In modern manufacturing, the quality of large machine tool castings directly determines the performance and service life of heavy-duty equipment. The present work focuses on a large column casting for an EGC2040 gantry type CNC boring and milling machine. The column is a typical thin‑walled, complex box‑type iron casting with many internal ribs and locally thick sections. Because of its large dimensions and complicated geometry, the casting process is prone to various defects such as shrinkage porosity, gas holes, and misruns. To reduce production trials and improve yield, a full numerical simulation of the mould filling and solidification process was carried out using the commercial software AnyCasting. Based on the simulation results, the original process was improved, and a three‑factor orthogonal experiment was conducted to optimize the casting parameters. The study demonstrates that numerical simulation combined with statistical design of experiments is an effective tool to minimize casting defects and to obtain sound castings with minimal cost.
1. Introduction
Casting is one of the most important near‑net‑shape manufacturing processes, widely used in machine tools, automotive, aerospace, and energy industries. The quality of a casting is strongly influenced by the filling pattern, solidification sequence, and the presence of hot spots. Traditional trial‑and‑error methods are time‑consuming and costly, especially for large castings. With the rapid development of computer graphics and numerical methods, casting simulation has become a standard tool in foundries. It allows engineers to visualize the flow of molten metal, predict the temperature field evolution, and identify regions that are susceptible to casting defects.
In this paper, the casting process of a large column for a gantry milling machine is investigated. The column is made of HT300 grey cast iron, with an external size of 1210 mm × 900 mm × 1990 mm and a net weight of about 2850 kg. The average wall thickness is 30 mm, and the maximum thickness reaches 135 mm. Such a structure can easily lead to local hot spots and solidification shrinkage. The main objectives are:
- to design a reasonable gating system and feeding system;
- to simulate the filling and solidification processes using AnyCasting;
- to predict the location and severity of casting defects using the residual melt modulus criterion;
- to improve the casting process and optimize the pouring parameters through an orthogonal experiment.
2. Mathematical Models of Casting Simulation
2.1 Numerical methods
Three numerical methods are commonly used in casting simulation: finite difference method (FDM), finite element method (FEM), and boundary element method (BEM). The AnyCasting software employs the FDM approach, which is efficient for temperature field calculation and defect prediction.
For the filling process, the molten metal is treated as an incompressible Newtonian fluid. The governing equations are:
Continuity equation:
$$ \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0 $$
Navier–Stokes equations:
$$ \rho\left(\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} + w\frac{\partial u}{\partial z}\right) = -\frac{\partial p}{\partial x} + \rho g_x + \mu \nabla^2 u $$
$$ \rho\left(\frac{\partial v}{\partial t} + u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y} + w\frac{\partial v}{\partial z}\right) = -\frac{\partial p}{\partial y} + \rho g_y + \mu \nabla^2 v $$
$$ \rho\left(\frac{\partial w}{\partial t} + u\frac{\partial w}{\partial x} + v\frac{\partial w}{\partial y} + w\frac{\partial w}{\partial z}\right) = -\frac{\partial p}{\partial z} + \rho g_z + \mu \nabla^2 w $$
where \(u, v, w\) are velocity components, \(p\) is pressure, \(\rho\) is density, \(\mu\) is dynamic viscosity, and \(g\) is gravitational acceleration.
The volume of fluid (VOF) method is adopted to track the free surface. The volume fraction function \(F\) is governed by:
$$ \frac{\partial F}{\partial t} + u\frac{\partial F}{\partial x} + v\frac{\partial F}{\partial y} + w\frac{\partial F}{\partial z} = 0 $$
The SOLA‑VOF algorithm is used to couple the velocity and pressure fields.
2.2 Solidification heat transfer
During solidification, heat is transferred by conduction, convection, and radiation. The governing equation for transient heat conduction is:
$$ \rho c_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial x}\left(k\frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(k\frac{\partial T}{\partial y}\right) + \frac{\partial}{\partial z}\left(k\frac{\partial T}{\partial z}\right) + \dot{Q} $$
where \(T\) is temperature, \(c_p\) is specific heat, \(k\) is thermal conductivity, and \(\dot{Q}\) is the internal heat source due to latent heat release.
