In modern manufacturing, the demand for lightweight materials has driven the extensive application of aluminum alloys in industries such as marine, vehicle manufacturing, aerospace, and aviation. Sand casting foundry processes are particularly valued for their ability to produce complex-shaped parts efficiently and economically. However, a persistent challenge in sand casting foundry is the formation of coarse solidification microstructures, which often lead to defects like shrinkage porosity and segregation, thereby degrading the mechanical properties of cast components. To address this, pulsed magnetic field (PMF) technology has emerged as a promising non-contact method for melt treatment, capable of refining grains and improving performance without introducing impurities. In this study, I developed and numerically simulated a novel pouring cup for sand casting foundry applications that integrates a pulsed magnetic field generator directly into the melt delivery system. This work encompasses laboratory simulation experiments, multi-physics finite element modeling, and industrial-scale foundry trials to validate the design.
The pouring cup is a critical component in the sand casting foundry gating system. It receives molten metal from the ladle, controls flow, and helps separate slag. Traditional pouring cups, however, offer no metallurgical treatment capability. By redesigning the pouring cup to incorporate a pulsed magnetic field source, it becomes possible to treat the melt in situ before it enters the mold cavity, thereby promoting grain refinement and enhancing final product quality. This article presents a comprehensive investigation covering experimental parameter optimization, numerical simulation of electromagnetic, flow, and thermal fields, and finally the construction and testing of two different pouring cup configurations suitable for different mold sizes.
1. Laboratory Simulation of Pulsed Magnetic Field Treatment
To establish the optimal electromagnetic parameters for the pouring cup design, I first conducted controlled experiments that simulated the sand casting foundry pouring process. The material used was ZL205A, a high-strength cast aluminum alloy with composition listed in Table 1. The experimental procedure involved melting the alloy in a medium-frequency induction furnace at 730°C, holding for 300 s, and then applying a pulsed magnetic field to the melt surface from a distance of 10 mm using a coil connected to a pulse power supply. The treatment duration was 90 s, after which the melt was cooled to 700°C and poured into preheated graphite molds.
| Cu | Mn | Ti | Cd | V | Zr | Si | B | Al |
|---|---|---|---|---|---|---|---|---|
| 4.76 | 0.321 | 0.165 | 0.151 | 0.005 | 0.096 | 0.046 | 0.017 | Bal. |
I examined the effect of the rate of change of magnetic flux density, dB/dt, on the solidification structure. Table 2 lists the experimental matrix with different excitation frequencies, duty cycles, peak currents, and resulting dB/dt values.
| Sample No. | Frequency (Hz) | Duty cycle (%) | Peak current (A) | dB/dt (mT/s) |
|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 |
| 2 | 20 | 20 | 100 | 3150 |
| 3 | 40 | 20 | 100 | 8000 |
| 4 | 50 | 20 | 100 | 150000 |
Metallographic specimens were taken from both the edge and center of each cast sample, etched with Keller’s reagent, and observed with an optical microscope. The average grain size was determined using the linear intercept method. Figure 1 in the original work illustrates the microstructures; here I summarize the key quantitative findings. As shown in Table 3, the application of a pulsed magnetic field significantly refined the primary α-Al phase. At dB/dt = 8000 mT/s, the edge grain size was refined from 71.53 μm to 52.34 μm, a reduction of 26.83%, while the center grain size decreased from 80.45 μm to 62.46 μm, a 22.36% reduction. Interestingly, further increasing dB/dt to 15000 mT/s led to coarsening, indicating an optimal window.
| dB/dt (mT/s) | Edge grain size (μm) | Center grain size (μm) |
|---|---|---|
| 0 | 71.53 | 80.45 |
| 3150 | 61.31 | 69.67 |
| 8000 | 52.34 | 62.46 |
| 15000 | 61.59 | 70.67 |
Mechanical property tests on the cast alloys revealed that the optimized pulsed magnetic field substantially improved strength and ductility. Table 4 presents the tensile properties and hardness for selected conditions. At dB/dt = 8000 mT/s, the yield strength increased from 125 MPa to 160 MPa (28% improvement), the ultimate tensile strength increased from 206 MPa to 241 MPa (17.5% improvement), and the elongation improved from 6% to 11.5% (91.7% relative increase). Hardness values at the edge and center increased from 55.3 HV and 51.2 HV to 62.5 HV and 56.0 HV, respectively. Fracture surface analysis indicated that the refined microstructure promoted a transition from shallow, sparse dimples to deep, densely packed dimples, confirming enhanced toughness.
