SAMPE Journal - July/August 2024 - 9

Extruder Sizing Calculations
To correctly size the components of the extruder,
the ideal throughput had to be determined. For
testing purposes, the extruder was sized for the
smallest build volume that is considered LFAM.
This size is a 1 m3
generic tooling component design that can be
used to aid in the sizing. A two-bead wall is often
standard in LFAM for easier part planning. For the
estimation of the required throughput, the length
of extrusion per layer is estimated at 4A+12B. With
A and B both set as 1 m which is the maximum tool
size for this build volume, the extruded length per
layer is 16 m.
The next step in sizing is to estimate the
Figure 3. Proposed design (bottom) versus current extruders.
a melt pump to the end of the extruder to more
closely control the volumetric output. The length of
this section can vary but at a minimum it is as long
as the transition or metering section. When looking
at the function of the melt pump, it can be referred
to as an external metering device. This would make
it a redundant system with the metering section of
the screw. This is why the design of the extruder
explained in this paper will replace the metering
section of the screw with a melt pump, thereby
decreasing the overall weight and length of the
system without sacrificing the advantages that can
be gained by having a melt pump in the system. A
diagram showing the proposed method is shown in
Figure 3. As shown, removing the metering section
of the screw would allow for enough space to add
the benefits of a melt pump without additional
length beyond the original screw design. This is
because the melt pump gears are typically the
screw diameter and the typical L/D ratio for these
extruders is 24:1. This means that 20% of the length
of the extruder is 4.8 meaning that the metering
section is 4.8 times the diameter of the screw. By
removing this section there is ample room for
adding a gear pump without exceeding the original
extruder length.
throughput required to maintain the 16 m extruded
length per layer. Assuming a 5 mm wide and 2.5
mm tall bead from a 5 mm nozzle, the volume per
layer is 0.00019 m3
build volume. In Figure 4 is a
. For maximum layer bonding
without the previous layer being so hot that a new
deposited layer deforms the part, an estimated
layer time for this part is about 3 min. By taking
the density of a typical LFAM material such as
carbon fiber reinforced ABS with a density of 1.14
g/cc, the weight of each layer can be determined
and then divided by the layer time to get the
required throughput for the extruder. In this case
the required throughput is 4.3 kg/hr. To account for
some differences in part design and layer times, a
small buffer will be added to this throughput and
the required throughput that will be used in the
design of this extruder is 4.5 kg/hr (approximately
10 lb/hr).
Motor Sizing
Although extruders may be rated for a specific
throughput, they are often able to reach a much
lower throughput for high-temperature materials
because the maximum torque of the extruder motor
would be reached. This can cause the extruder itself
to jam up and the screw unable to turn which is why
it is so important to size the motor appropriately
for the planned materials to be printed. This
was done by first calculating the specific energy
required to extrude each material. The specific
energy formula used in this calculation can be seen
in Equation 1. This equation assumes that cp
is the
specific heat capacity of the thermoplastic, DT is
the difference between the inlet and outlet extruder
Figure 4. Sample toolpath for LFAM tooling.
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JULY AUGUST 2024
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SAMPE JOURNAL |
9
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SAMPE Journal - July/August 2024

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