which was run. In this case, we started with a yield of about 82% and ended up with a yield of 86.7% after 6 simulations were run.

26. This graph shows the values of the constraint (Material Density) for each run. The final value was 0.9999, which indicates a sound casting.

27. Here the system has plotted the values which it tried for the Vertical Scale (the height) of the riser. The final value was 80% of the original value.

28. And a final plot shows the Horizontal Scale values which were tried. The riser ended up about 91% of its original diameter.

29. Another way to view results is to select View Iteration Data from the menu…

30. … which brings up an Excel spreadsheet that shows what happened in each successive simulation that was run by OPTICast®.

31. The result?

32. Process yield was increased about 5%, and quality was maximized, in 6 simulations run automatically by OPTICast®.

33. Now, let’s look at a more complex example.

34. This is a large steel casting, imported from a CAD system. Typically, we might first run a simulation of this casting with no gates or risers, to see what the “natural” order of solidification might be. This helps us decide where to place gates and risers.

35. We can examine the final temperature distribution…

36. … the Progressive Solidification…

37. … or an “X-Ray View” showing molten metal during solidification. By looking at these plots, we decide on an initial design of gates and risers to produce this casting.

38. Based on this information, we establish a rigging design for this casting as shown below. The next step is to create an Optimization Project for this casting.

39. First, we designate the end riser as Riser 1, and specify to the system that this is a Design Variable.

40. Next, we select Riser 2…

41. … and Riser 3 …

42. … and Riser 4 …

43. … and finally, Riser 5. Each of these risers will be allowed to independently vary its height and diameter.

44. We can easily establish the “Pin Point” (the contact point) for each riser by hiding the casting, rotating the view, and then clicking on the riser contact point to establish the (x,y,z) coordinates of the Pin Point.

45. Now we specify a Constraint. In this case, we select Material Density (macroporosity) and set a minimum value of 0.994.

46. Finally, we select Yield Maximization as the Objective Function.

47. Selecting Start Optimization Run from the menu will begin the automatic process of optimizing this design.

48. When the Optimization Run is complete…

49. … we can view the results by first plotting the Objective Function. Here, the yield started at about 48% and reached about 78% after 100 cycles. Note how the system initially got the yield up into the range of 60%-70%, and then found a way to increase it to 78%.

50. Plotting Material Density shows the soundness of the casting in each design cycle. The final value was 0.9954, which was above the specified constraint.

51. We can view the progress that OPTICast® made in deciding the size of each riser. Here, we have plotted the progressive changes in the height of Riser 1.

52. And here are the progressive values showing the diameter of Riser 1. We can plot the values for all of the risers this way…

53. … or we can view a spreadsheet showing all of the values for all of the designs investigated.

54. The final design is available to load and view as a model in SOLIDCast®. Notice the reduction in size of each of the risers.

55. The final view shows a plot of Material Density (shrinkage). With the design as given by OPTICast®, shrinkage is confined to the risers, and the casting appears sound.

56. The Final Result? The process yield was increased from 48% to 78%, with all five risers individually designed to produce a sound casting – with no operator intervention!

57. Some Questions Why did it take 100 iterations? The number of runs is roughly the square of the number of design variables. In this case, we had the height and diameter of five risers as design variables, so there were 10 total design variables. (10x10 = 100) We could have reduced the number of design variables to 5 if we had held the riser height constant and allowed only the diameters to vary.

58. More Questions… How long did this optimization take? On a 500-MHz PIII computer, this run took 10 hours (six minutes per simulation). This time would have been less than 3 hours on a 1.7-GHz P4 computer. The number of nodes used in each simulation was about 250,000.

59. More Questions… What processes can I use OPTICast® for? Any process that can be simulated with SOLIDCast® can be optimized with OPTICast®. This means that green sand, chemically-bonded sand, permanent mold and investment processes, in ferrous and non-ferrous alloys, can all be optimized.

60. More Questions… Are there any special considerations for optimizing a casting process design? In general, you should use the minimum number of nodes possible in order to reduce processing time. Also, be aware that OPTICast® is changing the size of features in the model, so if there is a possibility that some features may overlap, shape priorities must be set properly. Non-casting material (gates, risers, feeders) must be…

61. Special considerations (Cont’d): …created with “Riser” material in the SOLIDCast® model. This means that these components need to be separate shapes in the model. The number of design variables should be kept as low as possible to reduce the number of runs. OPTICast® has a special mode (called a Parameter Study) that allows you to check how much a specific design variable influences the outcome – so you know whether it’s worth designating this as a DV.

62. More Questions… What can I use as design variables? Any geometric feature (riser, gate, feeder or casting) that is a separate shape in the SOLIDCast® model can be designated a design variable. Also, the initial temperature of the casting alloy or any material can be a DV.

63. More Questions… What can I use as a constraint? You can specify a minimum value for Yield, Material Density, Temperature Gradient, Cooling Rate, Niyama Criterion, and Hot Spot Criterion. You can specify a maximum value for Solidification Time (just in the casting, or in casting and risers), FCC Criterion and Critical Fraction Solid Time. You can select more than one constraint for an optimization run.

64. More Questions… What can I use as an objective function? The objective function can be Yield, Material Density, Temperature Gradient, Cooling Rate, Niyama Criterion, Hot Spot Criterion, FCC Criterion, Solidification Time, or Critical Fraction Solid Time. You can tell the system to maximize or minimize the objective function. Only one objective function can be specified for each optimization run.

65. What kind of cost reduction is possible with OPTICast®? A few examples…

66. Cost Savings Example 1: 250 pound steel casting 100 castings produced per month 10% yield improvement Annual Savings:$ 21,240

67. Cost Savings Example 2: 8 pound permanent-mold aluminum casting 3600 castings produced per month 5% yield improvement Annual Savings:$ 3,670

68. The next generation of Solidification Modeling

69. Where can I find more information? Contact Finite Solutions, Inc: Dave SchmidtPhone: 847-398-5162 Email: FiniteIL@aol.comFiniteIL@aol.com Larry SmileyPhone: 513-821-5220 Email: LSmiley1@aol.comLSmiley1@aol.com