Large steel casting production has long been a critical challenge in the manufacturing industry due to the high tendency for defects such as shrinkage porosity, shrinkage cavities, hot tearing, gas entrapment, and sand inclusion. The quality control of these massive components is notoriously difficult because the solidification and filling processes are hidden from direct observation and cannot be easily verified through trial-and-error approaches. This is especially true for large steel casting components used in heavy machinery, where failure is not an option. This study, derived from a major national science and technology project, focuses on the front beam of a 20,000-ton horizontal extruder for hard-to-deform alloys. The front beam is a key load-bearing component, weighing 365 tons, making it a perfect case study for developing a comprehensive numerical simulation protocol for large steel casting processes.
The fundamental challenge in large steel casting lies in the fact that the casting process involves multiple, coupled physical phenomena, including heat transfer, fluid flow, and solid mechanics. The high pouring temperatures, large thermal gradients, and significant section thickness variations in large steel casting components create ideal conditions for defect formation. In this work, I employed the finite element method (FEM) using the ProCAST software, a leading tool in the field of casting simulation. The core objective was to analyze the formation mechanisms of shrinkage and hot tearing defects in a large steel casting and to develop an optimized process design that eliminates these defects, thereby ensuring the structural integrity and reliability of the final product. By conducting a thorough numerical analysis of the temperature field, flow field, and stress field during the casting of the extruder front beam, I aimed not only to solve the specific problem at hand but also to establish a robust, generalizable methodology for numerical simulation that can be applied to other large steel casting projects, thereby reducing design cycles and production costs.
1. Solidification Process and Temperature Field Analysis of the Front Beam
The solidification of a large steel casting is governed by the complex interplay of heat conduction, convection, and radiation. The accuracy of the temperature field simulation is the cornerstone of predicting shrinkage defects, as it directly determines the location of hot spots (isolated liquid regions) and the feeding efficiency of risers. In my analysis, the Fourier heat conduction equation serves as the foundation for the thermal model, while the latent heat released during phase transformation is carefully considered using the enthalpy method.
For a 3D Cartesian coordinate system, the governing equation for heat conduction during solidification is given by:
$$ \rho c_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( k \frac{\partial T}{\partial x} \right) + \frac{\partial}{\partial y} \left( k \frac{\partial T}{\partial y} \right) + \frac{\partial}{\partial z} \left( k \frac{\partial T}{\partial z} \right) + Q $$
where \( \rho \) is the density (\( kg/m^3 \)), \( c_p \) is the specific heat capacity (\( J/(kg \cdot K) \)), \( T \) is the temperature (°C), \( t \) is the time (s), \( k \) is the thermal conductivity (\( W/(m \cdot K) \)), and \( Q \) is the latent heat source term. The treatment of boundary conditions is critical for accurate prediction. In the simulation of this large steel casting, I defined three main types of heat transfer boundaries:
- Conduction: At the casting-mold interface, which is described by the Fourier law: \( q = -k \frac{\partial T}{\partial n} \). Since the casting and mold are different materials, ‘COINC’ interface conditions were used, allowing for a temperature drop across the interface by defining an interface heat transfer coefficient (HTC).
- Convection: Heat transfer from the external mold surface to the ambient air, described by Newton’s law of cooling: \( q = h_c (T_f – T_w) \). Here, \( h_c \) stands for the convective heat transfer coefficient, \( T_f \) represents the fluid temperature, and \( T_w \) denotes the wall temperature.
- Radiation: Heat transfer from the exposed surfaces of the casting, particularly within open risers, to the surroundings, which follows the Stefan-Boltzmann law: \( q = \epsilon \sigma_0 T_s^4 \). In this equation, \( \sigma_0 \) is the Stefan-Boltzmann constant, \( \epsilon \) represents the surface emissivity, and \( T_s \) stands for the absolute surface temperature.
