4 Notes
1. Process can be adapted for use with other materials and/or 3D
printers.
2. Over- or under-extrusion can be implemented on other 3D
printing machines. However, different calculation for the feeding parameter might be necessary depending upon the hardware. For example, Ultimaker 3 printer (Ultimaker) makes a
different usage of the extrusion parameter E within the G-code:
instead of the volume of the extruded material, as for the Ultimaker 2, the value of E represents the length of the filament fed
into the machine. The G-code for this printer would look
exactly like the one shown in the previous section; only the
numerical value for the parameter E would be different. For
example, we assume that the spool of material is made of a
filament of diameter d spool and that the diameter of the nozzle
is d nozzle . Within a movement between two points at a distance
l from each other, it is possible to equate the volume of material
before and after the extrusion. Using L as the length of filament
fed into the printer from the back, we obtain
lπ
d nozzle
2
2
¼ Lπ
d spool
2
2
:
By definition E ¼ L. The value of E correspondent to the
nozzle size is therefore given by
E nominal ¼ L nominal ¼ l
d nozzle
d spool
2
¼ l β nominal :
Thus, the parameter that controls the diameter of the
printed filament in the Ultimaker 3 printer machine is
β ¼
d filament
d spool
2
,
from which we can calculate the expected printed diameter as
d filament ¼ d spool
ffiffiffi
β
p :
3. From the graph plotted in Fig. 2, the diameter that is possible
to extrude is in the range [d nozzle , 2d nozzle ]. It is suggested to
avoid filaments with a diameter smaller than the nominal diameter of the nozzle as this would increase the variability in the
dimension of the printed filament.
4. The master calibration curve, such as the one presented in
Fig. 2, must be constructed for each machine and each nozzle
size to assess the accuracy of the process and identify the upper
and lower limits achievable.
38
Alessandra Bonfanti et al.
1. Process can be adapted for use with other materials and/or 3D
printers.
2. Over- or under-extrusion can be implemented on other 3D
printing machines. However, different calculation for the feeding parameter might be necessary depending upon the hardware. For example, Ultimaker 3 printer (Ultimaker) makes a
different usage of the extrusion parameter E within the G-code:
instead of the volume of the extruded material, as for the Ultimaker 2, the value of E represents the length of the filament fed
into the machine. The G-code for this printer would look
exactly like the one shown in the previous section; only the
numerical value for the parameter E would be different. For
example, we assume that the spool of material is made of a
filament of diameter d spool and that the diameter of the nozzle
is d nozzle . Within a movement between two points at a distance
l from each other, it is possible to equate the volume of material
before and after the extrusion. Using L as the length of filament
fed into the printer from the back, we obtain
lπ
d nozzle
2
2
¼ Lπ
d spool
2
2
:
By definition E ¼ L. The value of E correspondent to the
nozzle size is therefore given by
E nominal ¼ L nominal ¼ l
d nozzle
d spool
2
¼ l β nominal :
Thus, the parameter that controls the diameter of the
printed filament in the Ultimaker 3 printer machine is
β ¼
d filament
d spool
2
,
from which we can calculate the expected printed diameter as
d filament ¼ d spool
ffiffiffi
β
p :
3. From the graph plotted in Fig. 2, the diameter that is possible
to extrude is in the range [d nozzle , 2d nozzle ]. It is suggested to
avoid filaments with a diameter smaller than the nominal diameter of the nozzle as this would increase the variability in the
dimension of the printed filament.
4. The master calibration curve, such as the one presented in
Fig. 2, must be constructed for each machine and each nozzle
size to assess the accuracy of the process and identify the upper
and lower limits achievable.
38
Alessandra Bonfanti et al.