Measurement and Modeling of Forces in Extrusion-Based Additive Manufacturing of Flexible Silicone Elastomer With Thin Wall Structures

Silicone elastomer deposited using direct extrusion additive manufacturing (AM) has demonstrated great potential for fabricating a wide variety of custom flexible thin wall structures such as pneumatic actuators and parts with high elongation and fatigue life [1–3]. This AM process is particularly advantageous over other AM methods, such as selective laser sintering, photopolymer jetting, and fused deposition modeling (FDM), because it enables the use of a wide variety of commercially available silicone elastomers, denoted as silicones, with broad material properties ranging from 3 to 90 Shore A hardness, up to 1100% elongations, −65 °C to 177 °C functional temperature range, long fatigue life, high chemical and UV resistance, and reasonable cost [4,5].

In material extrusion AM, a nozzle moves line-by-line and layer-by-layer to extrude material on the AM part to create a three-dimensional object. Unfortunately, this process generates forces which can deform and skew a soft and flexible AM part. This is a key challenge for extrusion-based AM of flexible silicone thin wall structures because silicone's low elastic modulus, ranging around 0.5–30 MPa, makes the parts easily deformable by forces generated during the extrusion of high-viscosity silicone fluid. Generally, the taller and thinner the part becomes, the greater the impact of the AM forces. By adjusting extrusion process parameters (e.g., flowrate, layer height, nozzle size, and acceleration), the ratio of AM forces to the parts' bending moment of inertia can be reduced and the maximum height of a soft, thin wall structure can be greatly increased.

During the extrusion-based silicone AM process, force on the workpiece is imparted in three modes: (1) machine vibration and build plate movement, (2) tangential and normal forces caused by silicone deposition and the nozzle tip, and (3) gravity force. Forces due to machine vibration and build plate movement can be overcome through control of accelerations, stationary build plates using a prismatic-input delta robotic 3D-printer, and increasing the stiffness of the 3D-printer. Silicone deposition can create tangential forces due to the dragging or pulling of the extruded silicone between the AM part and the moving nozzle tip and normal forces due to the momentum of the extruded silicone impacting the AM part. Additional tangential and normal forces may also be created from the nozzle side and bottom surfaces dragging through the deposited material. Finally, gravitational forces may cause creep or negatively affect thin overhanging structures but can be overcome through silicone cure methods and geometric design.

External forces have always existed in extrusion-based AM but were ignored for process parameter selection until soft materials and flexible parts became more prevalent. With rigid parts, such as those made from acrylonitrile butadiene styrene produced using FDM, a type of extrusion-based AM processes, the molten thermoplastic solidifies quickly after deposition from the nozzle (typically within seconds) and has high rigidity once cooled. This high rigidity allows the solidified material to resist forces imparted on it from the AM process. However, when silicone is used instead, the liquid silicone that is extruded from the nozzle may go through a chemical reaction to cure. This curing process typically takes minutes to hours, creating a high likelihood that subsequent layers of material will be deposited on the uncured, liquid form of the material. This allows for high interlayer bonding strength but makes parts extremely susceptible to the forces previously described. Additionally, even if the silicone or other soft material was able to cure in seconds, the cured state can still be extremely flexible and prone to deformation by the AM forces.

Although deformation of the soft silicone AM parts has been observed within and between the extruded layers [2,3], the research to measure and quantify the forces during the extrusion-based AM process is still lacking. Compliant silicone structures can be skewed by forces in the mN level. Therefore, understanding and modeling the forces in extrusion-based soft silicone AM is important. Plott et al. [3] showed that an adjacent line spacing increase of just 0.05 mm can significantly reduce the tensile strength of the part due to the creation of internal voids between adjacent silicone lines. If a silicone part is deformed by even a fraction of a millimeter, there is the potential for reduced tensile strength of over 30% [3]. Furthermore, if the deformation is too large, overall part accuracy can quickly deteriorate and lead to a failed AM process.

