Extrusion, Fibre Spinning, Composites and Rubber Processing

This chapter answers the remaining items of Section XE5.7, Polymer Processing: “Electrospinning; Solution and melt spinning; … Filament winding; SMC; BMC; DMC; Extrusion; … pultrusion; … Rubber processing in two-roll mill, internal mixer, twin screw extruder.” It teaches the single-screw and twin-screw extruder, die swell, the spinning routes for fibres, the continuous and compound routes for composites, and the three machines of rubber processing. The numericals are extruder drag-flow output, fibre diameter from draw-down, pultrusion die residence time and internal-mixer batch mass from the fill factor.

1. Single-screw extruder: zones, screw geometry and output

A single-screw extruder is a rotating screw in a heated barrel, fed by a hopper. Along the screw there are three zones. In the feed zone the channel is deep and the pellets are conveyed forward as a solid bed. In the compression (transition) zone the channel depth falls, the solid is squeezed, and heat from the barrel and from viscous shear melts it, a thin melt film forming at the barrel wall. In the metering zone the channel is shallow and constant, so the melt is homogenised and pumped at a steady rate to the die. The compression ratio is the feed-zone channel depth divided by the metering-zone depth (commonly 2 to 4); L/D (barrel length over diameter) is typically 20 to 30, and a larger L/D gives better melting and mixing.

In the metering zone the output is the difference between a drag flow, caused by the barrel wall dragging melt forward relative to the screw, and a pressure (back) flow leaking back along the channel against the die pressure. Neglecting leakage over the flight, Q_drag = ½ π² D² N h sinφ cosφ, with D the screw diameter, N the speed in rev/s, h the channel depth and φ the helix angle; the pressure flow is Q_p ∝ h³ ΔP / μ and reduces the net output Q = Q_drag − Q_p. Output is proportional to speed; a high die resistance (small die, cold, viscous melt) cuts it; a deeper metering channel raises the drag flow in proportion to h but the pressure flow as h³.

⚠️ Worked example: open-discharge output
D = 60 mm, N = 60 rpm = 1 rev/s, h = 3 mm, square pitch (pitch = D) so tanφ = pitch/(πD) = 1/π, φ = 17.66°, sinφ cosφ = 0.2890; no die pressure, so Q = Q_drag. Q = ½ × 9.870 × (0.060)² × 1 × 0.003 × 0.2890 = 1.54 × 10⁻⁵ m³/s = 15.4 cm³/s. With melt density 0.78 g/cm³, mass flow = 12.0 g/s = 43.3 kg/h. The trap is using degrees or rpm directly: N must be in rev/s and all lengths in metres.

2. Die swell, melt fracture and the twin-screw extruder

When a polymer melt leaves the die the extrudate becomes thicker than the die opening. This die swell (extrudate swell) is elastic recovery: shear in the die stretches and orients the chains, and the stored normal stresses relax at the exit. The swell ratio B = D_extrudate / D_die exceeds 1 and rises with wall shear rate, with molecular weight and with elastic character of the melt. It falls with a longer die (L/D larger, so the chains relax inside), and with a higher melt temperature. Designers compensate by making the die smaller than the product or by drawing down. At still higher stress the surface becomes rough (sharkskin) and then irregular (gross melt fracture), setting an upper limit on output.

A twin-screw extruder has two screws in a figure-of-eight barrel. Co-rotating intermeshing screws are self-wiping and give strong distributive and dispersive mixing, good devolatilisation and short, controlled residence time: they are the standard compounding machines (fillers, glass fibre, pigments, reactive extrusion). Counter-rotating screws behave as positive-displacement pumps, with low shear and good pressure build, used for heat-sensitive PVC pipe and profile. The single-screw machine remains the cheapest pump for plain melting and shaping, but its mixing is poor and its output varies with die pressure; the intermeshing twin-screw conveys more positively, so output depends less on the die.

3. Spinning of fibres: melt, solution and electrospinning

A spinneret is a plate of fine holes through which polymer is forced to form filaments. In melt spinning the polymer melts, is extruded, and the filaments are cooled and solidified in a stream of air before take-up; no solvent is needed (nylon, polyester, polypropylene). Solution spinning is for polymers that decompose before melting or cannot be melted. In dry spinning the solution is extruded into a hot gas stream that evaporates the solvent (cellulose acetate, some acrylics); in wet spinning it is extruded into a coagulation bath where the polymer precipitates (viscose, many acrylics); dry-jet wet spinning inserts an air gap before the bath and gives very oriented high-strength fibres such as aramid.

