A 23-blade rotor with 1.3 mm walls is a casting problem before it is a machining problem
Micro turbine engines sit in a distinctive corner of propulsion: the smallest units are only about 5 mm in diameter, thrust ranges from 30 N to 500 N, and demonstrators have reached thrust-to-weight ratios of 8–10, comparable to or better than much larger turbojets. Because of that combination, they have moved from laboratory demonstrators into reconnaissance UAVs and target drones, and the rotor is the component that decides whether the whole machine meets its rating.
The turbine rotor carries the entire aerodynamic and thermodynamic duty of the engine. In service the blades see centrifugal loading at high rotational speed, thermally induced stress as the gas temperature swings, and alternating aerodynamic loads from the high-pressure gas path; the gas environment is around 800 °C, at which creep and fatigue resistance of the blade alloy become the limiting material properties. Blade reliability therefore sets both the thermodynamic parameters the engine can be tuned to and its service life.
Manufacturing, however, is where the geometry becomes decisive. The rotor examined here is a nickel-base superalloy turbine with 23 twisted blades distributed uniformly around an annulus (Table 1). Blade length is 13 mm, the tip section is only 1.3 mm thick, and the gap between adjacent blade roots is 2 mm. A twisted, streamlined aerofoil of that thickness cannot be cut economically by milling, and machining would in any case introduce stress concentrations exactly where fatigue resistance matters most. Near-net-shape investment casting is the practical route: the wax pattern carries the aerofoil, and the ceramic shell reproduces it without a cutting tool ever touching the blade surface.
| Parameter | Value or requirement |
|---|---|
| Rotor outer diameter | 83.4 mm |
| Hub bore diameter | 54.4 mm |
| Blade count | 23, uniformly spaced |
| Blade length / form | 13 mm, twisted aerofoil |
| Minimum wall thickness | 1.3 mm at the blade tip |
| Root-to-root gap between blades | 2 mm |
| Alloy | Nickel-base superalloy (Cr 17–21, Nb+Ta 4.75–5.5, Mo 2.8–3.3, Ti 0.75–1.15, Al 0.30–0.70, Ni 50–55, Fe balance, wt.%) |
| Dimensional tolerance | CT3 |
| Surface roughness | Ra 3.2 µm |
| Internal quality | No shrinkage porosity, cracks or distortion |
The tolerance requirement is what separates investment casting from the alternatives. Lost-wax casting reaches CT4–CT6 as a matter of routine and CT3 with tighter process control, against CT10–CT13 for sand casting and CT5–CT7 for die casting; as-cast roughness falls in the 3.2–6.4 µm band, with 0.8–1.6 µm attainable in premium work. That capability comes at a price: the process chain has many steps, each with its own parameters, and thin-walled parts accumulate error from step to step.
From wax to shell: what the process chain demands of a simulation model
Lost-wax casting is old technology that was rebuilt around aerospace tolerances. Beeswax pattern materials were used for large bronze castings in China some 4,000 years ago; the modern industrial version emerged during the Second World War, when cobalt-base alloys developed for surgical implants were found to be suitable for aircraft turbocharger wheels and could not be machined affordably. Investment casting then moved from military production into civil aero engines and, later, into hydro, petroleum and chemical equipment. Two late-20th-century developments shaped current practice: rapid-solidification investment casting for thin-wall, high-precision aluminium parts, commercialised by Howmet, and fast-drying silica sol binders of the Ludox SK type produced by Rolls-Royce. In China, the industry grew from ethyl-silicate binders introduced with Soviet practice in the 1950s; because ethyl silicate was scarce and expensive, ammonium-chloride-treated water glass became the standard binder for automotive and general engineering castings, and it still accounts for a large share of domestic output. Modern shops often combine the two, using silica sol on the face coats and water glass on the backup coats to trade cost against surface quality.
Numerical simulation of the process has followed a similar trajectory. Solidification modelling began in the 1960s with finite-difference treatments and was validated on automotive cylinder blocks; mould-filling simulation arrived in the 1980s, when fluid-mechanics formulations were adapted to gravity casting, first in two dimensions and then in full three dimensions. Commercial finite-element codes now couple filling, solidification, radiation and stress, and are used in aerospace casting because the shell must be modelled as a participating thermal body rather than a boundary condition.
