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FGF Extrusion Consistency and a Quick Detour into Statistics

Our Fused Granulate Fabrication (FGF) 3D printers rely on a single-screw plasticating extruder to convert pellets and flakes into molten plastic that can be 3D printed. It is a well known issue that single-screw extruders can suffer from flow surging if not controlled/tuned properly. Flow surging is an unwanted variation in extrusion rate (e.g. pounds of material per hour), and can negatively impact 3D print quality. 
As a group, we recently watched some videos of Thermwood’s awesome LSAM additive machines, which include mechanisms to avoid flow surging. This caused us to wonder if our FGF printers exhibit flow surging. To test this, we performed an experiment with Greengate rPETG pellets. We ship this material standard with our FGF machines, and have well-established printing parameters.

A GBX 2 printer was heated to T0=200C, T1=190C, and T2 = 175C and allowed to equilibrate for 10 minutes after reaching temperature. A DAQ-connected scale was placed 150 mm below the nozzle to record the mass of extrudate over time. The scale was set to record mass at 3.5 Hz. Then the PETG material was extruded over the scale for ~13 minutes using an extruder speed of 6.7 RPM. The mass of extrudate over time is plotted in Figures 1-3. The slope of the line is the extrusion throughput in grams per second. To convert to a more standard unit, multiply g/s by 3.6 to get kg/hr.

 

Figure 1: Mass of rPETG extrudate over 800 seconds using 6.7 RPM extrusion speed

 

It is clear from Figure 1 that the data is not perfectly linear. A linear regression returns an R2 value of over 0.99, but visually, there is non-linearity. Due to the nature of single-screw extrusion and of the experimental design, the non-linearity leading up to ~300 seconds was likely caused by oozing. As the machine sat at elevated temperature, the extruder oozed out some material. Therefore, it took a few minutes for the extruder to reach steady-state temperature and pressure. 

Zooming in to the period between 400-500 seconds (Figure 2), the data begins to look much more linear. It’s likely that by this point, the extruder has reached steady state temperature and pressure, so a linear throughput would be expected.

 

Figure 2: Mass of rPETG extrudate over 100 seconds.

 

Zooming in a bit further (Figure 3) actually causes the picture to become less clear. While the data are mostly linear (R2=0.967), there are some plateaus where the mass does not change for 1-2 seconds. At this scale, the resolution of the scale becomes a limiting factor. The scale uses a 5 kg load cell, which has a possible error of 0.05% (2.5 grams). Taking this at face value, one might conclude that the data in Figure 3 are meaningless because they span only ~3 grams. Additionally, this load cell can exhibit creep of up to 1.6 g/min. With these limitations in mind, there are still ways to extract meaningful insights from the data. 

Figure 3: Mass of rPETG extrudate over 25 seconds.

 

A known mass can be weighed on the scale to check accuracy, repeatability, and drift. In a laboratory environment, this would be performed using calibration weights. However, we’re proponents of scrappy (not crappy) DIY. Repeatability and accuracy were calculated by placing an aluminum block of known mass (64.6 g +/- 0.1 g) on the scale eight times. The piece of aluminum was then left on the scale for 4 minutes to capture any drift. Both of these experiments are captured in Figure 4.

Figure 4: Repeatability and drift experimental data for 5 kg load cell.

 

The calculated repeatability was +/- 0.07 grams, which is significantly smaller (and better) than the stated value from the manufacturer. The average sensor bias was -1.5 g. During the four minute drift portion of the experiment, the measurement drifted roughly -0.06 g/min, which is again smaller than the stated value. 

Taking these statistical measurements into account, it is safe to assume that the data presented in Figures 1-3 is a good representation of the system. Errors due to repeatability and drift are negligible, and sensor bias does not significantly affect slope of the line (extrusion rate). Therefore, we think it safe to assume that, in this case, the GBX2 was not experiencing significant flow surging. Of course, there are many caveats to this statement:

  • Performing these experiments in another environment could result in different extruder and sensor performance
  • This experiment was performed with the extruder stationary in the X and Y directions, and therefore does not capture any effects due to movement during printing
  • This only for one material. It is entirely possible that flow surging could be present with a different material.
  • The experiment was performed over a ~20 minute period, and was not repeated. It is possible that the period of flow surging is larger than 15-20 minutes, and we didn’t pick up on it. It is also possible that if we ran these experiments again, we would see different results.
  • A single set of printing parameters (temperatures and extruder RPM) was used in this experiment. Using different parameters could certainly affect the results.

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