Calculating the optimum output for a single-screw extruder can take lots of time, as it involves the specifics of the extruder and many polymer characteristics. But you can get a rough estimate of the potential output if you know the drive horsepower of your machine and the thermal characteristics of one of the materials you’ll be running, combined with experience with a similar process.
If a typical melt temperature for the process and the specific heat of the polymer are known, getting to your first output estimate can be fairly simple. In most cases, the change in temperature from the polymer entering the extruder to the temperature exiting the extruder (ΔT) accounts for about 90% of the total energy converted from the screw rotation for smooth-barrel extruders. Use that as the basis for an output estimate. The other 10% is consumed in solids feeding, pressurization, and mechanical losses.
Let’s use HDPE sheet extrusion as an illustration, where the average melt-temperature range is 400-450 F. If you take 425 F as an average melt temperature, and the polymer goes into the extruder at room temperature (75 F), the change in temperature is 350° F. We know the average specific heat of HDPE is 0.55 BTU/lb-°F. For 1000 lb/hr of output, the energy requirement can be calculated as:
1000 lb/hr x 350°F x 0.55 BTU/lb-°F = 192,500 BTU/hr.
Convert BTU to horsepower and you get:
192,500 BTU/hr x 0.000393 = 74.86 hp.
However, this is only the energy for heating the polymer. In addition to the previously mentioned 10% usage, there are losses in energy to the gear reducer, to the surroundings and to any extruder-cooling systems . The magnitude of those losses is typically an additional 20-25% on all but the newest extruders. So taking all factors into account, the drive size must be increased by 30-35% above what is necessary to handle just the heating of the polymer.
In the above scenario, 74.86 hp/0.65=115.2 hp would be enough drive power to turn the screw using full motor load or capacity. But you’ll need some reserve power to prevent hitting the current limit, so best bump that up by an extra 15-20%, taking the total to 115.2/0.80=144.0 hp. This last adjustment is just to allow the motor load to be at approximately 80% of full load at full speed. You might be able to reduce this margin and run closer to full load, as motors are designed to operate indefinitely at full load.
This can be broken down to the following formula for conservatively estimating output based on the available hp:
Available hp/(0.000748 x specific heat x ΔT) = Output (lb/hr)
Substituting values into the equation:
150 hp/(0.000748 x 0.55 BTU/lb x 350° F) = 1041.7 lb/hr
Use the correct temperature rise and specific heat. Different processes require different melt temperatures with the same polymer. The temperature rise is from your process experience; the specific heats are available on the internet. A Spirex publication, Plasticating Essentials, lists some specific-heat values (right).
The above calculation is only the first estimate of the potential output. Screw torque and L/D also have to be considered to get that final number. Horsepower is the power available, but torque capacity is the measure of turning power that rotates the screw.
Torque (in.-lb)=(hp x 63025)/maximum rpm
This affects performance because the force to turn the screw is reduced proportionally as the maximum screw speed increases. The screw should be designed for a specific output to match the available torque. If the torque is low—meaning the maximum screw speed is high—then the specific output must be lowered by using shallower screw channels. As the channels are made shallower, the melt temperature will be increased until it is no longer within the processing window. As a result, horsepower is not in itself a complete description of extruder power.
Lastly, determine if the L/D is long enough to handle feeding, melting, and pressurizing requirements at the rate determined. The effects of torque and L/D require screw-design smarts in order to be properly estimated. The formula based on heating the polymer is only an estimate of potential output.
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 firstname.lastname@example.org or (724)651-9196.