Why tooling-free casting suits one-off and small-batch wheels
The economics of wheel manufacture change abruptly when the batch size is one. Gravity casting, low-pressure die casting and squeeze casting all depend on a permanent metal mould; forging and flow forming depend on dies and dedicated presses. Tooling amortised over tens of thousands of parts is cheap per unit, but amortised over a single set it dominates the price and adds weeks to the delivery time. Investment casting inverts this constraint: the pattern, not the mould, carries the geometry, and a pattern can be printed directly from CAD data. The shell is consumed with every pour, but no metal tooling ever has to be cut.
Removing the tooling does not remove the metallurgical problem. A passenger-car wheel is a thick disc feeding a thin rim, so the natural solidification sequence runs from the rim towards the hub and leaves the last liquid exactly where service loads are highest. In the design examined here the disc is 41.25 mm thick while the rim wall falls to 8.63 mm, a ratio of roughly five to one. Any gating solution must therefore reverse the thermal sequence, keep the thin sections from freezing during filling, and place the final shrinkage outside the part.
The route explored in this article combines a selective-laser-sintered polystyrene pattern with a gypsum shell and vacuum pouring. Three candidate pouring positions were computed and compared by finite-element simulation, the surviving layout was optimised with a three-factor orthogonal array, and the resulting process was used to cast and test a complete wheel. The account below follows that sequence: geometry and allowances, gating and feeding calculations, shell design, simulation, parameter optimisation, fabrication, and inspection.
Geometry, allowances and the decision to cast the holes solid
The component is a symmetric passenger-car wheel with a maximum envelope of φ480 mm × 220 mm and a nominal cast mass in the range of 10 kg. Five thickness zones govern the thermal design (Table 1).
| Zone | Feature | Thickness (mm) |
|---|---|---|
| L1 | Wheel disc | 41.25 |
| L2 | Spoke | 17.22 |
| L3 | Rim wall | 11.70 |
| L4 | Rim wall, outer section | 8.63 |
| L5 | Inner flange | 9.92 |
Five bolt holes and one valve-stem hole were not cast. The bolt holes measure 7.12 mm minimum diameter against a 41.25 mm height, a height-to-diameter ratio well above the customary limit of 5 for holes that are cored in investment casting; the valve hole satisfies the ratio but sits close to the thin rim, where the metal front would be disturbed, and a printed polymer pattern cannot hold the tolerances of an inclined small bore. All six were therefore filled solid in the pattern and drilled after casting, which also removes the risk of shell cracking around slender printed cores.
Allowances follow conventional investment-casting practice for an aluminium alloy in a gypsum shell. The linear contraction allowance was set to 1.6%, the mid-value of the combined contribution of pattern shrinkage (0.4–0.6%), mould dehydration (0–0.5%) and solidification contraction of the alloy (1.1–1.3%), which together span 1.5–2.0%. A machining allowance of 3.5 mm per face was applied, consistent with a maximum dimension in the 400–630 mm band. Draft was biased towards the larger values recommended for bulky, complex castings: 0°15′ on the outer rim and 1°30′ on the inner rim for wall heights below 20 mm, and 0°10′ and 1°10′ respectively on the spokes, where wall heights reach 20–50 mm. Fillets were taken as one quarter of the mean adjacent wall thickness, giving 2.5/1.3 mm at the inner and outer flanges (inner/outer radius), 2.2/1.1 mm at the rim, 3.0/1.5 mm at the wheel well, 4.3/2.2 mm at the spokes and 10.3/5.2 mm at the disc.
The alloy is ZL101A (AlSi7Mg type, Si 6.5–7.5 wt%, Mg 0.2–0.4 wt%, Fe ≤0.2, Cu ≤0.2, Mn ≤0.1, Zn ≤0.1, Ti ≤0.2, Al balance), chosen for fluidity, low linear contraction and a low hot-tearing tendency. Its liquidus and solidus are 612 °C and 557 °C, density 2.67 g/cm³, specific heat 0.963 J/(g·°C), thermal conductivity 0.151 W/(mm·°C).