Given the massive size of the component, the front beam was simulated using a quarter model to save computational resources while maintaining high precision. The casting material selected for this large steel casting is ZG230-450, a carbon steel widely used for heavy machinery due to its excellent weldability and machinability. The material’s thermodynamic properties were calculated using ProCAST’s thermodynamic database, considering its specific chemical composition.
| Element | C | Si | Mn | P | S |
|---|---|---|---|---|---|
| Content | ≤0.20 | ≤0.50 | ≤1.20 | ≤0.04 | ≤0.04 |
The mechanical properties of the material at room temperature provide a baseline for evaluating the stress field later. The yield strength is 230 MPa, the tensile strength is 450 MPa, and the elongation is 22%. The liquidus temperature is calculated to be 1498°C and the solidus temperature is 1435°C. For the thermal analysis, the initial temperature of the molten metal was set to 1580°C.
1.1 Prediction of Shrinkage Defects in the Steel Casting
Shrinkage porosity and cavities are among the most severe defects in large steel casting. They form when the volumetric contraction during solidification cannot be compensated by the remaining liquid metal. The key to preventing these defects is to ensure a proper solidification sequence, ideally directional solidification towards the risers. In my research, I employed three distinct methodologies to predict the location and severity of shrinkage defects within the steel casting.
The first method is the critical solid fraction criterion. This approach assumes that when the solid fraction of a region exceeds a critical value, the flow of liquid metal becomes impossible, isolating that region. The defect forms if an isolated liquid island is found. For steel casting, the critical solid fraction is typically set to 0.7. The second method is the temperature gradient method. It posits that a small temperature gradient in the late stages of solidification increases the likelihood of dispersed micro-porosity. The third, and most widely used, is the Niyama criterion. The Niyama criterion calculates the ratio of the local temperature gradient \( G \) to the cooling rate \( R \), expressed as \( \frac{G}{\sqrt{R}} \). A low value indicates a high risk of micro-porosity.
$$ Niyama = \frac{G}{\sqrt{R}} $$
For large steel casting, the critical threshold for this criterion is typically taken as 1.1. Initially, I performed a simulation of the casting without any risers to identify the natural hot spots and to guide the initial riser design. The results showed that the large thick sections in the middle of the casting and the side vertical plates contained isolated liquid regions at later stages of solidification, indicating a high risk of shrinkage defects.
Based on the hot spot analysis, I divided the casting into four equilibrium sections and designed risers for each section. The initial design used sand risers for the main thick sections and smaller blind risers for the vertical plates.
| Component | Riser Type | Dimensions (mm) | Weight (kg) | Number of Risers |
|---|---|---|---|---|
| Main Thick Sections | Cylindrical Open Riser | D=2400, H=2400 | 91,096 | 2 |
| Vertical Side Plates | Oblong Blind Riser | B=600, L=H=900 | 2,877 | 6 |
The initial simulation of this large steel casting with sand risers revealed two critical issues. First, the chilling effect of the blind risers was insufficient for the vertical side plates, leading to isolated liquid phases forming within the casting body itself. Second, the use of ordinary sand risers resulted in poor feeding efficiency (around 14%), requiring excessively large riser dimensions and lowering the overall process yield. To address these issues, I modified the casting process by incorporating insulating and exothermic riser sleeves, adding padding (feeding aids), and incorporating external chills.
| Feature | Initial Process | Optimized Process |
|---|---|---|
| Open Riser Type | Sand | Exothermic & Insulating Sleeve |
| Open Riser Dimensions | D=2400mm, H=2400mm | D=1835mm, H=2202mm |
| Blind Riser Type | Sand | Insulating Sleeve (70mm) |
| Blind Riser Dimensions | B=600mm, L=H=900mm | B=700mm, L=H=1050mm |
| Feeding Aids (Padding) | None | Added to vertical plates |
| External Chills | None | 8 chills per side of vertical plate |
The solidification sequence of the optimized process was drastically improved. The temperature distribution in the casting, monitored at several key points (as shown in the cooling curves, Figure 2-15a), demonstrated that the vertical plates now cool faster at the bottom due to the chills, and the top sections remain hot due to the insulating risers. This established a smooth temperature gradient from the bottom to the top of the casting body, effectively directing solidification towards the risers. The isolated liquid regions were entirely contained within the riser system. The Niyama criterion prediction for the optimized process confirmed that the shrinkage porosity was absent from the casting body and confined to the risers, thus validating the design and ensuring the integrity of the large steel casting.