Between spinneret and take-up the filament is stretched by the faster take-up roll: the draw-down ratio = take-up speed / extrusion speed at the hole. For a cylindrical filament of constant density, mass conservation gives v_ex d_hole² = v_take d_fibre², so d_fibre = d_hole √(v_ex / v_take). Further drawing (stretching below the melting point) orients the chains and raises strength.

Electrospinning uses an electric field in place of a mechanical take-up. A polymer solution (or melt) is fed to a needle held at a high voltage of the order of 10 kV, a grounded collector sits some centimetres away, and the drop deforms into a Taylor cone; above a critical field a charged jet is ejected, whips and thins by instability while the solvent evaporates, and lands as a non-woven mat of nanofibres (diameters from tens of nanometres to about a micrometre). Voltage, flow rate, needle-collector distance, and solution concentration and viscosity control the diameter: too dilute a solution gives beads instead of fibres, and a higher concentration gives thicker, bead-free fibres. Uses are filters, tissue scaffolds and wound dressings.

🧠 Worked example: fibre diameter by draw-down
Hole diameter 0.40 mm, extrusion speed 0.05 m/s, take-up 1500 m/min = 25 m/s. Draw-down ratio = 25/0.05 = 500. d_fibre = 0.40 mm × √(0.05/25) = 0.40 × 0.0447 = 0.0179 mm = 17.9 µm. The diameter falls as the square root of the draw-down ratio, not linearly.

4. Composites processing: filament winding, SMC, BMC/DMC and pultrusion

Filament winding: continuous fibre rovings pass through a resin bath and are wound under tension onto a rotating mandrel while a carriage traverses; the winding angle sets the properties. Hoop winding (near 90° to the axis) resists hoop stress; helical winding carries axial load. For a closed-ended thin cylinder under internal pressure, hoop stress is twice the axial stress, and a netting analysis gives the balanced helical angle tan²α = 2, α = 54.7° to the axis. It makes pressure vessels, pipes and tanks with high fibre content, and the mandrel is removed after cure.

SMC (sheet moulding compound) is a ready-to-mould sheet of thermoset polyester resin paste, filler and chopped glass fibre, formed between carrier films and thickened (matured) chemically, often with magnesium oxide, until it handles like leather; it is compression moulded in a hot mould into large panels such as car body parts, with flow that carries fibres. BMC (bulk moulding compound) and DMC (dough moulding compound) are the same material under two names: a thick putty or dough of resin, filler and shorter chopped fibre, supplied as a log or rope and compression, transfer or injection moulded. SMC has longer fibres and higher strength; BMC and DMC have shorter fibres, higher filler, and flow into more intricate shapes.

Pultrusion pulls (not pushes) continuous fibre rovings and mats through a resin bath, a pre-former and a heated die in which the resin cures, then a pulling unit and saw. It makes constant-cross-section profiles (rods, beams, ladder rails) with high unidirectional fibre content and excellent axial strength. The line speed is limited by cure: the residence time in the die, t = die length / line speed, must be at least the cure time at die temperature. Because the section is constant, the process cannot make varying shapes.

🧠 Worked example: pultrusion line speed
A resin needs 4 min in the die to cure. With a 1.2 m heated die, the maximum line speed is 1.2 m / 4 min = 0.30 m/min. With a 1.2 m die at 0.30 m/min the residence time is 1.2 / 0.30 = 4.0 min.

5. Rubber processing: two-roll mill, internal mixer, twin-screw extruder

Raw rubber is tough and elastic, so compounding rubber has three stages: mastication (softening by mechanical chain scission, which lowers molecular weight and viscosity, especially for natural rubber), mixing (adding fillers such as carbon black, oils, activators and antidegradants) and sheeting/forming. Curatives (sulphur and accelerators) are added last and at a low temperature to avoid scorch, premature vulcanisation.

