I focus on the numerical simulation and process optimization of an annular titanium alloy component produced by sand casting. Titanium alloys are attractive for aerospace, engine, rocket, and high-temperature structural applications because they combine high specific strength, good corrosion resistance, and useful service temperatures between 350 °C and 600 °C. Among the available manufacturing routes, sand casting remains an important production method for thick, large, and moderately complex titanium parts. Compared with forging, sand casting can offer better material utilization for certain geometries. Compared with additive manufacturing, sand casting is often more productive for single pieces or small batches of large annular components. Compared with powder metallurgy, sand casting can avoid some of the residual porosity and interstitial contamination problems that may limit mechanical performance. Therefore, I treat sand casting as the central manufacturing route in this investigation.
Sand casting of titanium alloys is not without difficulty. The freezing range of titanium alloys can be relatively wide, and the thermal conductivity is low. These characteristics promote steep thermal gradients, isolated hot spots, and feeding channels that freeze before the last liquid regions can be replenished. In annular and conical components with stepped wall thickness, the thick sections act as hot spots, while thin sections cool rapidly and may cut off the path for liquid metal feeding. Shrinkage cavity and shrinkage porosity defects are therefore common in sand casting when the gating and riser system is not properly designed. I address this problem by combining three-dimensional finite element simulation with production trials. The simulation is used to locate hot spots, predict shrinkage defects, compare preliminary designs, and guide the final optimization. The production trials are used to validate the predicted defect locations and to calibrate the simulation assumptions, especially the effect of gas evolution in the sand mold.
The component I study is an annular titanium alloy casting with a conical, rotationally symmetric shape. Its largest outer diameter is approximately 600 mm, its smallest outer diameter is approximately 370 mm, and its overall height is approximately 180 mm. The wall thickness is not uniform. Most of the wall thickness lies between 12 mm and 45 mm, and the cross-section contains two distinct thick-wall regions. These thick regions behave as thermal masses during cooling. The first thick region is near the upper part of the casting, and the second is near the lower flange. Because the geometry is annular, the hot spots tend to form closed or semi-closed loops rather than isolated points. This annular hot-spot pattern is important because it influences both the location and the shape of the final shrinkage defects. A single riser or a single gate may not feed the entire loop effectively, so the feeding design must consider the circumferential continuity of the hot zone.
The alloy is ZTC4 titanium alloy. Its nominal chemical composition is summarized in Table 1. The main alloying elements are aluminum and vanadium, with controlled amounts of iron, silicon, carbon, nitrogen, hydrogen, and oxygen. The balance is titanium. The narrow ranges for interstitial elements are important because oxygen, nitrogen, hydrogen, and carbon can strongly affect fluidity, solidification behavior, and final mechanical properties. For sand casting, the alloy composition also influences the freezing range, the latent heat release, and the viscosity of the liquid metal. I use the composition as the input for thermodynamic and thermophysical property calculations.
| Element | Nominal Range (wt.%) | Role in Sand Casting Solidification |
|---|---|---|
| Al | 5.5–6.8 | Alpha stabilizer, affects liquidus temperature and fluidity |
| V | 3.5–4.5 | Beta stabilizer, influences freezing range |
| Fe | ≤0.30 | Impurity control, may affect phase stability |
| Si | ≤0.15 | Impurity control, minor effect on solidification |
| C | ≤0.10 | Interstitial, affects melt cleanliness |
| N | ≤0.05 | Interstitial, affects fluidity and toughness |
| H | ≤0.015 | Interstitial, must be minimized in titanium sand casting |
| O | ≤0.20 | Interstitial, strong effect on strength and ductility |
| Ti | Balance | Matrix element |
I set up the sand casting simulation with a transient heat-transfer formulation. The governing energy equation for the alloy and the mold can be written as shown in Eq. (1) and Eq. (2). In these equations, the release of latent heat is coupled to the solid fraction rate. The heat transfer between the casting and the sand mold is controlled by an interfacial heat-transfer coefficient. The mold is assumed to be alumina-based sand, and the initial mold temperature is 200 °C. The pouring is gravity-driven and static, with a pouring time of approximately 6 s. The alloy is ZTC4, and the mold material is bauxite sand. I use the finite element method to discretize the geometry and solve the coupled thermal problem.