Investment casting imposes four requirements that a sand-casting model does not:
- The model must contain the casting, the gating system and a shell of realistic thickness, because the shell controls heat extraction.
- The shell is preheated and soaked before pouring, so its initial temperature is high and radiation between shell and surroundings cannot be neglected in the way it can for a thick sand mould at room temperature.
- Walls are thin, so heat lost during filling is not negligible and the temperature field is transient from the first instant of fill.
- Thermophysical and mechanical properties must be temperature dependent over the whole liquidus-to-room-temperature interval.
The simulations described below therefore rest on a set of explicit simplifications: constant viscosity, a single-phase Newtonian and incompressible melt of fixed density, no oxide inclusions or gas bubbles, heat transfer between shell and environment and between shell and metal treated as conduction only (radiation and convection neglected), and a shell of uniformly good permeability with no atmospheric pressure effect.
Tooling: a left-right split with 23 loose blocks
Pattern accuracy propagates directly into casting accuracy, so the die is the first place where the specification is won or lost. Cavity dimensions were scaled by the alloy contraction. For a casting that shrinks against a core, the linear contraction is
$$\frac{\Delta L}{L}=\left(\alpha_{a}-\alpha_{m}\right)\left(T_{e}-T_{0}\right)$$
where $\alpha_{a}$ and $\alpha_{m}$ are the thermal expansion coefficients of alloy and die material, $T_{e}$ the temperature at which the casting leaves the die, and $T_{0}$ room temperature; without a core, $T_{e}$ is replaced by the solidus temperature, since contraction begins as soon as solidification is complete. With $\alpha_{a}=19.8\times10^{-6}$ mm/(mm·°C), a solidus of 1108 °C and a room temperature of 23 °C, the alloy term alone gives about 2.2%, and this value was used to enlarge the cavity.
The die body is machined from LD8 forged aluminium, which cuts faster than steel with less tool wear. Because the 13 mm twisted blades sit only 2 mm apart at the root, a simple vertical parting is impossible: the die opens left-right, with the aerofoil formed by 23 individual loose blocks extracted one at a time through a circular groove on their top face, and the upper hub formed by an aluminium core. A locating block fixes the first loose block so that the remaining 22 can be assembled to the required fit. The 23 blocks are the most demanding parts of the tool: mating faces are held to ±0.01 mm, blade-forming surfaces to Ra 0.8 µm and block-to-block contact faces to Ra 1.6 µm, with R0.3 mm fillets at the blade root and R1 mm at block corners.
The base plate was split into two pinned halves because the lower boss contains a hexagonal feature that cannot be machined in one piece; the boss is machined separately and assembled to the plate to ±0.01 mm. An early design placed the loose blocks against the outer circumference of the base plate, but that interfered with the finish turning of the plate on a CNC lathe, so the blocks were relocated to the plate centre, where an internal pocket is milled and pinned. Wax is injected sideways into an annular runner that feeds the cavity from all four sides of the aluminium core, which fills the thin blade passages evenly and avoids short runs. Overall die size is about 290 mm across for an 83.4 mm part.
Gating: feeding the last section to freeze
Solidification in this rotor proceeds from blade tip inward: the 1.3 mm tip freezes first, the section thickens toward the root, and the last metal to freeze is the hub, which is subsequently bored or turned. The gating system must therefore feed the hub last and keep a liquid path open to the blade roots throughout. A top-poured sprue-plus-ingate layout was chosen, two castings per mould, with the ingate placed at the hub.