| Parameter | Initial Process | Optimized Process |
|---|---|---|
| Total Metal Weight (t) | 610.5 | 523.9 |
| Process Yield (%) | 59.79% | 69.67% |
| Casting Quality | Defects Present | Sound, No Defects |
2. Mold Filling Process and Flow Field Analysis
The filling of the mold cavity is a critical stage for large steel casting, often determining the presence of surface and internal defects. Improper gating system design can lead to turbulent flow, air entrapment, mold erosion, and oxide film formation. For the extruder front beam, a stepped gating system is required to ensure that the molten metal enters the mold cavity progressively from the bottom up. This minimizes the risk of splashing and allows for smooth, sequential filling. The design of such a system for a large steel casting relies heavily on fluid dynamics principles.
The fundamental governing equations for the incompressible, viscous flow of molten metal are the continuity equation and the Navier-Stokes equations. These are solved numerically to predict the flow patterns within the casting. The continuity equation for incompressible flow is:
$$ \frac{\partial u_x}{\partial x} + \frac{\partial u_y}{\partial y} + \frac{\partial u_z}{\partial z} = 0 $$
where \( u_x, u_y, u_z \) are the velocity components in the x, y, and z directions, respectively. The N-S equations in the three coordinate directions are solved to obtain the momentum distribution. For example, the equation in the x-direction is:
$$ \rho \left( \frac{\partial u_x}{\partial t} + u_x \frac{\partial u_x}{\partial x} + u_y \frac{\partial u_x}{\partial y} + u_z \frac{\partial u_x}{\partial z} \right) = \rho g_x – \frac{\partial p}{\partial x} + \mu \left( \frac{\partial^2 u_x}{\partial x^2} + \frac{\partial^2 u_x}{\partial y^2} + \frac{\partial^2 u_x}{\partial z^2} \right) $$
where \( p \) is the pressure, \( \mu \) is the dynamic viscosity, and \( g_x \) is the gravitational acceleration component. These equations were solved by the ProCAST solver to simulate the filling process, providing critical insights into velocity fields, free surface behavior, and potential for defects in this large steel casting.
2.1 Design and Analysis of a Stepped Gating System
Based on the casting weight of 523.9 tons and the requirement to pour the metal using multiple ladles, the total pouring time was designed. Each ladle had a nozzle with a diameter of 100 mm and a flow rate of 190 kg/s. With four ladles pouring simultaneously, the total pouring time \( t \) was calculated. The gating system was designed as an open system, where the total cross-sectional area increases from the sprue to the ingates to prevent aspiration. The critical aspect of a stepped gating system is the ‘inversion’ or ‘turbulent mixing’ of flow from different layers, often leading to defects. We simulated the initial design and identified the phenomenon of random pouring (乱引). This occurs when the effective pressure head of the molten steel is so high that the liquid flows into the mold from multiple layers of the sprue simultaneously, causing splashing and oxidation. The initial simulation showed velocities as high as 5 m/s in the runners, and the flow pattern was chaotic.
| Component | Initial Diameter (mm) | Optimized Diameter (mm) |
|---|---|---|
| Main Sprue | 140 | 140 |
| Runner | 140 | 140 |
| Ingates (1st level) | 100 | 100 |
| Ingates (2nd & 3rd level) | 100 | 120 |
To mitigate the turbulent filling, I implemented a multi-faceted optimization strategy. First, the connection runner to the auxiliary sprue was repositioned to be at the same height as the first level of ingates. This change significantly reduced the static pressure head in the auxiliary sprue, preventing premature flow through the upper ingates. This design change was validated by comparing the hydraulic pressure in the two designs. By applying Bernoulli’s principle, we can calculate the effective pressure head difference. For the initial design, the pressure loss in the auxiliary sprue is less than in the optimized design. This means the pressure head at the upper inlets is smaller in the optimized design, which helps prevent the flow from entering the mold cavity too early.
