In the present work, I investigate the solidification process of a tail roller manufactured by lost foam castings. The tail roller is a rotating cylindrical component widely used in mining conveyor tail shaft assemblies. In the conventional foundry route, water-glass sand is often employed for moulding and core making. However, water-glass sand has poor collapsibility, and this makes the subsequent cleaning and knockout operations time-consuming and labour-intensive. Lost foam castings, also known as expendable pattern casting or EPC, provide a near-net-shape alternative. In this technique, a polystyrene foam pattern is assembled into a cluster, coated with refractory paint, dried, embedded in dry unbonded sand, and compacted by vibration. During pouring, the liquid metal replaces the vaporized foam pattern and solidifies to form the casting. The main advantage of lost foam castings is that binders, cores, and draft angles can be eliminated for many components, which reduces machining allowance and improves dimensional accuracy. However, the solidification stage is critical because the gas pressure generated by the foam decomposition, the permeability of the coating, and the vacuum level can influence feeding behaviour. I therefore used a numerical simulation approach to compare an original casting process with an improved process for this tail roller.
1. Introduction and Objectives
My objective is to optimize the lost foam castings process for a tail roller made of ZG30Mn2 cast steel. This material requires a sufficiently long feeding path and a sound temperature gradient to avoid shrinkage cavities and porosity. I first built a three-dimensional CAD model of the tail roller, then used the HuazhuCAE solidification simulation package to analyze two different gating and riser designs. The first design uses a middle-injection gating system with a cylindrical top riser. The second design replaces the top riser with an approximately spherical side riser and adds an internal chill on the cylindrical inner surface. I compare the predicted solidification sequences and porosity distributions. My simulation results demonstrate that lost foam castings can be made sound and economical if the riser geometry and chill location are chosen correctly. The improved process not only reduces shrinkage defects but also simplifies pattern assembly and riser removal. Throughout this article, I emphasize that solidification simulation is an indispensable tool for designing robust lost foam castings, especially for steel castings where feeding is difficult and the process window is narrow.
Lost foam castings differ from conventional sand casting in several ways. The foam pattern remains in the mould during pouring, and the decomposition products must escape through the refractory coating and the sand. This imposes a particular thermal boundary condition at the metal-mould interface. In addition, the absence of a binder means that the sand has a low mechanical strength until vacuum is applied, so the solidifying casting can move or deform if the pattern stiffness is insufficient. The vacuum not only holds the sand compact but also removes the pyrolysis gases. The heat transfer coefficient at the metal-foam interface is not constant; it changes with time, gap formation, gas pressure, and coating thickness. Therefore, the solidification behaviour of lost foam castings is more complex than that of conventional green-sand castings. A reliable simulation must therefore include realistic material properties, boundary conditions, and process parameters.
In the first part of my study, I review the geometrical features of the tail roller. In the second part, I describe the mathematical model and the equations used by the solidification solver. In the third part, I present the original process and its simulated solidification sequence. In the fourth part, I introduce the improved side-riser and chill design and compare it with the original design. Finally, I provide practical recommendations for the production of sound tail-roller lost foam castings.
2. Three-Dimensional Modeling of the Tail Roller
I constructed the three-dimensional model of the tail roller with UG NX. The part is a body of revolution, so the most efficient modeling strategy is to draw a two-dimensional cross-section and then revolve it around the rotation axis. The tail roller has a generally cylindrical envelope, with flanges and bosses near the two ends. The casting is designed with machining allowance on the thickest functional surfaces, making the nominal wall thickness relatively uniform. This uniform wall thickness is favourable for producing lost foam castings because it promotes gradual solidification from the thinner sections toward the thicker sections. The model includes only the casting geometry, not the foam pattern or the gating system. I exported the solid body in STL format for the simulation and also for the foam-pattern cutting process in lost foam castings. The CAD model is essential because it defines the exact volume and surface area, from which the solidification modulus can be calculated. I used the same CAD model for both the original and improved process simulations, so the only changes were the feeding systems and the chill.