Ingate size was fixed by the usual proportionality to the last-to-freeze section, whose equivalent dimension $D_{c}$ and area $A_{c}$ follow:
$$D_{g}=(0.6\sim1.0)\,D_{c}\qquad A_{g}=(0.4\sim0.9)\,A_{c}$$
With the hub section at 15 mm, the ingate was sized at Ø15 mm on the inner side, Ø19.4 mm on the outer side, 17.4 mm tall and drafted at −10°. The sprue is a 30 × 30 × 160 mm bar and the pouring cup a cone of Ø130 mm top, Ø62 mm bottom and 61 mm height at −45° draft, so that the sprue freezes after the ingate and the cup after the sprue. A machined wax ring was added around the blade tips and welded into the pattern assembly to stiffen the blade row against distortion during handling and shell building. Machining stock was 2 mm on the inner and outer bosses, with 15 mm at the bore, which is also the feeding path.
Three initial process parameters were set from alloy data and shop experience. Shell preheat was fixed at 850 °C — high enough to suppress chill-induced short runs and to drive off volatiles, low enough not to slow cooling and coarsen the structure excessively. Pouring temperature was set at 1480 °C, roughly 100–150 °C above the liquidus, with the upper part of that range permitted for thin sections. Pouring rate was estimated from an empirical relation for gravity casting that scales with casting height and inversely with wall thickness and pouring temperature, giving 39.6 mm/s, rounded to 40 mm/s for the simulation.
Baseline simulation: cracks and shrinkage at the blade tips
The assembly was modelled in three dimensions and meshed in ProCAST 2011 with 1 mm elements on the casting and 5 mm elements on the gating system, producing 63,526 surface elements and 362,729 volume elements; the 8 mm shell was generated from the casting surface. The alloy database was evaluated at a cooling rate of 1 K/s, giving a liquidus of 1332 °C, a solidus of 1108 °C and a latent heat of 295 kJ/kg. Temperature-dependent conductivity and specific heat were supplied for both alloy and shell (Table 2), with Young’s modulus and Poisson’s ratio entered as functions of temperature.
| Material | Property | 300 °C | 400 °C | 500 °C | 600 °C | 700 °C |
|---|---|---|---|---|---|---|
| Superalloy | $\lambda$, W/(m·°C) | 17.8 | 18.3 | 19.5 | 21.2 | 22.7 |
| $c_{p}$, J/(kg·°C) | 481.3 | 493.8 | 514.8 | 539.1 | 573.4 | |
| Shell (silica sol + zircon, 4.5–5 layers, 8 mm) | $\lambda$, W/(m·°C) | 0.61 | 0.59 | 0.59 | 0.59 | 0.62 |
| $c_{p}$, kJ/(kg·°C) | 0.97 | 1.02 | 1.06 | 1.09 | 1.11 |
Casting, gating and shell were coupled with a coincident interface and a heat transfer coefficient of 500 W/(m²·°C), a typical value for metal-to-shell contact in this process; the casting-to-gating interface was set as equivalent, since both are the same alloy. Gravity was applied at 9.8 m/s² along the sprue axis — without it the melt does not fill at all — and cooling was by natural air convection. The run was advanced at 5 steps per second for up to 10,000 steps, with temperature and velocity written every 5 steps and the calculation stopped when the whole model reached 300 °C.
The governing equations are the standard incompressible formulation. Mass conservation gives
$$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$$
momentum conservation in vector form gives the Navier–Stokes relation
$$\rho\left[\frac{\partial \mathbf{u}}{\partial t}+\left(\mathbf{u}\cdot\nabla\right)\mathbf{u}\right]=-\nabla P+\mu\nabla^{2}\mathbf{u}+\rho\mathbf{g}$$
and the free surface is tracked by a volume function
$$\frac{\partial F}{\partial t}+u\frac{\partial F}{\partial x}+v\frac{\partial F}{\partial y}+w\frac{\partial F}{\partial z}=0$$
Energy transport in the melt and heat conduction in the shell are described by
$$\rho c_{p}\frac{\partial T}{\partial t}=\lambda\left(\frac{\partial^{2}T}{\partial x^{2}}+\frac{\partial^{2}T}{\partial y^{2}}+\frac{\partial^{2}T}{\partial z^{2}}\right)+Q$$
with latent heat released over the freezing interval handled by an enthalpy formulation,
$$H=\int_{0}^{T}\rho\,c_{p}(T)\,\mathrm{d}T$$
Under the baseline parameters the mould filled in about 3.4 s, with melt velocity between 0.22 m/s and 3.31 m/s and temperature between 1430 °C and 1480 °C. Flow was orderly, without jetting or splashing. The problem appeared at 2.7 s, before filling was complete: parts of the blade row had already begun to freeze while metal was still entering the cavity, so the last volumes to fill were fed through a partially solid blade. The predicted defect map showed short-run and cold-shut conditions on the blades, and, in the solidification stage, an isolated hot spot near the blade tip that persisted while the mid-span had already cooled. Solid fraction maps confirmed that this region remained liquid long after the surrounding aerofoil, cutting it off from the ingate and leaving it to solidify without feeding. Predicted shrinkage porosity coincided with that location.
