Extrusion Process: Screw Design, Flow Mechanics and Die Geometry

Melt flow and cooling line setup - Visual reference for Extrusion Process: Screw Design, Flow Mechanics and Die Geometry

1. Why This Topic Matters

Extrusion is the continuous polymer processing method used to manufacture pipes, films, sheets, profiles, and wire insulation. The single-screw extruder converts solid polymer pellets into a homogeneous melt via three functional screw zones: Feed Zone, Compression/Melting Zone, and Metering Zone. Understanding screw $L/D$ ratio, compression ratio, drag flow ( $Q_{drag}$ ), pressure backflow ( $Q_{pressure}$ ), and flight leakage flow ( $Q_{leakage}$ ) governs throughput stability, melt temperature uniformity, and dimensional tolerances.

2. Learning Objectives

By completing this lesson, you will be able to:

Analyze the 3 functional zones of a single-screw extruder ( $L/D = 24:1 - 30:1$ ).
Calculate net volumetric throughput ( $Q_{net} = Q_{drag} - Q_{pressure} - Q_{leakage}$ ) combining drag flow, pressure backflow, and leakage flow.
Derive flight-clearance leakage flow ( $Q_{leakage}$ ) from radial clearance and geometry-supported 10 metering flight turns.
Compare coat-hanger film dies, spiral mandrel blown film dies, and annular pipe dies.

3. Core Theory & Extruder Architecture

graph TD
    A["Hopper Solid Feed (Pellets / Flakes)"] --> B["Feed Zone (Solids Conveying, Constant Channel Depth Hf)"]
    B --> C["Compression Zone (Melting & Tapered Channel Depth Hf to Hm)"]
    C --> D["Metering Zone (Homogenization & Constant Shallow Channel Depth Hm)"]
    D --> E["Breaker Plate & Screen Pack (Contaminant Filter & Backpressure)"]
    E --> F["Extrusion Die (Shaping Orifice: Pipe / Sheet / Profile)"]

4. Equations & Net Throughput Calculation

4.1 Screw-Channel Fluid Mechanics Model

The net volumetric flow rate $Q_{net}$ in the metering section equals drag flow $Q_{drag}$ minus pressure backflow $Q_{pressure}$ minus flight clearance leakage $Q_{leakage}$ :

Q_{net} = Q_{drag} - Q_{pressure} - Q_{leakage}

ext{Drag Flow: } Q_{drag} = rac{1}{2} pi^2 D^2 N h sinphi cosphi

ext{Pressure Flow: } Q_{pressure} = rac{pi D h^3 Delta P}{12 mu L_{axial}}

ext{Flight Clearance Leakage Flow: } Q_{leakage} = rac{pi D delta^3 Delta P_{turn}}{12 mu e} cdot N_{turns}

Key Note

[!NOTE] Leakage Flow Geometry & Fluid Mechanics Derivation: For a standard square-pitched screw ( $D = 60 ext{ mm}$ , pitch $p = 60 ext{ mm/turn}$ ), the $600 ext{ mm}$ axial metering length contains exactly $N_{turns} = 600 / 60 = 10 ext{ turns}$ . The pressure drop per flight turn is $Delta P_{turn} = 8.0 ext{ MPa} / 10 ext{ turns} = 8.0 imes 10^5 ext{ Pa/turn}$ . Per-turn leakage across radial clearance $delta = 0.10 ext{ mm}$ over flight land width $e = 5.0 ext{ mm}$ is $Q_{leak,turn} = 8.378 imes 10^{-9} ext{ m}^3/ ext{s}$ . Total leakage across all 10 metering turns is $Q_{leakage} = 10 imes 8.378 imes 10^{-9} = 8.378 imes 10^{-8} ext{ m}^3/ ext{s} = mathbf{0.0838 ext{ cm}^3/ ext{s}}$ . Because leakage flows backward from pushing face to trailing face across radial clearance, it opposes forward net throughput.