Gating and feeding: from pouring time to riser modulus
The pouring time was estimated from the empirical relation
$$t = K\left(G_L \cdot S\right)^{1/3}$$
where $G_L$ is the metal mass taken for the calculation (casting plus the assumed gating fraction), $S$ the mean wall thickness including machining allowance (19.1 mm) and $K$ a thickness coefficient taken as 1.5. The mean rise velocity of the metal front in the mould cavity follows from the casting height $H = 220$ mm:
$$v_L = \frac{H}{t}$$
For a mean wall thickness of 19.1 mm, the minimum permissible rise velocity is 10–20 mm/s; all three layouts exceed 20 mm/s, so none of them is at risk of cold shuts from an insufficiently fast front. The choke area was then obtained from the choked-flow relation
$$A_{\text{choke}} = \frac{G}{0.31\, t\, u \sqrt{H_p}}$$
with a resistance coefficient $u = 0.4$ and a mean static head $H_p = 16$ cm, which for the bottom-pour layout gives $A_{\text{choke}} \approx 3.2$ cm², i.e. 320 mm². Runner and sprue sections were scaled from the choke by the ratios $\sum S_{\text{ingate}} : \sum S_{\text{runner}} : \sum S_{\text{sprue}} = 1 : 1.1 : 1.2$ for the two layouts that use a runner, and by 1 : 1.15 for the side-pour layout, which omits the runner altogether. Table 2 collects the resulting figures for the three candidate layouts.
| Layout | $G_L$ (kg) | Gating fraction (%) | $t$ (s) | $v_L$ (mm/s) | Choke area (mm²) | Sprue (mm²) | Runner (mm²) | In-gate (mm²) |
|---|---|---|---|---|---|---|---|---|
| Bottom pour | 15.5 | 45 | 9.9 | 22.2 | 320 | 390 | 350 | 320 |
| Side pour | 16.1 | 50 | 10.1 | 21.8 | 443 | 520 | — | 450 |
| Top pour | 18.2 | 70 | 10.6 | 20.8 | 513 | 630 | 580 | 520 |
Feeding was sized with the modulus method. The casting modulus $M_c = V_c / A_c$ follows from a volume of 3.9 × 10⁶ mm³ and a heat-transfer surface of 8.7 × 10⁴ mm², giving 45 mm. The contraction modulus is $M_s = f_1 M_c$ with $f_1 = 0.55$, giving 25 mm, and the riser body and neck moduli are
$$M_r = f_1 f_2 f_3 M_c \qquad M_n = f_4 f_p M_s$$
where $f_2$ is a balancing coefficient, $f_3$ a pressure coefficient, $f_4$ a neck-length coefficient and $f_p$ a neck flow-efficiency coefficient. The coefficients differ by layout because the risers differ in shape and duty (Table 3).
| Layout | Riser type | $f_2$ / $f_3$ | $M_r$ (mm) | $f_4$ / $f_p$ | $M_n$ (mm) | Riser body (mm) | Neck (mm) |
|---|---|---|---|---|---|---|---|
| Bottom pour | Annular waist, on outer flange | 1.0 / 1.1 | 27 | 0.9 / 0.5 | 11 | 24 × 20, R5 | 24 × 6 |
| Side pour | Single cylindrical-spherical, at rim base | 1.4 / 1.5 | 52 | 1.1 / 0.6 | 17 | 55 × 50, R5 | 55 × 20 |
| Top pour | Eight columnar, on the runners | 1.5 / 1.6 | 60 | 1.2 / 0.7 | 21 | 85 × 24, R5 | 24 × 24 |
Four chills of 80 × 30 × 25 mm, each 0.6 times the local wall thickness, were placed symmetrically on the inboard face of the disc to steepen the gradient between the disc and the surrounding spokes and to push the last liquid towards the risers rather than into the hub.
Three pouring positions and what each one implies
Bottom pour. Metal enters through a long sprue and runner at the lowest point and rises through the cavity, which minimises impact on the shell wall and gives the thickest section the lowest position. The penalty is a long, cold flow path and a riser that must feed uphill.
Side pour. Metal enters through a narrow slit at the rim base, which leaves a small contact area that can be snapped off after casting and shortens the flow path. The layout abandons the runner, but the entry sits at a thin wall and feeds the disc only indirectly.
Top pour. Eight symmetric runners deliver metal directly into the disc from above, each with its own columnar riser. The sprue is short, the risers are vertical and open to the top of the shell, and the pattern has straight, unobstructed paths to escape during burnout.
Shell design: wall thickness, venting and pattern removal
The gypsum shell must be thick enough to withstand handling and pouring but thin enough to remain dimensionally stable during dehydration. A geometric estimate based on the casting envelope ($l$ = 480 mm, $b$ = 480 mm, $h$ = 220 mm) gives a minimum wall of 55.3 mm; allowing for the 1.5–2.0% linear contraction of the setting gypsum and for shop-floor handling, the wall was set to 57 mm.