One important consideration for lost foam castings is that the foam pattern must have a density low enough to minimize gas generation and carbon defects, but high enough to survive handling and coating. For steel castings such as ZG30Mn2, I usually select an expanded polystyrene foam with a density of about 16 to 20 kg per cubic metre. The pattern is coated with a water-based refractory paint with a thickness of about 0.2 to 0.4 mm. The coating acts as a permeable barrier that allows decomposition gases to pass into the sand while preventing the liquid metal from penetrating the mould. I also used dry silica sand with a mean grain size of approximately 30 to 50 AFS. The sand was compacted by vibration, and a vacuum of about 0.03 to 0.06 MPa was applied during pouring. These parameters are common for lost foam castings and were held constant in both simulations.
| Parameter | Value |
|---|---|
| Casting material | ZG30Mn2 |
| Casting density | 7,800 kg/m³ |
| Liquidus temperature | 1,515 °C |
| Solidus temperature | 1,435 °C |
| Pouring temperature | 1,550–1,600 °C |
| Pouring time | 21.0 s |
| Initial mould temperature | 20 °C |
| Negative pressure | 0.04 MPa |
| Refractory coating thickness | 0.3 mm |
| EPS foam density | 18 kg/m³ |
| Heat-transfer coefficient at metal-mould interface | 500–1,200 W/(m²·K) |
3. Mathematical Model of Solidification
Solidification simulation is based on the transient heat-conduction equation with latent-heat release. The governing equation that I used in the present study is:
$$\rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + \rho L \frac{\partial f_s}{\partial t} \tag{1}$$
In this expression, T is temperature, t is time, rho is density, c_p is specific heat, k is thermal conductivity, L is latent heat, and f_s is the solid fraction. The last term represents the release of latent heat during solidification. For the solidification range of ZG30Mn2, I assumed that the solid fraction varies linearly with temperature between the liquidus and solidus:
$$f_s(T) = \begin{cases} 0, & T > T_l \\[2mm] \dfrac{T_l – T}{T_l – T_s}, & T_s \le T \le T_l \\[2mm] 1, & T < T_s \end{cases} \tag{2}$$
This linear relationship is a useful approximation for cast steels because the freezing range is relatively narrow. The latent heat release strongly affects the dynamic of the mushy zone and therefore the formation of shrinkage porosity in lost foam castings. To evaluate the feeding ability of a riser, I used the solidification modulus, which is defined as the ratio of volume V to cooling surface area A:
$$M = \frac{V}{A} \tag{3}$$
The solidification time can then be estimated with Chvorinov’s rule:
$$t_s = B \, M^n \tag{4}$$
where B is a mould constant and n is close to 2 for sand moulds. A larger modulus means that a casting section solidifies more slowly. The modulus is a convenient way to design risers because a riser must have a modulus larger than the modulus of the hot spot that it feeds. For the riser design, I selected the riser modulus with a safety factor f_r between 1.1 and 1.3:
$$M_r = f_r \, M_{\text{hot spot}} \tag{5}$$
For a cylindrical riser of diameter D and height H, the modulus is:
$$M_{\text{cylinder}} = \frac{D H}{4H + 2D} \tag{6}$$
For a spherical riser of diameter D, the modulus is much easier to calculate because the sphere has a small surface-to-volume ratio:
$$M_{\text{sphere}} = \frac{D}{6} \tag{7}$$
The gating system dimensions were checked by applying the continuity equation. For a poured weight W, a filling velocity v and a pouring time t, the total effective ingate area A_g satisfies:
$$A_g = \frac{W}{\rho \, v \, t} \tag{8}$$
This equation helps to ensure that the mould cavity fills quickly enough to avoid cold shuts, but not so violently that the foam pattern is displaced or the coating is eroded. Finally, to evaluate microporosity, I used the Niyama criterion. This criterion relates the thermal gradient G and the local cooling rate CR:
$$N_y = \frac{G}{\sqrt{CR}} \tag{9}$$
In steel castings, the risk of microporosity is generally high when N_y is smaller than about 1 in the corresponding temperature unit. The Niyama criterion was computed from the simulated temperature history and assisted me in comparing the quality of the original and improved lost foam castings.
Feeding through the mushy zone can also be analyzed with Darcy’s law. The pressure drop of the liquid metal flowing through a dendritic network is proportional to the local viscosity, the flow velocity, and the inverse permeability of the solid skeleton:
$$\frac{\Delta P}{L} = \frac{\mu}{K_p} \, v_l \tag{10}$$
where K_p is the permeability of the mushy zone, mu is the dynamic viscosity, and v_l is the superficial liquid velocity. If the pressure drop becomes too large, the liquid cannot feed the shrinkage and microporosity forms. This equation underlines why it is necessary to maintain a steep temperature gradient and an open liquid path in lost foam castings. The simulation post-processor translated these physical conditions into a shrinkage-porosity risk map.
