The production of centrifugally cast composite rolls is a cornerstone of modern metallurgy, essential for the hot rolling of metals. This process fundamentally involves pouring a high-alloy steel melt into a rapidly rotating metallic mold—the cold mold or chill—to form a wear-resistant outer shell under centrifugal force. After this shell has completely solidified, the rotation is stopped, and a spheroidal graphite cast iron melt is statically poured into the core to achieve a metallurgical bond. The quality of this centrifugally formed outer layer is paramount, directly dictating the performance and service life of the final roll. Among various influencing factors, such as the G-factor (centrifugal gravity multiple), the wall thickness of the metallic mold stands out as a critical yet often empirically determined parameter. A faster solidification rate in the outer layer refines the microstructure, reduces segregation, and ultimately enhances mechanical properties like hardness and wear resistance. This study employs numerical simulation using ProCAST software to systematically investigate the relationship between the wall thickness of a grey cast iron cold mold and the solidification kinetics of the outer layer for three common roll alloys. The primary goal is to move beyond empirical rules and establish a theoretically and numerically informed optimal mold wall thickness.
Mathematical Modeling of the Solidification Process
To accurately simulate the transient thermal history during centrifugal casting, a robust mathematical model is required. Based on the specific characteristics of horizontal centrifugal pouring, the following assumptions are made to formulate the governing equations for heat transfer:
- Axisymmetric Radial Dominance: Given that the length of the roll barrel significantly exceeds its diameter (typically with an L/D ratio between 1:3 and 1:4), heat transfer is considered primarily radial. Heat loss from the two ends of the roll is negligible and thus treated as an adiabatic boundary condition.
- Uniform External Conditions: Due to high-speed rotation, the convective heat exchange at the outer surface of the grey cast iron mold is assumed uniform. Consequently, the temperature fields in both the mold and the solidifying shell are axisymmetric.
- Interfacial Contact Resistance: The powerful centrifugal force ensures intimate contact between the solidifying shell and the mold wall. The thermal resistance at this interface is modeled solely as the effect of the applied refractory coating.
- Initial Conditions: The pour is assumed to be instantaneous. Therefore, the initial temperature of the grey cast iron mold is its preheat temperature, and the initial temperature of the molten outer layer is its pouring temperature.
- Temperature-Dependent Properties & Latent Heat: The temperature-dependent thermophysical properties (density, specific heat, thermal conductivity) of all materials are considered. The latent heat of fusion for the outer layer alloy is treated using the enthalpy method or an equivalent specific heat method, where the latent heat is released according to a prescribed function (e.g., a quadratic relationship) between the liquidus and solidus temperatures.
Based on these assumptions, the governing partial differential equations for the two-dimensional, axisymmetric, transient heat conduction problem are established. For the mold domain (denoted by subscript ‘m’), the equation is:
$$
\rho_m c_m \frac{\partial T}{\partial t} = \frac{1}{r} \frac{\partial}{\partial r} \left( k_m r \frac{\partial T}{\partial r} \right) + \frac{\partial}{\partial z} \left( k_m \frac{\partial T}{\partial z} \right)
$$
For the solidifying outer layer domain (denoted by subscript ‘c’), which includes a source term for latent heat release, the equation is:
$$
\rho_c c_{c,eff} \frac{\partial T}{\partial t} = \frac{1}{r} \frac{\partial}{\partial r} \left( k_c r \frac{\partial T}{\partial r} \right) + \frac{\partial}{\partial z} \left( k_c \frac{\partial T}{\partial z} \right)
$$
where the effective specific heat \( c_{c,eff} \) incorporates both sensible heat and the release of latent heat \( L \) as a function of the solid fraction \( f_s \):
$$
c_{c,eff} = c_c – L \frac{\partial f_s}{\partial T}
$$
Where:
\( \rho \) = density (kg/m³)
\( c \) = specific heat (J/(kg·K))
\( k \) = thermal conductivity (W/(m·K))
\( T \) = temperature (K)
\( t \) = time (s)
\( r, z \) = radial and axial coordinates (m)
\( L \) = latent heat of fusion (J/kg)
\( f_s \) = solid fraction.