Fluid modeling has been applied to study the material flow and heat dissipation in AM. Die swelling is the radial expansion of the liquid material as it moves from a compressed, high pressure state within the nozzle to atmospheric pressure as it leaves the nozzle [6]. The swelling ratio, or the maximum diameter of the extruded material divided by the nozzle diameter, is typically 1.05–1.3 for FDM extrusion processes and is dependent on the material properties and process parameters [7,8]. Bellini [7] used computational fluid dynamics to create a two-dimensional model of the extruded material spreading process during and after deposition from the nozzle onto the build plate. Since the behavior of the melted filament in the extrusion nozzle is typically shear thinning, a power law dependency of the viscosity for the shear rate is used. One variation of the model included a nozzle tip as a contact condition, while another variation neglected the nozzle tip. Results showed that the presence of the nozzle tip added stability to the material flow and smoothed and flattened the top surface of the deposited material. Subsequent layers were modeled by rerunning the model using the geometry results from the previous layer as the base [7]. The literature review reveals a lack of study on the measurement of forces and part deformation due to forces in extrusion-based AM. This is particularly important for the AM of soft silicone flexible thin wall structures and will be investigated in this study.

The forces caused by extrusion-based AM of silicone are first introduced. Details of the experimental setup for silicone extrusion and force measurement are then presented. Results of tangential and normal forces created during the AM process are discussed and compared. Single wall towers were built based on different AM process parameters to validate the predictive deflection resistance model. Finally, results from the study are applied to the AM of a hollow thin wall silicone prosthetic hand.

Key factors affecting the magnitude of forces in extrusion-based AM of silicone include the silicone viscosity, flowrate, nozzle speed, nozzle tip diameter, layer height, extruded silicone material mechanical properties, and geometry and material properties of the surface for deposition. Figure 1 shows the free body diagrams of four scenarios in extrusion-based AM. From Figs. 1(a)–1(d), the flowrate, Q, is gradually increased. In Fig. 1(a), the extruded silicone is leaving the nozzle such that it is deposited onto a deposit layer or build plate without contacting the nozzle's exterior surface. This scenario is not commonly seen in extrusion-based AM because it is more difficult to control the part shape and where the material deposition is occurring. Three main force components in this scenario are F_ng—normal force caused by the weight of the silicone line, F_nd—normal force caused by deposited silicone decelerating, and F_td—tangential force caused by the nozzle as it drags and stretches the extruded silicone on the deposit layer or build plate.

In Fig. 1(b), Q is increased and the left side of the nozzle drags through the extruded bead of silicone, acting to flatten the top surface. In this scenario, the three forces (F_ng, F_nd, and F_td) that existed in the previous scenario are present with the addition of the fourth force, F_tn, which is the tangential force caused by nozzle movement through the deposited silicone, and the fifth force, F_nn, which is the normal force caused by the nozzle interacting with the deposited silicone. Additionally, since more silicone is being deposited in a given space, F_ng will increase due to an increase in weight, F_nd will increase due to the greater momentum of the material as it leaves the nozzle and decelerates on the deposit layer/build plate, and F_td will decrease since the extruded silicone will not be stretched as much by the nozzle movement.

In Fig. 1(c), Q is increased further causing the silicone to flow forward from the inner diameter of the nozzle as it contacts the deposit layer. This outward push of silicone will create a flow field that leads in front of the nozzle opening. Through this phenomenon, it is expected that F_td = 0 since the extruded silicone is no longer being stretched by the nozzle movement. Conversely, F_ng and F_nd are expected to increase for the same reasons described in the previous scenario.

Finally, in Fig. 1(d), Q is increased so much that the material flow field has moved in front of the nozzle, causing the side of the nozzle to drag through the material in addition to the bottom surface of the nozzle. In this scenario, it is expected that F_ng, F_nd, and F_tn will all be at the greatest level among four scenarios.

With an understanding of force originates in a given silicone AM scenario, it is important to measure the magnitude of these forces in each scenario. By determining these magnitudes, the process parameters can be optimized to minimize the part deformation and improve the accuracy and reliability of the extrusion-based AM for silicone and other soft materials. Section 3 explains the experimental setup to measure these forces.

This section outlines the silicone material, AM machine and setup, experimental design, and displacement to force conversion for force measurement of the silicone extrusion-based AM.

A one-part oxime cure silicone elastomer (Dow Corning^® 737, Dow Chemical, Midland, MI) was used as the base material for all experiments in the study. This silicone has a 33 Shore A durometer hardness, over 300% elongation, over 1.2 MPa tensile strength, and a specific gravity of 1.04 [9]. This silicone has a zero shear rate viscosity of about 62.5 Pa·s and begins curing with exposure to atmospheric moisture [1]. The viscosity was chosen since it is low enough for extrusion through the tapered nozzle tips and high enough to prevent self-leveling after extrusion, allowing the silicone to hold its shape. Once exposed to moisture, the silicone has a skin-over time of 3–6 min, a tack-free time of 14 min, and a cure to handling time of 24 h [9]. Since the skin-over time is lower than the layer times in the experiment, we assume each layer is extruded on a previously uncured layer.