| dB/dt (mT/s) | Yield strength (MPa) | Tensile strength (MPa) | Elongation (%) | Edge hardness (HV) | Center hardness (HV) |
|---|---|---|---|---|---|
| 0 | 125 | 206 | 6.0 | 55.3 | 51.2 |
| 3150 | 134 | 222 | 8.2 | — | — |
| 8000 | 160 | 241 | 11.5 | 62.5 | 56.0 |
| 15000 | 142 | 228 | 9.3 | — | — |
The grain refinement mechanism can be explained thermodynamically. During pulsed magnetic field treatment, the melt absorbs electromagnetic energy, which lowers the critical nucleation energy barrier. The modified free energy change for nucleation can be expressed as:
$$ \Delta G_m^* = \frac{16 \pi \sigma_{sl}^3}{3 \left[ \Delta G_v + \frac{1}{2} \mu_0 \Delta \chi_{S-L} H^2 \right]^2} $$
where $\mu_0$ is the vacuum permeability, $\Delta \chi_{S-L}$ is the difference in magnetic susceptibility between solid and liquid phases, $H$ is the magnetic field strength, and $\Delta G_v$ is the volume free energy change. The nucleation rate $I$ is then given by:
$$ I = n_s^* \varepsilon v_n e^{-\Delta G_m^*/(kT)} e^{-Q/(kT)} $$
The presence of the magnetic field reduces $\Delta G_m^*$, thereby increasing the nucleation rate and promoting the formation of fine, equiaxed grains. These laboratory results provided the design targets for the pouring cup: a dB/dt in the range 8000–15000 mT/s, and a magnetic field processing volume covering at least 25% of the total melt to ensure effective treatment.
2. Multi-Physics Mathematical Model of the Pouring Cup
To design a pouring cup that integrates a pulsed magnetic field generator, I utilized COMSOL Multiphysics software to establish a coupled electromagnetic, fluid flow, and heat transfer model. The pouring cup geometry was based on an industrial sand casting foundry configuration with dimensions of 834 mm × 700 mm × 590 mm and a maximum melt capacity of 1.6×10⁸ mm³. Two design variants were considered: a plug-type pouring cup for large molds and a smaller annular pouring cup for small molds. The simulations used the actual melt properties for ZL205A and ZL114A, with temperature-dependent thermal conductivity and specific heat as shown in the original work. The magnetic permeability of all materials except the ferrite core was set to unity; the core followed a B-H curve.
The governing equations for the electromagnetic field are derived from Maxwell’s equations, with the displacement current neglected due to the low frequency and high conductivity of the melt. The relevant equations are:
$$ \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t} \approx \mathbf{J} $$
$$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} $$
$$ \nabla \cdot \mathbf{B} = 0 $$
$$ \mathbf{J} = \sigma \mathbf{E} $$
The Lorentz force and Joule heating are computed as:
$$ \mathbf{F} = \mathbf{J} \times \mathbf{B} $$
$$ Q = \mathbf{J} \cdot \mathbf{E} $$
For the fluid flow and heat transfer, the melt was assumed to be an incompressible Newtonian fluid, with buoyancy modeled by the Boussinesq approximation. The continuity, momentum, and energy equations are:
$$ \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{U}) = 0 $$
$$ \frac{\partial (\rho \mathbf{U})}{\partial t} + \nabla \cdot (\rho \mathbf{U} \mathbf{U}) = \nabla \cdot (\mu_{eff} \nabla \mathbf{U}) – \nabla P + \mathbf{S}_m $$
$$ \frac{\partial (\rho T)}{\partial t} + \nabla \cdot (\rho \mathbf{U} T) = \nabla \cdot \left(\frac{k}{c_p} \nabla T\right) + S_{th} $$
Here $\mu_{eff} = \mu_l + \mu_t$ is the effective viscosity, and the momentum source term $\mathbf{S}_m$ includes thermal buoyancy and the time-averaged Lorentz force. The standard $k-\epsilon$ turbulent model was employed to account for turbulent mixing, with transport equations for turbulent kinetic energy $k$ and dissipation rate $\epsilon$:
$$ \frac{\partial (\rho k)}{\partial t} + \nabla \cdot (\rho \mathbf{U} k) = \nabla \cdot \left[ \left(\mu + \frac{\mu_t}{\sigma_k}\right) \nabla k \right] + G_k – \rho \epsilon + S_k $$
$$ \frac{\partial (\rho \epsilon)}{\partial t} + \nabla \cdot (\rho \mathbf{U} \epsilon) = \nabla \cdot \left[ \left(\mu + \frac{\mu_t}{\sigma_\epsilon}\right) \nabla \epsilon \right] + C_1 \frac{\epsilon}{k} G_k – C_2 \rho \frac{\epsilon^2}{k} + S_\epsilon $$
where the model constants are $C_1=1.44$, $C_2=1.92$, $\sigma_k=1.0$, $\sigma_\epsilon=1.3$, and $C_\mu=0.09$. The source terms $S_k$ and $S_\epsilon$ incorporate damping functions to handle the solidification region, as defined in the original model.
