Single-Screw Extruder 1.3

Calculate extruder throughput, pressure and drive online

With this online calculation tool you can technically size a single-screw extruder and determine the steady-state operating point of an extrusion line. Using screw geometry, material and rheology data, speed and the geometry of the extrusion die, the tool calculates throughput, head pressure, die pressure loss, screw torque and required drive power. The unknown quantity is the throughput Q*, not the retraction U_ret of the injection screw.

The tool is suitable for preliminary sizing of single-screw extruders, extrusion screws, dies and drives, as well as for technical comparisons of variants. The focus is the actual operating point where the characteristics of the screw and extrusion die intersect.

What can be calculated with the single-screw extruder?

The calculation combines screw, polymer melt, extrusion die and drive into a single technical model.

• Q* — volumetric throughput
• ṁ — mass throughput
• p_head — head pressure at the screw end
• M_screw,calc — calculated screw torque
• P_drive — required drive power
• F_axial — axial load estimate
• Δp_die — pressure loss in the extrusion die
• F_wall — diagnostic wall shear force
• p(l) — pressure profile along the screw and die
• Screw characteristic ∩ die characteristic
• machine checks and power reserves

Determine the operating point of extruder and die

The steady-state operating point is determined from the intersection of the screw and die characteristics. The target throughput Q* is the one for which:

p_screw,out(Q) = Δp_die(Q) + p_outlet

For discharge to atmosphere and when using gauge pressure, p_outlet = 0.

This makes it possible to examine how changes in screw geometry, speed, material viscosity or die cross-section influence the actual throughput and head pressure.

Screw throughput and pressure build-up

During extrusion, the screw rotates continuously and conveys the polymer through the feed, compression and metering zones. The model takes into account the actual zone layout L_f → L_c → L_m and the change in channel depth in the compression zone.

For the metering zone:

dp/dz = (Q_D − Q) / K_s

The Brent solver determines Q* so that the screw and die characteristics intersect.

• Q_D — Drag-Flow
• Q_P — Pressure-Flow
• Q = Q_D − Q_P
• γ̇_screw — Scherrate in der Screw
• η_screw — local melt viscosity in the screw

Feed zone and solids conveying

For solids conveying in the feed zone, friction between polymer, barrel and screw and the resulting pressure build-up are taken into account. The model follows Darnell–Mol / Schneider / Tadmor — not the Iwko-θ(U) of the injection screw.

• p_feed — feed pressure (optional; otherwise p₀ = ρ_bulk · g · D)
• ρ_bulk — bulk density
• f_b bzw. μ_barrel — Reibung am Zylinder
• f_s bzw. μ_screw — Reibung an der Screw
• θ — conveying angle according to Darnell–Mol
• k_s — axialer Druckaufbaukoeffizient

Calculate the extrusion die and die pressure loss

The pressure loss in the extrusion die depends on profile geometry, land length L_d, throughput and local melt viscosity.

The total die pressure loss is composed of several sub-sections:

Δp_die = Σ Δp_i

Depending on the model, adapter, contraction, preformer and land are taken into account.

• A — cross-sectional area
• P_w — benetzter Umfang
• D_h — hydraulischer Durchmesser
• A_wall — wall area
• C_shape — Formfaktor
• γ̇_die — shear rate in the die
• η_die — local viscosity in the die
• τ_w,mean — mittlere Wandschubspannung
• τ_w,max — maximale Wandschubspannung

Wall shear force in the die

F_wall is not an additional Coulomb resistance. For the polymer melt, the following approximation applies:

F_wall ≈ Δp · A = τ_w · P_w · L

This avoids counting die resistance twice.

Rheology and melt viscosity

Polymer melts are usually non-Newtonian. The apparent viscosity depends in particular on temperature and shear rate.

• η_eff — effective melt viscosity (Level 1 or derived from K)
• n — Power-Law-Exponent
• K — Konsistenzindex (0 = aus η_eff bei γ̇_ref)
• γ̇_ref — reference shear rate for K = η_eff · γ̇_ref⁽¹⁻ⁿ⁾ (default 100 s⁻¹)
• α_T — Temperaturkoeffizient
• ρ — Schmelzedichte

If K = 0, the consistency index is determined from η_eff and γ̇_ref:

K = η_eff · γ̇_ref⁽¹⁻ⁿ⁾, Default γ̇_ref = 100 s⁻¹.

The screw and die are evaluated at their respective local shear rates. Therefore η_screw = η_die must not be enforced in general.

Calculate screw torque and drive

For drive sizing, the torque is determined from the loads in the different screw zones.

• M_solid — Feststoffdrehmoment
• M_compression — torque of the compression zone
• M_visc,z — viskoser Drehmomentanteil in z-Richtung
• M_visc,x — viskoser Drehmomentanteil in x-Richtung
• M_pressure — druckbedingter Drehmomentanteil (signed)
• M_melt — Schmelzedrehmoment
• M_polymer — resultierendes Polymerdrehmoment
• M_screw,calc — calculated screw torque

Taking the mechanical efficiency η_mech, service factor and load type into account, service and design torque are derived from this.

• M_service — Service-Drehmoment
• M_design — Auslegungsdrehmoment
• P_screw — screw power
• P_motor,req — required motor power
• n_motor — Motordrehzahl
• M_motor,req — required motor torque

Estimate the axial force of the extruder screw

Head pressure creates an axial load on the screw and therefore on the thrust bearing.