4. Original Casting Process
The original process uses a middle-injection gating system. Liquid metal enters the casting through two ingates located at the middle height of the tail roller. The runner is horizontal and the sprue is vertical. I calculated the ingate area from the continuity equation and verified the dimensions with the HuazhuCAE filling module. The original process also includes a cylindrical top riser placed on the top flange of the casting. The sprue has a cross-sectional area of 5.04 square centimetres and a height of 250 millimetres. The runner has a cross-sectional area of 4.62 square centimetres and a length of 412 millimetres. The ingate has a cross-sectional area of 4.20 square centimetres and a length of 55 millimetres. The riser is a cylinder with a diameter of 70 millimetres and a height of 140 millimetres. These dimensions are summarized in Table 2.
| Component | Cross-section or shape | Main dimensions |
|---|---|---|
| Sprue | Circular | Area 5.04 cm², height 250 mm |
| Runner | Trapezoidal | Area 4.62 cm², length 412 mm |
| Ingate | Rectangular | Area 4.20 cm², length 55 mm |
| Top riser | Cylindrical | Diameter 70 mm, height 140 mm |
I simulated the solidification process of this original design for the tail roller. The simulation started after the mould cavity was filled. The initial temperature distribution was set according to the pouring temperature and the pouring time. The bottom parts of the casting and runner solidified first because they were in contact with the dry sand at room temperature. After about 90 seconds, the lower portion of the casting had already formed a solid shell, and the remaining liquid was confined to the middle and upper sections. After about 167 seconds, the central regions of the tail roller began to solidify, while the thick flanges at the two ends were still liquid. The top riser and the upper part of the casting remained liquid for a longer time. After about 534 seconds, the casting was essentially solid, and the only liquid remaining was in the top riser and in the connecting neck. The final shrinkage cavities were mostly located inside the top riser. This result is good in the sense that the casting itself did not contain macroscopic shrinkage cavities. The main problem is that the top riser must be removed by flame cutting and grinding, which increases the cleaning time and reduces the productivity of the foundry.
Another issue with the original top-riser design is that the foam pattern assembly is complicated. A vertical riser requires an additional foam part and a fragile joint at the top surface of the casting. During vibration compaction, the tall riser may bend or break if the pattern is not supported. In lost foam castings, any distortion of the foam pattern directly affects the final casting geometry. Therefore, although the original process produced a technically sound casting, it was not the most robust or economical design for mass production. I decided to optimize the riser position and geometry while maintaining the same quality level.
5. Improved Process with Side Riser and Chill
The improved process is based on two modifications. First, I replaced the cylindrical top riser with an approximately spherical side riser. Second, I placed a chill on the inner cylindrical surface of the tail roller. The position of the side riser was chosen at the last-solidifying region of the casting, as indicated by the original simulation. The chill was sized and positioned so that it would solidify the inner surface earlier and displace the hot spot toward the riser. This creates a directional solidification condition that is very desirable for lost foam castings because the feeding path remains open until the end of solidification.
The side riser has a shape similar to a sphere. A sphere offers a larger modulus for a given volume than a cylinder, and therefore it remains liquid longer. The modulus of the spherical side riser is:
$$M_{\text{sphere}} = \frac{D}{6} \tag{11}$$
In practice, I adjusted the diameter of the side riser so that its modulus was at least 1.2 times the modulus of the adjacent hot spot. The improved feeder was also connected to the casting by a short neck, and the neck was designed to remain open until the casting body had solidified. The natural consequence is that any shrinkage that must be compensated by the riser will be taken from the riser itself, not from the casting. Because the side riser is located on the outside surface of the cylindrical tail roller, it can be removed more easily during knockout or after a light cleaning. There is no need to cut a long vertical riser from the top flange, and the foam pattern assembly is therefore simplified.