The initial and boundary conditions complete the mathematical model:
Initial Conditions (at \( t = 0 \)):
$$ T_{mold}(r,z,0) = T_{preheat} $$
$$ T_{casting}(r,z,0) = T_{pour} $$
Boundary Conditions:
At the outer radius of the grey cast iron mold, a convective heat flux condition is applied due to air cooling during rotation:
$$ -k_m \frac{\partial T}{\partial r} \bigg|_{r=R_{out}} = h_{air}(T_{surface} – T_{ambient}) $$
At the interface between the casting and the mold, a thermal contact resistance \( R_{int} \) (representing the coating) is applied:
$$ -k_c \frac{\partial T}{\partial r} \bigg|_{r=R_{int}^-} = \frac{T_{casting} – T_{mold}}{R_{int}} = -k_m \frac{\partial T}{\partial r} \bigg|_{r=R_{int}^+} $$
At the inner free surface of the outer layer (before core pouring), a radiation/convection condition is applied.
Geometric Modeling and Simulation Setup
A three-dimensional model is constructed to accurately capture the geometry, though the thermal problem is essentially axisymmetric. Commercial CAD software is used to create the solid model of the assembly, which consists of the grey cast iron cold mold, the refractory coating layer, and the volume representing the outer layer melt. A representative roll barrel dimension is selected for each alloy case study. This solid model is then imported into the preprocessor of the ProCAST software for finite element mesh generation. An automatic tetrahedral meshing algorithm is employed, with careful attention paid to refining the mesh in critical regions such as the coating layer and near the mold-casting interface to ensure solution accuracy. The final mesh consists of several hundred thousand elements, each assigned a material identifier (grey cast iron, coating, high-Ni-Cr iron, etc.). The key material properties used in the simulation for the grey cast iron mold and the outer layer alloys are summarized in the table below.
| Material | Density, ρ (kg/m³) | Thermal Conductivity, k (W/(m·K)) | Specific Heat, c (J/(kg·K)) | Liquidus Temp. (°C) | Solidus Temp. (°C) | Latent Heat, L (kJ/kg) |
|---|---|---|---|---|---|---|
| Grey Cast Iron (Mold) | 7100 – 7300 | ~40 – 55 (temp. dependent) | ~500 – 600 (temp. dependent) | – | – | – |
| High Nickel Chromium Iron | ~7600 | ~25 – 35 | ~600 – 700 | ~1320 | ~1200 | ~270 |
| High Chromium Iron | ~7500 | ~20 – 30 | ~650 – 750 | ~1380 | ~1250 | ~280 |
| High Chromium Steel | ~7700 | ~30 – 40 | ~550 – 650 | ~1450 | ~1350 | ~250 |
| Refractory Coating | ~2500 | ~1.0 – 1.5 | ~1100 | – | – | – |
The boundary conditions are applied as per the mathematical model. The initial mold temperature is set to a standard preheat of 150°C to prevent thermal shock and aid in coating drying. The pouring temperatures for the outer layer melts are set according to standard practice for each alloy. The simulations are run for a time sufficient to capture the complete solidification of the outer layer for each configuration.
Effect of Grey Cast Iron Mold Wall Thickness on Outer Layer Solidification
The core of this investigation involves running a series of simulations where the only variable changed is the wall thickness of the grey cast iron cold mold. For each of the three primary outer layer alloys, the solidification history is monitored at a critical point—typically at the mid-length and mid-thickness of the outer layer—to determine the cooling rate.
Case 1: High Nickel Chromium (Hi-Ni-Cr) Iron Outer Layer
A mold with an internal cavity diameter of 730 mm and a barrel length of 3050 mm was modeled. The target outer layer thickness was 90 mm, with a 1.5 mm thick quartz-based coating applied to the grey cast iron mold surface. The pouring temperature was 1360°C.