The computational domain included the melt, coil, ferrite core, and surrounding air. A structured hexahedral mesh was used for the melt and coil, while the air region used tetrahedral elements. Boundary conditions are summarized in Table 5.
| Physical field | Location | Condition |
|---|---|---|
| Magnetic field | Outer air boundary | Far field, $\mathbf{B}=0$ |
| Flow field | Free surface | Initial velocity = 0 |
| Flow field | Side walls | No-slip stationary wall |
| Temperature | Free surface | $\lambda \frac{\partial T}{\partial n} = h(T-T_{env})$, $h=25\ \mathrm{W/(m^2K)}$ |
| Temperature | Side and bottom walls | Thermally insulated |
The numerical solution was obtained using the finite element method. The pulsed current waveform was implemented as an interpolated periodic function in the coil domain. Because the magnetic Reynolds number is small, the flow effect on the magnetic field was neglected, enabling a one-way coupling from electromagnetic to flow and thermal fields. The time-averaged Lorentz force and Joule heating were added as source terms to the momentum and energy equations, respectively. This approach improved computational efficiency while maintaining accuracy.
3. Numerical Simulation Results
3.1 Comparison of Different Coil Configurations
I first evaluated three possible coil layouts for the plug-type pouring cup: single-sided, inner ring, and symmetric. Figure 2 from the study shows the magnetic flux density distribution in the melt within the range 10–131 mT, which was considered effective for grain refinement. The single-sided configuration produced concentrated magnetic field near one end, leaving a large untreated volume. The inner ring configuration produced a hemispherical-shaped distribution around the coil but with weaker central strength. The symmetric configuration gave two separate lobes. The volumes within the 10–131 mT range were 2.68×10⁷ mm³, 4.37×10⁷ mm³, and 3.05×10⁷ mm³, corresponding to 17.87%, 29.13%, and 20.33% of the total melt, respectively. Therefore, the inner ring configuration with an opposite (counter-directional) coil winding was selected as it satisfied the dB/dt requirement (10480 mT/s) and maximized the treated volume.
| Configuration | Untreated Fraction (%) | Processed Volume (mm³) | Processed Fraction (%) |
|---|---|---|---|
| Single-sided | 82.13 | 2.68×10⁷ | 17.87 |
| Inner ring (opposite) | 70.87 | 4.37×10⁷ | 29.13 |
| Symmetric | 79.67 | 3.05×10⁷ | 20.33 |
3.2 Influence of Magnetic Field Direction
The direction of current in the two inner coils was studied. When both coils produced magnetic fields in the same direction, the vector plots showed diverging and converging patterns at different phases, but the decay was faster and the treated volume was smaller (3.13×10⁷ mm³, 20.89%). When the currents were opposite (heterodirectional), the magnetic field formed a vortex-like distribution, promoting more uniform exposure and increasing the treated volume to 4.37×10⁷ mm³ (29.13%). Thus, the opposite-direction configuration was adopted.
