Disk-shaped castings combine rotational symmetry with highly nonuniform section thickness. A mining flatbed wheel is a demanding example: a thin web connects a heavy hub to a wear-resistant rim, and the same part must carry payload, absorb impact, and resist abrasive service conditions. The manufacturing problem is therefore not simply to fill a round cavity. It is to keep the thin web from freezing prematurely while feeding the thick rim and hub sections through the final stages of solidification. Investment casting offers the dimensional control and surface quality needed for such geometries, but gating, shell preheating, pouring conditions, and melt mobility all influence whether shrinkage porosity opens at the hot spots.
Component, Duty, and Castability
The reference component is a mining flatbed wheel made of ZG35CrMnSi cast steel. Its envelope is 350 mm × 400 mm × 114 mm, with a 350 mm rim diameter and a 120 mm hub bore. The thin 10 mm web is the main filling constraint, while the 36 mm hub wall and the flanged rim store heat and feed the surrounding thin sections during cooling.
| Parameter | Value |
|---|---|
| Mass | 33.46 kg |
| Envelope | 350 × 400 × 114 mm |
| Rim outside diameter | 350 mm |
| Hub inside diameter | 120 mm |
| Hub wall thickness | 36 mm |
| Rim flange width / thickness | 25 / 15 mm |
| Web thickness | 10 mm |
| Slot size | 30 × 20 mm |
ZG35CrMnSi was selected for its combination of strength and toughness in a cast steel wheel. Its calculated liquidus and solidus temperatures are 1479 °C and 1111.8 °C, respectively. The high melting point and relatively large solidification shrinkage of cast steel make feeding design more critical than in low-melting alloys; the material is also sensitive to gas pickup and oxide entrapment when filling is turbulent.
| C | Si | Mn | P | S | Cr | Ni | Cu | Mo | V |
|---|---|---|---|---|---|---|---|---|---|
| 0.35 | 0.75 | 1.2 | 0.03 | 0.03 | 0.8 | 0.3 | 0.25 | 0.15 | 0.05 |
The quality requirements are strict. The wheel must be free of through cracks, with only small localized cracks permissible at the rim top or end faces and only after repair. Hub-surface porosity is limited to three spots, each no larger than 16 mm², less than 3 mm deep, and separated from the next by more than 30 mm. These requirements make open shrinkage on the tread or hub unacceptable and shift the process focus toward feeding rather than cosmetic finishing.
The main castability problem is the thermal mass distribution. The rim bottom and the junction between the rim and the web are the dominant hot spots, with additional hot regions where the hub and flange meet the base plate. These regions cool slowly, collect liquid over a long period, and tend to form isolated pools once the thin web has frozen. If those pools cannot draw feed metal from the gating system, shrinkage porosity appears at exactly the locations that carry wheel loads.
Process Architecture: Wax Pattern, Ceramic Shell, and Gating
Investment casting was selected because the ceramic shell can reproduce the rim profile and thin web with better dimensional consistency and surface finish than a conventional sand mold, while avoiding the oxide-film and gas-entrapment problems associated with some low-pressure die-casting routes. The process chain used a mid-temperature pattern wax, a multilayer ceramic shell, and a mid-height side-gating concept with the final ingates located at the thick lower section of the wheel.
The pattern material was an HK-168 mid-temperature wax with a melting range of 87.7–93.3 °C, softening point of 71–78 °C, linear shrinkage of 0.7–0.95%, and ash content below 0.02%. The face coat used fused corundum, the backup coat used bauxite clinker, and the binder was silica sol. The shell was built in five to seven layers, dried at 22–25 °C and 40–60% relative humidity, with 10–12 h per layer, and the finished shell was required to hold dimensional tolerance within ±1 mm.
Four gating concepts were compared: bottom pour, top pour, stepped pour, and mid-height side pour. Bottom pour gives smooth filling but a long flow path and a high risk of cold shut at the top of the wheel. Top pour fills quickly but impinges on the upper cavity and works against sequential solidification. Stepped gating combines the two but adds complexity. The selected mid-height system reduced direct impact on the cavity top and filled the upper part faster than a bottom-pour system, while retaining a controllable flow path.