The experimental setup for force measurement of extrusion-based AM of silicone is shown in Fig. 2. The system consists of six key components:

1. (1)

   A prismatic-input delta robotic 3D-printer as a motion control platform based on an open-source FDM machine (Rostock Max™ V3 by SeeMeCNC^®, Goshen, IN). The AM machine allows for the XYZ nozzle movement independent of the stationary build plate.

2. (2)

   A progressive cavity pump and its controller (model preeflow eco-PEN 450 pump and model EC200 controller by Viscotec, Töging am Inn, Germany) to dispense the silicone with a dosing accuracy of ±1% [10].

3. (3)

   Syringe barrels (model optimum by Nordson EFD, Westlake, OH) pressurized to 70±10 kPa which feed the progressive cavity pump with silicone while preventing the introduction of air bubbles into the silicone.

4. (4)

   A tapered nozzle with either 22 gauge (0.41 mm), 25 gauge (0.25 mm), or 27 gauge (0.20 mm) tip inner diameter (Model SmoothFlow™ by Nordson EFD, Westlake, OH) to deposit the silicone on the cantilevered plate.

5. (5)

   A brass cantilevered beam to measure the small AM force during material deposition. The beam has a polylactic acid base, a polylactic acid top plate, and a mirror. The length of cantilever beam for force measurement, h in Fig. 2(a), is 156 mm. The width and thickness of the beam is 25.83 and 0.82 mm, respectively.

6. (6)

   A laser displacement sensor (model LK-G10 by Keyence, Itasca, IL) with 0.02 μm repeatability and ±0.03% linearity over ±1 mm measuring range. The laser displacement sensor was connected to a display panel (model LK-GD500 by Keyence, Itasca, IL) and the LK-Navigator software (keyence) which records the sensor displacement data. A 3 Hz low-pass filter was used to smooth the data since the nozzle moves about the square test part at approximately 1 Hz. Due to the sensitivity of the force measurement setup, each moving component is isolated from one another and fixed to an optical table with vibration dampening.

Additionally, a high-speed camera (Model 100K, FASTCAM-1024PCI by Photron, San Diego, California, USA) with a 5.6× magnification lens operating at 500 frames per second was used to visualize the extrusion process and identify interaction between the nozzle tip and the extruded silicone.

To test the effects of key parameters on the forces experienced by a soft part created through extrusion-based AM, a parametric study was performed. Three key process parameters were varied: flowrate Q, layer height t, and nozzle diameter d_i, as listed in Table 1. The nozzle speed in the layer, v, was held constant at 20 mm/s. The parameter range was selected based on the previous studies in extrusion-based silicone AM [2,3] and preliminary exploration of process parameters for the AM of silicone thin wall structures.

A rounded-edge square part, as shown in Fig. 3, was utilized for silicone extrusion experiments. This part features a single line wall thickness with 25 × 25 mm side spacing and 3 mm total height. Four corners of the square are rounded with 4 mm radius to avoid rapid acceleration during the silicone AM process. The part is printed using a continuously increasing layer height, rather than the discrete jump in height for each layer, to further minimize any rapid acceleration.

Figure 4 shows the AM of this rounded-edge square part on the cantilevered build plate. The square was centered on the platform such that two opposite sides were parallel and the other two opposite sides were perpendicular to the long axis of the cantilever beam. Due to this print orientation relative to the cantilever beam, specific displacements (and forces) are measured at different sections of the part building process.

Looking first at point A₁ in Fig. 4(a), the nozzle is moving parallel to the long axis of the cantilever beam. At this point, only the normal force, F_n, can deflect the beam. According to point A₁ on the cantilever displacement versus time graph, Fig. 4(f), the deflection of the beam at A₁ is small due to F_n since the effective moment arm for F_n is only 12 mm versus the 197 mm moment arm for F_t. Section 3.4 explains this in further detail.

As the nozzle rounds the corner and moves to point A₂ in Fig. 4(b), F_t deflects the beam along the direction of the nozzle movement with a 197 mm moment arm, while F_n deflects the beam in the opposite direction of the nozzle movement with a 12 mm moment arm. From Fig. 4(f), the displacement at point A₂ (about 0.014 mm) is much higher than that at point A₁, indicating that forces which comprise F_t are well detected by the experimental setup in comparison to F_n.

