Investment casting produces complex metal parts by surrounding a sacrificial pattern with a ceramic shell, removing the pattern, and pouring liquid metal into the resulting cavity. When the pattern is made by selective laser sintering (SLS) from polystyrene powder, the digital model can move from CAD to a cast metal part in days rather than weeks. The trade-off is a dimensional chain: STL tessellation, layer-based sintering, wax infiltration, shell firing, and alloy solidification each shift the geometry. For thin-walled parts such as impellers and diffusers, those shifts can exceed the machining allowance before the first metal part is poured.
The dimensional chain in SLS-based investment casting
The process route is sequential: CAD model → STL file → SLS polystyrene prototype → wax-infiltrated pattern → ceramic shell → alloy casting. Each stage can be represented by a directional transfer coefficient. If \(L_0\) is the CAD dimension, \(L_1\) the SLS prototype, \(L_2\) the pattern after primary wax infiltration, and \(L_3\) the casting, the chain can be written as
$$L_1=\alpha_1 L_0,\qquad L_2=\alpha_2 L_1,\qquad L_3=\alpha_3 L_2$$
so that the combined CAD-to-pattern coefficient is
$$L_2=\alpha_{2/0}L_0,\qquad \alpha_{2/0}=\alpha_1\alpha_2$$
The coefficients are not material constants. They depend on powder grade, layer thickness, laser energy density, part orientation, powder-bed thermal history, shell system, and alloy. Their value is that they make the dominant directions and size ranges visible before compensating a complex part.
SLS pattern accuracy: data, layer, and process window
STL tessellation is the first loss. A curved surface is approximated by planar triangles, so a coarse chord tolerance truncates curvature before the part reaches the machine. Reducing chord tolerance from 0.08 mm to 0.003 mm raised the triangle count from 70,258 to 814,858 in a representative case, improving geometric fidelity while increasing file size and slicing load. Layer thickness introduces a second approximation: a large layer leaves a visible stair-step on free-form surfaces, and wax infiltration may not fill those steps completely. For investment casting patterns, the surface must be smooth enough for the ceramic shell to reproduce it.
The SLS process window used for polystyrene patterns in this route is summarized below. The values are specific to the machine, powder, and geometry, but they show the parameter set that produced the transfer data discussed later.
| Parameter | Value |
|---|---|
| Pattern material | Polystyrene powder |
| Preheat temperature | 95 °C |
| Laser | CO₂ laser, maximum 60 W |
| Laser power | 30 W |
| Spot diameter | ≤0.32 mm |
| Layer thickness | 0.14 mm |
| Scan speed | 3000 mm/s |
| Scan spacing | 0.31 mm |
| Build envelope | 310 mm × 310 mm × 255 mm |
On a stepped linear specimen, the measured SLS error was strongly direction-dependent. The X-direction relative error moved from about −1.0% to +1.1% along the specimen; the Y-direction stayed negative, between about −1.0% and −1.6%; the Z-direction changed most sharply, from +5.857% at a small Z height to −0.444% at the largest Z height. The sign change matters. Small Z sections are dominated by first-layer warpage, secondary sintering, and powder adhesion, which tend to enlarge the part. As Z height increases, bulk sintering shrinkage becomes more influential and the error moves negative. Around Z dimensions above 22 mm, the SLS prototype approached a smaller, more stable relative error.
| Stage | X | Y | Z | Relation |
|---|---|---|---|---|
| CAD model to SLS prototype | 0.99142 | 0.99425 | 1.01504 | \(L_1=\alpha_1L_0\) |
| SLS prototype to primary wax-infiltrated pattern | 0.99872 | 1.00145 | 1.00071 | \(L_2=\alpha_2L_1\) |
| Wax pattern to 304 stainless steel casting | 0.99259 | 0.99399 | 0.99509 | \(L_3=\alpha_3L_2\) |
| Combined CAD to primary infiltrated pattern | 0.99015 | 0.99569 | 1.01576 | \(L_2=\alpha_{2/0}L_0\) |
For an axisymmetric diffuser, the X coefficient was applied to both radial directions, giving a radial coefficient of 0.99015; the direct Y product is listed for completeness. The Z coefficient above 22 mm was 1.01576. These values show why a single “shrinkage factor” is inadequate for a complex part: the radial and vertical directions do not behave identically, and the vertical behavior changes with height.