The simulation campaign was conducted in three phases to efficiently pinpoint the optimal thickness. The first phase used a coarse sampling: 50, 100, 150, 250, and 300 mm wall thicknesses. The cooling curves extracted from a point 50 mm from the mold wall showed a clear non-linear trend. The second phase focused on the 100-230 mm range with a 20 mm increment. The third and most refined phase sampled the 110-200 mm range with a 10 mm increment. The key metric analyzed was the instantaneous cooling rate \( \left( -dT/dt \right) \) during the initial solidification period (first 200-300 seconds). The ranking of cooling rates from the final, most detailed simulation phase is presented below.
| Rank (Fastest to Slowest) | Mold Wall Thickness (mm) | Relative Cooling Rate Trend |
|---|---|---|
| 1 | 160 | Highest |
| 2 | 150 | Very High |
| 3 | 140 | High |
| 4 | 170 | High |
| 5 | 130 | Moderately High |
| 6 | 180 | Moderate |
| 7 | 120 | Moderate |
| 8 | 190 | Moderate |
| 9 | 200 | Lower |
| 10 | 110 | Low |
| 11 | 100 | Lowest |
The data reveals a distinct peak in the cooling rate at a grey cast iron mold wall thickness of approximately 160 mm. This non-monotonic behavior can be explained by two competing thermal effects: the thermal mass effect and the thermal resistance effect.
The instantaneous cooling rate of the solidifying metal can be conceptually related to the heat extraction dynamics. A simplified, lumped-capacitance-like analysis (though not strictly applicable) helps illustrate the point. The driving force for cooling is the temperature difference, but the rate is controlled by the total thermal resistance in the path.
Let \( \dot{Q} \) be the heat flux from the casting. In the initial moments, it can be approximated as being limited by the series of resistances: the conductive resistance of the solidified shell \( (R_{shell}) \), the interfacial coating resistance \( (R_{coat}) \), and the conductive resistance of the mold wall \( (R_{mold}) \). For a cylindrical mold wall:
$$
R_{mold} \approx \frac{\ln(r_{out}/r_{in})}{2 \pi k_{mold} L}
$$
where \( r_{out} \) and \( r_{in} \) are the outer and inner radii of the grey cast iron mold, and \( k_{mold} \) is its thermal conductivity.
- Thin Mold (e.g., 50-100 mm): \( R_{mold} \) is small. However, the thermal mass (heat capacity) of the thin grey cast iron mold is low. It heats up rapidly, quickly reducing the temperature gradient \( \Delta T \) across the mold-casting system, which is the primary driving force for heat flow. Thus, the cooling rate of the casting drops quickly.
- Increasing Thickness (e.g., 100-160 mm): The thermal mass increases significantly, allowing the mold to act as a more effective heat sink without a rapid temperature rise at the interface. Although \( R_{mold} \) increases slightly with thickness, its negative impact is outweighed by the positive effect of the increased heat sink capacity. The net result is an increasing cooling rate.
- Optimal Thickness (~160 mm): A balance is reached where the heat sink capacity is substantial, and the added conductive resistance of the thicker grey cast iron wall is not yet detrimental. This yields the maximum initial cooling rate.
- Very Thick Mold (>160 mm): The conductive resistance \( R_{mold} \) of the grey cast iron becomes the dominant limiting factor. Despite its enormous heat capacity, the heat cannot be conducted through the thick wall to the external cooling surface fast enough to further increase the initial extraction rate from the casting. Therefore, the cooling rate begins to decline.
Case 2: High Chromium Iron (Hi-Cr Iron) Outer Layer
For this case, a larger mold was analyzed: internal cavity diameter of 890 mm, barrel length of 3150 mm, with a composite outer layer design (95 mm base layer + 38 mm intermediate layer). A 1.5 mm zircon-based coating was used. The pouring temperature was higher at 1450°C. Based on findings from the first case, the simulation directly explored the 100-200 mm thickness range in 10 mm increments. The temperature evolution was tracked at a similar location within the outer layer.
The resulting ranking of cooling rates during early solidification was remarkably consistent with the first case:
Cooling Rate Trend: 160 mm > 150 mm > 140 mm > 170 mm > 130 mm > 180 mm > 120 mm > 190 mm > 200 mm > 110 mm > 100 mm.
This confirms that the underlying thermal principles governing the optimal thickness of the grey cast iron mold are largely independent of the specific outer layer alloy, at least within the family of iron-based alloys. The primary factors are the thermophysical properties of the mold material itself and the interfacial conditions.
