This study investigates the effects of pouring temperature and mold temperature on shrinkage defects in sand casting processes for automotive engine cylinder heads. Using InteCAST simulation software, we analyze defect formation mechanisms and establish quantitative correlations between process parameters and porosity levels. The results provide actionable insights for optimizing sand casting parameters to minimize shrinkage defects in complex castings.
1. Materials and Computational Methods
The cylinder head casting material is Ru450 vermicular graphite iron, with the following chemical composition:
| Element | C | Si | Mn | P | S | Mg |
|---|---|---|---|---|---|---|
| Content (%) | 3.6-3.8 | 2.3-2.6 | 0.3-0.5 | <0.05 | <0.02 | 0.015-0.025 |
The numerical simulation considers heat transfer during solidification using the governing equation:
$$
\frac{\partial}{\partial x}\left(k\frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(k\frac{\partial T}{\partial y}\right) + \frac{\partial}{\partial z}\left(k\frac{\partial T}{\partial z}\right) = \rho C_p\frac{\partial T}{\partial t} + L\frac{\partial f_s}{\partial t}
$$
Where:
$k$ = thermal conductivity (W/m·K)
$T$ = temperature (°C)
$\rho$ = density (kg/m³)
$C_p$ = specific heat (J/kg·K)
$L$ = latent heat (J/kg)
$f_s$ = solid fraction
2. Process Parameter Optimization
Experimental matrix for sand casting simulation:
| Case | Pouring Temp (°C) | Mold Temp (°C) | Shrinkage Count |
|---|---|---|---|
| 1 | 1360 | 20 | 28 |
| 2 | 1370 | 20 | 22 |
| 3 | 1380 | 20 | 25 |
| 4 | 1390 | 20 | 31 |
| 5 | 1400 | 20 | 35 |
| 6 | 1360 | 30 | 24 |
| 7 | 1370 | 30 | 26 |
| 8 | 1380 | 30 | 29 |
| 9 | 1390 | 30 | 33 |
| 10 | 1400 | 30 | 38 |
The correlation between process parameters and defect formation is quantified by:
$$
r_{PT} = \frac{\sum_{i=1}^{n}(x_i – \bar{x})(y_i – \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i – \bar{x})^2\sum_{i=1}^{n}(y_i – \bar{y})^2}}
$$
Where:
$r_{PT}$ = Pearson correlation coefficient for pouring temperature
$x_i$ = pouring temperature values
$y_i$ = corresponding shrinkage counts
3. Thermal Analysis and Defect Prediction
The critical solidification time for shrinkage prevention in sand casting can be estimated by:
$$
t_{crit} = \frac{V}{A} \cdot \frac{\rho L}{h(T_m – T_0)}
$$
Where:
$V$ = volume of thermal center (m³)
$A$ = surface area (m²)
$h$ = heat transfer coefficient (W/m²·K)
$T_m$ = melting temperature (°C)
$T_0$ = initial mold temperature (°C)
4. Multi-Objective Optimization
Parameter sensitivity analysis reveals:
| Factor | Sensitivity Index | Contribution (%) |
|---|---|---|
| Pouring Temperature | 0.82 | 64.7 |
| Mold Temperature | 0.41 | 23.1 |
| Interaction Effect | 0.29 | 12.2 |
The optimal window for sand casting parameters satisfies:
$$
\begin{cases}
1360 \leq T_{pour} \leq 1375\,^\circ\mathrm{C} \\
20 \leq T_{mold} \leq 35\,^\circ\mathrm{C} \\
\Delta T_{gradient} \geq 85\,^\circ\mathrm{C/cm}
\end{cases}
$$
5. Industrial Validation
Field tests in sand casting production showed 37% reduction in shrinkage defects when implementing optimized parameters:
| Metric | Before | After | Improvement |
|---|---|---|---|
| Defect Rate | 5.8% | 3.6% | 37.9% |
| Yield | 69.3% | 72.1% | 4.0% |
| Energy Use | 1.24 kWh/kg | 1.17 kWh/kg | 5.6% |
The relationship between sand casting parameters and quality metrics follows:
$$
Q = 0.78T_p^{-0.32} + 1.45T_m^{0.15} – \frac{2.17}{\ln(\Delta t_{fill})}
$$
Where:
$Q$ = quality index (0-1 scale)
$T_p$ = pouring temperature (°C)
$T_m$ = mold temperature (°C)
$\Delta t_{fill}$ = filling time (s)
6. Conclusion
This comprehensive analysis demonstrates that sand casting process optimization requires balanced control of thermal parameters. The established numerical models and correlation equations enable effective prediction and mitigation of shrinkage defects in complex castings, particularly for automotive components requiring high structural integrity.