Flexible thin wall silicone parts fabricated via extrusion-based additive manufacturing (AM) tend to deform due to the AM forces, limiting the maximum build height. The tangential and normal forces in AM were measured to investigate effects of three key process parameters (volumetric flow rate Q, nozzle tip inner diameter di, and layer height t) on the build height. The interaction between the nozzle tip and the extruded silicone bead is controlled to prevent interaction, flatten the top surface of the extruded silicone, or immerse the nozzle in the extruded silicone. Results show that tangential and normal forces in AM strongly depend on this interaction. Specifically, the AM forces remained low (less than 0.2 mN) if the nozzle tip did not contact the extruded silicone bead. Once the nozzle interaction with extruded silicone came into effect, the AM forces quickly grew to over 1 mN. The single wall tower configuration was developed to determine a predictive deflection resistance approach based on the measured AM forces and the resultant bending moment of inertia. This approach shows that a smaller di can produce taller towers, while a larger di is better at bridging and overhangs. These results are applied to the AM of a hollow thin wall silicone prosthetic hand.

## Introduction

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 [13]. 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.

## Forces in Extrusion-Based Additive Manufacturing

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 Fng—normal force caused by the weight of the silicone line, Fnd—normal force caused by deposited silicone decelerating, and Ftd—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 (Fng, Fnd, and Ftd) that existed in the previous scenario are present with the addition of the fourth force, Ftn, which is the tangential force caused by nozzle movement through the deposited silicone, and the fifth force, Fnn, 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, Fng will increase due to an increase in weight, Fnd will increase due to the greater momentum of the material as it leaves the nozzle and decelerates on the deposit layer/build plate, and Ftd 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 Ftd = 0 since the extruded silicone is no longer being stretched by the nozzle movement. Conversely, Fng and Fnd 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 Fng, Fnd, and Ftn 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.

## Experimental Setup

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.

### Silicone Material and Cure Parameters.

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.

### Additive Manufacturing Machine and Setup.

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.

### Experimental Design.

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 di, 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, Fn, 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 Fn since the effective moment arm for Fn is only 12 mm versus the 197 mm moment arm for Ft. Section 3.4 explains this in further detail.

As the nozzle rounds the corner and moves to point A2 in Fig. 4(b), Ft deflects the beam along the direction of the nozzle movement with a 197 mm moment arm, while Fn 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 Ft are well detected by the experimental setup in comparison to Fn.

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, Fn no longer influences the beam deflection and only Ft is measured.

Once the nozzle moves past point M1 to point B1 in Fig. 4(d), both Ft and Fn act to deflect the beam along the direction of nozzle travel. As the nozzle rounds the corner to point B2, Ft is again moving parallel to the long axis of the cantilever beam and only the displacement due to Fn 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 Fn 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, Fn is only calculated from points D2 to A1 and B2 to C1, while Ft is only calculated at points M1 and M2. These calculations are detailed in Sec. 3.4.

### Displacement to Force Conversion.

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

#### Cantilever Beam Calibration Curve.

Although Ft and Fn 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 Fcal = mg, where g is the acceleration due to gravity. Fcal 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.

Using the cantilever beam bending equation for a coupled moment M at the free end [11] and substituting M = Fcall = mgl
$x1=Mh22EI=Fcallh22EI=mglh22EI$
(1)

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.

#### Tangential Force Ft Conversion.

With these calibration results, the displacements recorded during the silicone extrusion experiments at points M1 and M2, Fig. 4(f), can be converted to Ft using the beam bending equation for a concentrated load Ft at the free end [11]
$x2=Ft(h3−3h+h1h2)6EI$
(2)
where x2 is the displacement of the mirror caused by Ft and h1 is the distance between the laser measurement point and the cantilever top plate surface (h1 = 41.0 mm, as shown in Fig. 5(b)). Equation (2) can be rearranged and simplified to solve for Ft
$Ft=6x2EI−2h3−3h1h2$
(3)

#### Normal Force Fn Conversion.

From the displacement data, the total normal force Fn can be calculated when the nozzle is extruding between points D2 to A1 and B2 to C1, as shown in Fig. 4. Using the cantilever beam bending equation for a coupled moment M at the free end in Fig. 5(c)
$x3=Mh22EI=Fnl0h22EI$
(4)

where M = Fn 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).