The diagnosis was straightforward: a single ingate per casting gave an insufficient feed path into a thin, high-surface-area blade row, and the 850 °C shell removed heat too quickly from the thinnest sections.
Redesign: four symmetric ingates and a hotter shell
The gating system was rebuilt with four symmetric ingates added at the ring, drafted at −8°, to shorten the feed distance to the blade roots and increase the volume of metal available for feeding. The revised assembly was remeshed at the same element sizes, giving 110,604 surface and 611,529 volume elements, with boundary and initial conditions unchanged so that the comparison isolates the design change.
| Metric | Baseline (single ingate) | Redesign (four ingates) |
|---|---|---|
| Surface / volume elements | 63,526 / 362,729 | 110,604 / 611,529 |
| Fill time | ≈3.4 s | ≈2.96 s |
| Fill velocity range | 0.22–3.31 m/s | 0.37–5.59 m/s |
| Fill temperature range | 1430–1480 °C | 1440–1480 °C |
| Premature freezing during fill | Yes, from 2.7 s | No |
| Isolated hot spot at blade tip | Present | Reduced but present |
| Predicted blade defects at 850 °C preheat | Short run, cold shut, shrinkage | Shrinkage only, reduced |
| Predicted defects at 950–1050 °C preheat | — | None detected |
Filling remained orderly. Melt entered through the lower ingates at 1.4 s and the mould was full at 2.96 s with no short run, and the velocity field showed about 1.0 m/s at the ingates, indicating an active feed during solidification. The hot spot near the blade tip nevertheless survived, which pointed to the thermal boundary conditions rather than the gating layout: with a shell at 850 °C and metal at 1480 °C, the temperature difference across the thin tip is large enough that local overheating cannot be equalised by conduction along the blade.
A preheat sweep was therefore run at 850, 950 and 1050 °C, holding everything else constant. At 850 °C, shrinkage porosity remained at the outer ring. At 950 °C and 1050 °C, no cold shuts, shrinkage cavities or porosity were predicted anywhere in the casting. The mechanism is consistent with the cooling behaviour of thin sections: a hotter shell slows heat extraction, keeps a temperature gradient from root to tip instead of a local peak, and allows the ingates to remain liquid long enough to feed the last volume to freeze. The process window was accordingly set at a pouring temperature of 1480–1500 °C, a pouring rate of 40–50 mm/s, and a shell preheat of 950–1050 °C.
Residual stress, distortion and hot tearing
The stress calculation reused the thermal solution, with the alloy treated as an elasto-plastic material, a yield stress of 950 MPa at 20 °C falling to 930 MPa at 100 °C, 718 MPa at 800 °C, 10 MPa at 1139 °C and 2 MPa at 1330 °C, and a temperature-dependent plastic modulus. Total strain was decomposed into elastic, plastic and thermal increments. The shell was displacement-constrained and symmetry conditions applied on the symmetry plane.
Elastic thermal stress scales as
$$\sigma=\alpha E\,\Delta T$$
so it is the difference in cooling rate between thick and thin regions, not the absolute temperature, that drives residual stress here. The hub, the blade root and the region in contact with the ingates cool slowly; the blade tips cool fastest, and the resulting misfit generates the stress field. Effective stress rises monotonically from the hub outward as solidification proceeds, reaching 920–950 MPa at the blade tip after the casting has cooled to room temperature — at, but not above, the 950 MPa yield strength of the alloy at 20 °C, so the tip retains most of that stress as residual stress rather than shedding it by plasticity.
