In contemporary manufacturing, the advancement of computer simulation technology has established itself as an indispensable guide for casting process design and scheme formulation, gaining widespread recognition and application within the industry. However, it is crucial to understand that simulation technology primarily serves as an evaluative tool for pre-designed process plans; it does not inherently generate the optimal solution. The integration of Design of Experiment (DOE) optimization techniques within specialized software like Cast Designer represents a significant leap forward. This enables the iterative improvement of output responses within a simulated environment, paving the way for the intelligent optimization of casting process schemes. This article details the application of this methodology to a challenging marine gas turbine steel casting part.
The subject of this study is a complex shell-type casting part for a marine gas turbine, assembled from segments. The material specification is ZG10Cr14Ni5Mo2 steel, with a total mass of approximately 104 kg. This casting part presents significant manufacturing challenges due to its intricate geometry, featuring walls with thicknesses ranging from 8 mm to 30 mm. This substantial variation in wall thickness creates pronounced thermal gradients during solidification, making it prone to shrinkage defects. The primary engineering objective was to develop a casting process that achieves the optimal balance between casting quality (minimizing defects) and production cost (maximizing yield).
Foundational Process Design and DFM Analysis
The initial phase of designing a robust process for such a complex casting part begins with a comprehensive assessment of its manufacturability. Utilizing the Design for Manufacturability (DFM) module within Cast Designer software, a systematic analysis was conducted. This analysis encompassed several key factors:
- Mass Distribution Index (MDI): Evaluating the overall distribution of mass to identify potential stability and filling issues.
- Heat Distribution Index (HDI): A critical analysis that predicts areas of thermal concentration (hot spots) which are susceptible to shrinkage porosity and cavities. The HDI calculation considers three-dimensional geometry and environmental thermal effects without running a full solidification simulation, providing rapid and flexible insights. The HDI results for this shell casting part clearly indicated two main regions with significant thermal mass, identifying them as high-risk zones for defect formation.
- Draft Angle and Undercut Analysis: Ensuring the part can be successfully removed from the mold or core boxes.
- Ejection Force Evaluation & Core Pull System Design: Assessing mechanical requirements for tooling design.
The HDI map served as the primary guide for the initial placement of feeding systems. An initial scheme employing two top risers and two side risers was conceived. However, a subsequent HDI evaluation of this scheme revealed inadequate feeding potential in the central region and the lower lateral sections of the casting part. This feedback prompted a redesign.
The optimized feeding system layout, as shown in the software’s assessment, was adjusted to incorporate one top riser and four side risers. This configuration provided a more uniform and effective feeding coverage for the problematic thermal zones identified earlier. Following the riser scheme finalization, the gating system was designed using the software’s automated runner design wizard. Based on fundamental inputs like casting part weight, dimensions, and material properties, the software calculates key process parameters such as filling time and flow velocity, and subsequently derives the required cross-sectional areas for the sprue, runners, and ingates. All these parameters are dynamically linked to the 3D geometry, allowing for real-time adjustments and evaluations.
| DFM Analysis Component | Purpose for the Shell Casting Part |
|---|---|
| Heat Distribution Index (HDI) | Identify hot spots and guide riser placement. |
| Mass Distribution Index (MDI) | Assess overall mass balance for process stability. |
| Draft/Undercut Check | Ensure moldability and proper part ejection. |
| Riser Design Aid | Provide data-driven suggestions for feeder size and location. |
Design of Experiments (DOE) for Systematic Evaluation
While the DFM-guided design offered a viable solution, the quest for the optimal balance between quality (minimized shrinkage) and cost (maximized yield) required a more systematic exploration. A Design of Experiments (DOE) study was set up within Cast Designer to quantitatively evaluate the influence of key process variables. For this complex casting part, two critical responses were defined:
- Shrinkage Volume (Quality Metric): The total volume of shrinkage porosity/cavity predicted by the simulation, to be minimized.
- Yield Rate (Cost Metric): The ratio of the final casting part weight to the total poured weight (casting + risers + gating). This should be maximized to reduce material cost.
These two objectives are inherently conflicting: larger risers reduce shrinkage but lower the yield. The DOE aimed to map this trade-off space. Five factors were selected for investigation, each with discrete levels, as outlined below:
| Factor | Symbol | Level 1 (Low) | Level 2 (Medium) | Level 3 (High) |
|---|---|---|---|---|
| Top Riser Size | $R_t$ | Small | Medium | Large |
| Side Riser 1 Diameter | $D_{s1}$ | Small | Medium | Large |
| Side Riser 2 Diameter | $D_{s2}$ | Small | Medium | Large |
| Chill Presence | $C$ | None | 1 Chill | 2 Chills |
| Pouring Temperature | $T_p$ | 1540°C | — | 1580°C |
A full factorial design would require $3 \times 3 \times 3 \times 3 \times 2 = 162$ unique simulation runs. The software efficiently managed this matrix, executing all simulations and collecting the response data for each combination of factor levels. The results can be visualized in a trade-off plot, where each point represents one simulation outcome. The Pareto front—the set of points where one objective cannot be improved without worsening the other—becomes clearly visible. Points in the lower-right quadrant of such a plot represent the most desirable outcomes: high yield with low shrinkage.