As the nozzle continues to travel past A₂ and reaches point M₁ in Fig. 4(c), the nozzle is directly above the cantilever beam. At this point, F_n no longer influences the beam deflection and only F_t is measured.

Once the nozzle moves past point M₁ to point B₁ in Fig. 4(d), both F_t and F_n act to deflect the beam along the direction of nozzle travel. As the nozzle rounds the corner to point B₂, F_t is again moving parallel to the long axis of the cantilever beam and only the displacement due to F_n is detected. This cycle then repeats but in the opposite direction as the nozzle moves from point B₂ to C₁, C₂ to D₁, and D₂ to A₁, as seen in Figs 4(e) and 4(f).

In Fig. 4(f), there is a slope from points A₂ to B₁ and C₂ to D₁. This can be due to F_n creating a moment on the beam, the momentum of the cantilever beam and top plate, and potential extrusion variations on the corners where the velocity might vary. Because of these potential effects, F_n is only calculated from points D₂ to A₁ and B₂ to C₁, while F_t is only calculated at points M₁ and M₂. These calculations are detailed in Sec. 3.4.

This section describes the procedure of converting the measured displacement of the cantilever beam to F_t and F_n. Three free body diagrams, as shown in Fig. 5, are used to derive the force equations.

Although F_t and F_n could be approximated from the measured beam displacements using the classic cantilever beam bending theory and elastic modulus assumptions, a calibration curve was created for validation and improved force estimation accuracy.

To obtain the calibration curve, a series of six small metallic washers with various masses (m) were placed on the top plate at a known distance, l, from the center of the cantilever beam, Fig. 5(a). These masses create a normal force F_cal = mg, where g is the acceleration due to gravity. F_cal creates a coupled moment M at the free end of the cantilever beam which causes the displacement x₁ of the mirror. This displacement is measured by the laser displacement sensor (Fig. 2). Six masses for calibration were adjusted to make the range of displacement x₁ within that which was observed during the AM experiments. Results of these six coupled moments, corresponding displacements, and calibration line are shown in Fig. 6. The relationship between the mass and its moment on the cantilever beam and the displacement of the beam is linear in the measured range.

where h is the distance from the fixed base of the cantilever beam to the laser measurement point (h = 156 mm in this study), E is the elastic modulus of the beam material, and I is the moment of inertia of the beam. Together, EI is the experimentally determined constant of the beam. It is also assumed that the top plate is rigid and the mirror has a negligible effect on the overall beam bending.

Rearranging Eq. (1) and substituting the linear fit in Fig. 6, the constant EI = 105 kN mm² is calculated.

Additionally, since dimensions of the cantilever beam can be measured, the moment of inertia, I, can be calculated and substituted in EI to determine the modulus of the beam, E. The moment of inertia for a rectangular beam is $I=(bd3/12)$⁠, where b = 25.83 mm and d = 0.82 mm. The parameters I = 1.19 mm⁴ and E = 88.9 GPa, which are reasonable for the brass cantilever beam material.

where M = F_n l₀ and l₀ is the distance from the center line of the cantilever beam to the center of the nozzle when extruding between points D₂ to A₁ and B₂ to C₁ (12 mm), as shown in Fig. 5(c).

While this equation provides the total normal force, F_n, it is also possible to calculate the three force components which compose the total normal force, F_nd, F_ng, and F_nn.

• F_nd: The force component F_nd is the normal force caused by deposited silicone decelerating as it impacts the build plate or part. Using the equation for jet forces on a stationary plate, the normal force component F_nd can be calculated

  $Fnd=QρV$

  (6)

where $ρ$ is the density of the silicone and V is the silicone exit speed from the nozzle.

Since values of Q (0.10–0.40 ml/min), $ρ$ (1040 kg/m³), and V (12.6–212.2 mm/s) are known from the process parameters and silicone material, F_nd can be calculated. Results are shown in Fig. 7. The smaller the nozzle, the greater F_nd becomes for a given Q.

