The traditional sand casting foundry process often relies heavily on the experience of engineers and extensive trial-and-error methods to determine the optimal process parameters. This approach leads to long development cycles, high costs, and inefficient use of materials. With the rapid advancement of computer technology and numerical simulation, the digitalization of casting technology has become an inevitable trend in the sand casting foundry industry. Numerical simulation tools like Procast enable the prediction of filling, solidification, and defect formation, thus significantly reducing the need for physical prototypes. In this study, I apply the three-dimensional casting simulation software Procast to model the gravity casting of a steel casting in a sand mold. The filling and solidification processes are simulated to obtain temperature field distributions and casting defects such as shrinkage porosity and shrinkage cavities. Based on the analysis, the sand casting foundry process is optimized to eliminate defects and improve product quality.
Mathematical Models in Sand Casting Foundry Simulation
The gravity sand casting process involves the flow of high-temperature molten metal into a complex mold cavity with free surfaces, accompanied by heat transfer to the surrounding sand and air. The governing equations are based on the conservation of mass, momentum, and energy. In Procast, the flow model couples the Navier-Stokes equations with the Fourier heat conduction equation, and the solidification model includes latent heat effects.
The continuity equation for incompressible flow is:
$$ \nabla \cdot \mathbf{u} = 0 $$
The momentum equations (Navier-Stokes) in three dimensions are:
$$ \rho \left( \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + w \frac{\partial u}{\partial z} \right) = -\frac{\partial p}{\partial x} + \mu \nabla^2 u + \rho g_x $$
$$ \rho \left( \frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + w \frac{\partial v}{\partial z} \right) = -\frac{\partial p}{\partial y} + \mu \nabla^2 v + \rho g_y $$
$$ \rho \left( \frac{\partial w}{\partial t} + u \frac{\partial w}{\partial x} + v \frac{\partial w}{\partial y} + w \frac{\partial w}{\partial z} \right) = -\frac{\partial p}{\partial z} + \mu \nabla^2 w + \rho g_z $$
The energy equation with latent heat release during solidification is:
$$ \rho c_p \left( \frac{\partial T}{\partial t} + \mathbf{u} \cdot \nabla T \right) = \nabla \cdot (k \nabla T) + \rho L \frac{\partial f_s}{\partial t} $$
where \( \rho \) is density, \( \mathbf{u} \) is velocity vector, \( p \) is pressure, \( \mu \) is dynamic viscosity, \( g \) is gravity, \( c_p \) is specific heat, \( k \) is thermal conductivity, \( T \) is temperature, \( L \) is latent heat, and \( f_s \) is solid fraction.
To predict shrinkage defects, Procast uses the Niyama criterion:
$$ M = \frac{G}{\sqrt{R_c}} $$
where \( G \) is the temperature gradient and \( R_c \) is the cooling rate. In steel sand casting foundry, a value of \( M \geq 1 \) is generally considered critical for avoiding centerline shrinkage.
Material Properties and Simulation Setup
The casting material is ZG35Cr26Ni12 heat-resistant steel, with the chemical composition shown in Table 1. The sand mold properties are typical of silica sand with a binder. Table 2 summarizes the thermophysical properties used in the simulation.
| Element | C | Si | Mn | Cr | Ni | S | P | Fe |
|---|---|---|---|---|---|---|---|---|
| Content | 0.35 | 2.00 | 2.00 | 26.00 | 12.00 | 0.04 | 0.04 | Balance |
| Property | Steel | Sand mold |
|---|---|---|
| Density (kg/m³) | 7800 | 1600 |
| Liquidus temperature (°C) | 1450 | — |
| Solidus temperature (°C) | 1380 | — |
| Latent heat (kJ/kg) | 270 | — |
| Thermal conductivity (W/mK) | 30 (solid), 25 (liquid) | 0.7 |
| Specific heat (J/kgK) | 670 | 800 |
The 3D model of the casting was created in Pro/ENGINEER, exported in STL format, and imported into Procast. The mesh consisted of tetrahedral elements with a size of approximately 10 mm in the casting and 20 mm in the mold. The gravity filling simulation used a velocity inlet at the sprue with a pouring temperature of 1550°C. Heat transfer coefficients between the casting and mold were set to 500 W/m²K, and between the mold and ambient air to 10 W/m²K.