Analysis of the DOE results via parallel coordinate plots and main effects charts revealed key insights:
– The dimensions of Side Riser 1 ($D_{s1}$) and Side Riser 2 ($D_{s2}$) were identified as the most significant factors influencing both shrinkage volume and yield for this specific casting part geometry.
– The size of the Top Riser ($R_t$) also had a direct and substantial impact, though its effect was slightly secondary to the side risers in this configuration.
– Interestingly, within the tested ranges, Chill presence ($C$) and Pouring Temperature ($T_p$) showed a relatively minor influence on the two target responses for this steel casting part.
This DOE analysis successfully mapped the design space, but the optimal configuration might lie between the discrete levels chosen for the initial experiment.
Genetic Algorithm (GA) Based Intelligent Optimization
To search for the absolute optimum configuration within a continuous variable space, a Genetic Algorithm (GA) optimization was employed. Unlike DOE, which evaluates pre-defined points, GA is an evolutionary search technique that iteratively “breeds” better solutions. It starts with a population of random designs, evaluates their fitness (based on our objectives), and selects, crosses over, and mutates the best performers to create a new generation. This process repeats until convergence.
For optimizing this shell casting part, the GA was configured with the following continuous parameters:
| Parameter | Variable | Lower Bound | Upper Bound | Step |
|---|---|---|---|---|
| Top Riser Height | $H_t$ | 120 mm | 160 mm | 10 mm |
| Top Riser Taper Angle | $\theta_t$ | 60° | 64° | 2° |
| Side Riser Diameter | $D_s$ | 90 mm | 110 mm | 5 mm |
| Riser Aspect Ratio | $AR = H_t / D_t$ | 1.0 | 1.5 | 0.1 |
The multi-objective optimization problem was formally defined as:
$$
\text{Minimize: } F_{\text{shrinkage}}(H_t, \theta_t, D_s, AR)
$$
$$
\text{Maximize: } F_{\text{yield}}(H_t, \theta_t, D_s, AR)
$$
$$
\text{Subject to: } 120 \leq H_t \leq 160, \quad 60 \leq \theta_t \leq 64, \quad 90 \leq D_s \leq 110, \quad 1.0 \leq AR \leq 1.5
$$
The GA proceeded to evaluate hundreds of design variants. The final output is a refined Pareto frontier, a curve representing the best possible compromises between shrinkage and yield. One optimal solution identified from this frontier for the production of this specific casting part is summarized below:
| Optimized Parameter | Value | Resulting Performance | Value |
|---|---|---|---|
| Top Riser Height ($H_t$) | 130 mm | Yield Rate | 65.1 % |
| Top Riser Angle ($\theta_t$) | 62° | Shrinkage Volume | 254.64 mm³ |
| Side Riser Diameter ($D_s$) | 90 mm | – | – |
| Riser Aspect Ratio ($AR$) | 1.0 | – | – |
This optimized design represents a significant achievement: it maintains a high yield rate of over 65% while predicting a very low and acceptable level of shrinkage porosity for the finished casting part, effectively achieving the target balance between cost-effectiveness and quality assurance.
Conclusion and Outlook
The integrated application of DFM analysis, DOE, and GA-based optimization within a unified simulation environment like Cast Designer provides a powerful methodology for the advanced development of casting processes. For the complex shell casting part discussed, this approach facilitated:
- Informed Initial Design: DFM analysis, particularly HDI, provided a scientific basis for the initial placement of risers and identification of critical zones, moving away from reliance solely on experience.
- Quantitative Trade-off Understanding: The DOE study systematically quantified the cause-effect relationships between key process factors (riser sizes) and critical performance metrics (shrinkage, yield), identifying the most influential variables.
- Discovery of Global Optima: The Genetic Algorithm transcended the limitations of testing pre-selected discrete levels, performing an intelligent search within a continuous variable space to find Pareto-optimal solutions that perfectly balance the conflicting objectives of quality and cost for this specific casting part.
The final optimized process scheme, derived from this intelligent workflow, ensures robust quality control for shrinkage defects while maximizing the material yield of the expensive alloy. This methodology significantly reduces the time and cost associated with traditional trial-and-error methods. It establishes a replicable framework for the design and optimization of casting processes for other complex and critical casting parts, pushing the boundary towards fully digital, intelligent, and data-driven foundry engineering.