# An Outline of Fused Deposition Modeling: System Models and Control Strategies

^{*}

## Abstract

**:**

## 1. Introduction

- Offline:
- →
- slicing;
- →
- path planning;

- Online:
- →
- motion control;
- →
- extrusion control.

## 2. Systems

#### 2.1. Extrusion

#### 2.1.1. Single-Screw

#### 2.1.2. Filament Extruder

- Slippage $\lambda $ causes loss of speed given by$${v}_{f}=\frac{\omega r}{1-\lambda},$$
- Deformation occurs in the filament indentation as a result of the compression exerted by the roller teeth, which can cut into the filament.

- Direct: the motors are mounted directly on top of the liquefier. The load on the end-effector is higher, but the movement of the filament is more constrained and hence more controlled;
- Bowden: only the liquefier is mounted on the printing head, while the motors are placed in a fixed position of the machine, diminishing the load on the end-effector. However, the filament needs to cover some distance from the rollers to the liquefier, which may lead to bending and buckling.

- Filament advancement: when the feeding speed increases, the filament takes less time to cover the channel of the liquefier. At constant heat flow, the point along the liquefier in which the phase shift of the filament occurs (called transition point ) moves further towards the nozzle. In the extreme case, the filament does not melt completely and reaches the nozzle in the solid state.
- Backflow: at the transition point, the liquid portion of the material partially fills the thin air layer that separates the solid filament from the channel wall (see Figure 3). This creates a region where a portion of the liquid flows in the opposite direction of the feeding speed and recirculates, reducing the shear stress in the liquefier and leading to a drop in the feeding force.

#### 2.2. Deposition

#### 2.2.1. Strand Geometry

#### 2.2.2. Surface Roughness

#### 2.2.3. Global Structure

- $s<w$ can cause considerable distortions in new the layers;
- Smaller h and s lead to smaller porosity and better surface roughness.

## 3. Control

#### 3.1. Offline

#### 3.2. Online

#### 3.2.1. Single-Screw

#### 3.2.2. Filament Extruder

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Scheme of the single-screw extruder: 1—solid polymer; 2—hopper; 3—barrel; 4—screw; 5—heaters; 6—die; 7—extrudate; A—solid conveying zone; B—pre-melting zone; C—melting zone; D—melt conveying zone; E—melt flow zone. Image from reference [30].

**Figure 2.**Scheme of the extruder in FFF applications. Image from reference [33].

**Figure 4.**Scheme of the assumed cross-section of the deposited strand. ${v}_{e}$ is the extrusion speed (i.e., the exiting velocity of the extrudate from the nozzle), ${v}_{h}$ the printing speed (i.e., the linear velocity of the EE), d the diameter of the nozzle, and h the high of the deposited strand, which is often assumed to be equal to the distance between the nozzle and the substrate z.

**Figure 5.**Bottom view of an extruder with a spreading head. The extrudate flows from the nozzle with radius ${r}_{i}$, while ${r}_{e}$ is the radius of the spreading head. L denotes how much the extrudate expands on the y axis during the printing with respect to the internal die, and w is the total width of the extrudate.

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**MDPI and ACS Style**

Martini, M.; Scaccia, M.; Marchello, G.; Abidi, H.; D’Imperio, M.; Cannella, F.
An Outline of Fused Deposition Modeling: System Models and Control Strategies. *Appl. Sci.* **2022**, *12*, 5400.
https://doi.org/10.3390/app12115400

**AMA Style**

Martini M, Scaccia M, Marchello G, Abidi H, D’Imperio M, Cannella F.
An Outline of Fused Deposition Modeling: System Models and Control Strategies. *Applied Sciences*. 2022; 12(11):5400.
https://doi.org/10.3390/app12115400

**Chicago/Turabian Style**

Martini, Michele, Massimiliano Scaccia, Gabriele Marchello, Haider Abidi, Mariapaola D’Imperio, and Ferdinando Cannella.
2022. "An Outline of Fused Deposition Modeling: System Models and Control Strategies" *Applied Sciences* 12, no. 11: 5400.
https://doi.org/10.3390/app12115400