Application to a Sand Casting Foundry Component
A large valve body weighing 7.12 tons was selected as the case study. The geometry featured thick sections that could cause hot spots and shrinkage defects. Two possible casting orientations (Scheme 1 and Scheme 2) were evaluated using Procast’s hot spot and shrinkage prediction modules. The results are shown in Table 3.
| Scheme | Number of hot spots | Total shrinkage volume (mm³) | Location of largest shrinkage |
|---|---|---|---|
| 1 | 5 | 12,348,921 | Multiple dispersed |
| 2 | 3 | 4,387,286.4 | Two concentrated areas near top flange |
Scheme 2 was chosen because it concentrated the shrinkage in two accessible locations, simplifying riser design. The two main shrinkage volumes were 64,897.9 mm³ and 43,786,386.5 mm³ (the latter dominated). Figure 1 illustrates the predicted shrinkage distribution for Scheme 2.
Based on the shrinkage locations, two risers were designed: an oblong open riser and a cylindrical open riser. The riser dimensions were calculated using the modulus method with a contraction allowance of 5%:
$$ M_r = \frac{V_r}{A_r} $$
where \( V_r \) is the riser volume and \( A_r \) is the cooling surface area. For safe feeding, the riser modulus must be larger than the casting modulus at the feeding zone. The results are summarized in Table 4.
| Riser type | Diameter (mm) | Length (mm) | Height (mm) | Modulus (mm) |
|---|---|---|---|---|
| Oblong | 510 | 760 | 640 | 102.26 |
| Cylindrical | 640 | 740 | 640 | 104.32 |
The gating system included two circular sprues (diameter 70 mm), eight circular ingates (diameter 50 mm), and four trapezoidal runners (top width 50 mm, bottom width 55 mm, height 45 mm). The complete sand casting foundry process layout is shown in Figure 1.
Simulation Results and Defect Analysis
The initial simulation of the gated casting predicted shrinkage porosity distribution as shown in Figure 2. Most of the shrinkage was captured inside the risers, but some scattered porosity remained along the bottom circumference of the casting, where localized hot spots created isolated liquid pools during solidification. Table 5 quantifies the defect locations and volumes.
| Location | Volume (mm³) | Percentage of total |
|---|---|---|
| Oblong riser | 1,240,000 | 68.0 |
| Cylindrical riser | 480,000 | 26.4 |
| Bottom circumference (6 spots) | 102,000 | 5.6 |
| Total | 1,822,000 | 100 |
These bottom defects were unacceptable for the valve body, which required pressure tightness. To eliminate them, I applied chills (copper blocks) at the corresponding locations on the mold. The chills increased the local cooling rate, thus avoiding hot spots. The modified gating system is shown in Figure 3.
The simulation was rerun with chills. The resulting shrinkage distribution is given in Table 6.
| Location | Volume (mm³) | Status |
|---|---|---|
| Oblong riser | 1,310,000 | Accepted (removed) |
| Cylindrical riser | 505,000 | Accepted (removed) |
| Bottom circumference | < 500 | Virtually eliminated |
The maximum remaining porosity in the casting body was less than 0.01% by volume, well below the industry standard for such components. The optimized sand casting foundry process successfully shifted all significant defects into the risers, which would be cut off after solidification.
Production Validation
Physical trials were conducted in the foundry using the optimized process. The castings were inspected by X-ray and sectioning. No shrinkage cavities were found. Mechanical testing showed tensile strength and elongation meeting the specifications. The successful outcome confirms that the Procast simulation accurately predicted the defect formation and guided the process improvement. The use of numerical simulation reduced the development time from several months to weeks and eliminated multiple costly trial castings.
Conclusion
In this work, I have demonstrated the application of Procast software to the sand casting foundry process for a heavy steel casting. By simulating filling, solidification, and defect formation, I identified hot spots and designed appropriate risers and chills. The key conclusions are:
- The numerical model based on Navier-Stokes and Fourier equations, combined with the Niyama criterion, effectively predicts shrinkage porosity in sand casting foundry.
- Orientation of the casting significantly affects hot spot distribution; simulation allows rapid evaluation of alternatives.
- Riser dimensions can be optimized using modulus calculations integrated into the software.
- Local chills successfully eliminated residual porosity without increasing overall cost.
- Production results validate the simulated predictions, confirming the reliability of Procast for sand casting foundry process design.
The methodology presented here can be generalized to other sand casting foundry applications, enabling faster development cycles, higher first-time yield, and improved product quality. Future work will extend the approach to consider other defect types such as gas porosity and hot tearing, and incorporate multi-criteria optimization.