The two-roll mill has two horizontal, water-cooled rolls turning towards each other at different speeds (a friction ratio, commonly about 1 : 1.2), so the rubber in the nip is sheared and folded; it masticates, blends in ingredients and delivers sheet, and the operator cuts and cross-blends the band. It is flexible and cheap but open, slow, operator-dependent and gives poor temperature control. The internal mixer (Banbury type) is a closed chamber with two counter-rotating rotors (tangential or intermeshing) and a ram; a batch is loaded through the hopper, the ram presses the charge into the high-shear zone, and the compound is dropped at a set temperature or energy. It mixes large batches fast with good dispersion and little dust, and the fill factor (typically about 0.7) is the fraction of the chamber volume occupied by compound. The dropped batch is sheeted on a two-roll mill, where curatives are often added.

The twin-screw extruder can mix, devolatilise and form continuously, giving uniform temperature history and consistent quality, and is used for continuous rubber compounding and for feeding profile extrusion; the single-screw cold-feed rubber extruder shapes tyre treads and tubing. Mixing in a mixer is batch, in the extruder continuous.

🧠 Worked example: internal-mixer batch mass
Chamber volume 100 L, fill factor 0.70, compound density 1.15 kg/L. Batch mass = 100 × 0.70 × 1.15 = 80.5 kg. Overfilling hinders circulation and mixing; underfilling lets the stock slip and gives poor shear.

Key takeaways

  • A single-screw extruder has feed, compression and metering zones; open-discharge output is the drag flow ½π²D²N h sinφ cosφ, reduced by pressure flow when the die resists.
  • Die swell is elastic recovery, larger at high shear rate and molecular weight and smaller for a longer die; twin-screw machines mix and devolatilise better than single-screw ones.
  • Melt spinning needs no solvent; dry spinning evaporates it, wet spinning precipitates the polymer in a bath; fibre diameter ∝ √(extrusion speed / take-up speed).
  • Electrospinning draws a charged jet from a Taylor cone to make nanofibre mats; low concentration gives beads.
  • Filament winding uses a mandrel (balanced helix 54.7°), SMC and BMC/DMC are compression-moulded compounds, and pultrusion is a pulled constant-section process limited by cure time in the die.
  • Rubber is masticated, mixed and sheeted; curatives go in last and cold to avoid scorch; the internal mixer works in batches at a fill factor near 0.7.

Practice questions (16)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. In a conventional single-screw extruder, melting of the pellets is completed mainly in the

    1. feed zone, where the channel is deepest and the pellets are first heated and compacted
    2. compression (transition) zone, where the channel depth falls and shear and barrel heat melt the solid bed
    3. die land, long after the melt has left the screw and is only being shaped
    4. hopper throat, by conduction of heat from the cooling water of the feed section
    Show answer

    Answer: B — compression (transition) zone, where the channel depth falls and shear and barrel heat melt the solid bed

    The channel depth falls through the transition zone, squeezing the solid bed against the hot barrel so that a melt film forms and the bed is consumed. The feed zone only conveys solid, the metering zone homogenises the melt, and the hopper throat is deliberately kept cool to prevent bridging.

  2. Die swell of a polymer melt leaving a capillary die is reduced by

    1. raising the wall shear rate through the die by increasing the output
    2. using a polymer of higher molecular weight and broad elastic response at the same temperature
    3. shortening the die land so that the chains have less time to relax before exit
    4. lengthening the die land at constant output, so that chains relax before the exit
    Show answer

    Answer: D — lengthening the die land at constant output, so that chains relax before the exit

    Swell is stored elastic strain; a longer land gives the stresses time to relax before exit, so swell falls. A higher shear rate or higher molecular weight stores more elasticity, and a shorter land leaves less time to relax, so each of those increases swell.

  3. For heat-sensitive PVC pipe extrusion, a counter-rotating twin-screw extruder is often preferred because it

    1. operates at very high screw speed so that maximum shear heating melts the PVC quickly
    2. conveys positively at low shear and builds pressure steadily, limiting degradation
    3. needs no barrel heating and works as a ram without any screw action at all
    4. removes the need for any heat stabilisers in the PVC compound formulation
    Show answer

    Answer: B — conveys positively at low shear and builds pressure steadily, limiting degradation

    Counter-rotating screws act as positive-displacement pumps with low shear and short, uniform residence time, which suits PVC that degrades if overheated. They do not remove the need for stabilisers, and high shear heating is what must be avoided.

