In-line measurement of extrusion force and use for nozzle comparison in filament based additive manufacturing

In FFF, a filament in wire form is fed to an extruder. (Fig. 1) This is driven by a feed wheel attached to a motor with the torque M_M. The feeding force F_F is generated by converting the rotational movement at the motor into a translational movement at the filament and can be calculated with the radius of the drive wheel r_M as follows:

On the opposite side of the filament, a pressure wheel provides the necessary contact force F_C on the filament. To enable the filament to be conveyed, the following condition must be met with μ₀ as the coefficient of friction.

Current models calculate with perfect friction (μ₀ = 1), without taking into account deformation of the filament or the feeding wheels. Investigations [3, 14, 19‐21] and practical experience show that the power transmission depends on the penetration capacity of the feed wheel into the filament (hardness of the filament), filament diameter variations as well as deposits and wear on the feed wheel. More deposits on the feeding wheels or lower penetration capacity into the filament mean that F_C must become larger, as presumably μ₀ becomes smaller. In order to compensate for deformations on the filament or to be able to adjust F_C the pressure wheel can be moved towards the filament via springs. If F_C is caused by a spring, as shown in Fig. 1, it can be calculated with the spring constant k and the spring displacement Δs using Hooke's law:

The smaller the radius of the filament or the greater the wear on the feeding wheels or smaller their radius r_M and r_W, the smaller Δs and thus F_C becomes.

In the area of the heating element, the material is transferred from the solid to the almost liquid state. At this boundary layer, the solid material acts as a piston and begins to feed the liquid material in negative z-direction. If the filament has sufficient stiffness in relation to the length from the feeding wheel to this boundary layer and is guided tightly in a barrel, bending or even buckling is avoided [5, 20]. The inner diameter of the barrel cannot be equal to the filament diameter due to increasing friction. This creates a gap where friction can be largely neglected.

The feeding force F_F can be described as follows via the force equilibrium in a control volume, see red area in Fig. 1, following [10]:

Here F_p,1, F_p,0 und F_p,C are the forces of the melt on the surface of the control volume in the z-direction. In the case of free extrusion and a large distance of the nozzle from a substrate, F_p,0 = 0 can be assumed. F_τ,B, F_τ,C and F_τ,N are the forces due to tangential stresses on the control volume in the z-direction. If no bending occurs on the filament or no moments are induced, F_p,1 is equal to F_F.

The forces or the pressure loss in the control room can be described using Hagen-Poiseuille law [3]. Here, a laminar flow is assumed due to the low feeding velocity v_F. According to [10], the following equations result for the individual forces:

Here p is the pressure, τ_ns the shear stress on the surface of the cone and τ_rz the shear stress component on the barrel surface. According to [10], the forces F_τ,C, F_τ,N have a small influence on F_F. At high v_F the shear stresses become larger and thus the influence of the shear forces F_τ,B; F_τ,C and F_τ,N on F_F.

The gap between the filament and the cylinder can cause a backflow [10, 20] of the melt. This has a particular influence on heat transfer at this point, so that it cannot be neglected, especially at high feeding velocities v_F. Serdeczny et al. [10] refer to this as the transition from a stable to an unstable extrusion. Above a certain v_F, the reflux causes an oscillation in the feeding force [11, 15].

The test rig (Fig. 2) has a rotary encoder (a) that records the length of the filament fed to the extruder and its actual speed. The feeding unit (c) has an adjustment option for the contact force (b). The feeding wheel on the motor shaft and the pressure wheel are dynamically linked to each other via gear wheels, so that the filament is actively fed into the extruder from two sides. The polymer is plasticised at the heating element (f). A heat break with a compressed air cooler (e) provides the necessary thermal bridge. The molten material is discharged at the nozzle (g). The force F_S is detected with a ring load cell "Burster Miniature Ring Load Cell Type 8438" (d) with integrated strain gauges.

The weight forces of the extruder G_L and the melt plus extrudate G_M are recorded with the force sensor and are deducted from the measurement result by taring. After taring the weight forces, the measured extrusion force is F_E.

During a measurement, the temperature at the heating element T_H and the feeding velocity v_f are setting parameters. The average extrusion force \(\overline{{F }_{\mathrm{E}}}\) is calculated over the extrusion time.

Before recording forces in the test, the ring force sensor was calibrated using standardised weights.

A bolt was placed on the ring force sensor. A wire attached to the bolt was passed through the centre of the extruder. The measured force at the sensor F_S was zeroed with the masses of the bolt and the wire. Outside the die, a standardised weight was attached to the wire. The mass of the weight was previously checked with a precision balance. F_S was recorded and the mean value of the recorded forces \(\overline{{F }_{\mathrm{S}}}\) was calculated.

Using the gravitational acceleration g = 9.81 mm/s², the weight force can be calculated as the nominal force from the mass of the weight. The corresponding values can be seen in Table 1. The maximum difference between the nominal and the measured force is 264 mN. The mean deviation is maximum 8 mN and the standard deviation maximum 13 mN.

