# Extrusion: A Simple Way to Evaluate Extruder Screws

While there’s lots of data that influences screw design, processors usually don’t have access to it. So instead, try calculating drag flow to see if your screw is working properly.

## Related Topics:

The design of extrusion screws can include an almost infinite amount of data when all the polymer properties, performance requirements, and the details of the extrusion system are considered. Most processors do not have much of this information at hand or know how to apply it to determine if the screw is producing the correct output.

As a result, a lot of misconceptions used in the industry prevail, and screws continue to be built in designs that are not optimized. So how do you know if your screws are working properly? One of the most useful evaluations is the relatively simple calculation of drag flow. Drag flow is simply half the volume of one turn of the metering section per second at a specific screw rpm, which, when multiplied by a units conversion and the melt specific gravity of the polymer, is a very accurate approximation of the output in lb/hr at no head pressure.

The calculation was developed and verified in the early 1950s, primarily by researchers at Western Electric, as follows:

1/2 π2 D2HN(sinѲ)(cosѲ) = in.3/sec

You can make a little more accurate by adding a shape factor, which represents the width-to-depth ratio of the screw channel. The shape factor compensates for the edge effects of the flights and the channel shape. For most screws, a shape factor for the metering section of 0.95 works well. So:

0.95 (0.5) π2 D2HN(sinѲ)(cosѲ) = in.3/sec

Further, a large percentage of extrusion screws use a standard pitch (flight pitch equals screw diameter) in the metering section, as it represents the best combination of overall performance in most cases. This simplifies the term (sinѲ)(cosѲ) to 0.289.

Additionally, (π2) can be simplified to 9.87 and N is in revolutions/ sec so by adding 1/60 the screw rpm can be substituted directly:

(0.95) (0.5) (9.87) (0.289)(1/60) D2HN = in.3/sec

0.02258 (D2HN)= in.3/sec

Where

• D = Screw diameter
• H = Channel depth
• N = Screw rpm

So as a first evaluation of the screw performance in in.3/sec, the only thing you need to know is the channel depth in the metering section. It’s assumed you know the screw diameter and the screw rpm.

Since the output is in in.3/sec, it needs to be converted to lb/hr for comparison. If you multiply by 130 you get lb/hr. But since extrusion screws are volumetric devices, the output must be further corrected for the melt specific gravity of the polymer (not the solid specific gravity) by multiplying by that number. Melt specific gravities are available on the internet for all the common polymers. At that point you’ll have the estimated output at no head pressure based on the metering-channel depth.

At low head pressures (<2000 psi) this is a pretty accurate number in most cases. At higher pressures, or with a very low-viscosity polymer, a second calculation may be needed to correct for the loss in output due to head pressure.

It should be noted that this calculation is for a single-stage screw. For a two-stage (or more) vented screw, the channel depth for the calculation is the first metering section, and it is very accurate estimate because the first metering section has no head pressure if the vent is open.

So what if the output is significantly different than the calculation? There are a host of things that can cause reduced output, but they require more information and more calculations and will be described by further articles. The most common cause of the actual output falling below the theoretical output of the metering section is inadequate feed capacity. Less common is a severe melting limitation whereby the screw becomes plugged with solid polymer.

There are externally measured symptoms that can lead to pretty firm conclusions about these issues without much knowledge of screw design. Another cause is a design where the feeding, melting and metering sections are not balanced, or if there is some restrictive mixer or other device affecting the output. But that requires a screw drawing and a complete analysis by someone with screw-design expertise.

The calculation above approximates what the output should be and indicates whether further investigation is appropriate. Despite all the variables involved in screw design, the drag flow in the metering section is a very good indicator of expected output, because for good screw balance, most designs are based on the metering section.

ABOUT THE AUTHOR: Jim Frankland is a mechanical engineer who has been involved in all types of extrusion processing for more than 40 years. He is now president of Frankland Plastics Consulting, LLC. Contact jim.frankland@comcast.net or (724)651-9196.

## Editor Pick

SPE Extrusion Division Holding May 'Mini-Tec'

Slated for May 1-2 in Charlotte, program will feature tutorial presentations on Day 1, and advanced presentations relating to the extrusion of PET and PLA formulations on Day 2.