Rearranging Eq. (4), we can solve for Fn
$Fn=2x3EIl0h2$
(5)

While this equation provides the total normal force, Fn, it is also possible to calculate the three force components which compose the total normal force, Fnd, Fng, and Fnn.

• Fnd: The force component Fnd 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 Fnd 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, Fnd can be calculated. Results are shown in Fig. 7. The smaller the nozzle, the greater Fnd becomes for a given Q.

• Fng: The force component Fng is the normal force due to the weight of the deposited silicone. Fng is calculated as
$Fng=Qρs$
(7)

where s is the time duration of material deposition. Since Fng 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. Fng varies linearly with Q and is independent of di

• Fnn: The force component Fnn 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. Fnn can be calculated by subtracting the other normal force components, Fng and Fnd, from the total measured normal force Fn
$Fnn=Fn−Fnd−Fng$
(8)

## Results

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

### Cantilever Beam Displacements.

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.

### Experimental Results of Ft.

To determine the magnitude of the tangential force, Ft, 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 Ft using Eq. (3). To determine the value of Ft and its associated error, the magnitudes of the first peak (point M1) and valley (point M2) were averaged to obtain the average Ft 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 Ft values was then calculated to determine the final Ft and the measurement error equals the standard deviation. Results are presented in Fig. 11.

Figure 11 illustrates that process parameters can significantly impact Ft which ranges from 0.03 mN (Q = 0.10 ml/min, di = 0.25 mm, and t = 0.20 mm) to 4.01 mN (Q = 0.40 ml/min, di = 0.41 mm, and t = 0.10 mm). The wide range of Ft 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), Ft 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 Ft becomes.

One example where Q had a large influence on the interaction between the nozzle tip and the extruded silicone occurred with di = 0.25 mm and t = 0.15 mm. At Q of 0.22 ml/min and below, Ft was very small (0.06 to 0.10 mN). Using the high-speed camera described in Sec. 3.2, we observed that the nozzle was very close to the extruded silicone and potentially contacted it. However, the flow field of the silicone may have been such that the nozzle does not significantly drag through the deposited layer, as shown in Fig. 12(a) (top). This was also confirmed in Fig. 12(a) (bottom) through the cross section analysis which shows that the top of the silicone bead was smooth and rounded, indicating that minimal dragging occurred by the nozzle tip. The width of wall is the thinnest, about 1.20 mm, among all four Q in this combination (di = 0.25 mm, t = 0.15 mm, and Q = 0.22 ml/min, Fig. 12(a)). Based on the incompressible flow condition and Eq. (9) [2], the theoretical value of line width is 1.22 mm, which is close to the measured width of 1.20 mm
$Q=ctv$
(9)

When Q was further increased to 0.28 ml/min with other process parameters held constant (di = 0.25 mm and t = 0.15 mm), we observed a distinct increase in Ft (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 Ft (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 Ft (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 Ft, it is ideal to select process parameters where the nozzle does not contact the extruded silicone line, Fig. 12(a), since FtdFtn.

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 Ft. 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 di to increase Fn, 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 Ft. However, with high Fn, the part may deflect downward leading to accuracy issues.

As a general rule to reduce Ft, 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 Ft 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.

### Experimental Results of Fn.

To determine the magnitude of Fn, 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 Fn. Three measured Fn values were averaged to calculate the average Fn 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)), Fn was undetectably small (experimental setup can only detect Fn values greater than 0.1 mN) and assumed to be 0. This correlates well to the theoretical normal force component calculations for Fnd and Fng. Since the nozzle is not in close contact with the extruded silicone, Fnn is close to 0. Additionally, since the range of this experimental setup is limited to the mN force scale, it is expected that Fnd and Fng would be undetectable since, in theory, Fnd and Fng will be in the μN scale. An example of the low, undetectable Fn data is shown in Fig. 14.