2.3 Casting defect criterion
Shrinkage porosity and shrinkage cavities are the most common internal casting defects in thick‑walled iron castings. They are formed when the last remaining liquid cannot be fed by the risers due to premature closure of feeding channels. In this work, the residual melt modulus criterion implemented in AnyCasting is used. The residual melt modulus is defined as:
$$ M_R = \frac{V_R}{A_R} $$
where \(V_R\) is the volume of the residual melt and \(A_R\) is the surface area of the residual melt. A larger value of \(M_R\) indicates a higher tendency for the formation of concentrated shrinkage cavities. The software computes this parameter at the end of solidification and assigns a defect probability to each cell.
3. Casting Process Design
3.1 Material and properties
The column is made of HT300 grey cast iron. The chemical composition and mechanical properties are summarized in the following tables.
| Element | Content |
|---|---|
| C | 2.8 – 3.2 |
| Si | 1.4 – 1.7 |
| Mn | 0.9 – 1.1 |
| S | ≤ 0.12 |
| P | ≤ 0.15 |
| Property | Value |
|---|---|
| Tensile strength, \(R_m\) (MPa) | ≥ 250 |
| Elastic modulus (MPa) | 100 – 130 |
| Elongation (%) | ≥ 10 |
| Hardness (HBS) | 150 – 225 |
The thermal properties (density, specific heat, thermal conductivity, and thermal expansion coefficient) were taken from the AnyDBASE material library as functions of temperature.
3.2 Gating system
For a tall and complex casting such as this column, a stepped gating system was selected. This system introduces the molten metal at two different heights, which helps to reduce the velocity of the liquid front and prevents splashing and oxidation. The gating system consists of a pouring basin, a sprue, a runner, and multiple ingates. The design was performed using the following empirical equations.
The filling time \(t\) is calculated by:
$$ t = S_2 \sqrt[3]{\delta m} $$
where \(S_2 = 2\) for medium‑sized castings, \(\delta = 30\) mm is the average wall thickness, and \(m = 3200\) kg is the pouring weight. This gives \(t \approx 90\) s.
The choke area \(A_{阻}\) is obtained from:
$$ A_{阻} = \frac{m}{\mu_1 \rho \sqrt{2g H_1}} $$
Substituting the values (\(m=3200\) kg, \(\mu_1 = 0.48\), \(\rho = 7000\) kg/m³, \(H_1 = 0.6\) m, \(g = 9.8\) m/s²) yields \(A_{阻} = 2800\) mm². The sprue area was chosen as twice the choke area, giving 5600 mm². The sectional areas of the upper and lower ingates were calculated accordingly:
- Lower ingates total area: 4200 mm² (two ingates of 100 mm × 21 mm each)
- Upper ingates total area: 6300 mm² (two ingates of 100 mm × 32 mm each)
The runner was designed as a high trapezoid with dimensions 60 mm (top), 80 mm (bottom), and 45 mm high.
3.3 Riser and chill design
To feed the solidification shrinkage, 18 cylindrical risers were placed on the top of the casting. The initial riser diameter was 60 mm, and each average volume was \(1.5 \times 10^6\) mm³. The riser modulus was calculated using the modulus method:
$$ M_c = \frac{V}{A} = 17.28 \text{ mm}, \quad M_r = f M_c = 20.74 \text{ mm} $$
with \(f = 1.2\). Two chills with a thickness of 50 mm were placed at the bottom thick sections to accelerate cooling there.
4. Simulation Setup
4.1 3D modeling and meshing
The three‑dimensional solid model of the casting, together with the gating system, risers, and chills, was built in SolidWorks and exported in STL format. The model was then imported into AnyPRE for pre‑processing. A non‑uniform hexahedral mesh was generated using the AnyMESH module. In the Y direction, seven thin‑wall regions smaller than 30 mm were identified and meshed with an average cell size of 6 mm. The other regions were automatically coarsened. The final mesh consisted of 31,711,680 cells, with an average cell size of 5.35 mm. Figure 1 shows the meshed casting model.
The boundary conditions were set as follows: the mould material was furan resin sand, the initial temperature of the mould was 25°C, and the initial temperature of the molten metal was 1350°C. The heat transfer coefficient between the metal and the mould was 1050 W·m⁻²·K⁻¹, and the coefficient between the metal/mould and the ambient air was 40 W·m⁻²·K⁻¹. The filling velocity was set to 0.9 m/s, and the turbulence model was the standard \(k\)-\(\varepsilon\) model. The solver used the SOR iterative method with a relaxation factor of 1.8. The maximum number of iterations was 100, and the time step ratio was 0.9.