Explicit Input Parameter Table for Reproduction

Input Parameter	Symbol	Value	Unit	Definition
Screw Outer Diameter	$D$	$0.060$	$ext{m}$	$60 ext{ mm}$ outer screw diameter
Metering Channel Depth	$h$	$0.0025$	$ext{m}$	$2.5 ext{ mm}$ metering flight depth
Screw Rotational Speed	$N$	$1.50$	$ext{rev/s}$	$90 ext{ rpm}$ rotational speed
Helix Flight Angle	$phi$	$17.65^circ$	Degrees	Square-pitched screw ( $sinphicosphi = 0.2889$ )
Metering Zone Axial Length	$L_{axial}$	$0.60$	$ext{m}$	$600 ext{ mm}$ metering section length
Metering Flight Turns	$N_{turns}$	$10$	Turns	$L_{axial} / ext{pitch} = 600 / 60 = 10 ext{ turns}$
Die Head Backpressure	$Delta P$	$8.0 imes 10^6$	$ext{Pa}$	$8.0 ext{ MPa}$ ( $80 ext{ bar}$ ) die head pressure drop
Melt Dynamic Viscosity	$mu$	$300$	$ext{Pa}cdot ext{s}$	Dynamic viscosity at processing shear rate
Radial Flight Clearance	$delta$	$0.00010$	$ext{m}$	$0.10 ext{ mm}$ radial clearance gap
Flight Land Width	$e$	$0.0050$	$ext{m}$	$5.0 ext{ mm}$ axial flight land width

Worked Numerical Example:

Problem: Calculate drag flow $Q_{drag}$ , pressure backflow $Q_{pressure}$ , flight leakage $Q_{leakage}$ , net volumetric throughput $Q_{net}$ , and HDPE mass output $dot{m}$ ( $ho = 0.90 ext{ g/cm}^3$ ) using the parameter table above.

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Solution:

Calculate Drag Flow ( $Q_{drag}$ ):

Q_{drag} = rac{1}{2} imes pi^2 imes (0.060)^2 imes 1.50 imes 0.0025 imes 0.2889 = 1.923 imes 10^{-5} ext{ m}^3/ ext{s} = mathbf{19.23 ext{ cm}^3/ ext{s}}

Calculate Pressure Backflow ( $Q_{pressure}$ ):

Q_{pressure} = rac{pi imes 0.060 imes (0.0025)^3 imes (8.0 imes 10^6)}{12 imes 300 imes 0.60} = rac{0.02356}{2160} = 1.091 imes 10^{-5} ext{ m}^3/ ext{s} = mathbf{10.91 ext{ cm}^3/ ext{s}}

Calculate Flight Leakage Flow ( $Q_{leakage}$ ):

Q_{leak, turn} = rac{pi imes 0.060 imes (0.00010)^3 imes (8.0 imes 10^5)}{12 imes 300 imes 0.0050} = rac{1.508 imes 10^{-7}}{18} = 8.378 imes 10^{-9} ext{ m}^3/ ext{s}

Across 10 geometry-supported metering turns:

Q_{leakage} = 10 imes 8.378 imes 10^{-9} = 8.378 imes 10^{-8} ext{ m}^3/ ext{s} = mathbf{0.0838 ext{ cm}^3/ ext{s}}

Calculate Net Throughput ( $Q_{net}$ ) and HDPE Mass Output ( $dot{m}$ ):

Q_{net} = 19.23 - 10.91 - 0.0838 = mathbf{8.236 ext{ cm}^3/ ext{s}}

dot{m} = 8.236 ext{ cm}^3/ ext{s} imes 3,600 ext{ s/hr} imes 0.90 ext{ g/cm}^3 = 26,684.6 ext{ g/hr} = mathbf{26.69 ext{ kg/hr}}

5. Industrial Applications

HDPE Water Pipe Extrusion: Annular basket-die extrusion in Vadodara cluster. (Illustrative Indian industry scenario based on BIS certified pipe manufacturing).

6. Key Takeaways & Glossary

$L/D$ Ratio: Ratio of screw flighted length to outside diameter ( $24:1$ to $30:1$ standard).
Compression Ratio: Ratio of feed channel depth to metering channel depth ( $2.5:1$ to $3.5:1$ ).

7. Sources & Standard References

ISO 294-1:2017 — Plastics — Injection moulding of test specimens of thermoplastic materials, ISO.
Rauwendaal, C. (2014). Polymer Extrusion, 5th Ed., Hanser Publishers.