• F_ng: The force component F_ng is the normal force due to the weight of the deposited silicone. F_ng is calculated as

  $Fng=Qρs$

  (7)

where s is the time duration of material deposition. Since F_ng changes over time and the rounded-edge square part is axisymmetric, the amount of silicone deposited on one layer between the points D₂ to A₁ and B₂ to C₁ was calculated. The nozzle moves at a speed v = 20 mm/s and the length between those points (D₂–A₁ and B₂–C₁) is approximately 20 mm, therefore the weight of silicone deposition for 1 s was calculated. These results are shown in Fig. 8. F_ng varies linearly with Q and is independent of d_i

• F_nn: The force component F_nn is the normal force caused by the nozzle interaction with the silicone and is dependent on the level of normal compression between the extruded silicone and the nozzle tip. F_nn can be calculated by subtracting the other normal force components, F_ng and F_nd, from the total measured normal force F_n

  $Fnn=Fn−Fnd−Fng$

  (8)

The force results obtained from the experimental tests are presented in this section.

Following the procedure outlined in Sec. 3, displacements of the cantilever beam were recorded throughout 54 different experiments corresponding to the process parameters listed in Table 1. An example of a displacement versus time graph is shown in Fig. 9. In the beginning layers (0–4 s), there is a significant variability due to (1) inconsistencies in the initial material flow Q from the extrusion pump as internal pressure builds in the nozzle before equilibrium pressure/flow is reached, (2) variations in initial layer height due to imperfect build plate/nozzle leveling, and (3) over or under extrusion on the initial layers due to a nondeformable build plate. To compensate for this, the initial displacement data was ignored until a more uniform, periodic displacement was observed, typically after 5 s.

To determine the magnitude of the tangential force, F_t, the first 20 peaks were selected after equilibrium was reached. As shown in Fig. 10, a least squares fit was imposed on the data to identify midpoints of the displacement peaks (points M₁ and M₂ in Fig. 4).

These peak displacements were converted to F_t using Eq. (3). To determine the value of F_t and its associated error, the magnitudes of the first peak (point M₁) and valley (point M₂) were averaged to obtain the average F_t for a given layer. This step was then repeated for the next ten layers to compensate for any potential measurement drift. The average of these F_t values was then calculated to determine the final F_t and the measurement error equals the standard deviation. Results are presented in Fig. 11.

Figure 11 illustrates that process parameters can significantly impact F_t which ranges from 0.03 mN (Q = 0.10 ml/min, d_i = 0.25 mm, and t = 0.20 mm) to 4.01 mN (Q = 0.40 ml/min, d_i = 0.41 mm, and t = 0.10 mm). The wide range of F_t is due largely to the interaction between the nozzle tip and the deposited silicone, as shown in Fig. 1. In general, if the nozzle tip is not dragging through the deposited silicone bead, Fig. 1(a), F_t is significantly lower than if the nozzle tip is dragging through the deposited silicone bead, Figs. 1(b)–1(d). The more extruded silicone the nozzle tip is dragging through, the greater F_t becomes.

When Q was further increased to 0.28 ml/min with other process parameters held constant (d_i = 0.25 mm and t = 0.15 mm), we observed a distinct increase in F_t (0.27 mN). Using the high-speed camera and cross section analysis, the back edge of the nozzle is confirmed to have slightly dragged through the deposited silicone bead, Fig. 12(b) (bottom). The width of the wall increased to 1.57 mm (versus 1.56 mm calculated based on the incompressible flow condition in Eq. (9)).

Increasing Q further to 0.34 ml/min, we again observed an increase in F_t (1.38 mN). Through the high-speed camera images and cross section analysis in Fig. 12(c), a greater area of the nozzle was dragging through the deposited silicone but there was still no buildup on the front of the nozzle. The width of the wall was 1.80 mm (versus 1.89 mm calculated based on the incompressible flow condition in Eq. (9)).

Finally, with Q increased to the highest level, 0.40 ml/min, we saw the largest average F_t (1.54 mN). Through the high-speed camera and cross section analysis in Fig. 12(d), the nozzle was dragging through the deposited silicone and excess silicone was building up on the sides of the nozzle. The width of the wall was 2.24 mm (versus 2.22 mm calculated based on the incompressible flow condition), the thickest among all four flow rates.

From these results, we conclude that to minimize the tangential force F_t, it is ideal to select process parameters where the nozzle does not contact the extruded silicone line, Fig. 12(a), since F_td ≪ F_tn.

There are several approaches that can achieve this result with varying degrees of success. For example, selecting a large layer height, t, may prevent the nozzle from contacting the extruded silicone and yield a low F_t. However, if this layer height is too large, then the extrusion accuracy can be negatively affected. Additionally, this higher layer height may reduce the compression on the extruded silicone layers below, making it more difficult to achieve a “voidless” mesostructure [2,3].

