In the aerospace industry, titanium alloys are widely used due to their high strength-to-weight ratio, excellent high-temperature resistance, and corrosion resistance. Among various manufacturing processes, sand casting is a cost-effective method for producing large and thick-walled titanium components, such as pumps, valves, and structural parts. However, the sand casting process often introduces defects like shrinkage porosity and cavities, especially in complex geometries with varying wall thicknesses. This study focuses on optimizing the gating and risering system for an annular titanium alloy casting using numerical simulation to mitigate these defects. We employ ProCAST software to analyze thermal behavior, predict defect distribution, and refine the design through iterative simulations and experimental validation.
The annular titanium alloy casting examined in this work has a conical rotational symmetry with a maximum outer diameter of 600 mm, a minimum outer diameter of 370 mm, and a height of 180 mm. Wall thickness varies between 12 mm and 45 mm, featuring two distinct thick sections that are prone to defect formation. To address this, we first conducted a structural analysis to identify critical areas. The casting’s geometry was modeled, and simulations were performed under typical sand casting conditions, including a mold preheat temperature of 200°C and a pouring time of 6 seconds. The material used is ZTC4 titanium alloy, whose chemical composition is detailed in Table 1.
| Al | V | Fe | Si | C | N | H | O | Ti |
|---|---|---|---|---|---|---|---|---|
| 5.5–6.8 | 3.5–4.5 | ≤0.30 | ≤0.15 | ≤0.10 | ≤0.05 | ≤0.015 | ≤0.20 | Bal. |
Thermophysical properties of ZTC4, such as thermal conductivity, density, enthalpy, and viscosity, are crucial for accurate simulation. These parameters were derived using the Scheil model in ProCAST and are plotted as functions of temperature. For instance, thermal conductivity $\lambda(T)$ can be expressed as:
$$ \lambda(T) = \lambda_0 + \alpha T $$
where $\lambda_0$ is the base conductivity and $\alpha$ is a temperature coefficient. Similarly, density $\rho(T)$ follows:
$$ \rho(T) = \rho_0 (1 – \beta (T – T_0)) $$
with $\rho_0$ as reference density and $\beta$ as the thermal expansion coefficient. Enthalpy $H(T)$ and viscosity $\mu(T)$ are modeled using polynomial fits based on experimental data. These properties are essential for solving the governing equations of fluid flow and heat transfer during sand casting, which include the continuity equation, Navier-Stokes equations, and energy equation:
$$ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0 $$
$$ \rho \left( \frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v} \right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \rho \mathbf{g} $$
$$ \rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (\lambda \nabla T) + Q $$
where $\mathbf{v}$ is velocity, $p$ is pressure, $\mathbf{g}$ is gravity, $c_p$ is specific heat, and $Q$ represents heat sources.
Mesh independence is critical for reliable simulations. We evaluated four mesh sizes (3 mm, 6 mm, 9 mm, and 12 mm) and compared temperature profiles at a specific point in the casting. The error relative to the 3 mm mesh was calculated, and simulation times were recorded. Results showed that a 6 mm mesh for the casting region, 9 mm for gates and risers, and 12 mm for the pouring cup provided an optimal balance between accuracy and computational cost. This approach ensured that the sand casting process simulation was both efficient and precise.
| Mesh Size (mm) | Simulation Time (hours) | Temperature Error (%) |
|---|---|---|
| 3 | 48 | 0.0 |
| 6 | 24 | 1.2 |
| 9 | 12 | 2.5 |
| 12 | 6 | 5.0 |
Initial simulations of a single casting without gating system revealed two isolated hot spots—one at the top (Hot Spot A) and another at the lower flange (Hot Spot B). The modulus distribution and solidification field indicated that these areas are susceptible to shrinkage defects. Using the Niyama criterion, which predicts shrinkage porosity based on thermal gradients $G$ and solidification rates $R$, we identified defect-prone zones:
$$ Niyama = \frac{G}{\sqrt{R}} $$
Values below a critical threshold indicate high risk of shrinkage. Simulation results showed shrinkage cavities at Hot Spots A and B, along with minor linear porosity in adjacent regions. This analysis guided the design of initial gating systems for the sand casting process.
Two preliminary schemes were proposed. Scheme 1 involved feeding Hot Spot B through the gate and Hot Spot A via a riser, while Scheme 2 inverted the casting to position the thick flange at the top for riser feeding. Simulations of Scheme 1 showed that the feeding path interrupted at 53% solid fraction, leading to micro-shrinkage near the gate and linear porosity elsewhere, with a total defect volume of 4.9 cm³. In Scheme 2, a conical solidification gradient formed between the gate and hot spot, causing shrinkage cavities extending 14.5 mm into the casting body, with a volume of 38.4 cm³. These findings highlight the challenges in sand casting of titanium alloys and the need for optimized designs.
| Scheme | Defect Location | Defect Volume (cm³) | Remarks |
|---|---|---|---|
| 1 | Gate and remote areas | 4.9 | Linear porosity issues |
| 2 | Gate root and far end | 38.4 | Deep shrinkage into casting |
Experimental validation was conducted using vacuum arc melting and sand casting techniques. For Scheme 1, X-ray inspection confirmed large shrinkage cavities near the gate and extensive linear porosity in the flange, consistent with simulations. Scheme 2 also showed significant shrinkage at the gate root, requiring extensive repair. Discrepancies in defect volumes between simulation and experiment were attributed to gas evolution in sand casting, which was not fully accounted for in the model. To improve accuracy, we adjusted the MACROFS parameter in ProCAST, which controls macroshrinkage formation when the solid fraction exceeds a threshold.
Based on these insights, an optimized design was developed. The inner gate was redesigned as a conical shape with a gradient angle of 25° and increased height to 155 mm, aligning with the solidification gradient and shrinkage depth observed in previous schemes. This modification aimed to transfer shrinkage defects entirely into the gate, away from the casting body. Simulations of the optimized scheme showed that the feeding path remained open until 76% solid fraction, with the final solidification point located in the gate. Defect analysis confirmed that all shrinkage was confined to the gate region, with no significant defects in the casting.
Experimental trials of the optimized sand casting process demonstrated successful defect control. X-ray inspection and machining revealed no major shrinkage cavities in the casting body, meeting the stringent requirements of aerospace standards. This outcome validates the effectiveness of numerical simulation in optimizing sand casting processes for titanium alloys. The study establishes a standardized workflow for forward design, emphasizing parameters like solidification gradient angle and shrinkage depth. Future work should focus on quantifying the effects of gas evolution in sand casting to further enhance simulation accuracy.
In conclusion, this research demonstrates the critical role of numerical simulation in addressing shrinkage defects in titanium alloy sand casting. By integrating thermal analysis, defect prediction, and iterative design optimization, we developed a robust process that minimizes defects and improves product quality. The optimized gating system, with its conical gate and adjusted dimensions, effectively redirects shrinkage away from critical areas, ensuring the reliability of annular titanium castings. This approach can be extended to other complex geometries in sand casting, contributing to advancements in aerospace manufacturing.