In this study, we investigate the application of numerical simulation to optimize the lost wax investment casting process for rod-shaped titanium alloy castings. Titanium alloys are renowned for their low density, high strength, and excellent corrosion resistance, making them ideal for aerospace, marine, and sports equipment industries. The lost wax investment casting technique, as a near-net-shape manufacturing method, enables the production of complex and high-surface-quality titanium components. However, challenges such as poor fluidity and limited feeding capability due to titanium’s low density and high sensitivity to interstitial elements like hydrogen and oxygen often lead to defects like shrinkage porosity and residual stresses. To address these issues, we employ numerical simulation to analyze temperature fields, stress distributions, and defect formation, thereby refining the casting process and reducing trial-and-error costs in production.
The rod-shaped titanium alloy casting under examination features a length-to-width ratio of approximately 9.3:1, with uniform wall thickness at the ends but a significant thickness variation of 10.5:1 at the junction between the rod and the open root. Key technical requirements include using ZTC4 alloy, maintaining non-machined surfaces except for a φ10 mm hole, and adhering to GB/T 6414-2017 CT6 tolerance standards. Critical areas, such as the thick-thin transition zones and machined regions, must be free from cracks and defects, and the client prohibits hot isostatic pressing to minimize costs. Our primary objective is to design a gating system that ensures defect-free casting in these sensitive areas while minimizing residual stresses.
We designed two gating systems based on different solidification theories: sequential solidification and equilibrium solidification. The first scheme employed a top-gating system with the rod aligned vertically to promote directional solidification, using gates as feeders and incorporating anti-deformation supports. The gating ratio was set to 1:1.02:2.06 for an open system. The second scheme utilized a side-gating system with the rod placed horizontally, reducing flow and feeding distances, and a gating ratio of 1:1.02:1.5 to achieve balanced solidification. Numerical simulations were conducted to model filling, solidification, temperature fields, and stress distributions, identifying shrinkage defects and stress concentrations.
The simulation results for the sequential solidification scheme revealed that filling occurred progressively from the center outward, with solidification following a directional pattern. However, shrinkage defects formed at the thick-thin junctions and around the φ10 mm hole due to hot spots introduced by anti-deformation supports. Stress concentrations exceeded 300 MPa in these areas, increasing the risk of cracking during service. In contrast, the equilibrium solidification scheme demonstrated a more uniform temperature distribution during filling and solidification, with defects localized at gate connections and lower stress differentials below 100 MPa at critical zones. Despite improvements, stress peaks around 267 MPa were observed near gates, indicating potential deformation issues.
Based on these findings, we optimized the casting process by eliminating anti-deformation supports, casting the φ10 mm hole to reduce defect risks, and repositioning gates to the thick-thin junctions to act as effective feeders. The revised design promoted balanced solidification and minimized stress concentrations. Subsequent simulations confirmed that shrinkage defects were confined to gate areas, avoiding critical zones, and stress differentials were reduced to below 90 MPa, ensuring a more uniform stress distribution.
To validate the optimized process, we produced 100 castings using the lost wax investment casting method. Wax patterns were fabricated with medium-temperature wax, assembled into clusters, and coated with an 8.5-layer silica sol shell system approximately 12 mm thick, matching simulation parameters. After dewaxing and firing, castings were poured in a vacuum consumable furnace with a mold temperature of around 40°C, using ZTC4 alloy. Post-casting inspection included non-destructive testing and fluorescent penetrant inspection. Results showed a 98% first-pass acceptance rate for internal quality, with only two instances of high-density inclusions at thick-thin junctions, and 100% acceptance for surface cracks. Dimensional accuracy met CT6 standards, confirming the process efficiency without hot isostatic pressing.
In summary, numerical simulation proved instrumental in optimizing the lost wax investment casting process for rod-shaped titanium alloys. The equilibrium solidification-based gating system effectively addressed defect formation and residual stresses, enabling high-yield production. Key insights include avoiding unnecessary thermal junctions in uniform sections and utilizing gates for feeding in thick-varying regions. This approach underscores the value of simulation-driven design in enhancing manufacturing reliability and cost-effectiveness for complex titanium castings.
The governing equations for heat transfer and solidification in the simulation can be expressed using Fourier’s law and the energy conservation equation. The temperature field during solidification is described by:
$$ \frac{\partial T}{\partial t} = \alpha \nabla^2 T + \frac{L}{c_p} \frac{\partial f_s}{\partial t} $$
where \( T \) is temperature, \( t \) is time, \( \alpha \) is thermal diffusivity, \( L \) is latent heat, \( c_p \) is specific heat, and \( f_s \) is the solid fraction. For stress analysis, the thermo-elastic-plastic model is employed, with the stress tensor \( \sigma \) given by:
$$ \sigma = C : (\epsilon – \epsilon_t – \epsilon_p) $$
where \( C \) is the stiffness tensor, \( \epsilon \) is total strain, \( \epsilon_t \) is thermal strain, and \( \epsilon_p \) is plastic strain. The thermal strain is computed as \( \epsilon_t = \beta (T – T_0) \), with \( \beta \) as the thermal expansion coefficient and \( T_0 \) as the reference temperature.
To quantify the solidification behavior, we use the Niyama criterion for predicting shrinkage porosity, defined as:
$$ N_y = \frac{G}{\sqrt{\dot{T}}} $$
where \( G \) is the temperature gradient and \( \dot{T} \) is the cooling rate. A lower Niyama value indicates a higher risk of shrinkage defects. In our simulations, regions with \( N_y < 1 \, \text{K}^{1/2} \cdot \text{s}^{1/2} / \text{mm} \) were identified as critical for porosity formation.
The following table summarizes key parameters used in the numerical simulation for the lost wax investment casting process:
| Parameter | Value | Description |
|---|---|---|
| Alloy | ZTC4 | Titanium alloy composition |
| Mold Material | Silica Sol Shell | 8.5 layers, ~12 mm thickness |
| Mold Temperature | 40°C | Initial mold temperature for simulation and production |
| Pouring Temperature | 1700°C | Typical for titanium alloys in vacuum casting |
| Gating Ratio (Scheme 1) | 1:1.02:2.06 | Open system for sequential solidification |
| Gating Ratio (Scheme 2) | 1:1.02:1.5 | Open system for equilibrium solidification |
| Simulation Software | ProCAST | Used for finite element analysis of casting processes |
Another table compares the simulation outcomes for the two initial gating schemes, highlighting defects and stresses:
| Aspect | Sequential Solidification Scheme | Equilibrium Solidification Scheme |
|---|---|---|
| Filling Pattern | Center-outward progression | Gradient filling from side gates |
| Solidification Behavior | Directional, top-down | Balanced, following filling sequence |
| Shrinkage Defects | At thick-thin junctions and φ10 mm hole | At gate connections and hot spots |
| Max Stress in Critical Zones | >300 MPa | >267 MPa |
| Stress Differential | High (>100 MPa) | Moderate (<100 MPa) |
The optimization process involved iterative simulations to adjust gating positions and remove unnecessary features. The final design prioritized minimizing thermal gradients and stress concentrations. The effectiveness of the lost wax investment casting process was evident in the production yield, demonstrating the practicality of simulation-based design.
In conclusion, our study highlights the critical role of numerical simulation in advancing the lost wax investment casting of titanium alloys. By integrating solidification theories with finite element analysis, we achieved a robust process that meets stringent quality standards. Future work could explore dynamic feeding mechanisms or advanced alloy compositions to further enhance performance. The success of this approach reaffirms the importance of computational tools in modern manufacturing, particularly for high-value materials like titanium.