Wax infiltration: strength versus surface finish
An SLS polystyrene pattern is porous. Primary wax infiltration fills the interparticle voids and raises strength; secondary infiltration deposits a thin surface layer and improves finish. The two steps serve different purposes and therefore have different dimensional signatures.
Primary infiltration at 65 °C for 20 s gave the smallest dimensional deviation in the tested window. At lower temperature, wax viscosity was high, penetration was limited, and excess wax remained on the surface; at higher temperature, penetration increased but thermal expansion and wax pickup raised the deviation again. Secondary infiltration at 75 °C for 4 s produced the best surface quality. The single-side wax layer after secondary infiltration ranged from 0.0100 mm to 0.0683 mm, with an average of 0.0392 mm.
| Condition | Temperature / time | Main effect | Average surface roughness |
|---|---|---|---|
| As-built SLS pattern | — | Porous, powder-adhered surface | 33.928 μm |
| Primary infiltration | 65 °C / 20 s | Pore filling, strength increase | 25.137 μm |
| Secondary infiltration | 75 °C / 4 s | Surface smoothing, wax layer formation | 2.203 μm |
The surface roughness fell by about 93.5% from the as-built SLS pattern to the secondary-infiltrated pattern. That improvement is necessary for investment casting because the shell replicates the pattern surface. The dimensional cost is the wax layer itself: secondary infiltration mainly adds a thin, fairly uniform coating, while primary infiltration changes the bulk by filling pores. Treating them as one “waxing” step hides that distinction.
Shell and casting: where contraction enters
The ceramic shell was built with a silica-sol binder and a zircon face coat, followed by kaolin chamotte backup layers. The face coat used zircon powder with a 325 mesh size and zircon sand stucco at 80–120 mesh; transition and backup stucco used kaolin chamotte at 220 mesh and 16–30 mesh. The shell had 7–8 coats. After drying, it was fired in two stages up to 1000 °C, preheated to 1115 °C, and poured with 304 stainless steel at 1600 °C.
| Parameter | Value |
|---|---|
| Alloy | 304 stainless steel |
| Liquidus / solidus | 1454 °C / 1213 °C |
| Shell system | Silica sol binder; zircon face coat; kaolin chamotte backup; 7–8 layers |
| Shell preheat | 1115 °C |
| Pouring temperature | 1600 °C |
| Pouring rate, final trial | 3 kg/s |
| Casting tolerance grade | CT4–CT6 |
The casting stage introduced a negative dimensional error in all three directions. For wax pattern dimensions below about 20 mm, contraction was small enough to fall within the allowed range. Above 20 mm, contraction became clear, with an average shrinkage of about 0.75%. The casting coefficients were 0.99259 in X, 0.99399 in Y, and 0.99509 in Z. This is consistent with the physics: liquid and solidification shrinkage are partly fed by the gating system, while solid-state contraction and mechanical resistance from the shell determine the final deviation.
Complex diffuser impeller: deviation mapping
The demonstration part was a thin-walled 304 stainless steel diffuser impeller with a maximum outer diameter of 262.99 mm and a height of 142.85 mm. Eight blades are distributed on the upper section and sixteen on the side. Minimum wall thickness is 1.88 mm in the upper blades and 2.40 mm in the side blades, so the part is sensitive to both thermal gradients and pattern distortion.
After SLS building and primary wax infiltration at 65 °C, the pattern was scanned with a hand-held laser scanner and compared with the CAD model in Geomagic Control using best-fit alignment and 3D comparison. The overall average positive deviation was +0.4212 mm; the average negative deviation was −0.7269 mm. The sign pattern was not random. Outer surfaces tended to shrink, while inner surfaces tended to grow or shrink less.
| Region | Average deviation |
|---|---|
| Overall positive deviation | +0.4212 mm |
| Overall negative deviation | −0.7269 mm |
| Upper blade outer surface | −0.7712 mm |
| Side blade outer faces and junctions | −0.6461 mm |
| Top planar face | −0.7230 mm |
| Lower outer surface | −2.47135 mm |
| Side blade outer surface | −1.6918 mm |
The large negative deviation on the lower outer surface reflects the initial build condition: the first sintered layers lose heat to the powder bed and to the machine environment, and warpage can dominate before bulk sintering shrinkage takes over. Inner regions receive heat from the already sintered material, so their radial contraction is smaller. In the diffuser, the inner positive deviation was roughly half of the outer negative contraction. This thermal asymmetry is the reason a single radial compensation factor cannot bring every feature into tolerance on a large part.
