Torque in Filament Extrusion

Community-scale plastic recycling often involves melting shredded plastic and forcing it through a die to produce filament for 3D printing. The heart of many do-it-yourself extruders is a rotating screw that pressurizes and pushes molten polymer through a nozzle. Understanding the torque required to drive this screw helps makers choose an appropriate motor and gearbox so the extruder operates reliably without stalling. This calculator provides a first approximation of that torque by combining extrusion pressure, screw diameter and drivetrain efficiency.

When a screw extrudes plastic, it must generate enough force to overcome the pressure of the melt resisting flow through the die. The force on the screw is the product of pressure and the cross-sectional area of the screw bore. The torque is this force multiplied by the radius of the screw because torque is defined as force times lever arm distance. These relationships are captured by the equations below.

Here $F$ is force in newtons, $P$ is extrusion pressure in pascals, $A$ is the barrel cross-sectional area, $r$ is screw radius in meters and $\eta$ is drivetrain efficiency expressed as a fraction. Pressure arises from flow restrictions in the nozzle and from the viscosity of the molten plastic. Efficiency accounts for losses in gears, couplings and bearings that mean the motor must deliver more torque than the screw itself requires.

The calculator accepts screw diameter in millimeters, extrusion pressure in megapascals and drivetrain efficiency as a percentage. Internally it converts units to SI base units, computes the barrel area using $A=\pi r{2}^{}$, determines the force and multiplies by radius to find torque. Dividing by efficiency yields the motor torque requirement. The result is presented in newton-meters, a standard engineering unit that can be compared with motor specifications.

Extrusion pressure varies widely with plastic type, temperature and die geometry. Soft plastics like polyethylene may require as little as 2 MPa, while more viscous materials or small nozzle diameters can demand upwards of 10 MPa. Makers often determine pressure experimentally by measuring force on a plunger or by referencing industrial extrusion data. The table below provides ballpark pressures for common recycled plastics processed into 1.75 mm filament through a moderate-length die.

Screw diameter influences torque in two ways: a larger diameter increases both the area that pressure acts upon and the radius at which force is applied. Consequently, torque scales with the cube of diameter. Doubling the diameter increases torque eightfold assuming pressure remains constant. This highlights the importance of matching screw size to available motor power. Many DIY extruders repurpose auger bits or injection molding screws, so understanding this scaling helps avoid underpowered designs.

Drivetrain efficiency reflects mechanical losses. Gearboxes, chain drives and bearings each consume a portion of the motor’s effort. High-quality components can achieve efficiencies above 90 percent, but improvised or poorly aligned systems may drop below 60 percent. Selecting efficient components reduces motor size and energy consumption, but may increase cost. The calculator’s efficiency input allows users to explore these tradeoffs.

For example, consider a screw 20 mm in diameter extruding PLA at 4 MPa with an efficiency of 80 percent. The barrel area is 314 mm², the resulting force is 1,256 newtons and torque at the screw is 12.6 N·m. Accounting for efficiency, the motor must provide about 15.7 N·m. If the extruder uses a gearbox with a 10:1 reduction, the motor itself sees 1.57 N·m, which many hobby-grade DC motors can deliver. Changing to ABS at 6 MPa raises required torque proportionally to 23.6 N·m at the screw, illustrating why some materials are more challenging to extrude.

The calculator focuses on steady-state torque for continuous extrusion. In practice, startup torque can be higher due to initial static friction and the need to melt cold plastic. Providing a safety margin when selecting motors and gearboxes is prudent. Thermal management is also critical; excessive pressure from undersized nozzles can cause overheating or degradation of the polymer. Monitoring motor current during operation offers insight into real-time torque demands and can alert operators to jams.

Beyond recycling, understanding extruder torque benefits small-scale manufacturers developing bespoke filaments with additives such as wood flour, metal powders or colorants. These additives often change viscosity, requiring recalculated pressures and thus torque. The transparent formulas in this tool invite experimentation with new feedstocks. Because the calculator runs entirely in the browser with no external libraries, it can be embedded in offline guides for maker spaces or educational settings where internet access is limited.

By articulating the interplay between pressure, diameter and efficiency, this calculator demystifies a key aspect of extruder design. Makers can iterate digitally before committing to mechanical components, saving time and resources. The lengthy explanation serves searchers looking for detailed guidance on DIY filament production, a niche yet growing field as 3D printing becomes more accessible. With quantitative understanding, community recycling projects can transform waste plastic into valuable feedstock for digital fabrication, closing material loops and fostering local resilience.