Injection Moulding (2D): Plate Fill, Wall Cross-Section, Gate Freeze-Off and Cycle Timeline

Presets

Live readouts

Graphs

Temperature through the wall at the end of the fill

Cavity pressure over the cycle

Cooling time and cycle time versus wall thickness

Volumetric shrinkage versus packing pressure

Numerical checks

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How to use

Pick a preset and watch the cycle (Space pauses, R restarts). Every setting restarts the shot. Click the plate in the 2D view to move the probe of the wall cross-section. Graphs: temperature through the wall at the gate, mid-plate and far end; the cavity pressure over the cycle; cooling and cycle time against wall thickness; and shrinkage against packing pressure with and without packing.

The science

What you are looking at

One shot of an injection-moulding cycle for a flat plate (100 mm wide, variable length and thickness): the melt fills from the gate, cold mould walls freeze a skin, the gate freezes off and ends the packing, the core cools until the part can be ejected, and the part shrinks. The cycle time is dominated by cooling and so by the square of the wall thickness.

Equations used (identical in the 2D and 3D pages)

Cooling of a slab of thickness h from both faces held at the mould temperature T_w: theta(y,t) = sum over odd k of (4/(k pi)) sin(k pi y/h) exp(-k^2 pi^2 alpha t / h^2), theta = (T - T_w)/(T_m - T_w).
Cooling time until the centre reaches the ejection temperature T_e: t_c = h^2 / (pi^2 alpha) · ln[(4/pi)(T_m - T_w)/(T_e - T_w)].
Frozen skin during contact (semi-infinite conduction, no-flow temperature T_f): s(t) = 2 sqrt(alpha t) · erfinv[(T_f - T_w)/(T_m - T_w)].
Power-law melt tau = K gamma^n, slit flow: wall shear rate gamma_w = ((2n+1)/(3n)) 6Q/(W h_eff^2), pressure drop dP = 2 L K gamma_w^n / h_eff, with h_eff = h - 2 (0.6 s). If dP exceeds the 140 MPa machine limit only the fraction 140/dP of the flow length fills (short shot).
Gate freeze-off: the cooling-time formula applied to the gate thickness with T_f; packing time used t_p = min(setting, t_gate, t_c - t_fill).
Cycle time = t_fill + t_p + remaining cooling + 6 s mould open, eject and close.

Numerical checks run in the page

Finite-difference slab: the centre reaches T_e at the predicted t_c.
Fourier series against the finite-difference centre temperature.
Frozen-layer position from a finite-difference semi-infinite solid against the erf formula.
Velocity profile integrated across the slit against the imposed volume flow.

Honest simplifications

Textbook-scale model: constant thermal properties, frozen skin averaged by a factor 0.6 for the fill, no latent heat of crystallisation, no viscous heating in the pressure estimate (a bound is shown), a 1D plate with one gate, no weld lines, fibre orientation or warpage. The shrinkage and sink-depth numbers use an empirical packing-efficiency index and are illustrative trends, not predictions for a real tool. Material constants are round representative values, not a datasheet.

What to try

Standard PP plate versus Thin wall, slow fill: watch the fill pressure and the frozen skin.
Double the thickness: the cooling time rises about fourfold.
Gate too small: packing stops early and shrinkage rises even with high pressure.
Raise the mould temperature: thinner skin and easier fill but a longer cycle.