# Compensation for Geometrical Deviations in Additive Manufacturing

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## Abstract

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## 1. Introduction

## 2. State of the Art

#### 2.1. Causes for Geometrical Deviations in Additive Manufacturing

- Deviations in data preprocessing;
- Errors during material processing;
- Machine errors;
- Stochastic errors.

#### 2.2. Classical Methods to Compensate for Deviations in Additive Manufacturing

#### 2.3. Geometrical Deviation Compensation in Additive Manufacturing

## 3. Hypothesis

## 4. Materials and Methods

#### 4.1. Specimen and Manufacturing

#### 4.2. Compensation Algorithm

- Identification of the stochastic portion of the deviations;
- Automated and structured modification of manufacturing geometries.

## 5. Results and Discussion

#### 5.1. Geometrical Deviation in the Calibration and Compensation Cycles

#### 5.2. Evolution of the Part Deviations

#### 5.3. Stochastic Deviations

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

2D | two dimensional |

3D | three dimensional |

AM | additive manufacturing |

CAD | computer aided design |

MAE | mean absolute error |

SLS | selective laser sintering |

STD | standard deviation |

STL | stereolithography, standard tessellation language |

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**Figure 1.**Stacking of the components in the build chamber. Blue components were measured and compensated; cyan components were measured for reference and not compensated.

**Figure 2.**Flow chart of the compensation process for determining a suitable manufacturing geometry for AM in comparison to the forming tool compensation approach.

**Figure 3.**Compensated components for the calibration cycle (0) and two compensation cycles (1 and 2). The positions on the building platform of the parts a-e are detailed in Figure 1.

**Figure 4.**Reference components without compensation for the calibration cycle (0) and two compensation cycles (1 and 2). The positions on the building platform of the parts ${b}^{ref}$-${d}^{ref}$ are detailed in Figure 1.

**Table 1.**Separated stochastic errors of the compensation procedure conducted for the three reference parts. (mae: mean absolute error; std: standard deviation).

Part | Iteration 1 | Iteration 2 | Iteration 3 | Average | ||||
---|---|---|---|---|---|---|---|---|

Mae | Std | Mae | Std | Mae | Std | Mae | Std | |

${b}_{i}^{ref}$ | 0.113 | 0.150 | 0.111 | 0.141 | 0.108 | 0.135 | 0.111 | 0.142 |

${c}_{i}^{ref}$ | 0.115 | 0.145 | 0.100 | 0.132 | 0.115 | 0.144 | 0.110 | 0.140 |

${d}_{i}^{ref}$ | 0.090 | 0.123 | 0.085 | 0.116 | 0.097 | 0.125 | 0.091 | 0.121 |

average | 0.106 | 0.139 | 0.099 | 0.130 | 0.107 | 0.135 | 0.104 | 0.134 |

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**MDPI and ACS Style**

Hartmann, C.; Lechner, P.; Himmel, B.; Krieger, Y.; Lueth, T.C.; Volk, W.
Compensation for Geometrical Deviations in Additive Manufacturing. *Technologies* **2019**, *7*, 83.
https://doi.org/10.3390/technologies7040083

**AMA Style**

Hartmann C, Lechner P, Himmel B, Krieger Y, Lueth TC, Volk W.
Compensation for Geometrical Deviations in Additive Manufacturing. *Technologies*. 2019; 7(4):83.
https://doi.org/10.3390/technologies7040083

**Chicago/Turabian Style**

Hartmann, Christoph, Philipp Lechner, Benjamin Himmel, Yannick Krieger, Tim C. Lueth, and Wolfram Volk.
2019. "Compensation for Geometrical Deviations in Additive Manufacturing" *Technologies* 7, no. 4: 83.
https://doi.org/10.3390/technologies7040083