The parting plane was placed on the symmetry plane to simplify wax-pattern assembly and shell construction. The choke cross-section was calculated from the total poured mass, fill time, alloy density, and effective metal head. For a four-cavity tree, the total poured mass was 244.913 kg; at 1580 °C the alloy density was taken as 6962 kg/m³; and the design fill time was 12 s. These inputs gave a choke area of 44–47 cm². The calculated pouring speed was 278.46 mm/s, rounded to 280 mm/s. The initial layout used two ingates, A and B, placed at the thick lower section to promote feeding from the gate into the rim and hub.
Initial Simulation: Filling, Solidification, and the Hot-Spot Defect
The initial design was assessed with a finite-element casting simulation. The shell was represented as a 6 mm fused-mullite layer initially at 1000 °C, the alloy was poured at 1580 °C, and the mesh used 5 mm surface elements with approximately 4.49 million volume elements. The simulation tracked the free surface, velocity field, temperature field, and solid-fraction evolution through filling and solidification.
Filling began at about 2.6 s, when the melt entered the sprue. The lower pair of wheel cavities started to fill at about 4.4 s; the lower pair was full by 6.9 s; the upper pair began to fill at 7.7 s; and the entire tree was full at 13 s. The average filling velocity near the sprue inlet was 1.422 m/s, with local turbulence at the sprue bend and flow separation where the melt met the web and hub. At about 4.4 s, the flow front folded around the rim-web junction, creating a condition favorable to gas entrapment. The lower rim region was identified as the most likely location for shrinkage and entrapment defects.
Solidification followed the intended general sequence: the shell-side skin froze first, the thin web and upper rim lost heat rapidly, and the rim bottom, ingate junction, and sprue center remained liquid longest. Complete solidification was reached at 3187 s, when the system cooled to the solidus temperature of 1111.8 °C. Despite this macroscopically sequential pattern, the initial design left an isolated liquid region at the rim bottom and web junction. The predicted shrinkage-porosity index was 13.13%, concentrated in that hot spot.
The first correction was geometric rather than statistical. Two additional ingates, C and D, were added at the bottom of the wheel to enlarge the feeding area, and venting was added to improve gas escape. With the revised gating, the predicted shrinkage-porosity index fell to 8.87%. The improvement was substantial but incomplete: local porosity remained near the rim bottom and web, which indicated that the thermal profile still allowed a late-freezing pool to form after the thin sections had closed the feed path.
Response-Surface Optimization of Pouring Conditions
The remaining porosity was addressed by optimizing pouring temperature, pouring speed, and shell preheating temperature. Single-factor trials were first used to establish feasible ranges. Each level was evaluated three times, and the mean shrinkage response was used. These trials are conditional: each factor was varied while the other two were held at fixed values, so the resulting optima are local rather than global.
| Condition | Fixed variables | Best setting | Shrinkage-porosity index |
|---|---|---|---|
| Shell preheating temperature | 1580 °C pouring; 280 mm/s | 875 °C | 8.31% |
| Pouring speed | 1580 °C pouring; 1050 °C shell | 280 mm/s | 8.63% |
| Pouring temperature | 280 mm/s; 1050 °C shell | 1555 °C | 8.34% |
The shell-preheating response was U-shaped. Below 875 °C, the melt met a colder shell, the thermal gradient increased, and the thin web froze earlier. Above 875 °C, the shell and casting geometry were more strongly affected by the higher temperature, and the feeding path became less effective, so porosity rose again. The pouring-speed response had a clear minimum at 280 mm/s: higher speeds increased turbulence and gas entrapment, while lower speeds allowed the melt to lose fluidity before feeding was complete. The pouring-temperature response improved as superheat increased, but above about 1555 °C the melt’s gas pickup tendency increased and porosity rose again.