Gypsum is effectively impermeable, so the shell cannot vent through its walls. Two consequences follow. First, the shell was filled so that the risers and vents finished flush with its top face, giving the cavity a direct path to atmosphere; pouring under vacuum then removes most of the residual gas. Second, the pattern must leave the cavity before pouring, which constrains the gating layout: the assembly is inverted during burnout so that the melted polymer can drain through the gating rather than being trapped in a blind recess. Polystyrene has a high molecular weight, a long melting range and a high melt viscosity, so complete removal requires burnout above 500 °C; the schedule adopted peaks at 680 °C.
Numerical simulation of the three layouts
Filling and solidification were solved on a 20-million-cell mesh with the alloy and shell properties listed above. Boundary conditions were a metal-to-shell heat-transfer coefficient of 800 W/(m²·K), a shell-to-shell coefficient of 200 W/(m²·K) and a shell-to-air coefficient of 15 W/(m²·K); the melt surface tension was 0.914 N/m. The baseline schedule was a pouring temperature of 720 °C, a shell preheat of 250 °C and an inlet velocity of 5 cm/s. Defects were ranked with a residual-melt-modulus criterion, visualised as a probability map in which red marks the predicted shrinkage-porosity/cavity zone and blue the sound zone.
| Layout | Filling | Solidification | Predicted defects | Assessment |
|---|---|---|---|---|
| Bottom pour | Uneven front at 5–15% fill; turbulence and oxide entrainment at the disc; front temperature falls from about 700 °C to 600 °C between 65% and 80% fill | Rim solidifies first, disc last; the spoke freezes before the disc, isolating a liquid pool in the hub | Large red zone at the disc and hub bore | Rejected |
| Side pour | Intermittent turbulence at the thin rim near the gate; spokes fill before the disc at 25% fill; about 70 °C spread across the rim | Strongly asymmetric; the gated side stays near 640 °C while the far rim reaches 550 °C; part of the inner flange solidifies last | Smaller red zone, still at the hub bore | Rejected |
| Top pour | Disc fills first, then spokes, then the rim rises with a level front at near-initial temperature | Rim and flange freeze first (about 530 °C), disc and risers last (about 650 °C); final liquid in the risers | Red zone confined to the riser heads | Selected |
The bottom-pour result is instructive because it inverts the expected benefit. Placing the heavy section low does produce a quiet, bottom-up fill, but the same geometry leaves the disc above the spokes, so the riser loses hydraulic contact with the last liquid. The simulation showed the pool in the hub bore — the load-bearing seat of the wheel — which is unacceptable regardless of how small the predicted volume is.
The side-pour layout shortens the flow path and reduces the contact area, but the gate sits against a 8.6–11.7 mm rim wall, and the back pressure generated there fragments the front. The single large riser on one side also acts as a heat reservoir, so the two halves of the wheel solidify on different schedules. That asymmetry is more serious than the defect area alone suggests: a section that solidifies at different times on either side will not have a uniform grain structure or solute distribution, and the ductility of the casting suffers accordingly.
Only the top-pour layout produced a favourable sequence. Because the risers sit above the disc and are the last regions to freeze, the shrinkage is transferred out of the wheel and into metal that is cut off and remelted. The eight symmetric entries also give the gas in the cavity a short vertical path to the vents during vacuum pouring.
Orthogonal optimisation of pouring temperature, preheat and pouring rate
With the gating fixed, three process variables remained: pouring temperature (705, 720, 735 °C), shell preheat (230, 250, 270 °C) and pouring velocity (5, 10, 15 cm/s). A standard L9 array was simulated, and each run was scored with a defect index defined as the largest shrinkage-porosity/cavity cross-section divided by the total casting area, with the gating excluded.
| Run | Pouring temperature (°C) | Preheat (°C) | Pouring velocity (cm/s) | Defect index (%) |
|---|---|---|---|---|
| 1 | 705 | 230 | 5 | 12.837 |
| 2 | 705 | 250 | 10 | 8.577 |
| 3 | 705 | 270 | 15 | 5.168 |
| 4 | 720 | 230 | 15 | 2.064 |
| 5 | 720 | 250 | 5 | 0 |
| 6 | 720 | 270 | 10 | 0 |
| 7 | 735 | 230 | 10 | 0 |
| 8 | 735 | 250 | 15 | 0 |
| 9 | 735 | 270 | 5 | 1.125 |
The filling snapshots at 60% fill separate the runs into two groups. Runs 1–3, all at 705 °C, show a temperature drop of up to 80 °C across the front, and runs 1 and 2 end with a misrun at the outer flange; the last metal to freeze sits in the disc rather than in the riser. Runs 4–9 keep the front close to the inlet temperature and finish solidification in the riser heads. In the defect maps, runs 5–8 are clean outside the gating, whereas runs 1–4 and run 9 show shrinkage at the outer flange, worst in run 1 and mildest in run 4 and run 9.
