Large Aluminium Die-Casting Lab

Solidification time, mould filling and porosity of a big thin-walled casting. Drag the gate bar on the mould map; click the map to place a probe.

Mould map

Presets

Part, gate and process

Gate edge

Verdict and readouts

Graphs

Probe cell temperature

Shot profile: plunger speed (blue) and metal pressure (orange)

Part consolidation economics (illustrative)

Stamped parts replaced70

The stamped-assembly counts are simple rules of thumb set by the sliders, not data from any company. Joints = 1.6 per extra part, 8 spot welds per joint, 60 welds per robot, 0.25 mm tolerance per joint (root-sum-square).

Experiments

1. Solidification time vs (V/A)²: 1-D finite-difference solver against the closed formula (current melt, die and interface settings).

2. Fluidity length vs wall thickness at the current mean front speed: time-stepped lumped enthalpy integration against the closed form.

The science

What is being simulated

High-pressure die casting (HPDC) injects molten aluminium alloy into a steel die through a thin gate in tens of milliseconds, then holds pressure while the metal freezes. Inspired by publicly reported single-piece "giga-casting" of large vehicle underbody structures that replace dozens of stamped parts, this lab models a generic 1.6 m x 1.1 m thin-walled plate with ribs and thick bosses. Wall, rib, boss, gate and process values are illustrative, not any company's data.

Solidification time: Chvorinov's rule

The modulus M = V/A (volume over cooling area) sets how long a section stays liquid. Chvorinov: t_s = B (V/A)^n with n about 2 for mould-limited cooling. This lab uses the heat balance for a slab frozen against a die with interface conductance h:

t_s = (ρ H' / ΔT) [ M / h_eff + M² / (2 k_s) ]
1/h_eff = 1/h + 0.85 · 2√(t/π) / e_d, e_d = √(k ρ c)_die
H' = L + c·(T_pour − T_liq), ΔT = ½(T_liq+T_sol) − T_die

The M² term is the classic Chvorinov (n = 2) behaviour; the M term is interface/die limited, so thin die-cast walls show an effective exponent between 1 and 2. The 0.85 averaging factor of the die-side resistance was fitted once against the 1-D finite-difference solver (agreement within a few percent, see experiment 1). Junctions, rib crossings and bosses raise M locally by a "fillet" multiplier (hot spots). Those multipliers are illustrative modelling choices.

Mould filling, jet numbers, cold shuts

Plunger speed v₂ gives the flow rate Q = A_sleeve v₂; the gate velocity is v_g = Q / (gate length x gate thickness). Publicly typical gate velocities are about 30 to 60 m/s. At the gate Re = ρ v d / μ and We = ρ v² d / σ (d = gate thickness): Re about 10⁵ and We about 10⁴, so the jet is turbulent and atomises, which entrains air.

The front advances by an eikonal (fast-sweeping) solution with front speed proportional to the square root of the local section thickness (ribs fill first - "race-tracking"); times are scaled so that the cavity volume equals Q x t_fill. While travelling, the metal loses heat to the die; in a lumped model dT/dt = −h (T−T_die) / (ρ c M) above the liquidus and with c_eff = c + L/(T_liq−T_sol) in the mushy zone. The front is taken to choke at 30 % solid fraction. A cold shut / misrun is flagged where the arrival time exceeds that choke time; the fluidity length is L_f = v_front t_choke (Flemings-style).

Gas and shrinkage porosity

Gas: air is entrained when the slow-phase wave in the shot sleeve breaks (Froude number Fr = v₁/√(g h), h = melt depth) and when the gate jet is very fast; it gathers where the fronts arrive last, unless a vacuum is applied. The index is an illustrative 0-1 score, not a measured porosity.

Shrinkage: aluminium shrinks about 6.5 % on freezing. Intensification pressure p_int feeds liquid through the gate only while a liquid path to the cell exists. The lab finds, for every cell, the minimax freezing time along any path from the gate (bottleneck path); where that path closes before the cell has frozen, the remaining liquid fraction shrinks unfed. Pressure densification is modelled as removing up to 70 % of the unfed shrinkage at 80 MPa. Isolated thick bosses connected only through thin walls are the textbook result.

Cycle time and consolidation

Cycle = fixed handling overhead (38 s, illustrative) + slow shot + fill + hold until the last hot spot freezes + ejection dwell. Thick bosses lengthen the hold of the whole casting, so hot spots cost both quality and throughput. The comparison table counts parts, welded joints, robots and root-sum-square tolerance stack-up for a stamped assembly versus one casting.

Simplifications

2-D plan-view model; through-thickness conduction is in the modulus formula, in-plane conduction is neglected.
No coupled Navier-Stokes free-surface solver; the front is a geometric eikonal solution scaled by volume continuity.
Constant material properties; one alloy (Al-Si type, 555-595 degC).
Porosity indices are qualitative risk maps, not predictions for a real part.

References

Chvorinov, N. (1940) on casting solidification time; Flemings, M. C. (1974) Solidification Processing (fluidity); Campbell, J. (2015) Complete Casting Handbook (entrainment, feeding); Garber, L. W. (1982) and Brevick et al. on shot-sleeve critical velocity; Carslaw and Jaeger (1959) for semi-infinite conduction; Beckermann and Viskanta (1993) on mushy-zone heat capacity.

Independent educational model, not affiliated with or endorsed by any company named here; trademarks belong to their owners. Numbers are textbook-level/publicly reported approximations.