The hot-tearing indicator peaks at the same location, at the blade tips adjacent to the feed path. This is the expected pattern for a thin, isolated section that completes solidification while still connected to a much heavier, slowly freezing hub: contraction of the tip is constrained, the local ductility at the end of freezing is low, and a crack initiates. Since pouring temperature is the dominant lever on hot tearing, the upper part of the 1480–1500 °C window was specified deliberately: a hotter melt slows and equalises solidification in the thin sections and reduces the tendency to crack, at the cost of a coarser structure.
Distortion follows the same gradient. Displacement at the blade tips reached 0.6–0.9 mm in the X direction, growing from essentially zero at the rotor centre outward, and slightly more in Y, the direction in which gravity was applied. In Z, displacement was negligible. Because the alloy is a superalloy, distortion of this magnitude cannot be corrected after casting, which is why the preheat sweep matters: node cooling curves at the blade tip and root diverge sharply at 850 °C and converge at 950 °C and 1050 °C, and the first principal stress at both nodes is correspondingly lower at the higher preheats. At 850 °C the computed first principal stress exceeds the allowable yield stress at both nodes, so the material yields, deforms and locks in the deformation. Raising the preheat to 950–1050 °C keeps the stress below that threshold, which independently confirms the process window derived from the defect predictions.
Shell making and casting practice
The process design has to deliver the simulated boundary conditions in hardware. Wax patterns are injected from a medium-temperature wax (a paraffin–stearic acid blend, supplied ready-mixed, used at about 70 °C) because medium wax gives the surface finish needed for a small, thin part. Injection pressure is 0.3–0.5 MPa, die temperature 25–30 °C and dwell 3–5 s; patterns are quenched in water immediately after ejection to limit distortion, inspected for flash and sinks, cleaned of wax chips, and assembled into trees at 1–2 cm spacing.
Shell building uses a silica sol binder rather than water glass (Table 3). The comparison is not close for this application: water glass shells give Ra 12.5 µm and CT6–CT8 at a relative cost of 1.0 with a 14 h cycle, while silica sol shells give Ra 3.2–6.3 µm and CT4–CT6 at a relative cost of 6.0 with a 60 h cycle. For an 83.4 mm rotor with 1.3 mm walls and a Ra 3.2 µm requirement, the silica sol route is the only one that meets the drawing. The binder is GRJ-30 grade to HB5346-1986, with 29–31% SiO₂, Na₂O below 0.5%, density 1.20–1.22 g/cm³, pH 9–10, kinematic viscosity below 8 mm²/s and colloidal particle size 9–20 nm.
| Item | Water glass shell | Silica sol shell |
|---|---|---|
| Surface roughness, Ra | 12.5 µm | 3.2–6.3 µm |
| Dimensional tolerance | CT6–CT8 | CT4–CT6 |
| Shell build cycle | 14 h | 60 h |
| Relative casting cost | 1.0 | 6.0 |
| Typical use | Carbon steel valve bodies, low-alloy parts; sand casting replacement | Aero engine turbine rotors and stators, thin-walled parts with complex internal cavities |
Three slurries are used: a face coat that contacts the metal and must not react with it or its oxides, a transition coat that bonds face to backup, and a backup coat that supplies strength and resistance to deformation. Formulation and properties are given in Table 4. Mixing order matters — silica sol and wetting agent first, refractory added with lumps broken down, 1 h of stirring, then defoamer, then a further 2 h; total defoamer is capped at 0.3% and the batch is rejected if bubbles persist. Pattern trees are cleaned in a 1:1 mixture of ZF-301 emulsifying cleaner and tap water by dipping about ten times, then drained, dipped into slurry at 45° with rotation, inspected for bubbles and bare patches, and stuccoed in a fluidised bed at 45° with the tree turned to cover shadowed areas.
