1. Introduction
In the realm of precision investment casting, achieving high-quality cast components with minimal defects remains a critical challenge. Defects such as shrinkage porosity, microporosity, and deformation often arise due to complex interactions between process parameters, casting geometry, and material properties. This study focuses on optimizing the precision investment casting process for a stainless steel three-way valve body, which exhibited significant defects during production. By integrating numerical simulations with grey correlation analysis, we aim to identify the optimal combination of process parameters to enhance casting quality while reducing trial-and-error costs.
The term precision investment casting refers to a near-net-shape manufacturing technique renowned for producing intricate components with excellent surface finish. However, its sensitivity to process variables—such as pouring temperature, shell roasting temperature, and pouring time—demands systematic optimization. Traditional approaches rely heavily on empirical adjustments, which are time-consuming and resource-intensive. Here, we propose a data-driven framework that combines finite element simulations (via ProCAST) and statistical methods (grey correlation analysis) to streamline the optimization process.
2. Methodology
2.1 Problem Identification
The stainless steel three-way valve body, with a mass of 2.42 kg and varying wall thicknesses (4–24.96 mm), consistently exhibited defects in its original casting process. Shrinkage porosity (1.95 cm³) and deformation (0.0325 cm) were concentrated at thick-walled junctions, attributed to uneven heat dissipation and inadequate feeding during solidification (Figure 1).
2.2 Material and Simulation Setup
- Material: SCS16 stainless steel (chemical composition in Table 1).
- Simulation Software: ProCAST was used to model thermal behavior, utilizing thermophysical parameters for SCS16 and mullite ceramic shells (Figures 2a–2b).
- Mesh Configuration: The original top-pouring system was discretized into 195,858 surface elements and 45,906 volume elements (Figure 3).
Table 1: Chemical Composition of SCS16 Stainless Steel (wt%)
| Cr | Si | Mn | P | S | Ni | Mo | Fe |
|---|---|---|---|---|---|---|---|
| 17–20 | <1.5 | <2 | <0.04 | <0.04 | 12–16 | 2–3 | Bal. |
2.3 Orthogonal Experimental Design
To systematically evaluate the effects of key parameters, an L9 orthogonal array was designed with three factors and three levels (Table 2). The quality objectives were shrinkage porosity volume and deformation amount.
Table 2: Factors and Levels for Orthogonal Experiments
| Level | Pouring Temperature (°C) | Shell Roasting Temperature (°C) | Pouring Time (s) |
|---|---|---|---|
| 1 | 1,610 | 1,000 | 4 |
| 2 | 1,640 | 1,050 | 6 |
| 3 | 1,670 | 1,100 | 8 |
Table 3: Orthogonal Experiment Scheme (L9 Array)
| Trial | A (°C) | B (°C) | C (s) |
|---|---|---|---|
| 1 | 1,610 | 1,000 | 4 |
| 2 | 1,610 | 1,050 | 6 |
| 3 | 1,610 | 1,100 | 8 |
| 4 | 1,640 | 1,000 | 6 |
| 5 | 1,640 | 1,050 | 8 |
| 6 | 1,640 | 1,100 | 4 |
| 7 | 1,670 | 1,000 | 8 |
| 8 | 1,670 | 1,050 | 4 |
| 9 | 1,670 | 1,100 | 6 |
3. Grey Correlation Analysis
3.1 Data Preprocessing
Raw experimental data were normalized using the following equation to eliminate dimensional differences:yi=xi−min(xi)max(xi)−min(xi)yi=max(xi)−min(xi)xi−min(xi)
where xixi is the original value and yiyi is the dimensionless value.
3.2 Grey Correlation Coefficient Calculation
The grey correlation coefficient (δiδi) quantifies the similarity between experimental results and ideal outcomes:δi=min∣yi0∣+ρmax∣yi0−yi∣∣yi0−yi∣+ρmax∣yi0−yi∣δi=∣yi0−yi∣+ρmax∣yi0−yi∣min∣yi0∣+ρmax∣yi0−yi∣
where yi0yi0 is the reference sequence, and ρ=0.5ρ=0.5 (distinguishing coefficient).
3.3 Entropy Weight Method
To objectively assign weights to quality objectives, entropy values (ejej) and weights (wjwj) were calculated:Pij=λij∑i=1nλij,ej=−1lnm∑i=1mPijlnPij,wj=1−ej∑j=1n(1−ej)Pij=∑i=1nλijλij,ej=−lnm1i=1∑mPijlnPij,wj=∑j=1n(1−ej)1−ej
Table 4: Weight Distribution for Quality Objectives
| Objective | Weight (wjwj) |
|---|---|
| Shrinkage Porosity | 0.2873 |
| Deformation Amount | 0.7127 |
4. Results and Discussion
4.1 Grey Correlation Degree Ranking
The comprehensive grey correlation degree (GiGi) for each trial was computed as:Gi=∑j=1nwjδiGi=j=1∑nwjδi
Table 5: Grey Correlation Analysis Results
| Trial | Shrinkage Porosity (cm³) | Deformation (cm) | GiGi | Rank |
|---|---|---|---|---|
| 1 | 0.0954 | 0.0313 | 0.3660 | 7 |
| 2 | 0.0566 | 0.0239 | 0.9208 | 1 |
| 3 | 0.0446 | 0.0304 | 0.5644 | 3 |
| 4 | 0.0744 | 0.0320 | 0.3823 | 6 |
| 5 | 0.0714 | 0.0312 | 0.4115 | 5 |
| 6 | 0.0918 | 0.0313 | 0.3697 | 8 |
| 7 | 0.0711 | 0.0249 | 0.3849 | 4 |
| 8 | 0.1076 | 0.0322 | 0.3333 | 9 |
| 9 | 0.0561 | 0.0247 | 0.8088 | 2 |
The optimal parameters were identified as A1B2C2:
- Pouring Temperature: 1,610°C
- Shell Roasting Temperature: 1,050°C
- Pouring Time: 6 s
4.2 Factor Significance Analysis
Grey correlation mean range analysis revealed the relative influence of factors:
Table 6: Mean Range Analysis of Process Parameters
| Parameter | Mean Range (RR) | Significance Rank |
|---|---|---|
| Pouring Time (C) | 0.3476 | 1 |
| Pouring Temperature (A) | 0.2293 | 2 |
| Shell Temperature (B) | 0.2033 | 3 |
This indicates that pouring time has the most significant impact on casting quality, followed by pouring temperature and shell temperature.
5. Validation and Industrial Application
Under the optimized parameters, the precision investment casting process demonstrated remarkable improvements:
- Shrinkage Porosity: Reduced by 97% (from 1.95 cm³ to 0.0566 cm³).
- Deformation: Reduced by 27% (from 0.0325 cm to 0.024 cm).
The modified gating system ensured sequential solidification, eliminating isolated liquid zones and enhancing feeding efficiency. Production trials confirmed defect-free castings with dimensional accuracy, validating the robustness of the grey correlation approach.
6. Conclusions
- Grey Correlation Analysis: A highly effective tool for optimizing precision investment casting parameters, requiring minimal experimental data while delivering reliable results.
- Optimal Parameters: Pouring temperature = 1,610°C, shell roasting temperature = 1,050°C, pouring time = 6 s.
- Factor Significance: Pouring system design exerts the greatest influence on quality, followed by pouring time and temperature parameters.
This study underscores the synergy between numerical simulations and statistical methods in advancing precision investment casting. Future work will explore multi-objective optimization algorithms to further refine process robustness.