$$\rho C_p \frac{\partial T}{\partial t} = \nabla \cdot \left( k \nabla T \right) + \rho L \frac{\partial f_s}{\partial t} \tag{1}$$
$$\rho_m C_{p,m} \frac{\partial T_m}{\partial t} = \nabla \cdot \left( k_m \nabla T_m \right) \tag{2}$$
In Eq. (1), \rho is density, C_p is specific heat, T is temperature, t is time, k is thermal conductivity, L is latent heat, and f_s is solid fraction. In Eq. (2), the subscript m denotes the mold. The interfacial heat flux is expressed in Eq. (3), where h is the heat-transfer coefficient and T_c and T_m are the casting surface temperature and mold surface temperature, respectively.
$$q = h \left( T_c – T_m \right) \tag{3}$$
The solid fraction evolution is coupled to temperature through the latent heat term. I use a Scheil-type solidification model to estimate the fraction solid as a function of temperature. A simplified form is shown in Eq. (4), where T_L is the liquidus temperature, T_S is the solidus temperature, and k_0 is the partition coefficient. This expression is not intended to represent every microstructural detail, but it provides a reasonable basis for macro-scale feeding analysis in sand casting.
$$f_s = \left( \frac{T_L – T}{T_L – T_S} \right)^{\frac{1}{k_0 – 1}} \tag{4}$$
The thermophysical properties required by the simulation include thermal conductivity, density, enthalpy, and viscosity. I calculated these properties as functions of temperature using the alloy composition and a Scheil solidification model. The thermal conductivity of titanium alloys is relatively low, so heat extraction through the casting is limited. The density changes during solidification contribute to volumetric shrinkage. The enthalpy curve includes the latent heat release over the freezing range. The viscosity affects the fluidity during filling and the ease of feeding during solidification. These properties are not constant; they vary strongly with temperature, especially near the liquidus and solidus. Therefore, I use temperature-dependent property curves rather than room-temperature constants.
The simulation parameters are summarized in Table 2. The pouring temperature and mold temperature determine the initial thermal state. The pouring time influences the filling pattern and the initial temperature distribution. A longer pouring time can reduce turbulence but may also increase heat loss. A shorter pouring time can improve filling but may create more severe impingement and gas entrapment. For this annular sand casting, I maintain a relatively short pouring time of about 6 s to promote complete filling before significant freezing occurs. The mold preheat temperature of 200 °C is selected to reduce the thermal shock and to improve filling behavior, while still providing enough cooling capacity for the sand mold.
| Parameter | Value or Setting |
|---|---|
| Simulation software | ProCAST |
| Numerical method | Finite element method |
| Casting alloy | ZTC4 titanium alloy |
| Mold material | Bauxite sand |
| Mold preheat temperature | 200 °C |
| Pouring time | 6 s |
| Filling mode | Gravity, static pouring |
| Solidification model | Scheil model for thermophysical properties |
| Initial casting temperature | Above liquidus, controlled by pouring practice |
| Heat-transfer model | Transient conduction with interfacial heat transfer |
Mesh sensitivity is a critical issue in sand casting simulation. A very coarse mesh may smear the thermal gradients and misplace the hot spots. A very fine mesh may produce accurate results but requires a long computation time. I therefore performed a mesh independence study using four characteristic mesh sizes: 3 mm, 6 mm, 9 mm, and 12 mm. I compared the temperature history at the same internal location for each mesh size. The results are summarized in Table 3. The 3 mm mesh produced the smallest error but required the longest simulation time. The 6 mm and 9 mm meshes produced temperature curves close to the 3 mm reference. The 12 mm mesh produced a larger error and was considered too coarse for the casting body. Based on the trade-off between accuracy and efficiency, I assigned a 12 mm mesh to the pouring cup, a 6 mm mesh to the casting body, and a 9 mm mesh to the gating and riser transition regions.
