Plastic processing: injection moulding and extrusion

Why it matters

Enclosures, connectors, gears, cable sheaths, tubing and sensor housings in mechatronic products are mostly moulded or extruded polymer. Injection moulding makes millions of identical, finished parts at a cycle of seconds, and extrusion makes continuous profiles, pipes, film and wire insulation. Both machines are closed-loop controlled systems – screw position, speed, pressure and barrel temperatures – so understanding the physics helps you set and tune them.

Key ideas

Polymers for processing. Thermoplastics (PE, PP, PVC, PS, ABS, PA, PC, POM) soften on heating and harden on cooling, repeatedly, so they suit both processes and scrap can be reground. Thermosets (phenolics, epoxies) cure irreversibly and are mostly compression or transfer moulded. Polymer melts are highly viscous (roughly 10²–10⁴ Pa·s) and shear-thinning, and they shrink on cooling – much more if semi-crystalline (PP, PE, PA, POM: about 1–3 %) than if amorphous (PS, ABS, PC: about 0.4–0.8 %). Take actual shrinkage from the resin supplier's data sheet.

Injection moulding machine. A hopper feeds pellets into a heated barrel containing a reciprocating screw. The screw rotates to melt and convey material forward (plasticising) and, while doing so, retracts to build up a shot; it then acts as a ram and pushes the melt through the nozzle, sprue, runners and gate into the cavity. A clamping unit (toggle or hydraulic) holds the two mould halves shut against the cavity pressure.

Moulding cycle.

1. Mould closes and clamps.
2. Injection (fill) – controlled by screw speed.
3. Packing / holding – pressure is kept on to push extra melt in as the part shrinks, until the gate freezes.
4. Cooling – the longest stage; the screw plasticises the next shot meanwhile.
5. Mould opens and ejector pins push the part out. Cooling time grows with the square of wall thickness, so thin, uniform walls give fast cycles.

Mould features. Sprue, runners and gates (two-plate and three-plate moulds; hot-runner systems avoid runner scrap), cavity and core, cooling channels, ejector pins, vents, draft angles (typically 0.5–2°) so the part releases, and cavity dimensions enlarged by the shrinkage allowance.

Common moulding defects.

• Short shot – cavity not filled (low shot volume or pressure, cold melt, frozen gate, poor venting).
• Flash – melt squeezes into the parting line (clamp force too low, worn mould, excessive pressure).
• Sink marks and voids – thick sections shrink after the skin freezes (insufficient packing).
• Warpage – non-uniform cooling or orientation, often from ejecting too early.
• Weld (knit) lines – where two flow fronts meet; weaker zones.
• Burn marks – trapped air compressed and heated (poor venting).

Extrusion. A single-screw extruder has three zones: feed (deep flights convey solid pellets), compression/transition (flight depth reduces to compact and melt the polymer and expel air; compression ratio typically 2–4) and metering (shallow constant flights pump a uniform melt). About 2/3 or more of the melting energy comes from viscous shearing driven by the screw motor, the rest from barrel heaters. A breaker plate and screen pack filter the melt and build back-pressure. The die shapes the profile; downstream equipment (water bath or vacuum sizing, puller, cutter or winder) cools and draws it. Products: pipe, tube, rod, window profiles, sheet, blown film, wire coating.

Extruder flow. In the metering zone the rotating screw drags melt forward (drag flow), while the pressure built up against the die pushes some back (pressure flow). Net output Q = Q_d − Q_p, so output falls as die resistance increases. The operating point is where the screw characteristic meets the die characteristic.

Die swell and melt fracture. The extrudate swells on leaving the die because the stretched molecules recover elastically, so die openings are made smaller than the product. At very high extrusion rates the surface becomes rough (sharkskin) or grossly distorted (melt fracture).

Formulas

F_clamp = p_c·A_p

• F_clamp = clamping force (N); p_c = average cavity pressure (Pa; typically 20–100 MPa, depends on material and flow length); A_p = projected area of part and runners on the parting plane (m²).

t_c = (s² / (π²·α)) · ln[(4/π)·(T_m − T_w)/(T_e − T_w)]

• Cooling time (s) for a plate cooled from both faces. s = wall thickness (m); α = thermal diffusivity of the polymer (m²/s, about 1 × 10⁻⁷); T_m = melt temperature; T_w = mould wall temperature; T_e = ejection temperature (°C).

D_c = D_p / (1 − S) ≈ D_p·(1 + S)

• Cavity dimension D_c from part dimension D_p (mm) and fractional shrinkage S.

