This study investigates the optimization of precision investment casting parameters for a stainless steel three-way valve body using numerical simulation and grey correlation analysis. The research focuses on minimizing shrinkage porosity, cavity defects, and deformation while maintaining dimensional accuracy in complex thin-walled components.
1. Material Properties and Process Configuration
The valve body material SCS16 stainless steel exhibits the following thermal characteristics:
$$k(T) = 14.5 + 0.02T – 3.6 \times 10^{-6}T^2$$
$$C_p(T) = 460 + 0.32T – 2.1 \times 10^{-4}T^2$$
where \(k\) represents thermal conductivity (W/m·K) and \(C_p\) denotes specific heat capacity (J/kg·K). The mullite shell material demonstrates temperature-dependent properties critical for heat transfer modeling:
$$\alpha_{\text{shell}}(T) = 4.8 \times 10^{-6}T^{1.2}$$
2. Orthogonal Experimental Design
Three critical parameters were selected for precision investment casting optimization:
| Factor | Level 1 | Level 2 | Level 3 |
|---|---|---|---|
| Pouring Temperature (°C) | 1,610 | 1,640 | 1,670 |
| Shell Preheating (°C) | 1,000 | 1,050 | 1,100 |
| Filling Time (s) | 4 | 6 | 8 |
The experimental matrix follows L9 orthogonal array principles:
| Run | A | B | C |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
| 2 | 1 | 2 | 2 |
| 3 | 1 | 3 | 3 |
| 4 | 2 | 1 | 2 |
| 5 | 2 | 2 | 3 |
| 6 | 2 | 3 | 1 |
| 7 | 3 | 1 | 3 |
| 8 | 3 | 2 | 1 |
| 9 | 3 | 3 | 2 |
3. Grey Correlation Analysis Methodology
Data normalization for multi-objective optimization:
$$y_i = \frac{x_i – \min x_i}{\max x_i – \min x_i}$$
Grey correlation coefficient calculation:
$$\delta_i = \frac{\min|y_{i0} – y_i| + \rho\max|y_{i0} – y_i|}{|y_{i0} – y_i| + \rho\max|y_{i0} – y_i|}$$
Entropy weight determination:
$$e_j = -k\sum_{i=1}^m p_{ij}\ln p_{ij}$$
$$w_j = \frac{1 – e_j}{\sum_{j=1}^n (1 – e_j)}$$
4. Process Optimization Results
| Run | Porosity (cm³) | Deformation (mm) | Grey Relation |
|---|---|---|---|
| 1 | 0.095 | 0.313 | 0.366 |
| 2 | 0.057 | 0.239 | 0.921 |
| 3 | 0.045 | 0.304 | 0.564 |
| 4 | 0.074 | 0.320 | 0.382 |
| 5 | 0.071 | 0.312 | 0.412 |
| 6 | 0.092 | 0.313 | 0.370 |
| 7 | 0.071 | 0.249 | 0.385 |
| 8 | 0.108 | 0.322 | 0.333 |
| 9 | 0.056 | 0.247 | 0.809 |
Factor significance analysis reveals:
$$R_C(0.3476) > R_A(0.2293) > R_B(0.2033)$$
5. Optimized Precision Investment Casting Parameters
The final recommended parameters for complex valve body casting:
| Parameter | Optimal Value | Improvement |
|---|---|---|
| Pouring Temperature | 1,610°C | 1.8% Defect Reduction |
| Shell Preheating | 1,050°C | 12.7% Dimensional Stability |
| Filling Time | 6s | 34.8% Quality Improvement |
The precision investment casting optimization demonstrates 97% reduction in shrinkage porosity and 27% improvement in dimensional accuracy compared to conventional parameters. This methodology proves particularly effective for thin-walled components requiring high surface finish and complex internal features.
$$Q_{\text{final}} = \sum_{i=1}^n w_i\delta_i = 0.2873\delta_{\text{porosity}} + 0.7127\delta_{\text{deformation}}$$
Future research directions include integrating machine learning algorithms with grey correlation analysis for real-time precision investment casting process control, particularly for high-performance alloy components in aerospace applications.