Second, the flow rate from the ladles was controlled during the initial pouring stage. The pouring began at a lower flow rate and increased to the maximum rate after a short period. This soft start minimizes the impact velocity and prevents the initial jet of metal from splashing in the sprue well. Third, the cross-section of the upper ingates was enlarged to ensure that once the metal level reached them, they could handle the required flow smoothly without building up excessive back-pressure in the sprue.
The simulation results for the optimized gating system showed a dramatic improvement. The maximum velocity of the molten metal within the mold cavity was reduced to a safe 2.8 m/s. The flow front was much more stable, and the liquid level rose evenly. The phenomenon of random pouring was eliminated. The metal entered the mold cavity strictly through the first level ingates initially, and only began to flow from the second level when the metal level rose to cover the first level, and similarly for the third level. This sequential, layer-by-layer filling pattern is ideal for large steel casting, promoting the upward and directional solidification, and effectively avoiding the violent mixing and oxidation that leads to inclusions and gas pores.
3. Stress Field Analysis of the Solidifying Steel Casting
The formation of hot tears and residual stresses is a major cause of rejection in large steel casting. These defects develop during the solidification and subsequent cooling of the casting as a result of thermal gradients, differential contraction rates, and the restraining forces from the mold and cores. To predict these critical defects, I performed a stress field analysis using a thermal-elastic-plastic model. This model considers the material’s elastic behavior up to the yield point, followed by plastic flow, with all material properties (such as Young’s modulus, thermal expansion coefficient, and yield strength) being temperature-dependent.
The total strain increment \( d\{\varepsilon\} \) is composed of three parts: the elastic strain increment \( d\{\varepsilon_e\} \), the plastic strain increment \( d\{\varepsilon_p\} \), and the thermal strain increment \( d\{\varepsilon_T\} \):
$$ d\{\varepsilon\} = d\{\varepsilon_e\} + d\{\varepsilon_p\} + d\{\varepsilon_T\} $$
The stress-strain relationship is then given by:
$$ d\{\sigma\} = [D_{ep}] (d\{\varepsilon\} – d\{\varepsilon_T\}) $$
where \( [D_{ep}] \) is the elastic-plastic matrix. The thermal strain increment is calculated based on the current thermal expansion coefficient \( \alpha \) and the temperature change:
$$ d\{\varepsilon_T\} = \alpha dT + \frac{\partial \alpha}{\partial T} dT (T – T_0) $$
Before applying this to the complex geometry of the front beam, I first performed a highly illustrative parametric study on a simple stress frame specimen with a shape similar to a cross-section of the front beam. The study aimed to quantify how different process parameters influence hot tearing. The stress frame, which has a thick bar and a thin bar connected by a cross member, was simulated to investigate the stress distribution and deformation.
| Variable Variation | Max Equivalent Stress (MPa) | Hot Tearing (%) | Max Deformation (cm) |
|---|---|---|---|
| Clay-Sand Mold | 401.3 | 0.040 | 0.151 |
| Sodium Silicate-Sand Mold | 337.2 | 0.034 | 0.145 |
| No Fillets (Sand Mold) | 337.2 | 0.034 | 0.145 |
| With Fillets R5/R15 | 318.6 | 0.032 | 0.129 |
| Sand Mold + 2 Chills | N/A | 0.021 | N/A |
The study revealed that the mold material plays a significant role. Sodium silicate sand has a higher thermal diffusivity but a better high-temperature collapsibility than clay sand, reducing the resistance to casting contraction and lowering the stress. The results showed that adding fillets at the junctions of the bars significantly reduced the stress concentration and hence the hot tearing susceptibility. The addition of chills accelerated the cooling of specific areas, strengthening them and reducing the hot tears.