| Mesh Size (mm) | Relative Temperature Error Compared with 3 mm Mesh | Relative Simulation Time | Application in the Model |
|---|---|---|---|
| 3 | Reference, lowest error | Highest | Not used globally due to long runtime |
| 6 | Small | Moderate | Casting body |
| 9 | Acceptable | Moderate to low | Gating and riser transition zones |
| 12 | Largest | Lowest | Pouring cup and non-critical regions |
After setting the mesh and boundary conditions, I first simulated the casting without a gating and riser system. The purpose of this step was to identify the natural hot spots and the intrinsic shrinkage behavior of the annular geometry. I used the modulus method as a first indicator. The modulus M is defined in Eq. (5), where V is the volume and A is the heat-transfer surface area. Regions with a large modulus cool more slowly and tend to become hot spots. I also examined the solidification field and the location of closed iso-solid-fraction contours. A closed contour indicates an isolated liquid region that cannot be fed easily from the surrounding liquid metal. The results showed two main hot spots. The first hot spot, which I call hot spot A, is located near the top of the casting. The second hot spot, which I call hot spot B, is located near the lower flange. These two hot spots correspond to the two thick-wall regions identified from the wall-thickness distribution.
$$M = \frac{V}{A} \tag{5}$$
The shrinkage defects predicted for the casting without gating and risers are consistent with the hot-spot analysis. Shrinkage cavity A is located near the top hot spot, and shrinkage cavity B is located near the lower flange hot spot. In addition, a linear shrinkage porosity region, which I call defect C, appears adjacent to shrinkage cavity B. The linear morphology suggests that the feeding path was interrupted along a narrow band, so the last liquid could not be replenished. Because the component is annular, shrinkage cavity A and shrinkage cavity B each form a ring-like distribution around the circumference. This ring-like distribution is more difficult to feed than a compact isolated hot spot because liquid metal must travel along a curved path, and the thin sections between thick regions may freeze early. The main findings from this baseline simulation are listed in Table 4.
| Feature | Location | Cause | Predicted Defect |
|---|---|---|---|
| Hot spot A | Top thick-wall region | Large local modulus and slow cooling | Shrinkage cavity A, ring-like |
| Hot spot B | Lower flange region | Large local modulus and flange geometry | Shrinkage cavity B, ring-like |
| Defect C | Adjacent to lower flange hot spot | Interrupted feeding path | Linear shrinkage porosity |
I then designed two preliminary gating and riser schemes based on the baseline results. In the first scheme, the inner gate is positioned to feed hot spot B, while a riser is placed to feed hot spot A. The intention is to use the riser for the upper thick section and the gate for the lower flange. In the second scheme, the casting is inverted for pouring. The thick flange is placed at the top, and the riser is positioned to feed it directly. The intention is to use gravity and the top riser to improve feeding of the heaviest section. These two schemes are summarized in Table 5. Both schemes are intended to reduce shrinkage cavities in the casting body by moving the last solidification region into the gating or riser system.