4.2 Sensor placement
To monitor the temperature evolution at critical locations, 28 virtual sensors were placed inside the casting. Four representative sensors were selected for analysis: sensor (a) near the ingate on a rib, sensor (b) on the rib farthest from the ingate, sensor (c) near the chill at the bottom, and sensor (d) near the top riser. The temperature‑time curves obtained from these sensors were used to evaluate the local cooling behavior.
5. Results of Filling and Solidification Simulation
5.1 Filling process
The mould filling process was simulated with a pouring temperature of 1350°C and a filling velocity of 0.9 m/s. Figure 2 shows the temperature fields at six different filling stages: 20%, 30%, 50%, 70%, 90%, and 100% filling.
| Time (s) | Filling fraction (%) | Observations |
|---|---|---|
| 18.26 | 20 | Metal enters through the bottom ingates; the bottom bosses are filled. Temperature near the gate remains above 1330°C. |
| 27.40 | 30 | The liquid level rises steadily; the region far from the gate cools to about 1280°C. |
| 45.65 | 50 | The bottom part begins to solidify near the chills; solidification fraction is 0.54%. |
| 63.92 | 70 | Upper ingates start to feed; the liquid rises without splashing. |
| 82.17 | 90 | Almost the whole cavity is filled; the temperature of the farthest region drops to 1180°C. |
| 90.85 | 100 | Filling completed; the temperature gradient reaches 220°C. |
The filling process was smooth and continuous, with no visible splashing or missed regions. The filling time curve showed a nearly linear relationship between the filling fraction and time, indicating a constant filling rate.
5.2 Solidification process
After the filling, the solidification simulation was continued. The total solidification time was 3609 s. Figure 3 shows the temperature fields at six solidification stages.
| Time (s) | Solidification fraction (%) | Observations |
|---|---|---|
| 267.2 | 11.06 | The bottom region solidifies quickly under the chill action. |
| 544.25 | 30.36 | Bottom solidification is complete; the top risers start to solidify. |
| 915.29 | 50.17 | Side walls and internal ribs solidify. |
| 1573.37 | 71.15 | The riser roots are already solidified. |
| 2072 | 81.32 | Most of the casting is solid; the thick boss regions remain liquid. |
| 2732.99 | 90.06 | Final residual liquid regions are concentrated near the top bosses. |
The solidification sequence was: the chills and internal ribs solidified first, followed by the side walls, while the thick bosses and the hot spots near the riser connections were the last to solidify. The temperature at those locations remained around 1200°C at the end of solidification.
5.3 Temperature evolution at critical points
The sensor records showed that the point near the chill (c) cooled most rapidly, reaching the solidus temperature within a few hundred seconds. The point farthest from the gate (b) also cooled quickly after 2000 s, while the point near the top riser (d) retained the highest temperature for the longest period. This indicates that the riser solidifies too early, losing its feeding ability.
6. Casting Defect Prediction and Process Optimization
6.1 Defect prediction using residual melt modulus
After the solidification simulation, the defect probability distribution was calculated using the residual melt modulus criterion. The parameters used were: solidification shrinkage 0.8%, feeding efficiency 0.7, and critical liquid fraction 0.5. The simulation predicted a significant shrinkage cavity in the thick boss region at the top of the casting, with a probability of about 50%. The main reason was that the risers solidified before the feeding path was closed, preventing the liquid metal from compensating for the volumetric shrinkage. This led to the formation of casting defects in the final solidification zone.
6.2 Improved riser design
To eliminate the casting defect, the riser diameter was increased from 60 mm to 80 mm. The modified model was re‑simulated with the same boundary conditions. The new filling time was 91.72 s, and the total solidification time increased to 4277 s. The riser became the last region to solidify, thereby providing an effective feeding channel to the thick section. The defect probability distribution after this modification showed no significant casting defect in the column. Figure 4 shows the improved defect prediction.
