posted May 18, 2006 07:27 AM            

Fortunatly the cross sectional area for standard screw elements and kneading blocks is the same, so one only needs to find the open area and multiply it by the length.

Undercut elements, SME, TME, ZME, Tri-lobe and other such specialy elements require different calculations.

I've had good results using 1MI HDPE to purge with on these machines. Fiberglass can be added to the mix for extra cleaning action.

------------------
Best Regards,

Tom Cunningham

posted May 18, 2006 07:47 AM            

but..these are not working. I refferred one book...but...????

do you have such formule, by which I can calculate the areas.....

another question...for ZME....can I use water immersion (water displacement) method? how exactly will this method function?
regards...

posted May 18, 2006 10:35 PM            

5. Specific volume

Specific volume (SV) represents the approximate volume per screw outside diameter (OD) length of screws for traditional Erdmenger-type screw geometries. This calculation, which is useful in a number of other formulas, allows you to calculate the volume in the process section. SV is calculated as follows:

Specific volume=.94 x (OD2-ID2) x OD/1000

SV is denoted in cc/diameter of length (it’s always best to obtain SV data from the machine supplier, if possible),
OD=Screw outside diameter (each),
ID=Screw inside diameter (each).

For example: For a HSEI twin-screw extruder with a screw OD of 50 and an ID of 32 the SV is as follows:

SV=.94 x (502-322) x 50/1000 = 73.8 cc/dia

This number can also be used for rough scaling between different size machines that share geometric similarities (OD/ID ratio) and that are not too dramatically different in size. For instance:

Qtarget=Qreference x (volumetarget/volumereference)

For example, if a 45-mm twin-screw extruder has a SV of 60 cc/dia and is running at 150 kg/hr then it can be inferred that a 75-mm extruder with a SV of 240 cc/dia will process approximately four times the rate:

Qtarget (75 mm) = 150 x (240/60)=600 kg/hr

6. Fill % approximation

This formula provides the percentage of the available volume in the process section that is being utilized in the starved-fed HSEI twin-screw extruder. This calculation is useful to approximate a starting point as to where to run a process. The following formula can be used:

% fill = (Q x .2777)/(SV x rpm/60) x (SG x Ef)

Q=Flow rate in kg/hr,
Ef=Average forwarding efficiency (approx. 35% for a screw with 1?3 kneaders and 2?3 flighted elements, or .35),
SV=Specific volume of extruder in cc/dia,
rpm=Screw rpm,
SG=Specific gravity of the material being processed.
For example, a 40-mm extruder with an SV of 34.8 cc/dia is running 50 kg/hr at 200 rpm:

% fill = (50 x .2777)/[34.8 x (200/60)] x 1 x .35= .34, or 34% filled

This formula is a very rough estimation and is meant to provide some insight into the dynamics of a starved process section. More advanced/accurate calculations take into account the specific screw geometries, the viscosity of the melt, and the degree of screw fill.

This calculation might show that devolatilization intensive processes run at 30% (or less) screw fill because a highly starved process section increases the surface area of the melt pools under the vent. Another example could demonstrate that similar masterbatch formulations for film/fiber applications utilize a 40% volume, compared to 60% for injection molding applications, because of the comparative dispersive mixing requirements.

Higher fill levels result in a tighter residence time distribution (RTD) and less shear, and lower fill levels are associated with wider RTD and more shear. Fill level approximations help explain why different processes benefit from comparative fill level percentages.

7. Residence time

This formula provides the approximate residence time (RT) in the process section of an HSEI twin-screw extruder. As denoted above, the residence time distribution is highly dependent upon the degree of screw fill. The following formula can be used for RT:

RT(sec) = (SV x SG x L/D x %fill)/(Q x .2777)

RT=Residence time in seconds,
SV=Specific volume in cc/dia,
SG=Specific gravity,
L/D=L/D extruder ratio,
%fill=Degree of fill, expressed as a decimal (i.e. 40% = .4),
Q=kg/hr being processed.

For example, a 50-mm extruder with a SV of 70 cc/dia and 48 L/D, is running a material with a 1.1 SG at 270 kg/hr with an assumed 40% screw fill (.4), the following applies:

RT = (70cc/dia x 1.1 x 48 x .4)/(270 x .2777)
RT = 19.7 seconds

The RT formula provides insight as to how long materials are exposed to heat and shear in the process section.

8. Specific throughput

The specific throughput (ST) provides the output per rpm for a given process and can be calculated as follows:

ST=(kg/hr)/rpm

For example, if a 100-mm twin-screw extruder is successfully processing a formulation at 1000 kg/hr with 250 rpm, this equates to 4kg/rpm.

ST=1000/250= 4kg/rpm

Specific throughput provides a number that is proportional to the degree of fill and is used to process similar products at different rates on the same machine. For instance, if a product runs at 1000 kg/hr at 250 rpm, then for 2000 kg/hr on the same extruder 500 rpm is a good starting point. ST is often helpful to scale-up/down products on different size extruders, in that over time a process that runs 5 kg/hr on a 30-mm class machine will most likely equate to 50 kg/hr (or another rate) on a 60-mm class machine, and vice versa.

------------------
Best Regards,

Tom Cunningham

posted May 19, 2006 12:14 PM            

The above is a graph of typical fill factor levels in a twin screw. Twin screws are run starve fed, so the channels are not full. I'm not sure a partially filled channel will purge much at all. or perhaps only the pushing side of the flights.

The above shows some shear stress studies for a couple of twin screw processes. These show about 1/2 the length of the screw screw. Highest stresses are where resin is just melted. Minimal shear stress required to keep surfaces clean is about 30MPa. As can be extrapolated, much of the extruder will run at less than 30MPa. This indicates that the extruder surfaces will not be self cleaning while running as advertised in many cases. This is demonstrated by the need for cleaning and purging. Fortunatly the tight tolerances in a twin screw keep the stagnent material from building up a large volume.

Good purging of screw and barrel surfaces need a combination of high viscosity, high shear rates and surface contact in order to clean well. This is a difficult combination to get in a co-rotating twin screw extruder.

------------------
Best Regards,

Tom Cunningham
www.ExtrusionTechnicalServices.com

[This message has been edited by Tom C (edited May 19, 2006).]

[This message has been edited by Tom C (edited May 20, 2006).]

[This message has been edited by Tom C (edited May 20, 2006).]

posted May 19, 2006 07:55 PM            

------------------
Best Regards,

Tom Cunningham

posted January 17, 2010 10:17 AM            

I am a student at IIT roorkee.
I have done an extensive project on resident time calculation using these equations. Also i have successfully calculated zone wise resident time distribution.

posted January 17, 2010 07:00 PM            

Potente
Bigio
Vergnes

------------------
Best Regards,

Tom Cunningham