Another approach might utilize a low Q. However, as Q decreases (all else equal), the extruded line width becomes thinner. A thinner line width may become problematic for fabricating thin wall structures as it will have a low structural stiffness and be more susceptible to the deformation by AM forces.

Yet another approach could include the use of a very small d_i to increase F_n, the force at which the deposited silicone compresses extruded silicone layer. This could be used to push the deposited silicone out of the way from the nozzle, preventing the nozzle from dragging and creating a large F_t. However, with high F_n, the part may deflect downward leading to accuracy issues.

As a general rule to reduce F_t, it is recommended to select AM process parameters which create an extrusion scenario where the nozzle is very close to the deposited surface, as shown in Fig. 12(b), while still residing in the extrusion scenario shown in Figs. 1(a) and 12(a). This ensures a low F_t while at the same time compressing previous layers to minimize internal voids, maintaining deposition accuracy and having a bead width with enough structural stability for producing thin wall parts.

To determine the magnitude of F_n, regions from D₂ to A₁ and B₂ to C₁, as shown in Figs. 4 and 13, were identified in the displacement versus time graph. The difference of average displacement between regions D₂ to A₁ and B₂ to C₁ is 2x₃, as shown in the close-up view in Fig. 13. The parameter x₃ in three selected measurement regions equally spaced in the 3rd to 11th layers was identified. Equation (5) was used to convert the measured x₃ to F_n. Three measured F_n values were averaged to calculate the average F_n for a given set of process parameters.

In some of the displacement versus time data, especially with process parameter settings where the nozzle did not drag through the extruded silicone material (Fig. 1(a)), F_n was undetectably small (experimental setup can only detect F_n values greater than 0.1 mN) and assumed to be 0. This correlates well to the theoretical normal force component calculations for F_nd and F_ng. Since the nozzle is not in close contact with the extruded silicone, F_nn is close to 0. Additionally, since the range of this experimental setup is limited to the mN force scale, it is expected that F_nd and F_ng would be undetectable since, in theory, F_nd and F_ng will be in the μN scale. An example of the low, undetectable F_n data is shown in Fig. 14.

The normal force results, F_n, for all 54 process parameter combinations are shown in Fig. 15. These results show that F_n has a strong dependence on the process parameters, ranging from undetectable (< 0.1 mN) where the nozzle does not contact or come in close compression with the deposited silicone to 1.21 mN where significant compression takes place (d_i = 0.41, t = 0.15 and 0.10 mm, and Q = 0.4 ml/min).

A key observation is that F_n was undetectable if the nozzle was not dragging through the extruded silicone bead. However, the nozzle does not necessarily have to drag through the extruded silicone for a jump in F_n to occur. An example of this is shown in the following process parameters: d_i = 0.25 mm, t = 0.15 mm, and Q = 0.22 ml/min. From Fig. 12(a), we observe that the nozzle may slightly contact the extruded silicone bead with those parameters without dragging through the extruded material (cross section analysis shows that the top of the silicone bead was smooth and rounded, indicating that minimal dragging occurred by the nozzle tip). However, in Fig. 15, a distinct increase in F_n was observed at this parameter set. This indicates that the nozzle does not necessarily need to drag through the extruded silicone bead to create a detectable mN-scale F_n. It is hypothesized that in this scenario, the silicone is being compressed by the nozzle but the flow field of the silicone is such that minimal drag is created. In general, as Q is increased further, the degree to which the nozzle contacts the extruded silicone increases, causing an increase in F_n. Based on these results, F_nn is the dominating normal force component.

Experimentally measured F_t and F_n show similarities and differences. As the nozzle tip begins to contact the extruded silicone, there is a significant increase in both F_t and F_n. Based on this, we conclude that forces due to the nozzle tip contacting the extruded silicone, F_tn and F_nn, are much larger than the other force components caused by the silicone extrusion-based AM process. We also observed that once the nozzle begins to contact the extruded silicone, F_tn and F_nn increase as Q increases. A slight difference in the behavior of F_tn and F_nn is that F_nn tends to onset before F_tn in certain scenarios since the nozzle can contact the extruded silicone and influence the normal compression without significantly dragging through the extruded silicone bead. This is observed in the spikes at three process parameter combinations: (1) Q = 0.22 ml/min, t = 0.15 mm, and d_i = 0.25 mm; (2) Q = 0.22 ml/min, t = 0.10 mm, and d_i = 0.20 mm; and (3) Q = 0.40 ml/min, t = 0.20 mm, and d_i = 0.25 mm, where the ratio of F_n to F_t quickly jumps and then flattens out, as shown in Fig. 16.