3.3 Effect of Frequency and Duty Cycle
Simulations were performed for frequencies of 20 Hz, 40 Hz, and 50 Hz, each with duty cycles of 20%, 40%, and 50%. The results indicated that lower frequencies and higher duty cycles yielded lower dB/dt and larger treated volume, while higher frequencies with lower duty cycles produced higher dB/dt but smaller treated volume. For example, at 20 Hz and 50% duty cycle, dB/dt was 10480 mT/s, which lies within the target range, and the treated volume was 4.37×10⁷ mm³. The magnetic field decayed exponentially with distance from the coil, and higher frequency increased the attenuation rate. Figure 3 in the original thesis shows the field decay curves; here Table 7 summarizes the effective dB/dt and treated volume for selected cases.
| Frequency (Hz) | Duty cycle (%) | dB/dt (mT/s) | Processed volume (×10⁷ mm³) | Fraction (%) |
|---|---|---|---|---|
| 20 | 20 | 12450 | 2.96 | 19.73 |
| 20 | 40 | 10820 | 4.01 | 26.73 |
| 20 | 50 | 10480 | 4.37 | 29.13 |
| 40 | 50 | 14230 | 2.88 | 19.20 |
| 50 | 50 | 15100 | 2.61 | 17.40 |
3.4 Effect of Current Intensity
For the optimal frequency and duty cycle (20 Hz, 50%), I varied the peak current from 100 A to 200 A. As expected, increasing the current increased the Lorentz force and improved the penetration depth. The dB/dt increased from 5256 mT/s at 100 A to 7888 mT/s at 150 A and 10480 mT/s at 200 A. The volume fraction with magnetic induction >10 mT increased from 16.41% to 23.77% and 29.13%. The velocity magnitude at a monitor point increased from 0.031 m/s at 100 A to 0.049 m/s at 200 A, indicating stronger melt convection. The flow patterns showed that higher currents promoted a more uniform velocity distribution and reduced the stagnant zone in the center. Temperature distributions became more homogeneous with increasing current, as stronger forced convection enhanced heat exchange. Based on these results, 200 A was selected as the operating current.
| Current (A) | dB/dt (mT/s) | Processed volume fraction (%) | Point velocity (m/s) |
|---|---|---|---|
| 100 | 5256 | 16.41 | 0.031 |
| 150 | 7888 | 23.77 | 0.041 |
| 200 | 10480 | 29.13 | 0.049 |
3.5 Small Pouring Cup Simulation
For the small pouring cup intended for hand-ladle operation, an annular geometry with a 220 mm inner diameter and 200 mm depth was modeled. The maximum melt volume is 6.28×10⁶ mm³. Using the same selected electromagnetic parameters (20 Hz, 50% duty, 200 A), the simulation predicted dB/dt = 8960 mT/s, which is within the target range. The magnetic flux density exceeded 10 mT throughout the melt volume, meaning 100% treatment coverage. The flow field exhibited four vortices with a maximum velocity of 0.05 m/s. The temperature distribution showed a distinct vertical gradient, with cooler upper and warmer lower regions due to electromagnetic stirring, which helps homogenize the melt.
4. Experimental Validation of the Pouring Cup
4.1 Model Verification
Before manufacturing, I verified the numerical model by comparing simulated and measured magnetic flux densities at the same location in a prototype. The actual current waveform was loaded into the model, and the simulated peak value was 92 mT versus 98 mT measured, a difference of 6.52%. This reasonable agreement confirmed the reliability of the simulation approach for designing the sand casting foundry pouring cup.
4.2 Manufacture and Testing of the Plug-Type Pouring Cup
The plug-type pouring cup was manufactured with 304 stainless steel body, a funnel-shaped bottom, and an inner ring coil wound around a ferrite core. The coil consisted of 120 turns of 70 mm² conductor. The cup dimensions were 834 mm × 700 mm × 590 mm, with a maximum capacity of 1.6×10⁸ mm³. Two experiments were conducted: one without magnetic field and one with dB/dt = 10480 mT/s. The melt (ZL205A) was held at 730°C, treated for 240 s, then poured into a sand mold after cooling to 663°C. The results from the heat-treated castings (T5) are shown in Table 9.
| Condition | Tensile strength (MPa) | Elongation (%) | Hardness (HBW) |
|---|---|---|---|
| 0 mT/s | 236 | 3.5 | 116 |
| 10480 mT/s | 350 | 10.0 | 125 |
| Improvement | +48.31% | +185.71% | +7.76% |
Similarly, for ZL114A alloy tested in the same pouring cup, the T5 heat-treated tensile strength increased from 299 MPa to 344 MPa (+15.05%) and hardness increased from 96 HBW to 101 HBW (+5.21%). These improvements highlight the effectiveness of the pulsed magnetic field in a real sand casting foundry environment.