A Box–Behnken design was then used to capture interactions among the three variables. The response was the predicted shrinkage-porosity index, and the design space was set from the single-factor results.
| Factor | Low level (−1) | Center level (0) | High level (+1) |
|---|---|---|---|
| A: pouring temperature (°C) | 1530 | 1555 | 1580 |
| B: pouring speed (mm/s) | 270 | 280 | 290 |
| C: shell preheating temperature (°C) | 750 | 875 | 1050 |
The quadratic model was significant (p < 0.0001), with R² = 0.9893, adjusted R² = 0.9756, predicted R² = 0.9022, and a coefficient of variation of 3.38%. Lack of fit was not significant (p = 0.3437). The main effects ranked as pouring speed (F = 89.65, p < 0.0001), shell preheating temperature (F = 7.13, p = 0.0320), and pouring temperature (F = 5.90, p = 0.0455). The pouring-temperature × shell-temperature interaction was the strongest interaction (F = 67.71, p < 0.0001); the pouring-temperature × pouring-speed interaction was also significant (F = 9.82, p = 0.0165), while the pouring-speed × shell-temperature interaction was not (F = 1.38, p = 0.2791).
The statistical optimum was 1530 °C pouring temperature, 290 mm/s pouring speed, and 875 °C shell preheating temperature. Three replicate evaluations at this condition gave shrinkage responses of 5.12%, 5.07%, and 5.03%, with no significant difference from the model prediction (p ≥ 0.05). The optimum is not the same as the single-factor optimum: co-varying temperature and shell preheating shifts the best combination toward lower superheat and a higher pouring speed. Under the optimized condition, simulated filling was complete at 11.1 s. The wheel body showed no shrinkage porosity in the final simulation, although a small amount remained in the sprue, where it does not affect the casting.
Vibration-Assisted Filling: DEM Screening and Water-Model Validation
Even after parameter optimization, thin and complex sections can remain difficult to fill completely. Mechanical vibration was therefore introduced as a transient filling aid. The intent was not to replace gating design but to increase melt mobility, promote gas escape, and help the melt reach thin web and rim details before freezing. The screening work used a discrete-element method (DEM) model in which the melt was represented as a granular assembly. This is a comparative flow model, not a direct simulation of liquid-steel rheology, so the results are most useful for ranking vibration conditions.
| Parameter | Value |
|---|---|
| Particle diameter | 0.5 ± 0.1 mm |
| Particle density | 900 kg/m³ |
| Young’s modulus | 1 MPa |
| Poisson ratio | 0.4 |
| Friction coefficient | 0.3 |
| Restitution coefficient | 0.15 |
| Contact model | Hertz–Mindlin no slip |
| Time step | 1 × 10−5 s |
| Simulated filling time | 13 s |
| Particle count | 25,000 |
Frequency was varied from 10 to 115 Hz in 15 Hz steps. At low frequency, particle transport remained close to gravity-driven filling. As frequency increased, the particles gained more energy and penetrated farther into the sprue and ingates. At 55 Hz, 164 particles reached the ingate. At 85 Hz, the farthest transport distance reached 1100 mm and the particle count in the sprue reached 588. Above 85 Hz, transport slowed; at 100 and 115 Hz, excessive vibration disrupted rather than enhanced flow. The 85 Hz condition therefore gave the best filling response in the frequency sweep.
Amplitude was varied from 0.2 to 1.6 mm in 0.2 mm steps. At 0.6 mm, 478 particles entered the cavity. The 0.8 mm and 1.0 mm cases produced more uniform particle distribution, and the 1.0 mm case gave faster dispersion and better penetration of the cavity details. At 1.2 mm, flow became unstable; at 1.4 mm, sloshing and impact against the mold wall increased; and at 1.6 mm, local splashing and air entrapment appeared. The 1.0 mm amplitude was the best compromise between driving force and flow stability.
Directional vibration produced a clear ranking. Single-axis vibration improved filling relative to no vibration, but the effect depended on direction: vertical motion helped gravity-driven filling, while horizontal motion improved lateral spreading. Combined directions performed better because they reduced localized over-disturbance and distributed the driving force through the cavity. The ranking was XYZ > YZ > XZ > XY > Y > X > Z > no vibration. The three-axis case delivered 702 particles into the sprue, compared with 457 for YZ and 257 for XY, and gave the most complete filling of the complex wheel cavity.