A difference between the F_t and F_n measurements, assuming the nozzle is contacting the extruded silicone, is that a larger d_i creates a larger F_t and conversely creates a smaller F_n (all else equal), as shown in Fig. 16.

We hypothesize that since a larger nozzle size has a greater bottom surface area, it has a greater tendency to flatten the top surface of the extruded silicone bead, creating a larger F_t than a small nozzle.

Tall thin wall silicone structures are easily deformed by forces caused during the extrusion-based AM process. To explore the relationship between part structure, AM forces, and maximum part height, experiments were conducted to test the build height limit of single wall silicone towers with 10 mm × 10 mm base, as shown in Fig. 17(a), produced with process parameters in Table 1. In this study, the AM process continues to increase the height of the thin wall tower until its deformation caused by AM forces significantly deteriorates the part quality. The maximum tower height before deterioration was recorded and marked in Fig. 17(b). We observed that low F_n and F_t did not necessarily yield taller towers since those parameters typically produce thinner wall structures which are more easily deformed. Parameters are explored to correlate to the maximum tower height with forces and wall structure. Two parameters, called deflection ratios, were chosen:

1. (1)

   F_t/I, where I is the moment of inertia of the tower base bending cross section

2. (2)

   F_t/W_t, where W_t is the width of the thin wall

These deflection ratios have good predictability of the maximum tower height under different extrusion conditions. Note that the maximum tower heights for all 54 possible process parameter combinations were not tested in this experiment. Instead, a representative set of towers was produced corresponding to the key inflection points identified in the deflection ratio curves of Figs. 17 and 18.

Since tall thin wall parts are more sensitive to tangential forces than normal forces, the F_t measured in Sec. 4.2 is used in the numerator of the deflection ratio. For the denominator I of the deflection ratio, the base of the thin wall square structure is approximated as a hollow rectangular prism. The moment of inertia for a hollow rectangular prism is $I=(EF3−ef3/12)$⁠, where E and F are the outer dimensions of the rectangular prism and e and f are the inner dimensions of the rectangular prism [11]. For the 10 mm × 10 mm single wall square tower, E = F = 10 + c/2 mm and e = f = 10 − c/2 mm, where c is calculated using Eq. (9). Results of the F_t/I versus flow rate with the value of maximum tower height are shown in Fig. 17(b).

In Fig. 17(b), it is observed that F_t/I correlates well to the maximum tower height in most cases. In general, as F_t/I is reduced, the maximum tower height is increased, with the exception of d_i = 0.41 mm, t = 0.10 mm, and Q = 0.22 and 0.40 ml/min. It is hypothesized that the poor correlation for these parameters is due to a different tower failure mechanism than that of the other towers. A typical example of a failed tower due to rectangular prism bending is shown in Fig. 19(a). In this example, as the height of the tower grew, the tower deflection increased due to F_t until it no longer provided a stable platform for printing. The noncorrelating towers did not fail due to tower deflection, but rather due to an over extrusion and buildup of material, as shown in Figs. 19(b) and 19(c). In this case, the nozzle continually dragged the extruded silicone until the top of the tower closed off and could no longer provide a suitable printing surface.

Under low flow rate and small nozzle diameter conditions, the liquid rope coiling phenomenon [12] was observed. This is denoted as coil in Figs. 17(b) and 18.

To predict the maximum tower height in the over extrusion scenario, Figs. 19(b) and 19(c), a new deflection ratio, F_t/W_t, is explored. Figure 18 shows results of F_t/W_t versus Q with the maximum tower height marked. For Q = 0.22 ml/min and above at the t and d_i values tested, this deflection ratio provides a better correlation for the maximum tower height.

From these results, a smaller nozzle d_i has a more favorable force deflection ratio than a larger nozzle d_i. As d_i becomes smaller, the force deflection ratios (F_t/I and F_t/W_t) also become less dependent on Q and t. Based on these results, when selecting the process parameters for tall and thin structures, it is best to minimize d_i. When utilizing a small d_i, other parameters such as t and Q can be selected based on the desired surface finish and wall thickness.