| Scheme | Orientation | Feeding Strategy | Expected Advantage | Expected Risk |
|---|---|---|---|---|
| Scheme 1 | Normal orientation | Inner gate feeds lower hot spot B; riser feeds upper hot spot A | Direct feeding of lower flange | Long feeding path to remote regions |
| Scheme 2 | Inverted orientation | Thick flange at top; riser feeds top flange | Gravity-assisted feeding of thick section | Large shrinkage at gate root |
For Scheme 1, the solid fraction simulation shows that the feeding channel through the inner gate becomes interrupted when the overall solid fraction reaches approximately 53%. At that moment, an un-solidified region remains near the bottom of the casting. The predicted shrinkage defects include a micro-shrinkage region near the gate-to-casting connection with a volume of approximately 3.9 cm³, and a linear shrinkage region far from the gate with a volume of approximately 1 cm³. The defect locations are consistent with the baseline hot-spot analysis. The gate can feed the nearby lower flange, but it cannot reach the remote upper region effectively. The riser at the upper region is not sufficient to compensate for the isolated liquid pocket that forms there. Therefore, Scheme 1 reduces the local shrinkage near the gate but leaves a linear shrinkage defect in the distant region.
For Scheme 2, the inverted orientation changes the thermal gradient. The solid fraction simulation indicates that when the solid fraction is approximately 40%, feeding becomes difficult. The hot spot cools more slowly than the gate, so a conical solidification gradient forms between the gate and the hot spot. The gradient is wider at the top and narrower at the bottom, which means the gate freezes earlier than the hot spot. As a result, the feeding path is blocked. The predicted shrinkage defects for Scheme 2 include a large cavity near the gate root with a volume of approximately 38 cm³ and a depth of approximately 14.5 mm into the casting body. A small additional shrinkage defect with a volume of approximately 0.4 cm³ appears far from the gate. The large gate-root cavity is a serious concern because it penetrates into the casting body and would require extensive repair.
The simulation results for the two preliminary schemes are compared in Table 6. Scheme 1 has a smaller total shrinkage volume, but the defect is distributed as a linear porosity far from the gate. Scheme 2 has a larger total shrinkage volume, but the defect is concentrated near the gate root. In terms of post-processing, a concentrated defect near the gate may be easier to remove if it remains entirely within the gating system. However, in Scheme 2 the cavity penetrates about 14.5 mm into the casting body, so it is not acceptable without repair. In terms of casting integrity, Scheme 1 avoids a large gate-root cavity but produces a linear defect in a remote region. Neither preliminary scheme is fully satisfactory. This comparison motivated the optimized design.
| Scheme | Critical Solid Fraction for Feeding Interruption | Main Defect Location | Predicted Volume | Depth into Casting | Assessment |
|---|---|---|---|---|---|
| Scheme 1 | Approximately 53% | Near gate and remote linear region | 3.9 cm³ near gate; 1 cm³ remote | Not dominant; linear porosity | Remote linear shrinkage remains |
| Scheme 2 | Approximately 40% | Gate root and small remote region | 38 cm³ gate root; 0.4 cm³ remote | 14.5 mm at gate root | Large cavity penetrates casting body |
I also validated the two schemes through production trials. The production route includes mold preparation, drying, coating, high-temperature baking, preheating, gravity pouring in a vacuum consumable electrode arc skull furnace, and sand removal after solidification. For Scheme 1, the produced casting shows a large shrinkage cavity near the gate and a large linear shrinkage region far from the gate. These defect locations match the simulation predictions. For Scheme 2, the produced casting shows a large shrinkage cavity at the gate root, which also matches the simulation prediction. The gate-root cavity requires extensive weld repair, which is costly and may introduce additional quality risks. The experimental results are summarized in Table 7.
| Scheme | Observed Defect Location | Observed Defect Type | Agreement with Simulation | Production Consequence |
|---|---|---|---|---|
| Scheme 1 | Near gate and remote region | Large cavity near gate; linear shrinkage remote | Location consistent | Remote linear shrinkage requires repair or rejection |
| Scheme 2 | Gate root | Large shrinkage cavity | Location consistent | Extensive weld repair required |
One important observation from the trials is that the simulated shrinkage volumes are generally smaller than the actual shrinkage volumes. The predicted defect locations are accurate, but the volumetric predictions are conservative in the wrong direction. I attribute this difference primarily to gas evolution from the sand mold. In actual sand casting, the mold binder and moisture can release gas during pouring and solidification. This gas can be entrained or can influence the local pressure balance, increasing the tendency for shrinkage cavity formation. The simulation setup did not include a quantitative gas-evolution model. Therefore, the predicted shrinkage volume underestimates the real defect volume. To improve the quantitative agreement, I calibrated the macro-shrinkage formation parameter, MACROFS, using the experimental results. This parameter defines the critical solid fraction above which macroscopic feeding stops. When the local solid fraction exceeds this threshold, the remaining liquid cannot flow freely, and a macro-shrinkage cavity forms. By adjusting MACROFS, I brought the simulation closer to the observed behavior and used the calibrated model for the optimized design.