| Constituent | Face coat | Transition coat | Backup coat |
|---|---|---|---|
| Silica sol, kg | 10 | 10 | 10 |
| Zircon powder, kg | 36–40 | — | — |
| Calcined kaolinite, kg | — | 16–17 | 14–15 |
| Wetting agent, mL | 16 | — | — |
| Defoamer, mL | 12 | — | — |
| Slurry density, g/cm³ | 2.7–2.8 | 1.82–1.85 | 1.81–1.83 |
| Flow-cup viscosity, s | 32 ± 1 | 19 ± 1 | 13 ± 1 |
Drying is the step that decides shell quality, because the silica sol must gel and the interior must dry before the shell can carry its own weight and the metal. Temperature, air velocity and relative humidity dominate. The schedule in Table 5 holds the room at 23 ± 1 °C throughout, keeps humidity at 60–70% for the face and second coats and 40–60% for the backup and seal coats, introduces 6–8 m/s circulating air from the second coat onward, and allows 4–6 h, more than 8 h, more than 12 h and more than 14 h respectively. Stucco grades coarsen with each coat: 100/120 mesh zircon on the face, then 30/60 and 16/30 mesh calcined kaolinite.
| Shell layer | Slurry | Stucco | Temperature | Humidity | Air velocity | Drying time |
|---|---|---|---|---|---|---|
| Face | Face coat | 100/120 mesh zircon | 23 ± 1 °C | 60–70% | — | 4–6 h |
| Second | Face or transition coat | 30/60 mesh kaolinite | 23 ± 1 °C | 60–70% | 6–8 m/s | >8 h |
| Backup | Backup coat | 16/30 mesh kaolinite | 23 ± 1 °C | 40–60% | 6–8 m/s | >12 h |
| Seal | Backup coat | None | 23 ± 1 °C | 40–60% | 6–8 m/s | >14 h |
Dewaxing takes place in a steam autoclave with the pouring cup downward; the cycle is about 10 min, after which the moulds rest for 6 h before firing. Firing is in a tunnel furnace at 1050 °C for about 45 min, and the mould is poured immediately on removal, so the fired shell temperature and the specified 950–1050 °C preheat are the same condition rather than two separate operations. The superalloy is melted in a medium-frequency coreless induction furnace; most superalloys are vacuum induction melted, but this alloy and part size are compatible with air melting under the shell. Pouring follows the simulated window: 1480–1500 °C, 40–50 mm/s, filling a small casting in 5–10 s.
Post-cast processing includes shell removal, shot blasting, abrasive cleaning and dimensional inspection, followed by radiography or fluorescent penetrant inspection of the interior. Internal porosity, if found, is closed by hot isostatic pressing; surface defects are repaired by welding; the blade surfaces are finished by polishing with abrasive-loaded flexible wheels, which plastically deforms the surface layer rather than cutting it.
What the design chain establishes, and its limits
The sequence — cavity sized by a 2.2% contraction, left-right die with 23 loose blocks and a split base plate, top-poured sprue-and-ingate system later expanded to four −8° ingates, finite-element filling and solidification modelling, elasto-plastic stress and distortion analysis, and a silica sol shell schedule — converges on a single, self-consistent process window: pouring at 1480–1500 °C, pouring rate 40–50 mm/s, shell preheat 950–1050 °C. Defect prediction, residual stress at the blade tip and the node-level cooling curves at three preheats all point to the same conclusion, and the melting, dewaxing and firing steps were set to deliver that window in production rather than approximating it.
The limits are equally clear. The predictions rest on an assumption set that removes exactly the physics most relevant to a 1.3 mm wall: radiation between shell and environment, turbulent flow features during filling, oxide films and gas entrainment, and non-uniform shell permeability are all excluded, and interface heat transfer is a single typical value rather than a measured one. The reported effective stress of 920–950 MPa at the blade tip sits at the yield strength of the alloy at room temperature, which means the result is sensitive to the yield data used. And the acceptance of the design is computational: the parameters are validated against computed defect, stress and distortion fields, not against a documented series of production pours with radiographic acceptance statistics. A casting trial campaign at the three preheat levels, with sectioned or radiographed blades at the tip, is the natural next step before the window is frozen into a production specification.