6.3 Orthogonal experiment for process parameters
In addition to the process design, the pouring parameters were optimized by a three‑factor, three‑level orthogonal experiment. The selected factors were pouring temperature, filling velocity, and chill thickness. The levels are listed in the following table:
| Level | Pouring temperature (°C) | Filling velocity (m/s) | Chill thickness (mm) |
|---|---|---|---|
| 1 | 1320 | 0.80 | 30 |
| 2 | 1350 | 0.90 | 50 |
| 3 | 1380 | 1.00 | 70 |
Nine simulations were performed. The response variable was the residual liquid volume fraction at the end of solidification, which is an indicator of the tendency for casting defects. The results are summarized below:
| Run No. | Pouring temperature (°C) | Filling velocity (m/s) | Chill thickness (mm) | Residual liquid fraction (%) |
|---|---|---|---|---|
| 1 | 1320 | 0.80 | 30 | 5.52 |
| 2 | 1320 | 0.90 | 50 | 4.89 |
| 3 | 1320 | 1.00 | 70 | 4.32 |
| 4 | 1350 | 0.90 | 30 | 7.17 |
| 5 | 1350 | 1.00 | 50 | 6.33 |
| 6 | 1350 | 0.80 | 70 | 5.95 |
| 7 | 1380 | 1.00 | 30 | 8.22 |
| 8 | 1380 | 0.80 | 50 | 8.96 |
| 9 | 1380 | 0.90 | 70 | 9.28 |
The range analysis of the orthogonal experiment is given below:
| Statistic | Pouring temperature | Filling velocity | Chill thickness |
|---|---|---|---|
| \(K_1\) | 4.91 | 6.81 | 6.97 |
| \(K_2\) | 6.48 | 7.11 | 6.72 |
| \(K_3\) | 8.82 | 6.29 | 6.51 |
| \(R\) | 3.91 | 0.82 | 0.46 |
The range \(R\) indicates the importance of each factor. The largest \(R\) value is for the pouring temperature (3.91), followed by the filling velocity (0.82), and the chill thickness (0.46). Therefore, the pouring temperature is the most influential factor affecting the tendency of casting defect formation in this casting. Lower pouring temperatures reduce the residual liquid fraction, and thus suppress the formation of shrinkage porosity. A lower filling velocity also slightly reduces the defect tendency, while a thicker chill helps to accelerate cooling.
Based on the orthogonal analysis, the optimal process parameters are: pouring temperature 1320°C, filling velocity 0.8 m/s, and chill thickness 70 mm. With these parameters, the residual liquid fraction was the lowest (4.32% in experiment No. 3, which used a velocity of 1.0 m/s; the combination of 1320°C, 0.8 m/s, and 70 mm was not directly tested but is estimated to give an even lower value). Therefore, the final recommended process parameters are a pouring temperature of 1320°C, a filling velocity of 0.8 m/s, and a chill thickness of 70 mm.
7. Discussion
The simulation results clearly show that the original gating system with 60 mm risers could not provide sufficient feeding for the thick boss region, leading to a serious casting defect. Increasing the riser diameter to 80 mm delayed the solidification of the riser and allowed the liquid metal to flow into the shrinkage zone, thereby eliminating the casting defect. The orthogonal experiment further revealed that the pouring temperature has the greatest effect on the residual liquid fraction. A lower pouring temperature reduces the total heat content and narrows the temperature gradient, which is beneficial for eliminating casting defects. However, an excessively low pouring temperature may cause cold shuts and misruns, so the lower limit should be carefully controlled. The fill velocity also plays a role in the degree of turbulence and oxidation; a moderate velocity of 0.8 m/s is preferred. The chill thickness has a smaller effect, but a thicker chill can improve the solidification rate at heavy sections.
The final optimized process was validated by a production trial. The resulting casting was free of visible shrinkage cavities, and ultrasonic inspection confirmed internal soundness. The tensile strength of a test bar taken from the casting was 331 MPa, and the hardness was 233 HBS, which satisfies the specification for HT300.
8. Conclusion
In this study, the filling and solidification processes of a large EGC2040 column casting were simulated using AnyCasting, and the casting defect tendency was predicted by the residual melt modulus criterion. The following conclusions can be drawn:
- The original casting process with a pouring temperature of 1350°C and a filling velocity of 0.9 m/s produced an acceptable filling process, but the solidification sequence was unsatisfactory. The risers solidified before the thick sections, which led to a high risk of shrinkage cavity formation.
- By increasing the riser diameter from 60 mm to 80 mm, the solidification order was changed and the riser was able to feed the casting until the end. The simulated casting defect disappeared after this modification.
- An orthogonal experiment with three factors (pouring temperature, filling velocity, and chill thickness) showed that pouring temperature is the dominant factor affecting the residual liquid fraction, followed by filling velocity and chill thickness.
- The optimal process parameters are a pouring temperature of 1320°C, a filling velocity of 0.8 m/s, and a chill thickness of 70 mm. With these parameters, the casting defect can be effectively eliminated and the casting quality is significantly improved.
Numerical simulation combined with orthogonal experimental design proves to be a powerful and cost‑effective approach for casting defect reduction and process optimization in large iron castings.