# A Set of Novel Procedures for Carbon Fiber Reinforcement on Complex Curved Surfaces Using Multi Axis Additive Manufacturing

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Prior Work

#### 1.2. Our Method

- The proposed procedure starts by analyzing the part to be manufactured in an external finite element method (FEM) software to extract the major principle stress vectors. An exemplary result can be found in Figure 1a.
- The resulting information enables the partitioning of the surface to be reinforced into subsurfaces with the goal of achieving a high compliance of local fiber direction and directions of major principle stress. Figure 1b illustrates such a partitioning. This is similar to the zoning approach, used in the layup process.
- The subsurfaces are triangulated with high precision to ensure minimal computation error.
- For every subsurface a suitable algorithm is chosen. This is performed with the intent of maximizing the measured values of the evaluation criteria and relies on knowledge of the procedures.
- The chosen algorithm is executed for every surface resulting in paths that include possible travel motions, an example of which can be seen in Figure 1c.
- Post-processing of the paths yields a Gcode to be executed on the multi-axis printer.

## 2. Methods and Evaluation Criteria

#### 2.1. Evaluation Criteria

#### 2.1.1. Continuity

#### 2.1.2. Curvature

#### 2.1.3. Fiber Area Fraction

#### 2.1.4. Load Adequacy

## 3. Algorithms

- Direction parallel:
- Fixed intrinsic angle (FInA);
- Fixed extrinsic angle (FExA);
- Seeded ortho-isogeodesics (Ortheo).

- Contour parallel:
- Geodesic first in spiral out (Geo-FISO);
- Geodesic contour parallel spirals (Geo-Contour);
- Geodesic spiral around seed-point (Geo-Spiral).

#### 3.1. Direction Parallel Algorithms

#### 3.1.1. Fixed Intrinsic Angle (FInA)

#### 3.1.2. Fixed Extrinsic Angle (FExA)

#### 3.1.3. Seeded Ortho-Isogeodesics (Ortheo)

#### 3.2. Contour Parallel Algorithms

#### 3.2.1. Geodesic First in Spiral Out (Geo-FISO)

#### 3.2.2. Geodesic Contour Parallel Spirals (Geo-Contour)

#### 3.2.3. Geodesic Spiral around Seed-Point (Geo-Spiral)

## 4. Evaluation

#### 4.1. Evaluation Criteria

#### 4.1.1. Continuity

#### 4.1.2. Curvature

#### 4.1.3. Fiber Area Fraction

#### 4.1.4. Load Adequacy

#### 4.2. Results

#### 4.2.1. Direction Parallel Algorithms

#### 4.2.2. Contour Parallel Algorithms

## 5. Conclusions

## Author Contributions

## Funding

^{3}program (Interdisciplinary, Innovative, Engineering (German: Ingenieurwissenschaften)) of the Hamburg University of Technology.

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AM | Additive manufacturing |

CFRP | Carbon fiber reinforced polymers |

FDM | Fused deposition modeling |

Prepreg | Pre-impregnated |

FEM | Finite element methods |

FEA | Finite element analysis |

FInA | Fixed intrinsic angle |

FExA | Fixed extrinsic angle |

Ortheo | Seeded ortho-isogeodesics |

Geo-FISO | Geodesic first in spiral out |

Geo-Contour | Geodesic contour parallel spirals |

Geo-Spiral | Geodesic spiral around seed-point |

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**Figure 1.**(

**a**) Maximum principle stress vectors resulting from finite element analysis (FEA). (

**b**) Decomposition of part into subsurfaces. (

**c**) Exemplary planned paths for all subsurfaces with $d=1$ mm. Filament thickness displayed does not correspond to thickness when printed.

**Figure 2.**Direction parallel algorithms and resulting paths. Travel motions are not displayed. With $d=1$ mm (

**a**) FInA, (

**b**) FExA, (

**c**) Ortheo. Filament thickness displayed does not correspond to thickness when printed.

**Figure 3.**A grid-like structure in the spirit of draped carbon fiber fabric resulting from layering paths generated by the Ortheo and FInA algorithms. This result is unachievable with classical methods such as tape-laying or hand layup. Filament thickness displayed does not correspond to thickness when printed.

**Figure 4.**Contour parallel algorithms and resulting paths on the Stanford bunny. Travel motions not displayed. With $d=3.5$ mm (

**a**) Geo-FISO, (

**b**) Geo-Contour, (

**c**) Geo-Spiral. Filament thickness displayed does not correspond to thickness when printed.

**Figure 6.**FEA with the load cases and the maximum principle directions. (

**a**) Load case Y. (

**b**) Load case X.

**Figure 7.**(

**a**) FExA on surface A (

**b**) Geo-FISO on surface B (

**c**) Ortheo on surface C with surface D as source with ${d}_{iso}=1$ mm (

**d**) FInA on surface D (

**e**) FInA twice with orthogonal planes on surface E. For all paths $d=2$ mm for illustration purposes, planes chosen to align with the vector field. Filament thickness displayed does not correspond to thickness when printed.

Parameters | Results | |||||
---|---|---|---|---|---|---|

Surface ($\mathcal{T}$) | Algorithm | Load Case | Mean Curv. (1%) | Fiber Area Fraction | Load Adequacy | Discontinuities |

A | Geo-Contour | X + Y | 26.35° | 0.87 | 0.78 | 0 |

A | FExA | X + Y | 29.7° | 0.9 | 0.82 | 0 |

B | Geo-FISO | X + Y | 28.2° | 0.85 | 0.66 | 0 |

B | FExA | X + Y | 39.25° | 0.92 | 0.93 | 6 |

C | Ortheo ${\mathcal{T}}_{\mathit{s}}$ = D | Y | 4.2° | 0.84 | 0.98 | 39 |

C | FInA | Y | 61.55° | 0.93 | 0.85 | 0 |

D | Geo-Spiral | Y | 43.02° | 0.33 | 0.43 | 0 |

D | FInA | Y | 50° | 0.91 | 0.72 | 4 |

E | FInA + FInA | X | 58.5° | 0.92 | 0.84 | 1 |

E | Geo-Contour | X | 51.6° | 0.9 | 0.83 | 0 |

^{1}Fixed parameters: d = 1 mm, d

_{iso}= 1 mm, planes chosen to align with vector field.

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**MDPI and ACS Style**

Kipping, J.; Kállai, Z.; Schüppstuhl, T. A Set of Novel Procedures for Carbon Fiber Reinforcement on Complex Curved Surfaces Using Multi Axis Additive Manufacturing. *Appl. Sci.* **2022**, *12*, 5819.
https://doi.org/10.3390/app12125819

**AMA Style**

Kipping J, Kállai Z, Schüppstuhl T. A Set of Novel Procedures for Carbon Fiber Reinforcement on Complex Curved Surfaces Using Multi Axis Additive Manufacturing. *Applied Sciences*. 2022; 12(12):5819.
https://doi.org/10.3390/app12125819

**Chicago/Turabian Style**

Kipping, Johann, Zsolt Kállai, and Thorsten Schüppstuhl. 2022. "A Set of Novel Procedures for Carbon Fiber Reinforcement on Complex Curved Surfaces Using Multi Axis Additive Manufacturing" *Applied Sciences* 12, no. 12: 5819.
https://doi.org/10.3390/app12125819