The optimized design is based on Scheme 2 but with a modified inner gate geometry. I changed the inner gate to a conical shape. The conical gate provides a larger cross-section near the casting and a smaller cross-section away from the casting. This geometry helps to maintain a positive thermal gradient toward the gate. I set the gradient angle to approximately 25°, based on the solidification gradient observed in Scheme 1. I also increased the gate height to 155 mm, based on the measured shrinkage depth of 14.5 mm in Scheme 2. The taller gate provides additional liquid metal for feeding and shifts the last solidification region farther into the gate. The optimized parameters are listed in Table 8.
| Optimized Parameter | Value | Reason |
|---|---|---|
| Inner gate shape | Conical | Promotes directional solidification toward the gate |
| Gradient angle | Approximately 25° | Based on solidification gradient from Scheme 1 |
| Gate height | 155 mm | Based on measured shrinkage depth of 14.5 mm in Scheme 2 |
| Base gating orientation | Inverted from Scheme 2 | Places thick flange in a favorable feeding position |
| Critical solid fraction for feeding | Approximately 76% in optimized simulation | Feeding channel remains open longer; final solidification in gate |
| Defect target location | Inner gate | Keeps shrinkage out of the casting body |
In the optimized simulation, the solid fraction evolution shows that the feeding channel remains open until the solid fraction reaches approximately 76%. At that stage, the hot spot is still able to receive liquid metal from the inner gate. The final solidification point is located inside the inner gate, not in the casting body. The predicted shrinkage cavity is therefore fully transferred to the inner gate region. This result is significant because it means the casting body itself remains free of large macro-shrinkage defects. The optimized design effectively converts the gate into a sacrificial feeding reservoir. The annular hot spots are fed along the circumferential direction through the conical gate, and the last liquid contracts inside the gate, where it can be removed during cleaning and machining.
I then produced the optimized casting and inspected it by X-ray radiography and machining. The X-ray results show no large shrinkage cavity in the casting body. The internal quality meets the B-level requirement of the applicable titanium casting standard, GJB 2896A-2020. The machining results confirm that the gate contains the shrinkage defect and that the casting body is sound after gate removal. The final quality results are summarized in Table 9. Compared with the preliminary schemes, the optimized design reduces the defect volume in the casting body to an acceptable level and avoids the need for extensive weld repair. This demonstrates that the combination of numerical simulation and production validation can be used to solve shrinkage problems in annular titanium alloy sand casting.
| Quality Item | Preliminary Scheme 1 | Preliminary Scheme 2 | Optimized Scheme |
|---|---|---|---|
| Large cavity in casting body | Remote linear shrinkage present | Gate-root cavity penetrates body | No large cavity in body |
| Main defect location | Gate and remote region | Gate root | Inner gate |
| Repair requirement | High risk | Extensive weld repair | Limited to gate removal |
| X-ray result | Not acceptable | Not acceptable | Meets B-level requirement |
| Production outcome | Repair or rejection risk | High cost and risk | Acceptable casting body |
The optimization logic can be expressed in terms of feeding resistance and thermal gradient. The feeding flow through a mushy zone can be approximated by Darcy’s law, as shown in Eq. (6), where v is the superficial velocity, K is permeability, \mu is viscosity, P is pressure, \rho is density, and g is gravitational acceleration. When the solid fraction increases, the permeability decreases rapidly. Once the local solid fraction exceeds a critical value, the pressure drop required to feed the remaining liquid becomes very large, and feeding effectively stops. This critical value is related to the MACROFS parameter used in the simulation.