Q_d = ½·π²·D²·N·h·sin φ·cos φ

• Drag flow (m³/s). D = screw diameter (m); N = screw speed (rev/s); h = channel depth in the metering zone (m); φ = flight helix angle (17.66° for a square-pitch screw, pitch = D).

Q_p = π·D·h³·sin²φ·Δp / (12·η·L)

• Pressure (back) flow (m³/s). Δp = head pressure at the die (Pa); η = melt viscosity (Pa·s); L = metering length (m).

Q = Q_d − Q_p

• Net extruder output (m³/s); for a die, Q = K_s·Δp with K_s a die constant from its geometry.

Worked examples

Example 1 (injection moulding, standard). An ABS cover has a projected area of 120 cm² and wall thickness 3 mm. Average cavity pressure is 60 MPa, T_m = 240 °C, T_w = 50 °C, T_e = 100 °C and α = 1.0 × 10⁻⁷ m²/s. Find the clamping force and cooling time.

1. A_p = 120 cm² = 0.012 m²; F = p_c·A_p = 60 × 10⁶ × 0.012 = 720 000 N = 720 kN (about 73 tonnes-force; choose a machine of at least 80–100 t).
2. Ratio (4/π)(T_m − T_w)/(T_e − T_w) = 1.2732 × 190/50 = 4.838; ln 4.838 = 1.577
3. s²/(π²·α) = (3 × 10⁻³)² / (9.870 × 10⁻⁷) = 9.12 s
4. t_c = 9.12 × 1.577 = 14.4 s Answer: F ≈ 720 kN, t_c ≈ 14.4 s. Reducing the wall to 2 mm would cut cooling time to (2/3)² of this, about 6.4 s.

Example 2 (extruder output, GATE level). A single-screw extruder has D = 50 mm, square-pitch flights (φ = 17.66°), metering channel depth h = 2.5 mm, metering length L = 1.2 m and speed 60 rev/min. The melt viscosity is 100 Pa·s and the die head pressure is 10 MPa. Find the net output.

1. N = 60 rev/min = 1 rev/s; sin φ = 0.3034, cos φ = 0.9529.
2. Q_d = ½·π²·D²·N·h·sin φ·cos φ = 0.5 × 9.870 × 0.0025 × 1 × 0.0025 × 0.3034 × 0.9529 = 8.92 × 10⁻⁶ m³/s
3. Q_p = π·D·h³·sin²φ·Δp/(12·η·L) = π × 0.05 × (0.0025)³ × 0.09203 × 10⁷ / (12 × 100 × 1.2) = 1.57 × 10⁻⁶ m³/s
4. Q = Q_d − Q_p = 8.92 × 10⁻⁶ − 1.57 × 10⁻⁶ = 7.35 × 10⁻⁶ m³/s Answer: Q ≈ 7.35 × 10⁻⁶ m³/s = 7.35 cm³/s (about 26 L/h). Note D² = 0.0025 m² and h = 0.0025 m happen to be equal numbers here.

Common mistakes

• Using the total surface area of the part instead of the projected area on the parting plane for clamp force.
• Confusing a short shot (filling problem) with warpage (cooling or ejection problem).
• Expecting cooling time to scale linearly with wall thickness; it scales with thickness squared.
• Forgetting to enlarge the cavity for shrinkage, or using metal-casting shrinkage values.
• Treating extruder output as drag flow only and ignoring back-pressure from the die.
• Making the extrusion die the same size as the product and ignoring die swell.
• Using rev/min directly in the drag-flow formula, which needs rev/s for m³/s.

For GATE ME

• Polymer processing appears mainly through conceptual MCQs: thermoplastic versus thermoset, which process suits which product, moulding defects and their causes.
• Simple numericals on clamping force, shrinkage allowance and cooling time, and on extruder drag and pressure flow if the syllabus or university paper includes them. Practise one clamping-force and one extruder-flow calculation and link each defect to the process setting that cures it.

Quick check

1. Which stage of the injection moulding cycle is usually the longest?
2. A part has a projected area of 200 cm² and average cavity pressure 40 MPa. What clamp force is needed?
3. Why are extrusion dies made smaller than the final profile?
4. What is the effect on extruder output of a die with higher flow resistance?
5. Which defect results from too low a clamping force?

Answers: 1. Cooling. 2. 40 × 10⁶ × 0.02 = 800 kN. 3. To allow for die swell as the melt recovers elastically. 4. Head pressure rises, pressure back-flow increases and net output falls. 5. Flash.