In the test rig, the heatbreak is not only necessary for conveying by separating the solid and liquid phases of the plastic, but also serves to protect the ring force sensor from overheating. To check the influence of the cooling by the compressed air cooler on the temperature at the ring force sensor, the temperature at the ring force sensor was measured while simultaneously recording the force. The temperature of the heating element was varied from 25 to 350 °C, the pressure of the cooling air p_A from 50 to 150 kPa.

As Fig. 3a shows, the temperature at the force sensor increases as the temperature of the heating element increases. A higher cooling pressure p_A causes less heating of the ring load cell and improves the accuracy of the force sensor (lower slope of the force graph in Fig. 3b). According to these results, the measurement error with p_A = 150 kPa would be a maximum of 80 mN in a series of tests over the range of 250–350 °C. The following tests are carried out with a cooling pressure of 150 kPa.

For comparison, the nozzles "E3D V6", "Gühring PKD Printer Nozzle" and "3DVerkstan Olsson Ruby", each with a diameter of 0.4 mm, were used.

The “filamentworld PLA (blue)” was used as the reference material and the “extrudr GreenTEC Pro Carbon”, a PLA with 10% carbon short fibres. All the filaments tested had a diameter of 1.75 mm.

As the weight force of the melt and the extrudate G_M increases over the duration of a measurement Eq. (9), this may have an influence on the measured force. To investigate this, the nozzle was positioned at a height of 5–45 mm from the substrate. Mathematically, at most a negligible weight force of 0.02 mN should be added at a height of 45 mm. In the test, 500 mm PLA filament, the "filamentworld PLA (blue)", was extruded at T_H = 210 °C and v_F = 3 mm/s. The smaller the distance, the greater the force. The smaller the chosen distance, the more often material had to be removed from the die area during extrusion. At a height of 5 mm, the material could not always be removed in time. This led to a jamming of material at the nozzle entrance and thus to an increase in pressure in the extruder or to an increase of \(\overline{{F }_{\mathrm{E}}}\). For heights of 15 mm and more, values of \(\overline{{F }_{\mathrm{E}}}\) were determined with a mean value deviation of approx. 80 mN. This deviation of the mean values of \(\overline{{F }_{\mathrm{E}}}\) is about one-tenth smaller than the mean deviation within a measurement of approx. 850 mN. G_M thus has no significant influence on the measurement of F_E in the selected measuring range. In the following, a nozzle height of ≥ 15 mm was selected.

An important assumption in the calculation models is that the contact force on the filament F_C must always be greater than F_E/2 at perfect friction Eq. (2). This assumption is validated in the following.

The "filamentworld PLA (blue)" was extruded at a heating element temperature T_H = 210 °C and feeding velocities v_F of 2 – 6 mm/s and F_E was recorded. In the experimental setup, F_C is generated via two identical springs mounted in parallel. Two pairs of springs with spring rates of k = 2.842 and k = 7.164 and a maximum force tolerance of 1 N and 2 N were used. The spring displacement Δs and thus F_C was adjusted by turning the knurled head screw at the feeding unit (Fig. 2b). According to Eq. (3), the parallel mounting of the springs means an addition of the spring forces. The resulting contact forces F_C can be seen in Table 2.

Since the extreme case of slipping on the filament is considered first, the maximum extrusion forces F_E,max are considered. Accordingly, in Fig. 4, half of F_E,max (F_E,max/2) is compared with the contact force according to Eq. (2). The more F_E,max/2 is converging F_C, in this case the as the force limit, the less constant the filament is fed. A strong exceeding of the force limit of F_E,max/2 was not measured. It is assumed that in this case μ₀ from Eq. (2) falls below 1 and thus a slipping occurs on the filament. Thereby, the equation would continue to be valid, only feeding no longer takes place. The further the distance of F_E,max/2 from the force limit, the more constant the feeding becomes.

This relationship can also be illustrated by observing the mean deviation of the extrusion force F_E,md in Fig. 5. Up to F_C ≤ 20.9 N, F_E,md and thus the spread of F_E initially decreases. From F_C > 20.9 N the spread increases, although the corresponding F_E,max moves away from the force limit. One assumption here is a decreasing contact pressure due to the penetration of the feed wheels into the filament and the resulting reduction of Δs. Macro images (Fig. 6) of the filament fed with v_F = 3 mm/s confirm the assumption. At F_C = 9.5 N, no notch is visible on the contact side of the feed wheel (1). This confirms the assumption of μ₀ < 1. A peek F_E,max at F_C = 9.5 N can, therefore, be explained by non-uniform friction of the feed wheel. In addition, characteristic elevation of material (2) can be seen on the surface of the filament on the pressure side, which could represent shearing of the material due to a stop of the filament in the z-direction. In this case, no extrusion force would be measurable. A notch on the engagement side of the feed wheel (3), among others, can be seen at F_C = 20.9 N. Deep notches (4), without significant elevation, are produced F_C = 40.0 N. In order to quantify the depth of the notches d_N using the images, the software “LAS X” from “Leica Microsystems” was used. The mean value of d_N as a function of the contact force is shown in Fig. 5. The measurement shows a greater notch depth at low and high contact forces. The notch depth is smallest at F_C = 20.9 N. A comparison of F_E,md and d_N in relation to the contact force suggests a correlation. A reduction of Δs by d_N results in a reduction of F_C. If this is added to F_E,md, the result is a corrected form of the spread F_E,md,cor (Fig. 5). This graph is consistent with the expectation that the spread of corresponding extrusion forces decreases while distancing from the force limit in Fig. 4. Considering the corrected spread a mean deviation limit of approx. 1 N has been identified. Above the limit extrusion seems to be unstable, resulting in higher frequent fluctuations of F_E over time. The unstable region is shown in Fig. 4, red area. In summary, at T_H = 210 °C the PLA shows stable flow at feeding velocities of 2–3 mm/s and contact forces of about 20–40 N.