• F_axial,screw — Axialkraft der Screw
• F_{pressure,land} — Druckkraft im Landbereich
• F_wall,total — sum of sectional wall forces Δp · A (contraction: Level 1)

For the pressure force in the land section:

F_{pressure,land} = (p_land,in − p_outlet) · A_profile

What inputs are required?

Screw geometry

• D — screw diameter
• d — Kerndurchmesser
• L_f — length of the feed zone
• L_c — length of the compression zone
• L_m — length of the metering zone
• H_f — Kanaltiefe Feed
• H — Kanaltiefe Metering
• t — screw pitch
• e — Stegdicke

Solids conveying

• p_feed — feed pressure (optional; otherwise p₀ = ρ_bulk · g · D)
• ρ_bulk — bulk density
• f_b / μ_barrel — Reibung Zylinder
• f_s / μ_screw — Reibung Screw

Process parameters

• n — screw speed
• T — Massentemperatur
• T_die — melt temperature in the die
• p_outlet — Austrittsdruck
• target throughput — optional comparison value

Material data and rheology

• η_eff — effective melt viscosity (Level 1 or derived from K)
• n — Power-Law-Exponent
• K — Konsistenzindex (0 = aus η_eff bei γ̇_ref)
• γ̇_ref — reference shear rate for K = η_eff · γ̇_ref⁽¹⁻ⁿ⁾ (default 100 s⁻¹)
• α_T — Temperaturkoeffizient
• ρ — Schmelzedichte

Extrusion die and profile

• Profiletyp — Round bar, Rechteck, Rohr, U/C/L/T/I-H, Mehrkanal oder DXF
• L_d — land length
• D, b, h, D_a, D_i, B, H, t, b_f, t_w, t_f — profile-dependent dimensions
• Calculation mode — analytical, D_h approximation or 2D Poisson
• Adapter, contraction and preformer lengths as well as adapter-D

Drive and machine data

• i — gear ratio
• η_G — Getriebewirkungsgrad
• η_mech — mechanischer Wirkungsgrad
• P_nom — optionale Motor-Nennleistung
• M_max — maximales Motordrehmoment
• n_max — maximale screw speed
• p_max — maximum allowable pressure
• F_thrust,max — maximum allowable axial force
• K_peak — Belastungsfaktor
• F_D, F_P — Shape Factors

What results are output?

Operating point

• Q* — volumetric throughput
• ṁ — mass throughput
• p_head — Kopfdruck
• p_max,screw — maximaler Druck in der Screw
• l(p_max) — Position des maximum screw pressure
• Δp_die — die pressure loss
• F_axial,screw — Axialkraft der Screw
• F_{pressure,land} — Druckkraft im Landbereich
• F_wall,total — sum of sectional wall forces Δp · A (contraction: Level 1)
• p(l) — axiales Druckprofil

Screw

• Q_D — Drag-Flow
• Q_P — Pressure-Flow
• θ — conveying angle Darnell–Mol
• k_s — axialer Druckaufbaukoeffizient
• F_D, F_P, φ — Shape Factors und Steigungswinkel
• γ̇_screw, η_screw — screw shear rate and viscosity
• p_feed, p_feed,end, p_comp,end — zone pressures
• M_solid
• M_compression
• M_visc,z
• M_visc,x
• M_pressure (signed)
• M_melt
• M_polymer
• M_screw,calc

Extrusion die

• A
• P_w
• D_h
• A_wall
• C_shape and calculation method
• γ̇_die
• η_die
• τ_w,mean
• τ_w,max
• partial pressure losses of the individual head zones

Drive sizing

• M_service — Service-Drehmoment
• M_design — Auslegungsdrehmoment
• P_screw — screw power
• P_motor,req — required motor power
• n_motor — Motordrehzahl
• M_motor,req — required motor torque
• overall reserve and machine checks

Machine limits and variant comparison

In addition to the theoretical calculation results, machine limits such as n_max, p_max and F_thrust,max can be taken into account.

This makes it possible to compare different screw diameters D, geometries, speeds n, die cross-sections and rheology parameters.

What tasks is the calculation suitable for?

• Preliminary estimate of Q* and p_head
• sizing of screw motor and gearbox
• Estimate Δp_die
• Vergleich verschiedener screw diameter D
• Untersuchung des Einflusses der Drehzahl n
• evaluation of different rheological parameters
• Comparison with existing machine and die data

Model limits and notes

The calculation model is intended for technical preliminary sizing, plausibility checks and variant comparison. It does not replace a full three-dimensional flow, heat-transfer and melting simulation.

Barrier and mixing screws, flight leakage, partially filled screw channels and calibration, cooling and swelling are not fully represented in the current model stage.

In particular, η_eff is not a constant material property. It must match the material, temperature and relevant shear-rate range.

Calculation model

The current model version Single-screw extruder 1.3 takes into account the feed, compression and metering zones L_f → L_c → L_m, the pressure build-up of solids conveying and the intersection of the screw and die characteristic.

The screw geometry (φ, W, F_D, F_P) and the drive balance come from the same core as Injection Molding Machine 1.4.

Calibration, cooling and swelling are planned for extended model stages.