Simulation Results— Optimized Riser and the Chilling System
After the two preceding analyses, one might think that a reasonably good solution has been found. The gating sys- tem has been improved; the solidification pattern changed and fewer defects are present. This was also confirmed by the manufacturing foundry which is using this improved design at the present state. Thus it is a favorable state for a subsequent geometry optimization. Both of the previous designs weighed approximately 60 tons together with the riser and gating system. From Figures 13 and 14, it is seen that the major shrinkage pipe in the riser is still too far from the actual casting body to be critical. Therefore, there is room for a volume reduction to obtain an increased cast- ing yield. From now on, only the solidification results will be discussed since the gating system remained unchanged, and thus the filling pattern did not change.
The objective space for the optimization problem in Figure 15 is constructed by the two following objectives: mini- mize shrinkage porosity and minimize the remaining vol- ume of the top riser. The first objective is represented by the Weighted Volume Porosity which stands for the total volume of areas having issues with porosity. The remain- ing volume of the riser is then calculated as the geometri- cal volume of the riser minus the volume of the shrinkage pipe in the riser. Several features in that figure should be addressed. The blue line is the Pareto set which is com- prised of the non-dominated solutions, but, it is up to the
user to determine which solution out of the Pareto set will be the most desirable. In other words, the user has to fig- ure whether he/she wants to minimize the riser as much as possible, at the cost of increased porosity, or to have a po- rosity-free casting with a slightly larger riser. In our case, three distinct designs were selected. The first one, marked 1 in Figure 15, does not lie on the Pareto set and represents the most modest solution- i.e. the largest riser volume. It should be emphasized that although it may not be clear from the figure, solution 1 is dominated by solution 2. The second one, marked 2, resembles a single optimum case, the lowest amount of porosity, and the third one, marked 3, stands for a trade-off solution, see Figure 15.
The three designs have then been analyzed in the standard simulation environment. In order to obtain realistic tem- perature fields during solidification, filling has also been considered in the simulation, but its results are not shown here. The reason for choosing such designs was: The pri- mary aim has been to keep the level of porosity very low- possibly not above the value of the original design, but still increasing the casting yield. That is why the focus was put on the solutions very close to the Y-axis. More- over, the manufacturing foundry wanted to see different layouts-from “modest” to those “on the edge” to make a better comparison and decision as to which solution to se- lect for the subsequent production. From the optimization perspective it is given that the best solutions constitute the Pareto line, so why should we pick a design not on the Pareto line that is solution 1? Many foundries prefer a
Figure 13. Prediction of centerline porosity. International Journal of Metalcasting/Fall 10
Figure 14. Distribution of macroscopic shrinkage. 71
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