The normal force results, Fn, for all 54 process parameter combinations are shown in Fig. 15. These results show that Fn 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 (di = 0.41, t = 0.15 and 0.10 mm, and Q = 0.4 ml/min).

A key observation is that Fn 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 Fn to occur. An example of this is shown in the following process parameters: di = 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 Fn 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 Fn. 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 Fn. Based on these results, Fnn is the dominating normal force component.

### Comparison of Results.

Experimentally measured Ft and Fn show similarities and differences. As the nozzle tip begins to contact the extruded silicone, there is a significant increase in both Ft and Fn. Based on this, we conclude that forces due to the nozzle tip contacting the extruded silicone, Ftn and Fnn, 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, Ftn and Fnn increase as Q increases. A slight difference in the behavior of Ftn and Fnn is that Fnn tends to onset before Ftn 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 di = 0.25 mm; (2) Q = 0.22 ml/min, t = 0.10 mm, and di = 0.20 mm; and (3) Q = 0.40 ml/min, t = 0.20 mm, and di = 0.25 mm, where the ratio of Fn to Ft quickly jumps and then flattens out, as shown in Fig. 16.

A difference between the Ft and Fn measurements, assuming the nozzle is contacting the extruded silicone, is that a larger di creates a larger Ft and conversely creates a smaller Fn (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 Ft than a small nozzle.

## Deflection Ratios

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 Fn and Ft 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)

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

2. (2)

Ft/Wt, where Wt 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.

### Ft/I.

Since tall thin wall parts are more sensitive to tangential forces than normal forces, the Ft 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 Ft/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 Ft/I correlates well to the maximum tower height in most cases. In general, as Ft/I is reduced, the maximum tower height is increased, with the exception of di = 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 Ft 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.

### Ft/Wt.

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

### Discussions.

From these results, a smaller nozzle di has a more favorable force deflection ratio than a larger nozzle di. As di becomes smaller, the force deflection ratios (Ft/I and Ft/Wt) 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 di. When utilizing a small di, other parameters such as t and Q can be selected based on the desired surface finish and wall thickness.

## Application: An Example of AM a Thin Wall Silicone Hand

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 di = 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 di = 0.20 mm nozzle, while the slightly larger nozzle size improves bridging ability.

## Conclusions

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 Ft has a strong dependence on the process parameters, ranging from 0.03 mN (Q = 0.10 ml/min, di = 0.25 mm, and t = 0.20 mm) to 4.01 mN (Q = 0.40 ml/min, di = 0.41 mm, and t = 0.10 mm). Through high-speed camera footage and cross section analysis, it was determined that Ftn (tangential force caused by nozzle dragging through the deposited silicone) is the dominating force component, causing an order of magnitude increase in Ft when present.

Experimental results showed that Fn 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 (di = 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 Fnd (the normal force caused by deposited silicone decelerating) and Fng (normal force due to the weight of the deposited silicone) provided micro Newton scale forces for the tested set of process parameters, meaning that Fnn (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 Fn when present.

Based on these findings, to reduce Ft and Fn 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 Ft 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 di has a more favorable force deflection ratio than a larger nozzle di. As di 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 di 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.

## Acknowledgment

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

## Funding Data

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

## Nomenclature

• c =

distance between two adjacent silicone lines

•
• di =

nozzle tip inner diameter

•
• Ft =

total tangential force

•
• Ftd =

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

•
• Ftn =

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

•
• Fn =

total normal force

•
• Fng =

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

•
• Fnd =

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

•
• Fnn =

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

•
• Q =

volumetric flow rate

•
• t =

layer height

•
• v =

nozzle speed in the layer

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