WOBBLpulley.py
Will the hub of this sand cast aluminum pulley shrink and leave porosity?
MARGINAL
Freezes sound in 2.2 min, fed throughout by the risers, which freeze at 2.24 min, with at most 0.466% Niyama porosity.
freezes in
2.2 min
shrinkage pockets
0
worst porosity
0.466%
riser time ratio
1.02
Confidence medium
- process estimate: freezing times follow the latent heat (321 to 500 kJ/kg between sources, up to 40% on time) and the mold's heat uptake, which varies about 20% with sand and compaction
Simulation
Checks
| status | check | result |
|---|---|---|
| pass | mesh convergence | time for 99% of the casting to freeze settled: 127 -> 130 s over 2 meshes, last change 1.9% |
| pass | time step | half the time step moves the freezing time from 127 to 127 s (0.13%) |
| pass | energy balance | the cooling metal and sand give up 278 kJ, the rest of the mold takes it in and 0.00822 kJ leaves its outside, closing to 4.7e-07% |
| info | hand calculation | Chvorinov's rule with modulus V/A = 3.58 mm and mold constant 611 s/cm2 gives 1.31 min, and the casting freezes in 2.2 min here (1.68x), a spread that comes from a shape far from compact, which a single modulus cannot capture |
| pass | feeding | every part of the casting freezes before the metal on its path back to a riser does, so liquid can reach it as it shrinks |
| warn | riser | the risers freeze at 2.24 min, 1.02x the casting, and by hand the riser's modulus is 1.50x the casting's against the rule of thumb of 1.2x |
| warn | porosity | the dimensionless Niyama criterion gives at most 0.466% shrinkage porosity, at (-4.48, 7.07, -6.66) mm, with 5.8% of the casting over 0.1% |
| pass | units and sanity | poured at 720 C into silica sand, bonded at 25 C, a 151 cm3 casting frozen after 2.2 min |
How to fix it
Make the riser about 1.1x wider
The risers freeze at 1.02x the casting's time and should outlast it by 1.2x. Freezing time grows with the square of the modulus, so a riser about 1.1x the diameter, or an insulating sleeve, gives that margin.
Steepen the freezing toward the riser
Porosity of 0.466% at (-4.48, 7.07, -6.66) mm comes from a shallow thermal gradient late in freezing. Taper the section so it thickens toward the riser, or chill the far end, so that region freezes in a clear order.
Assumptions
- Wobbl guessed: no riser given, so Wobbl places risers over the hot spots by the modulus rule and checks them.
- No risers were given, so Wobbl placed 1 over the hot spots of a coarse freeze without them, each sized by the modulus rule: riser d=25 h=37.5 at -3.1,6.3,21.
- Aluminum A356 (Al-7Si-0.3Mg): liquidus 616 C, solidus 551 C, latent heat 403 kJ/kg, 151 W/(m K), 963 J/(kg K), 2670 kg/m3, shrinkage on freezing 5.57%. Sources: liquidus, freezing range, shrinkage and Niyama data from Carlson and Beckermann 2009; latent heat 403 kJ/kg as quoted for A356.0 by the ABM 2015 thermal analysis study (measured values run from 321 to 500 kJ/kg); density, conductivity and specific heat from MatWeb A356.0-T6; Scheil curve with k = 0.13 and the Al-Si eutectic at 577 C.
- Silica sand, bonded: 0.5 W/(m K), 1600 kg/m3, 1050 J/(kg K), 26.5 mm thick around the part, its outside cooled at 10 W/(m2 K) to 25 C. Sources: 0.5 W/(m K) and 1600 kg/m3 as in common foundry cost models (laser flash measurements give 0.34 to 0.4 W/(m K)); 1050 J/(kg K) is the 25 to 1300 C mean measured for silica sand in J. Japan Foundrymen's Society 49 (1977) 747.
- The cavity fills at once with metal at 720 C, so the gating and the cooling while it fills are not modeled.
- Metal and mold touch perfectly throughout. The air gap that opens as the casting shrinks slows cooling late in freezing, so real freezing times run somewhat longer.
- Shrinkage is fed only along paths of metal that freezes later. Gas porosity from hydrogen is not modeled, which assumes well degassed metal.
- Risers are blind cylinders sitting on the casting and poured at the same temperature. The part is cast the way it is drawn, with +z up.
- Porosity comes from the dimensionless Niyama criterion of Carlson and Beckermann (2009), with the thermal gradient and cooling rate taken 10% of the freezing range above the solidus.