  4. In wet spinning the polymer solution is extruded into

    1. a stream of hot air that carries off the solvent by evaporation as it leaves
    2. a cold air quench in which no solvent is present and the polymer is simply cooled
    3. a coagulation bath in which the polymer precipitates as filaments
    4. a high-voltage electric field between a charged needle and an earthed collector
    Show answer

    Answer: C — a coagulation bath in which the polymer precipitates as filaments

    Wet spinning precipitates the polymer in a liquid coagulation bath (viscose, acrylic). Hot gas evaporation is dry spinning, air quenching is melt spinning, and a needle-collector field is electrospinning.

  5. In electrospinning, a dilute polymer solution gives beaded fibres. Which change is most likely to give bead-free, thicker fibres?

    1. Increase the polymer concentration, raising viscosity and chain entanglement
    2. Dilute the solution further so that surface tension of the jet is reduced
    3. Remove the voltage altogether so that the jet is no longer whipped and thinned
    4. Replace the polymer by one of much lower molecular weight at the same weight concentration
    Show answer

    Answer: A — Increase the polymer concentration, raising viscosity and chain entanglement

    Beads form when chain entanglement is too low to stabilise the jet against surface tension; more concentration or higher molecular weight raises viscosity and entanglement and gives continuous, thicker fibres. Further dilution or lower molecular weight does the opposite, and without a field there is no electrospinning.

  6. Which pair of statements about pultrusion and filament winding is correct?

    1. Pultrusion pushes the fibre bundle through a cold die; winding uses a stationary mandrel and a fixed carriage
    2. Pultrusion gives parts of continuously varying section; winding can make only flat sheets and plates
    3. Pultrusion pulls fibre through a heated die to make constant-section profiles; winding lays rovings on a rotating mandrel
    4. Both are discontinuous batch processes that use chopped fibre only and need no mandrel or die
    Show answer

    Answer: C — Pultrusion pulls fibre through a heated die to make constant-section profiles; winding lays rovings on a rotating mandrel

    Pultrusion is a pulled, continuous process through a heated, shaped die that gives a constant section; filament winding places continuous rovings on a rotating mandrel. Both use continuous fibre, not chopped fibre, and pultrusion cannot vary the section.

  7. In compounding natural rubber, curatives are normally added

    1. first, before mastication, so that they disperse for the whole of the mixing time
    2. last and at low temperature, to avoid scorch (premature vulcanisation)
    3. only after the stock has already been fully vulcanised in the press
    4. at the highest temperature of the cycle, to ensure a uniform and complete cure
    Show answer

    Answer: B — last and at low temperature, to avoid scorch (premature vulcanisation)

    Sulphur and accelerators are added late and cool because mixing generates heat that would start crosslinking and cause scorch. Adding them first or at peak temperature invites scorch, and adding them after vulcanisation is meaningless.

  8. Two rolls of a laboratory mill turn at surface speeds in the ratio 1 : 1.2 towards each other. The main purpose of the speed difference is to

    1. impose shear in the nip that masticates and mixes the rubber
    2. cool the rubber by evaporation of moisture from the roll surfaces during milling
    3. reduce the power that the mill drive has to supply to the stock
    4. keep the nip gap exactly constant whatever the stock hardness
    Show answer

    Answer: A — impose shear in the nip that masticates and mixes the rubber

    Friction ratio gives a velocity gradient in the nip, so the stock is sheared and folded, which also lets the operator cut and fold the band. It increases rather than reduces power, and neither evaporative cooling nor gap control is its purpose.

  9. Select ALL correct statements about screw extrusion.

    1. The metering zone has a shallow, constant channel depth and pumps homogeneous melt to the die
    2. Open-discharge output is proportional to screw speed in the drag-flow model
    3. Compression ratio is metering-zone depth divided by feed-zone depth, so it is below 1
    4. A co-rotating intermeshing twin-screw extruder is a standard compounding machine
    Show answer

    Answer: A — The metering zone has a shallow, constant channel depth and pumps homogeneous melt to the die; B — Open-discharge output is proportional to screw speed in the drag-flow model; D — A co-rotating intermeshing twin-screw extruder is a standard compounding machine

    The metering zone, linear speed dependence of drag flow and the compounding role of co-rotating twin screws are correct. Compression ratio is feed depth divided by metering depth, so it is above 1.