$$\mathbf{v} = -\frac{K}{\mu} \left( \nabla P – \rho \mathbf{g} \right) \tag{6}$$
The formation of macro-shrinkage can be approximated by Eq. (7), where V_sh is the shrinkage volume, and f_s^{crit} is the critical solid fraction for feeding. In practice, the exact volume depends on the pressure boundary conditions, the permeability of the mushy zone, and the gas evolution in the sand mold. Nevertheless, Eq. (7) captures the idea that macro-shrinkage occurs when the local solid fraction exceeds the feeding threshold before the liquid can be replenished.
$$V_{sh} \approx \int_{V} \max \left( 0, f_s – f_s^{crit} \right) dV \tag{7}$$
I also used the Niyama criterion as a supplementary indicator. The Niyama parameter is defined in Eq. (8), where G is the thermal gradient and \dot{T} is the cooling rate. A low Niyama value indicates a high probability of shrinkage porosity. In sand casting, the cooling rate is relatively low, so the thermal gradient must be maintained to keep the Niyama value above the critical threshold. The conical gate and the increased gate height help to maintain a favorable thermal gradient from the casting body toward the gate. This reduces the risk of isolated liquid pockets in the casting body.
$$N = \frac{G}{\sqrt{\dot{T}}} \tag{8}$$
The cooling rate itself can be approximated from the freezing range, as shown in Eq. (9), where T_L is the liquidus temperature, T_S is the solidus temperature, and t_f is the local freezing time. A longer freezing time generally corresponds to a larger hot spot and a greater feeding demand. The annular geometry creates long freezing times in the thick sections, so the feeding system must be able to supply liquid metal over a sufficient distance. The feeding distance can be estimated by Eq. (10), where L_f is the feeding distance, K_f is an empirical coefficient, and M is the modulus. The optimized gate increases the effective modulus of the feeding path, which extends the feeding distance and allows the gate to feed the annular hot spots more effectively.
$$\dot{T} \approx \frac{T_L – T_S}{t_f} \tag{9}$$
$$L_f = K_f M \tag{10}$$
The thermal gradient angle in the optimized design is another important parameter. I define the gradient angle \theta as shown in Eq. (11), where \Delta T is the temperature difference over a characteristic distance \Delta x. A positive gradient angle toward the gate indicates that the gate remains hotter than the casting body, so the last liquid forms in the gate. This condition is desirable because it moves the shrinkage defect into the gate. In the optimized sand casting process, the 25° gradient angle provides a favorable directional solidification pattern without making the gate excessively large.
$$\theta = \arctan \left( \frac{\Delta T}{\Delta x} \right) \tag{11}$$
From a practical standpoint, the optimized sand casting process has several advantages. First, the conical inner gate improves feeding by maintaining a hot channel to the last liquid region. Second, the increased gate height provides a larger reservoir of liquid metal. Third, the inverted orientation places the thick flange in a position where gravity can assist feeding. Fourth, the calibrated MACROFS parameter improves the quantitative prediction of shrinkage volume. Fifth, the final solidification point is shifted into the gate, so the casting body remains sound. These measures are all compatible with the sand casting route and do not require a major change in mold material or pouring practice.
The experimental validation also highlights the limitations of simulation. The predicted defect locations are reliable, but the predicted volumes are sensitive to the gas-evolution behavior of the sand mold. In future work, I would incorporate a gas-evolution model that accounts for binder decomposition and moisture release. I would also measure the interfacial heat-transfer coefficient more accurately during the pouring and solidification stages. These improvements would make the simulation more quantitative. Nevertheless, the current approach is sufficient for process design because it correctly identifies the hot spots, the feeding paths, and the final defect locations. The optimization is based on relative comparisons between schemes, and the production trials confirm that the final scheme is robust.
