Residence Time Calculation for Extrusion - Polymer Processing

Hello and welcome to a new blog post. In a previous post, I presented the residence time calculation in injection moulding. Today we will focus on the extrusion process.

Residence time in extrusion is referring to the time, which a polymer pellet, and as consequence, polymer melt needs to travel from the melting zone until the end of the metering zone.

The online calculation

For an approximate calculation of the residence time, building the quotient of the volume of the extruder filled with melt and the volume flow of the melt is possible (underlying basic laws of physics):

Equation 1 - extrusion residence time (average residence time): t=V/Q

V = volume of the extruder filled with melt

Q = flow rate of the melt

t = extrusion residence time

This is the background of the online calculation tool shown below:

Check out the new tool here

In literature, extruder output (flow rate; kg/h) can be calculated by the following equation [3]:

The leakage flow is calculated by addition of mass flow rate (drag) and pressure flow rate minus the extruder output.

2nd way to calculate the average residence time

average residence time t = V/Q= (2 * z) / (v_bz *(1-a)) = 

z =dz = unwound channel length = L / sin φ

φ = outer slope angle f.e. 30.72°

L = screw length f.e. 14*D

D = screw diameter (mm)

n = RPM (1/min)

h = groove depth

b = π*D*sin φ-e

e =  bridge width

dp = pressure drop f.e. 20 bar = 20*10^5 Pa

v_bz = circumferential speed in Z direction = n*π*D*cos φ 

a = throttle coefficient = ((b*h^3)/(12*η))*(dp/dz)* (2)/(v_bz*b*h)

Example with following extrusion screw and process data

D=45 mm

L=14*D

h=3 mm

e=4.7mm

n=60 1/min

φ=30.72°

η = 800 PAs

1. calculate b = 67.52 mm

2. calculate v_bz = 121.53 mm/s

3. calculate  z = 1233.26 mm

4. calculate a = 0.25

5. calculate t = 2*1233,26 / 121,53 (1-0,25) = 27,07 s

Also as a general rule, the higher the temperature, the lower should be the melt residence time. 

Thanks for reading and #findoutaboutplastics

Greetings

Herwig Juster

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Literature:

[1] https://www.findoutaboutplastics.com/2017/10/how-to-calculate-residence-time-in.html

[2] https://www.extrusion-training.de/extruder-dimensionierung/

[3] Rao, Natti S. - Design Formulas for Plastics Engineers

[3] N. Rao: Design formulas for plastics engineers