Compensation and machining allowance
The measured chain was inverted to correct the CAD model before building. For a coefficient \(\alpha_{2/0}\), the correction factor is
$$K=\frac{1}{\alpha_{2/0}}$$
For the radial direction, the applied correction factor was 1.00985; for Z sections above 22 mm, it was 1.00339. The corrected STL was offset in Magics, rebuilt by SLS, primary-infiltrated, and scanned again. Most deviations after correction fell within ±0.5 mm. Machining allowance was then added to the as-cast blank. With a required machining allowance \(\mathrm{RMA}=1.4\) mm and casting tolerance \(\mathrm{CT}=0.56\) mm, the outer and inner allowances were
$$R_1=F+\mathrm{RMA}+\frac{\mathrm{CT}}{2}=F+1.68\ \mathrm{mm}$$
$$R_2=F-2\mathrm{RMA}-\frac{\mathrm{CT}}{2}=F-3.08\ \mathrm{mm}$$
where \(R_1\) is the outer blank dimension, \(R_2\) the inner cavity dimension, and \(F\) the final machined dimension. The outer surfaces received 1.68 mm of allowance; the inner cavity received 3.08 mm.
| Feature | Nominal | Before compensation | After compensation | Relative error before | Relative error after |
|---|---|---|---|---|---|
| Lower inner diameter | 166.27 mm | 165.92 mm | 166.26 mm | −0.211% | −0.006% |
| Lower outer diameter | 191.37 mm | 190.70 mm | 191.11 mm | −0.350% | −0.134% |
| Inner wall height | 123.85 mm | 123.23 mm | 123.62 mm | −0.501% | −0.186% |
| Maximum outer diameter | 269.80 mm | 268.09 mm | 268.77 mm | −0.634% | −0.382% |
The lower inner diameter was effectively corrected, with an average deviation of −0.014 mm. The maximum outer diameter improved but remained negative, because the outer powder bed had no comparable heat source and the thin blades cooled faster than the inner hub. In other words, the correction factor removed the systematic part of the error, but not the thermal gradient that produced it.
Casting simulation and trial validation
The gating system was designed for gravity investment casting with eight ingates. A first simulation in ProCAST used a 3 mm mesh on the casting, a 5 mm mesh on the gating, and a 10 mm shell. The filling sequence was bottom-up through the sprue and runners, with the upper blades filling by about 4.8 s and the side blades by about 9.1 s; the cavity was essentially full by about 14.1 s. Solidification was progressive from the thin blades toward the hub and finally the sprue, with completion at about 2086.7 s. Shrinkage porosity was concentrated in the gating system rather than in the blades.
The first trial pour still showed incomplete filling at the tips of the upper blades and defects near the lower side blades. The upper blades are thin and fill first, so air can be trapped before the metal arrives. The gating was revised by adding a blind riser to each of the eight upper blades for venting and an open riser to each side blade for venting and feeding. The revised shell was fired, preheated to 1115 °C, and poured at 1600 °C with a pouring rate of 3 kg/s. After knockout, cut-off, and blasting, the casting was complete, with no misrun and a clean contour.
Practical rules and limitations
The useful output of this chain is not a universal shrinkage number but a direction- and size-dependent correction procedure. Several rules follow from the data.
- Use separate radial and vertical coefficients. In the SLS stage, Z behaved differently from X and Y, and the Z error changed sign with height.
- Do not apply a small-Z coefficient to a large-Z section. Above about 22 mm, the SLS error became more stable; below that, warpage and secondary sintering dominated.
- Treat primary and secondary wax infiltration separately. Primary infiltration changes bulk dimensions and strength; secondary infiltration mainly adds a thin surface layer.
- Apply casting contraction only after the pattern stage is corrected. For 304 stainless steel in this shell system, dimensions above 20 mm shrank by about 0.75% on average.
- Where the powder bed has no heat-source compensation, increase the correction beyond the calculated value. For thin outer blades and similar low-thermal-mass features, a factor of 1.5–2 times the calculated compensation was more effective than the nominal correction.
These coefficients remain process-specific. A different SLS machine, powder batch, layer thickness, scan strategy, shell recipe, or alloy will shift them. The method is transferable: build a stepped or feature-rich coupon, measure the directional chain, invert it for the CAD offset, and validate by scanning the compensated pattern before committing to shelling and pouring. For complex investment castings, that validation step is often the difference between a corrected pattern and a corrected casting.