The chill is the second important element of the improved lost foam castings process. The chill was placed on the inner arc-shaped surface of the tail roller. The material of the chill was grey cast iron, and the chill was painted and dried before embedding. The chill accelerates solidification in the central region, where the heat would otherwise remain trapped. By increasing the temperature gradient locally, the chill moves the remaining liquid toward the side riser and improves feeding. The combination of a side riser and a chill is a common and effective way to control solidification in steel lost foam castings.
| Item | Original process | Improved process |
|---|---|---|
| Riser location | Top surface | Lateral surface |
| Riser shape | Cylindrical | Approximately spherical |
| Chill | Not used | Internal cylindrical surface |
| Pattern assembly | More complex vertical joint | Simpler side joint |
| Riser removal | Difficult flame cutting | Easy sawing / knockout |
| Feeding direction | From top downward | From side toward hot spot |
| Cleaning workload | High | Low |
6. Simulation Results of the Improved Process
I applied the same mesh size, material database, and boundary conditions to the improved process so that the comparison with the original process is meaningful. The solidification sequence of the improved process is controlled by the chill and the side riser. At about 192 seconds, the region near the chill had already solidified. This is expected because the chill extracts heat faster than the dry sand. At about 477 seconds, the two thick end sections of the tail roller were solidifying, and the central part of the casting had formed a solid shell. The remaining liquid was concentrated near the side riser and in the feeding neck. At about 807 seconds, the side riser still contained a small amount of liquid, while the casting itself was completely solid. This behaviour is exactly what a foundry engineer wants: the last liquid is in the riser, and the riser is able to feed the casting until the end of solidification.
The shrinkage-porosity prediction for the improved process shows very few internal defects in the functional part of the tail roller. The small amount of microporosity that remains is located in the areas with machining allowance or in non-stressed regions. These defects are not expected to affect the mechanical performance of the component. Compared with the original process, the improved process does not create new harmful porosity, and it greatly reduces the cost associated with riser removal. The use of the side riser also improves the productivity of lost foam castings because the same foam pattern can be cut and assembled more quickly. The simulation therefore confirms that the side riser combined with a chill is superior to the original top-riser design.
| Predicted feature | Original process | Improved process |
|---|---|---|
| First solidified region | Bottom of casting | Internal surface near chill |
| Intermediate solidification | Middle band and flanges | Flanges and outer walls |
| Last remaining liquid | Top riser and upper flange | Side riser |
| Macro-shrinkage in casting | Not observed | Not observed |
| Microporosity risk in functional area | Low | Very low |
| Riser removal cost | High | Low |
7. Discussion
The results of my simulation demonstrate a general principle for lost foam castings: the solidification pattern is controlled not only by the geometry of the casting but also by the arrangement of feeders and chills. A top riser can feed a cylindrical steel casting, but it may be inconvenient from the point of view of production. A side riser with a spherical shape and an appropriately placed chill can achieve the same or better casting soundness while lowering the amount of post-casting work. The reason is that the direction of solidification is more explicit: the chill cools the inner surface, the side riser remains hot, and the solidification front advances from the chill toward the riser. In this way, the feeding path is never blocked by an earlier solidified region.
I also compared the cooling time and gradient. The improved process used a spherical side riser because its modulus is equal to D divided by 6. For a cylindrical riser with the same diameter and a length of twice the diameter, the modulus is smaller than that of a sphere of the same diameter. Therefore, a spherical side riser can feed a larger volume of liquid for the same amount of metal. This is particularly important in lost foam castings because any metal above the minimum required for feeding represents unnecessary labour and material. The use of a spherical riser also reduces the surface area through which heat can escape, so the liquid remains hot for a longer time. The simulations confirmed that the side riser remained the last region to solidify in the improved process.
The chill played a key role in the improved process. Without the chill, the hot spot in a thick-walled cylindrical casting may be located at the geometrical centre of the wall. With the chill, I forced the hottest point to move away from the central region. The chill was placed on the internal cylindrical surface because this surface is not a critical machined surface in some portions of the tail roller. The chill must not leave a hard spot or an unacceptable metallurgical condition on the final component. Therefore, I selected a chill thickness that was large enough to alter the cooling rate but not so large that it caused a sharp discontinuity in the casting structure. In my design, the chill thickness was about 20 to 30 millimetres, and the chill was covered with a refractory coating before being embedded in the sand. This practice is common in lost foam castings and reduces the risk of blowholes caused by surface moisture or gases from the chill.
Another important observation is that the total solidification time of the improved process is longer than that of the original process. This may seem counterintuitive because the chill should accelerate cooling. However, the time of complete solidification includes the side riser itself. The side riser was intentionally designed to solidify after the casting, so the total freezing time of the entire assembly is longer. The casting body, however, solidifies earlier than in the original process because the chill increases the thermal gradient. Thus, the longer total time is not a problem. In fact, it is a sign that the riser is large enough to feed the casting. If the riser were too small, it would freeze too early and shrinkage would form in the casting. I therefore recommend judging the process from the shape of the solidification sequence rather than from the total solidification time alone.
