Arte SheetsLearn. Try. Understand.

Composites Manufacturing, Pultrusion Heated-Die Residence Time, Pull Force & Line Speed

Pultrusion Composite Die Residence Time & Pull Force Formula

Calculate Heated-Die Cure Residence Time (s), Net Fiber Cross-Section Area (mm²), Viscous-Gelation Die Wall Pull Force (kN), and Continuous Profile Mass Output (kg/h).

Crank pultrusion haul-off speed 80% too fast and the exothermic cure peak gets dragged OUTSIDE the chrome-plated steel die!

Continuous **FRP Composite Pultrusion** pulls unidirectional E-glass or carbon fiber rovings (`Fiber Volume Fraction V_f ≈ 0.55–0.68`) saturated with thermoset vinyl-ester, polyester, or epoxy resin through a multi-zone heated steel die of Length `L_{die}` (m), Cross-Sectional Area `A_p` (mm² -> **Net Fiber Area `A_f = A_p * V_f`** mm²), and Wetted Perimeter `P_{die}` (mm) at Haul-Off Speed `v` (`m/min`). Thermoset gelation and `>=92%` degree-of-cure conversion demand sufficient **Heated-Die Residence Time `t_{res} = (L_{die} / v) * 60`** (`s`, typically `75–140` s)—pull faster and the exothermic peak shifts past the die exit, causing centerline delamination cracks and uncured styrene blisters! Meanwhile, hydraulic reciprocating grippers must overcome **Die-Wall Shear Pull Force `F_{pull} = (P_{die} / 1,000) * L_{die} * tau_{avg}`** (`kN`, combining entrance viscous drag, bulk compaction pressure, and pre-shrinkage friction `tau_{avg}` kPa) while producing **Hourly Profile Throughput `dot_m = (A_p * 10^{-6}) * (v * 60) * rho_c`** (`kg/h`)!

Verify on a `480` mm² Structural E-Glass / Vinyl-ESTER Channel Pultrusion Line—Heated_Die_Length `L_{die}` = 1.20 m (B2), Gripper_Line_Speed `v` = 0.75 m/min (B3), Profile_Cross-Section `A_p` = 480 mm² (B4), Fiber_Volume_Fraction `V_f` = 0.62 (B5), Die_Cavity_Perimeter `P_{die}` = 140 mm (B6), Mean_Die-Wall_Traction `tau_{avg}` = 48.0 kPa (B7), and Cured_Composite_Density `rho_c` = 2,030 kg/m³ (B8): Die Residence Time holds `96.0` s (E2), Fiber Area equals `297.6` mm² (E3), Hydraulic Pull Force equals `8.06` kN (E4), and Line Output hits `43.85` kg/h (E5)!

Pultrusion Line KPI (L=1.20 m, Ap=480 mm², Vf=0.62, P=140 mm, v=0.75 vs 1.35 m/min)FormulaVerified Output
Die Cure Residence Time (s)(Die_Length_m / Line_Speed_m_min) * 6096.0 s (53.3 s under-cured @ 1.35 m/min!)
Net Fiber Cross-Section (mm²)Profile_Area_mm2 * Fiber_Vol_Fraction_Vf297.6 mm²
Hydraulic Gripper Pull Force (kN)(Perimeter_mm / 1000) * L_m * Shear_kPa8.06 kN
Continuous Mass Output (kg/h)(Area_mm2 * 1e-6) * (v * 60) * Density43.85 kg/h (78.93 kg/h @ 1.35 m/min)

Pultrusion Die Residence Time, Roving Fill Area, Wall Traction & Output Formula

Validate `Die_Length L_{die} > 0.3` m, `Line_Speed v > 0.05` m/min, `Area A_p > 10` mm², `Fiber_Fraction V_f` in `[0.30, 0.80]`, `Perimeter P_{die} > 10` mm, `Wall_Shear > 1` kPa, and `Density` in `[1,100, 2,400]` kg/m³!

=LET(ld_m, B2, vs_m, B3, ap_m, B4, vf_r, B5, pd_m, B6, tw_k, B7, rc_k, B8, IF(OR(ld_m <= 0.3, vs_m <= 0.05, ap_m <= 10, vf_r < 0.3, vf_r > 0.8, pd_m <= 10, tw_k <= 1, rc_k < 1100, rc_k > 2400), "Invalid Pultrusion Input", ROUND((ap_m * 0.000001) * (vs_m * 60) * rc_k, 2)))

Over-Sped 1.35 m/min Exotherm Blowout & Uncured Core Check (Set Line Speed B3 = 1.35 m/min)

Push haul-off speed to `v` B3 = 1.35 m/min without lengthening the `1.20` m die or adding RF preheating: Nominal Output E5 jumps to `78.93` kg/h, yet Die Residence Time E2 plunges to `53.3` s—pushing exothermic peak shrinkage outside the constrained die cavity and splitting thick web fillets!

=IF(ISTEXT(E5), E5, ROUND((B2 / B3) * 60, 1))

Try the example

Use the original values or change them to test your understanding.

Further reading