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included. T is methodol- ogy maintains the con- stant bounding box while gradually increasing the part complexity with the growing number of cores. T e fi rst case study

involves the train air brake casting shown in Figure 3. Using conventional processes, the design and assembly of eight cores are required. Beginning with a solid part, cores were added sequentially until the fi nal number of cores was reached. T e corresponding design attributes described in the complexity factor equations are shown in Table 2. In conventional pattern

conventional pattern making even in the case of no cores. In other words, the breakeven point is the lowest level of complexity for this family of castings at this quantity. However, for quantities

Fig 6. This graph depicts the total costs (tooling and fabrication) for Case Study 1 where conventional patternmaking costs are shown for 30, 100 and 1,000 units.

making, a tooling cost is associated with pattern and corebox fabrication. T e relationship between tooling costs per set of mold and the corresponding complexity factor is shown in Figure 4. Figure 5 shows the relationship between fabrication costs for both con- ventional pattern making and 3-D sand printing at diff erent levels of complex- ity for Case Study 1. For conventional pattern making production costs, the fabrication cost proportionally increases with increasing complexity: as cores are added, the cost in labor to assemble cores, cost of materials (i.e., sand, glue) and scrap costs all increase. It was observed that lower levels of

complexity lead to higher fabrication cost in 3-D sand printing than conventional

mold manufacturing approach. In the case of the part design with a complex- ity greater than 56, the fabrication cost of 3-D sand printing was lower than conventional pattern making. 3-D sand printing provides a unique advantage here by consolidating cores into single core. T is results in lower labor and scrap costs with higher numbers of cores. Figure 6 incorporates both tooling

and fabrication costs as a function of part design complexity. For conven- tional manufacturing, cost curves for quantities of 30, 100 and 1,000 were included to show that the costs of pat- terns and core boxes were amortized across the production volume. For a pro- duction volume below 30 castings, 3-D sand printing is more aff ordable than

greater than 30 castings, it depends on the level of part design complexity. As quan- tity increases, the breakeven point shifts to increasing levels of complexity. For production quanti- ties of 1,000 castings, the tooling cost per mold/set is so low that fabrication costs signifi cantly dominate and cost/complexity behavior is almost identical to the fabrication costs.

Case Study 2: Turbocharger In a second case study involving a

turbocharger, cores were sequentially added starting with a solid casting until the incorporation of all three cores (Fig. 7). However, in the case of this part design, the core geom- etries were diff erent for each sub-case, wherein the fi rst core is added in the shape of a cube and subsequently the cubic core is replaced by two cylindri- cal cores. Finally, the cylinders are replaced by the three actual cores. T e relationship between tooling

set and complexity factor is presented in Figure 8. Figure 9 presents the rela- tionship between fabrication costs for both conventional pattern making and 3-D sand printing at diff erent levels of complexity for the turbocharger. T e conventional patternmaking

Fig 7. Shown is the turbocharger casting and its core geometry in Case Study 2.

production costs increased as a func- tion of complexity; however, a drastic increase occurred between one cube- shaped core and two cylindrical cores. For 3-D sand printing, it also was observed that at lower levels of com- plexity the fabrication cost was higher than that of conventional manufactur- ing. Unlike the previous case study, the 3-D sand printing cost does not ‘‘level out’’ because the volume of the cores is signifi cantly increased due to the cylinders and the fi nal core geometry. For complexity factor values greater than 51, the fabrication cost of 3-D

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