Two interactions are worth separating. Raising preheat and pouring velocity together (runs 1 to 3) reduces the defect index monotonically, because a hotter shell absorbs less heat from the front and a faster fill shortens the time available for cooling. Raising temperature and preheat at a fixed low pouring velocity is not, however, uniformly beneficial: run 9 (735 °C, 270 °C, 5 cm/s) still shows a small rim defect. A slow fill of superheated metal increases liquid contraction and flattens the thermal gradient between the shell and the thin rim, so temperature and velocity must be raised together rather than independently.
| Level | Pouring temperature (°C) | Preheat (°C) | Pouring velocity (cm/s) |
|---|---|---|---|
| 1 | 26.582 | 14.901 | 13.962 |
| 2 | 2.064 | 8.577 | 8.577 |
| 3 | 1.125 | 6.293 | 7.232 |
| Range $R$ | 25.457 | 8.608 | 6.730 |
The ranges rank the factors unambiguously: pouring temperature (25.46) dominates, preheat (8.61) is second and pouring velocity (6.73) third, with the two secondary factors together contributing less than two thirds of the temperature effect. The level sums point to 735 °C, 270 °C and 15 cm/s, a combination absent from the array. A confirmation run at that setting returned a defect map with no red zone anywhere on the wheel, only in the riser heads.
The chosen parameters are at the upper end of each range, which deserves comment. A rim wall of 8.6–11.7 mm poured at 705 °C misruns, and manual pouring inevitably loses some superheat between the furnace and the mould, so margin on temperature is worth more than the additional liquid contraction it brings. The 270 °C preheat is also not an arbitrary optimum: it coincides with the temperature at which the shell leaves the burnout furnace, so the shell can be transferred directly to the vacuum vessel without a separate reheating step.
Fabrication: printed pattern, gypsum shell, vacuum pour
Pattern. The wheel model was sliced into 1237 layers of 0.2 mm, printed with a 0.3 mm line width, a scanner speed of 1400 mm/s and a powder-spreading speed of 1800 mm/s on a machine with a 1200 × 1200 × 600 mm build cylinder and ±0.2 mm accuracy, taking about 37.4 h. The polystyrene powder has a bulk density of 1.04 g/cm³, a glass transition near 100 °C and a heat-deflection temperature of 78 °C, so the printed body is dimensionally stable at room temperature but softens well below the shell’s service temperature. After printing and cooling, loose powder was brushed off and the pattern was infiltrated twice in wax at 45 °C for 2 h per cycle. The infiltration seals the surface porosity left by the sintering process, raises the surface finish of the pattern and hence of the casting, and adds green strength for handling.
Pattern assembly. The gating was machined from paraffin wax and bonded to the top of the pattern. Paraffin was chosen because it machines at high speed without coolant, causes negligible tool wear and bonds reliably to the infiltrated polystyrene.
Shell. The cluster was mounted in a ring flask on a wooden base plate, and the joint was sealed with molten rosin to prevent slurry leakage. Slurry was mixed and de-aired under 0.05 MPa, then poured as a thin stream with the flask tilted, tapping the base plate to release entrained air and gradually levelling the flask as the level rose. The vessel was then vented so that atmospheric pressure consolidated the slurry, and the block was dried in air for 24 h to remove bulk water slowly; rapid drying at this stage would induce the linear changes that later appear as dimensional error or cracks.
Burnout. The shell was heated at 1–2 °C/min with holds at 140, 180, 230, 350 and 450 °C, then held at 680 °C for 8 h and furnace-cooled to 270 °C. The slow ramp removes free and chemically bound water in stages and lets the pattern drain through the gating before it can build pressure inside a closed cavity.
Melting and pouring. The charge was preheated to 350–450 °C, melted, and refined with 0.7–0.75 wt% hexachloroethane added in three plunges for 3–5 min. Modification used 0.5–0.7 wt% Sr-810 at 730–750 °C followed by 0.5 wt% potassium fluorozirconate at 750–770 °C for 15–18 min. The melt was then held at 735 °C, skimmed and transferred to the vacuum vessel. The shell was evacuated to 0.02 MPa or below, poured at 15 cm/s, and the vessel was vented and pressurised within 40 s of the end of the pour, with the whole sequence kept under 60 s to crystallise the metal under positive pressure.