Metallographic analysis of the ZL205A casting body showed a clear refinement of primary α-Al dendrites from coarse rosette-like structures to fine equiaxed grains. The average grain size decreased from 62.27 μm to 50.64 μm, a refinement of 18.7%.
4.3 Small Pouring Cup Trials
A smaller annular pouring cup was constructed for use with a 304 stainless steel hand ladle (220 mm diameter, 200 mm depth). The coil was wound annularly with 120 turns (6 layers × 20 turns) and had an outer diameter of 404 mm and height of 220 mm. For the sand casting foundry test, ZL114A melt was held at 730°C, treated for 90 s, and then poured at 700°C. I tested multiple dB/dt values (0, 8960, 17600, 18400, 23000 mT/s) on test bar samples. The microstructure tests showed that the optimal grain refinement occurred at dB/dt = 8960 mT/s, where the grain size decreased from 77.66 μm to 60.89 μm (21.59% refinement). As shown in Table 10, the tensile strength, elongation, and hardness of the as-cast test bars increased by 20.14%, 75.78%, and 12.72% respectively, compared to the untreated condition.
| dB/dt (mT/s) | Tensile strength (MPa) | Elongation (%) | Hardness (HV) |
|---|---|---|---|
| 0 | 199.75 | 5.12 | 68.44 |
| 8960 | 240.00 | 9.00 | 77.14 |
| 17600 | 215.00 | 6.80 | 72.30 |
| 18400 | 220.00 | 7.10 | 73.50 |
| 23000 | 225.00 | 7.60 | 74.80 |
For the sand mold trials, castings were produced under dB/dt = 8960 and 23000 mT/s and compared with untreated castings. After T5 heat treatment, the mechanical properties are presented in Table 11.
| dB/dt (mT/s) | Tensile strength (MPa) | Elongation (%) | Hardness (HV) |
|---|---|---|---|
| 0 | 200.0 | 6.52 | 67.16 |
| 8960 | 262.0 | 9.02 | 81.68 |
| 23000 | 254.5 | 7.55 | 78.56 |
| Improvement at 8960 | +31.0% | +38.34% | +21.62% |
These industrial trials conclusively demonstrate that integrating a pulsed magnetic field into the pouring cup is a viable and effective technique for improving the quality of sand casting foundry aluminum components.
5. Conclusion
In this work, I developed two novel pouring cups for sand casting foundry applications, both incorporating a pulsed magnetic field generator directly into the melt path. Through laboratory experiments, multi-physics numerical simulation, and full-scale foundry trials, the following conclusions were established:
(1) Laboratory tests on ZL205A alloy showed that applying a pulsed magnetic field with a dB/dt of 8000 mT/s optimally refines the primary α-Al grains, reducing the average grain size by up to 26.83% and improving yield strength, tensile strength, and elongation by 28%, 17.5%, and 91.66%, respectively.
(2) Numerical simulation using COMSOL Multiphysics revealed that an inner-ring coil configuration with opposite current directions provides the largest magnetically treated volume (4.37×10⁷ mm³, 29.13% of the total) while maintaining a dB/dt of 10480 mT/s within the target range. Lower frequency (20 Hz) and higher duty cycle (50%) were optimal, and increasing current from 100 A to 200 A enhanced melt convection and thermal homogenization.
(3) For the small pouring cup, an annular coil design achieved dB/dt = 8960 mT/s with nearly 100% melt coverage. Industrial trials confirmed that this design improves the T5 heat-treated tensile strength of ZL114A castings by 31% and hardness by 21.62%.
(4) The successful integration of pulsed magnetic field treatment into the pouring cup represents a significant advancement for sand casting foundry technology, offering a non-contact, environmentally friendly method to enhance the microstructure and mechanical properties of aluminum alloy castings without the need for grain refiners or additional process steps.