The broader implication for sand casting of titanium alloys is that annular and conical geometries require special attention to feeding paths. Unlike compact castings, annular castings have circumferential hot spots that can be difficult to feed from a single gate. The gating system must provide a continuous path for liquid metal to reach all parts of the hot zone. A conical gate with a positive thermal gradient is an effective solution. It acts as a hot reservoir and a directional solidification promoter. The gate height must be sufficient to contain the final shrinkage cavity. The gate taper must be sufficient to keep the gate open while the casting is still solidifying. The gradient angle must be controlled so that the gate remains hotter than the casting body until the casting body is fully solid. These principles can be generalized to other thick annular titanium sand castings.
I summarize the key simulation equations and their roles in Table 10. These equations are not all independent; they form a coupled description of heat transfer, solidification, feeding, and defect formation. The heat-transfer equation determines the temperature field. The solid fraction equation determines the mushy zone evolution. The Darcy equation describes feeding resistance. The Niyama criterion indicates porosity risk. The modulus and feeding distance equations provide simple design guidance. The shrinkage volume integral relates the solid fraction to the final defect volume. Together, these relations explain why the optimized conical gate works and why the preliminary schemes fail.
| Equation | Description | Role in Sand Casting Optimization |
|---|---|---|
| Eq. (1) | Casting energy equation with latent heat | Predicts temperature and solidification evolution |
| Eq. (2) | Mold energy equation | Predicts sand mold heating and heat extraction |
| Eq. (3) | Interfacial heat flux | Controls heat transfer between casting and mold |
| Eq. (4) | Scheil solid fraction | Estimates fraction solid versus temperature |
| Eq. (5) | Modulus | Identifies hot spots and feeding demand |
| Eq. (6) | Darcy flow | Describes feeding resistance in the mushy zone |
| Eq. (7) | Shrinkage volume integral | Relates critical solid fraction to defect volume |
| Eq. (8) | Niyama criterion | Indicates shrinkage porosity risk |
| Eq. (9) | Cooling rate | Estimates local freezing time |
| Eq. (10) | Feeding distance | Estimates how far a gate or riser can feed |
| Eq. (11) | Gradient angle | Controls directional solidification toward the gate |
The final production outcome confirms that the optimized sand casting process is effective. The casting body contains no large shrinkage cavity. The shrinkage defect is transferred to the inner gate, where it is removed during gate cutting and machining. The X-ray inspection meets the B-level acceptance requirement. The process is repeatable because the key parameters are defined geometrically and thermally: conical gate, 25° gradient angle, 155 mm gate height, and a calibrated critical solid fraction. These parameters can be used as a starting point for similar annular titanium alloy castings. The main remaining uncertainty is the gas evolution from the sand mold. If gas evolution is high, the effective feeding threshold may decrease, and the shrinkage volume may increase. Therefore, mold baking, coating control, and moisture control remain important in actual sand casting production.
In conclusion, I have shown that numerical simulation can accurately predict the location of shrinkage defects in annular titanium alloy sand castings. The baseline simulation identified two ring-like hot spots and corresponding shrinkage cavities. Two preliminary schemes were designed and tested. Scheme 1 fed the lower flange but left remote linear shrinkage. Scheme 2 fed the upper flange but created a large gate-root cavity that penetrated the casting body. The optimized scheme used a conical inner gate, a 25° gradient angle, and a 155 mm gate height. The optimized solidification pattern kept the feeding channel open to approximately 76% solid fraction and placed the final solidification point inside the gate. Production trials confirmed that the casting body was free of large shrinkage cavities and met the required internal quality standard. The study provides a practical design method for sand casting of thick annular titanium components and demonstrates the value of combining simulation, experimental validation, and parameter calibration.