  10. Select ALL correct statements about fibre spinning.

    1. Melt spinning needs no solvent, because the polymer is melted and cooled in air
    2. Dry spinning evaporates the solvent into a hot gas stream
    3. Electrospinning needs a mechanical take-up roll running at kilometres per minute
    4. Electrospun mats are non-woven nanofibre webs
    Show answer

    Answer: A — Melt spinning needs no solvent, because the polymer is melted and cooled in air; B — Dry spinning evaporates the solvent into a hot gas stream; D — Electrospun mats are non-woven nanofibre webs

    Melt, dry and electro routes are described correctly. Electrospinning draws the jet with an electric field, not a high-speed mechanical roll.

  11. Select ALL correct statements about moulding compounds and composites processing.

    1. SMC is a thickened sheet of resin paste, filler and chopped glass fibre, compression moulded hot
    2. BMC and DMC are two names for the same dough-like compound with short fibres
    3. In pultrusion the maximum line speed equals die length divided by the required cure time
    4. Filament winding needs a split two-part mould clamped by a press
    Show answer

    Answer: A — SMC is a thickened sheet of resin paste, filler and chopped glass fibre, compression moulded hot; B — BMC and DMC are two names for the same dough-like compound with short fibres; C — In pultrusion the maximum line speed equals die length divided by the required cure time

    SMC, BMC/DMC and the pultrusion speed limit are correct. Filament winding uses a rotating mandrel, not a two-part press mould.

  12. Select ALL correct statements about rubber compounding equipment.

    1. An internal mixer processes closed-chamber batches under a ram and drops at a set temperature or energy
    2. A two-roll mill is open, so temperature control and operator dependence are drawbacks
    3. Mastication of natural rubber raises its molecular weight
    4. A twin-screw extruder can mix rubber continuously rather than in batches
    Show answer

    Answer: A — An internal mixer processes closed-chamber batches under a ram and drops at a set temperature or energy; B — A two-roll mill is open, so temperature control and operator dependence are drawbacks; D — A twin-screw extruder can mix rubber continuously rather than in batches

    Mixer, mill and continuous twin-screw statements are right. Mastication breaks chains, so molecular weight and viscosity fall.

  13. A single-screw extruder has D = 50 mm, N = 90 rpm, metering depth h = 2.0 mm and helix angle φ = 20°. For open discharge (no die pressure, no leakage) take Q = ½ π² D² N h sinφ cosφ with N in rev/s. Melt density is 0.80 g/cm³. The mass output is ____ kg/h (integer).

    Numerical answer — type the value.

    Show answer

    Answer: 34

    N = 90/60 = 1.5 rev/s. sin20° cos20° = 0.3420 × 0.9397 = 0.3214. Q = 0.5 × 9.8696 × (0.05)² × 1.5 × 0.002 × 0.3214 = 1.19 × 10⁻⁵ m³/s = 11.9 cm³/s. Mass = 11.9 × 0.80 = 9.52 g/s = 9.52 × 3600 / 1000 = 34.3 kg/h, so 34.

  14. A melt-spun filament is extruded through a 0.50 mm hole and solidifies to a 20 µm diameter fibre. Assuming constant density, a cylindrical filament and no later drawing, the draw-down ratio (take-up speed divided by extrusion speed) is ____ (integer).

    Numerical answer — type the value.

    Show answer

    Answer: 625

    Mass conservation: v_ex d_hole² = v_take d_fibre², so v_take / v_ex = (d_hole / d_fibre)² = (500 µm / 20 µm)² = 25² = 625. Using the diameter ratio itself (25) is the slip.

  15. A polyester resin needs 2.5 min inside a 1.5 m heated pultrusion die to cure fully. The maximum line speed is ____ mm/s (integer).

    Numerical answer — type the value.

    Show answer

    Answer: 10

    Residence time = die length / line speed ≥ 2.5 min, so v ≤ 1.5 m / 2.5 min = 0.60 m/min = 600 mm / 60 s = 10 mm/s.

  16. An internal mixer has a chamber volume of 250 L and runs at a fill factor of 0.72 with compound of density 1.18 kg/L. Each batch cycle (load, mix, drop) takes 4.0 min with no idle time. The compound output is ____ kg/h (integer).

    Numerical answer — type the value.

    Show answer

    Answer: 3186

    Batch mass = 250 × 0.72 × 1.18 = 212.4 kg. Batches per hour = 60 / 4.0 = 15. Output = 212.4 × 15 = 3186 kg/h.