Cleaning. The casting was air-cooled for 2 h, knocked out with a hard wooden mallet, and the residual gypsum in blind recesses and tight corners was removed with a high-pressure water jet at 0.1–0.2 MPa. The gating was cut off and the stubs ground flush.
Inspection: radiography and tensile testing
Radiographic inspection used a digital real-time X-ray imaging system on the disc, spokes and rim. Acceptance limits were set by zone: shrinkage no worse than level 3 at the disc and spokes and level 2 at the rim, gas porosity no worse than level 3–4 and pinholes no worse than level 3–4 depending on location, with cold shuts and cracks prohibited anywhere. Because X-rays are absorbed differently by different thicknesses and densities, a sound section appears as a smooth grey gradient, whereas pinholes and gas pores appear as round or elongated dark spots, shrinkage as foggy dark bands and cracks as thin irregular dark lines.
The radiographs showed uniform contrast across the disc, spokes and rim, with no banded bifurcation, no spot-like or pit-like dark features, and no bright speckle or mottled regions. On the acceptance criteria above, the casting is free of detectable pinholes, shrinkage porosity and cavities, cracks, and banded segregation.
Tensile specimens were cut from the spokes, the principal load path of the wheel, as flat proportional test pieces with $K = 5.65$ in accordance with GB/T 228.1-2010: 35 mm gauge length, 10 mm parallel width, 1 mm thickness, 20 mm transition radius and 100 mm overall length. Testing was carried out on a universal machine at a crosshead speed of 1 mm/min.
| Property | Measured | Specified minimum |
|---|---|---|
| Ultimate tensile strength (MPa) | 255 | 220 |
| Yield strength (MPa) | 235 | 140 |
| Elongation (%) | 8 | 7 |
The strength margin is large enough to be meaningful rather than marginal: 16% above the specified tensile strength and close to 70% above the specified yield strength, with elongation just above the 7% floor. For a thin-walled casting produced without any metal tooling, this combination indicates that the shell was sound, the melt was adequately degassed and modified, and the feeding path worked as the simulation predicted.
What the results do and do not establish
The case supports three conclusions and leaves several open. It shows that a printed polystyrene pattern in a gypsum shell can reproduce a complex wheel geometry with wall sections down to 8.6 mm, that the pouring position rather than the pouring parameters decides whether the hub is sound, and that a 3² factorial subset is sufficient to rank the process variables, with pouring temperature dominant by a factor of about three over pouring velocity.
It does not show that the simulated defect areas are quantitatively accurate. The model uses bulk thermophysical properties, constant interfacial heat-transfer coefficients and a shell treated as a homogeneous solid, whereas a real gypsum shell has a moisture gradient, a pore structure that changes with burnout and a thermal state that depends on how long it waits between the furnace and the vacuum vessel. The ranking of the three layouts is robust because it follows from the geometry of the feeding path; the absolute defect fractions in Table 5 should be read as relative indicators.
The orthogonal grid is also coarse. With levels spaced 30 °C apart in temperature and 5 cm/s apart in velocity, and with a strongly non-linear response between 705 °C and 720 °C, the true optimum may lie between the tested points. A finer grid around the transition, ideally with a fourth level, would locate it more precisely. On the materials side, the pattern is limited by the thermal expansion and ash residue of polystyrene, and the shell by the properties of a general-purpose dental/art gypsum; pattern binders with lower residue and a gypsum formulation with higher green strength and controlled permeability would both raise the achievable wall-thickness limit and surface quality.
Conclusion
A φ480 mm × 220 mm aluminum alloy wheel with a 41.25 mm disc and an 8.6 mm rim was designed, simulated and cast by investment casting with a 3D-printed polystyrene pattern and a 57 mm gypsum shell. Choke areas of 320, 443 and 513 mm² were calculated for bottom, side and top pouring respectively, with pouring times of 9.9–10.6 s and front rise velocities of 20.8–22.2 mm/s. Simulation rejected the bottom-pour and side-pour layouts because both leave the last liquid at the hub bore, and selected the top-pour layout, in which eight symmetric risers feed the disc and freeze last. A nine-run orthogonal array ranked pouring temperature above shell preheat above pouring velocity (ranges 25.46, 8.61 and 6.73) and produced an optimum of 735 °C, 270 °C and 15 cm/s, confirmed by a defect-free simulation. The cast wheel passed radiographic inspection and reached 255 MPa tensile strength, 235 MPa yield strength and 8% elongation, exceeding the 220 MPa, 140 MPa and 7% requirements for the alloy. The approach removes metal tooling from the production chain and is therefore suited to one-off and small-batch wheels, where the cost of a die cannot be amortised.