8. Practical Recommendations for Production
Based on my simulation and optimization of this tail roller, I can offer several practical recommendations for producing sound lost foam castings in steel. These recommendations are summarized in Table 5. First, the EPS foam pattern should have a low density, about 16 to 20 kg per cubic metre, to minimize gas generation. Second, the refractory coating must be thick enough to resist liquid metal erosion but permeable enough to allow gas evacuation. Third, the sand should be dry and free of fines, and the vibration time should be long enough to produce a rigid mould. Fourth, the negative pressure should be maintained between 0.03 and 0.06 MPa during pouring. Fifth, the pouring temperature should be controlled in the range of 1,550 to 1,600 °C for ZG30Mn2. Sixth, the pouring time should be around 21 seconds, as used in my simulation. Seventh, a spherical side riser should be preferred over a long top riser whenever the geometry allows it. Eighth, a chill should be placed on the inner surface to create directional solidification. Ninth, the riser neck should be designed with a modulus slightly smaller than the riser but larger than the hot spot, so that it remains open until the casting has solidified. Finally, the entire system should be checked with solidification simulation before the production tools are made.
| Process parameter | Recommended value or range |
|---|---|
| Pattern material | EPS foam, density 16–20 kg/m³ |
| Coating thickness | 0.2–0.4 mm |
| Coating drying temperature | 40–50 °C, air flow |
| Mould sand | Dry silica sand, AFS 30–50 |
| Vibration time | 60–90 s |
| Vacuum pressure | 0.03–0.06 MPa |
| Pouring temperature | 1,550–1,600 °C |
| Pouring time | 20–22 s |
| Riser type | Spherical side riser with short neck |
| Chill material | Grey iron, 20–30 mm thick |
| Chill position | Inner cylindrical surface of the tail roller |
| Inspection method | Ultrasonic testing and Niyama-criterion post-processing |
I would like to emphasize that the success of lost foam castings depends heavily on the repeatability of the pattern-making step. The foam pattern must be cut with sufficient accuracy, and the joints between the foam parts must be smooth and strong. The side riser in the improved process can be bonded to the main pattern with a smaller contact area than the top riser, which reduces the risk of deformation. The chill must be fixed securely to the pattern or placed in the mould before vibration, otherwise it may move during compaction. I used a thin layer of adhesive to attach the chill to the foam pattern in my proposed procedure. The coating must also cover the chill surface to avoid a reaction between the liquid steel and the chill surface. If this procedure is followed, the improved lost foam castings process can be transferred to mass production with high reliability.
9. Conclusions
In this article, I have presented a detailed solidification simulation and process optimization of a tail roller produced by lost foam castings. The following conclusions can be drawn from my work. First, the original top-riser process produced a casting without harmful shrinkage cavities, but the top riser increased the cleaning work and made pattern assembly more difficult. Second, by replacing the top riser with an approximately spherical side riser and placing a chill on the inner cylindrical surface, I was able to create a more favourable directional solidification sequence. Third, the improved process keeps the last liquid in the side riser, which is ideal for feeding the casting. Fourth, the simulation results show that the improved process has very low porosity risk in the functional area of the tail roller. Fifth, the improved process is more suitable for mass production because it simplifies the pattern assembly and the riser removal. Sixth, the combination of a spherical side riser and a chill can be recommended for similar cylindrical steel lost foam castings. I also verified that the solidification modulus, Chvorinov’s rule, and the Niyama criterion provide a reliable theoretical basis for riser and chill design. The use of numerical simulation is therefore essential to ensure the soundness and economy of lost foam castings.
The most important lesson from this study is that the geometry of the riser should be adapted to the actual production constraints, not only to the feeding calculation. The side riser is easier to integrate into an automated lost foam castings line, and the chill can be applied without affecting the final dimensions of the casting. The simulation gave me confidence that the improved process is both technically and economically superior. In future work, I plan to include the mould-filling stage and the gas-pressure evolution during foam decomposition to refine the thermal boundary conditions. I also intend to perform experimental pouring trials to validate the simulated porosity distribution. However, the current simulation already demonstrates that lost foam castings can be successfully produced for thick-walled steel parts such as tail rollers by using an optimized side-riser and chill system.