Current extruders have fixed feeding wheels or gradual adjustments of the contact force at the feeding unit. Compared to the use of springs, on one hand, this allows a high contact force and constant values of μ₀ near 1; on the other hand, the system does not react to variations in the filament diameter. In this case, either very deep or relatively small notches can be formed in the filament. In relation to the observations presented here, this can lead to larger differences in the material output.

To determine the boundary conditions of a PLA filament, the average extrusion forces \(\overline{{F }_{\mathrm{E}}}\) were compared to the feeding velocities v_F of 2– 6 mm/s and the contact force F_C as well as the heating element temperature T_H of 190–230 °C were then varied.

The influence of the contact force at constant T_H = 210 °C is shown in Fig. 7. With increasing v_F, \(\overline{{F }_{\mathrm{E}}}\) increases. With F_C of 20.9 N, 29.9 N and 40.0 N, there is a transition (Fig. 7, red area) to a steep increase of \(\overline{{F }_{\mathrm{E}}}\) at v_F von 3.5–4 mm/s. Using a higher F_C, \(\overline{{F }_{\mathrm{E}}}\) increases significantly at v_F > 3.5 mm/s. Here, a higher \(\overline{{F }_{\mathrm{E}}}\) can be achieved with a higher F_C, since at the same time the force limit is higher and higher F_E,max can be achieved. The mean deviation of the extrusion force F_E,md also increases more strongly from v_F > 3.5 mm/s than at lower feeding velocities. At F_C = 40.0 N it increases non-corrected from F_E,md ≈ 1.9 N to F_E,md ≈ 8.9 N, which means significant extrusion fluctuations.

As a comparison, the springs on the feeding unit were removed and a screw was used to press the pressure wheel onto the filament with a tightening torque M_C. Two torques were selected with M_C = 0.3 Nm (approximately the maximum holding torque of the extruder motor of 0.32 Nm) and M_C = 0.6 Nm. The contact force F_C could thus be calculated with the thread pitch of the screw P via the formula of frictionless work.

This results in F_C = 2.693 N at P = 0.7 mm and M_C = 0.3 Nm. This value seems very high compared to the contact force generated with the springs. It suggests that friction cannot be neglected and therefore the actual contact forces are lower. The torques were set with a torque screwdriver before each extrusion, while the pressure wheel was in contact with the filament. Figure 7 shows \(\overline{{F }_{\mathrm{E}}}\) using the two torques as a function of v_F. Up to the transition speed v_F = 3.5 mm/s, they differ little from those of the feeding unit with spring. The strong increase of \(\overline{{F }_{\mathrm{E}}}\) occurs at approx. v_F = 5 mm/s. The mean deviation of the extrusion force F_E,md also remains relatively low up to this speed. At v_F = 6 mm/s the two forces evolve in opposite directions. The forces at M_C = 0.6 Nm showing a high-frequent oscillation. In addition, an occasional clocking of the extruder motor can be observed. At v_F = 6 mm/s there is no feeding and continuous clocking. As long as the filament is moving, feeding can take place. Otherwise, exceeding the maximum holding torque of the extruder motor leads to a stop in feeding.

The results shown here show a strong correlation to the results of [11, 15], which also describe the transition from stable to unstable extrusion above a certain feeding velocity. In addition, an independence of this transition zone from the contact force on the filament is shown here. In stable extrusion, the contact force has little significance. In this study, the moment-controlled contact force allows a higher feeding velocity under stable conditions.

Figure 8 shows the influence of the heating element temperature T_H. The higher T_H, the lower \(\overline{{F }_{\mathrm{E}}}\). At faster v_F the processing material can absorb less heat due to a shorter heating time in the heating zone and F_E remains greater. Here the transition zone (Fig. 8, red area) is shown in relation to T_H. Using T_H and v_F below the transition a stable \(\overline{{F }_{\mathrm{E}}}\) and thus a stable extrusion is ensured.

This dependence of F_E on v_F has already been proven several times [11, 15]. The investigations with the experimental set-up described here confirm this relationship.