The vibration-assisted process was then checked with a room-temperature water model. The transparent mold used an acrylic sprue of 60 × 60 × 520 mm and ingates of 40 × 40 × 15 mm, with a PMMA cover and a sealed fixture. A three-axis electromagnetic shaker with a 500 × 500 mm table, 0–5 mm amplitude range, 1–600 Hz frequency range, and 100 kg payload was used, and flow was recorded at 1000 frames per second. The working fluid was water with 1.0% polyacrylamide, 1.0 mol/L sodium chloride, and 15% transparent soft particles, giving an apparent viscosity of 0.0030 Pa·s and a density of 1.40 g/cm³. The viscosity approaches the 0.002–0.003 Pa·s range used for liquid steel, but the density remains far below that of steel; the water model therefore reproduces filling topology and sequence rather than exact hydrodynamic equivalence.
| Metric | Water model | Numerical simulation | Relative difference |
|---|---|---|---|
| Filling time | 11.60 s | 11.1 s | 4.31% |
| Flow velocity | 1.48 m/s | 1.422 m/s | 3.92% |
| Liquid distribution uniformity | 0.95 | 0.94 | 1.05% |
| Filling sequence | Consistent | Consistent | — |
| Defect-prone locations | Consistent | Consistent | — |
The water model reproduced the filling sequence and the defect-prone locations within about 5% on the reported metrics. In the vibration tests, a nine-run, three-factor, three-level screening design covered amplitudes of 0.6–1.0 mm, frequencies of 55–85 Hz, and XY, YZ, and XYZ directions. At 85 Hz and 0.8 mm, the mean filling speed reached 105 mm/s, compared with 67 mm/s at the lower amplitude. The best overall combination was 85 Hz, 1.0 mm amplitude, and three-axis vibration, consistent with the DEM ranking.
Engineering Interpretation and Limits
The case shows that shrinkage in this wheel is primarily a feeding problem, not a bulk-filling problem. The initial gating could fill the cavity, but it could not maintain a feed path after the thin web froze. Adding lower ingates and vents reduced the hot-spot isolation; response-surface optimization then adjusted the thermal profile so that the late-freezing region was smaller and better fed. The important variables are coupled: shell preheating controls the thermal gradient, pouring speed controls turbulence and gas entrapment, and pouring temperature controls superheat and shrinkage. A single-factor optimum is therefore not a reliable production set point.
Vibration acts through a different mechanism. It raises melt mobility and helps gas escape during filling, but excessive frequency or amplitude can create wall gaps, unstable flow, or splashing that re-entrains gas. The window around 85 Hz, 1.0 mm, and three-axis vibration is a process window, not a universal setting. It depends on the mold mass, fixture stiffness, shell strength, and the vibration system’s coupling to the tree.
The evidence presented here is simulation-led, with water-model validation. It does not include cast-metal trials, X-ray or CT inspection of production wheels, tensile or fatigue testing, or production scrap data. The 5.07% response is a model-based shrinkage index, not a certified rejection rate. The water model also has a density mismatch relative to liquid steel, and the DEM model treats the melt as a granular analog. These limitations do not invalidate the comparative conclusions, but they do mean that industrial adoption requires cast trials, shell-cracking checks under vibration, dimensional-capability studies, and mechanical-property validation.
Conclusion
- The mining wheel’s thin 10 mm web and heavy rim and hub create hot spots at the rim bottom and web junction, making feeding design the central investment casting challenge.
- Mid-height side gating with lower ingates, a symmetry-plane parting line, and a silica-sol ceramic shell provided a workable process architecture for the ZG35CrMnSi wheel.
- Initial simulation predicted a 13.13% shrinkage-porosity index at the rim bottom and web junction. Adding ingates C and D plus vents reduced it to 8.87%.
- Response-surface optimization identified pouring speed as the strongest main effect, followed by shell preheating temperature and pouring temperature. The best combination was 1530 °C pouring temperature, 290 mm/s pouring speed, and 875 °C shell preheating temperature, with replicate responses of 5.03–5.12%.
- Vibration screening ranked three-axis vibration first, followed by YZ, XZ, XY, Y, X, Z, and no vibration. The best single setting was 85 Hz and 1.0 mm amplitude.
- The water model reproduced the simulated filling time, velocity, uniformity, and defect-prone locations within about 5%, supporting the process concept while leaving cast-metal validation as the next step.