The initial simulation of the large steel casting front beam with clay sand showed high equivalent stress regions, exceeding the 230 MPa yield limit, at the junctions between the casting and the gating system, around the tension holes (through-holes), and at sharp corners. This prediction aligned perfectly with the hot tearing criterion, which states that hot tearing occurs when the local equivalent stress exceeds the material’s yield strength in the mushy zone. The simulation of hot tearing distribution highlighted these exact locations as high-risk areas.
Based on the lessons learned from the stress frame experiment, I optimized the casting design to minimize stress in the large steel casting. The key changes were implemented to reduce mechanical restraint and improve stress distribution. The main modifications are detailed below:
| Parameter | Initial Plan | Optimized Plan |
|---|---|---|
| Molding Sand | Clay Sand | Sodium Silicate Sand |
| Core Sand | Clay Sand Core | Ester-cured Sodium Silicate |
| Casting Fillet Radius | 30 mm | 50 mm |
| Fillets at Gating contact | None | 10 mm radius |
| Shakeout Temperature | 400°C | 550°C |
| Pouring Temperature | 1580°C | 1550°C |
By changing the mold material to one with better high-temperature collapsibility, the restraint on the solidifying casting was greatly reduced. Increasing the fillet radius reduced the stress concentration at the corners. Raising the shakeout temperature allowed for a more gradual cooling process, reducing the thermal gradient and the associated residual stress build-up. I also specified the use of anti-seepage coatings on the mold and core surfaces, which reduces the friction between the casting and the mold, further lowering the risk of hot tearing in the large steel casting.
The stress field simulation results for the optimized plan were highly encouraging. The equivalent stress throughout the casting body remained below the yield limit of 230 MPa at all critical sections, including the tension holes and the other corner features. The hot tearing prediction for the optimized plan showed no tearing defects within the casting body. This confirmed that the process optimization was successful in mitigating the risk of hot tearing and excessive deformation in the large steel casting.
The deformation analysis of the optimized process showed a maximum deformation of approximately 44 mm, which is acceptable for a large steel casting of this size. The deformed state prediction is crucial in large steel casting as it helps engineers design the mold with a pre-deformation compensation (also known as ‘spring back’ compensation) to ensure the final machined and cast dimensions are within tolerance.
Conclusion
This comprehensive study, centered on the numerical simulation of the large steel casting front beam, successfully developed and validated a robust protocol for process optimization. The work systematically addressed the most common and severe defects in large steel casting production. Through the detailed analysis presented, several key conclusions and practical contributions were made:
The research confirmed that the ProCAST software suite is an excellent tool for predicting defects in large steel casting. The combined use of three prediction methods—namely the critical solid fraction, temperature gradient, and Niyama criterion—provided a comprehensive and accurate method for identifying shrinkage defects in the initial design. It was determined that for this specific large steel casting, the use of exothermic and insulating sleeves on risers is highly effective. The implementation of these sleeves led to a significant reduction in riser dimensions, which in turn increased the casting yield from approximately 60% to about 70% while successfully eliminating shrinkage porosity and cavities. The study of the filling process highlighted the dangers of turbulent flow in a stepped gating system for a large steel casting. The optimization of this critical system, achieved by repositioning the connecting runner and adjusting the inner gate cross-sections, successfully eliminated the chaotic ‘random pouring’ phenomenon. The optimized gating system enabled smooth, sequential filling, reducing the risk of gas entrapment and metal oxidation.
The investigation of the stress field revealed that using a mold material with better high-temperature collapsibility, such as sodium silicate sand, significantly reduces the restraint on the solidifying casting, thereby reducing the risk of hot tearing. It was also demonstrated that simple structural modifications, like increasing the radius of fillets, are powerful tools in reducing stress concentrations and preventing hot cracks. The combination of these process adjustments completely eliminated the risk of hot tearing in the casting body and kept deformation within acceptable limits.
Ultimately, this thesis provides a practical and effective example of how numerical simulation can be utilized to solve real-world manufacturing problems in the casting industry. It successfully transformed a trial-and-error approach into a scientific, predictable process. The developed methodology and the insights gained from this study offer valuable design references for future large steel casting production, contributing to shorter lead times, lower development costs, and higher quality, more reliable products.