Findings in Sec. 5 were applied to select process parameters which enabled the extrusion-based silicone AM of a prosthetic hand, as shown in Fig. 20. The geometry for this prosthetic hand was generated from an optical scan of an adult hand and then scaled down to a smaller size due to limitations generated by the large unsupported geometry and slow material cure speed creating a tendency for the structure to collapse under its own weight.

The angled base of the thumb and in-between the finger joints approximates support-less bridging sections [2] and the rest of the hand (especially the fingers) approximates the tall thin-walled structures.

The AM process parameters used were d_i = 0.25 mm, t = 0.21 mm, Q = 0.28, and v = 20 mm/s. Two lines were used for the main wall of the hand to provide a stable base for support-less bridging, while a single line wall was used for the fingers to minimize over extrusion at the tips of the fingers. The process parameters were selected since the deflection ratios were comparable to those found with the smaller d_i = 0.20 mm nozzle, while the slightly larger nozzle size improves bridging ability.

The tangential and normal forces imparted by the extrusion-based AM of silicone were experimentally determined for a variety of process parameter combinations. Experimental results showed that the F_t has a strong dependence on the process parameters, ranging from 0.03 mN (Q = 0.10 ml/min, d_i = 0.25 mm, and t = 0.20 mm) to 4.01 mN (Q = 0.40 ml/min, d_i = 0.41 mm, and t = 0.10 mm). Through high-speed camera footage and cross section analysis, it was determined that F_tn (tangential force caused by nozzle dragging through the deposited silicone) is the dominating force component, causing an order of magnitude increase in F_t when present.

Experimental results showed that F_n also has a strong dependence on the process parameters, ranging from undetectable (< 0.1 mN) where the nozzle does not contact the deposited silicone to 1.21 mN where significant compression takes place (d_i = 0.41 mm, t = 0.15 mm and 0.10 mm, and Q = 0.4 ml/min). Based on the fluid flow modeling, we predicted that F_nd (the normal force caused by deposited silicone decelerating) and F_ng (normal force due to the weight of the deposited silicone) provided micro Newton scale forces for the tested set of process parameters, meaning that F_nn (the normal force caused by the nozzle interaction with the silicone deposit layer) was the dominating force component causing an order of magnitude increase in F_n when present.

Based on these findings, to reduce F_t and F_n in extrusion-based AM, it is recommended to select process parameters where the nozzle tip does not drag through the deposited silicone. However, minimizing these forces may not directly translate to better parts. A deflection ratio utilizing F_t and the moment of inertia for a hollow rectangular prism was utilized to help determine the optimal process parameters for tall thin wall structure types. From these results, a smaller nozzle d_i has a more favorable force deflection ratio than a larger nozzle d_i. As d_i becomes smaller, the force deflection ratio also becomes less dependent on Q and t.

By minimizing the relevant deflection ratio based on AM forces and part geometry, it is possible to reduce the deflection of a tall thin walled silicone part during AM and enable a greater level of design freedom. Even though these experiments were performed using one type of silicone, it is expected that similar findings exist with other silicones and soft materials in extrusion-based AM.

It is also important to note that the process parameters suitable for tall and thin walled structures may increase the difficulty for producing a voidless structure ideal for maximizing tensile strength. This is because as the nozzle size d_i is decreased and the flowrate Q is increased, the distance the silicone spreads out over the cross section increases, requiring multiple layers of subsequent layer compression to achieve the theoretical wall width used for voidless cross section prediction.

Future work aims to develop a computational fluid dynamics model of this process and develop additional deflection ratios for other part types, enabling the creation of tall, thick- and thin-walled structures with high accuracy and mechanical strength.

We acknowledge the support and expertise from Dow Performance Silicones, in particular Dr. Rocky (Bizhong) Zhu.

• This research was partially funded by the National Science Foundation (CMMI Grant Nos. #1435177 and #1547073).

c =

distance between two adjacent silicone lines

d_i =

nozzle tip inner diameter

F_t =

total tangential force

F_td =

tangential force on deposit layer caused by the silicone bead dragging (F_td'—reactive force)

F_tn =

tangential force on deposit layer caused by the nozzle contact with the silicone (F_tn'—reactive force)

F_n =

total normal force

F_ng =

normal force on deposit layer caused by the weight of silicone (F_ng'—reactive force)

F_nd =

normal force on deposit layer caused by the deposition of the silicone (F_nd'—reactive force)

F_nn =

normal force on deposit layer caused by the nozzle interaction with the silicone (F_nn'—reactive force)

Q =

volumetric flow rate

t =

layer height

v =

nozzle speed in the layer