Case 3: High Chromium Steel (Hi-Cr Steel) Outer Layer
The third case studied a mold with an internal cavity diameter of 1250 mm and a barrel length of 2260 mm, aiming for an outer layer thickness of 105 mm. A 1.5 mm zircon-based coating and a pouring temperature of 1450°C were used. Again, simulations were run for grey cast iron mold wall thicknesses from 100 to 200 mm in 10 mm steps.
The results solidified the observed pattern:
Cooling Rate Trend: 160 mm > 150 mm > 140 mm > 170 mm > 130 mm > 180 mm > 120 mm > 190 mm > 200 mm > 110 mm > 100 mm.
The consistent peak at 160 mm across three different alloys, mold sizes, and pouring temperatures is a powerful finding. It strongly suggests that for a typical grey cast iron cold mold used in horizontal centrifugal casting of roll outer layers, a wall thickness in the vicinity of 150-170 mm provides the most favorable conditions for rapid initial solidification. For practical design purposes, considering manufacturing tolerances and the presence of features like keyways and stiffening ribs, a range of 140-160 mm is recommended.
Effect of Grey Cast Iron Mold Wall Thickness on Core Solidification
In the composite roll process, the core is poured statically after the outer shell has solidified. The heat flow path during core solidification is: Core → Solidified Outer Shell → Coating → Grey Cast Iron Mold → Ambient. The outer shell and the mold are already hot when core pouring begins. A supplementary simulation was conducted to assess whether the mold wall thickness significantly influences the much slower core solidification process. A system with an 890 mm inner diameter mold, a 130 mm thick solidified outer shell, and a core poured at 1390°C was modeled for mold thicknesses of 100, 120, 140, 160, 180, and 200 mm.
The total solidification time for the core was recorded for each case, as shown in the table below.
| Mold Wall Thickness (mm) | Total Core Solidification Time (seconds) | Time Difference from 100mm base (seconds) |
|---|---|---|
| 100 | 33840 | 0 (Reference) |
| 120 | 33896 | +56 |
| 140 | 33948 | +108 |
| 160 | 34011 | +171 |
| 180 | 34054 | +214 |
| 200 | 34115 | +275 |
The data indicates a very weak dependence. While a thicker grey cast iron mold wall does marginally increase the core solidification time (due to increased total thermal mass that must be warmed), the effect is negligible in practical terms—an increase of less than 0.8% even when doubling the mold wall thickness from 100 to 200 mm. Therefore, the choice of optimal mold wall thickness can be made based solely on the requirements for the outer layer solidification kinetics without concern for adversely affecting the core process.
Conclusions
Through the development of a theoretical heat transfer model and systematic numerical simulation using ProCAST software, this study has quantitatively elucidated the relationship between grey cast iron cold mold wall thickness and the solidification rate of centrifugally cast roll outer layers. The key findings are:
- Non-Linear Relationship: The initial solidification cooling rate of the outer layer does not increase monotonically with grey cast iron mold wall thickness. It exhibits a clear maximum at an optimal thickness.
- Optimal Thickness Identification: For the range of conditions and alloys simulated (High Nickel Chromium Iron, High Chromium Iron, and High Chromium Steel), the fastest initial solidification consistently occurs at a grey cast iron mold wall thickness of approximately 160 mm. A thickness range of 140-160 mm provides nearly optimal and robust performance, suitable for practical design considerations.
- Universal Thermal Principle: The optimal thickness is primarily governed by the balance between the heat sink capacity (favoring thicker molds) and the conductive thermal resistance (penalizing very thick molds) of the grey cast iron material itself. This principle appears transferable across different outer layer alloys and mold sizes.
- Negligible Impact on Core: The wall thickness of the grey cast iron mold has a minimal, practically irrelevant effect on the subsequent solidification time of the statically poured core material. The decision on mold thickness can therefore be optimized for the outer layer process alone.
This work demonstrates the significant value of numerical simulation in moving from empirical rules to a science-based design of centrifugal casting tools. Selecting a grey cast iron mold wall thickness within the identified optimal range promotes a faster-chilling outer layer, which is a critical step toward achieving a finer microstructure and enhanced performance in the final composite roll.