# An Automated Open-Source Approach for Debinding Simulation in Metal Extrusion Additive Manufacturing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Design for Debinding and Sintering

#### 2.2. Setup of the Finite Element Model

**C**describes the material matrix (consisting of the Young’s Modulus and the Poisson’s ratio of the material) and the displacement-strain-transformation matrix

**B**. Assembling the individual stiffness matrices leads to the following overall linear equation system:

#### 2.3. Automated Simulation Framework

## 3. Results

^{®}(Chair of Engineering Design and CAD, Bayreuth, Germany) [23], using the hybrid optimization algorithm TOSS (Topology Optimization for Stiffness and Strength) [32] with a target volume of 75%. The chassis diverter was manually redesigned in Creo parametric based on the Topology optimization result. All presented example parts are meshed using quadratic tetrahedral elements and an edge length of 2 mm.

#### 3.1. Staircase

#### 3.2. Sprocket

#### 3.3. Topology Optimized Chassis Diverter

## 4. Discussion

#### 4.1. Evaluation of Application Examples

#### 4.2. Impact for Design for Additive Manufacturing

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Sinter shrinkage behavior of metal EAM parts. The printing plane (x and y) shrinkage shows identical values, while the shrinkage in stacking direction (z) is significantly larger. The dashed lines represent the green-part and the solid lines the sintered metal-part.

**Figure 5.**Example parts selected for testing the automated simulation framework before scaling. (

**a**) staircase; (

**b**) sprocket; (

**c**) topology optimized chassis diverter.

**Figure 6.**Failure-plot of the debinding simulation of the staircase. (

**1**)–(

**6**) denote the number of the orientation, white dots represent the bottom plane, red areas indicate failure due to tension, and blue areas indicate failure due to compression.

**Figure 7.**Failure-plot of the debinding simulation of the sprocket. (

**1**)–(

**6**) denote the number of the orientation, white dots represent the bottom plane, red areas indicate failure due to tension, and blue areas indicate failure due to compression.

**Figure 8.**Failure-plot of the debinding simulation of the chassis diverter. (

**1**)–(

**6**) denote the number of the orientation, white dots represent the bottom plane, red areas indicate failure due to tension, and blue areas indicate failure due to compression.

**Figure 11.**Comparison of STEP (

**left**) and STL (

**right**) structure types, exemplary shown for the quadratic meshed staircase.

**Table 1.**Material data of [20] chosen as the default for the simulation framework.

Parameter | Value |
---|---|

Young’s modulus | 210,000 MPa |

Poisson ratio | 0.4 |

Density | 4.7 × 10^{−9} t/mm^{3} |

**Table 2.**Maximum stress limits for debinding simulation according to [20]. The tensile stress limit is abbreviated with ${\sigma}_{t,li{m}_{i}}$ and the compression stress limit with ${\sigma}_{c,li{m}_{i}}$.

Direction | Component | Limit |
---|---|---|

Printing plane (x and y) | ${\sigma}_{t,li{m}_{x,y}}$ | 6.0 kPa |

${\sigma}_{c,li{m}_{x,y}}$ | −7.0 kPa | |

Stacking direction (z) | ${\sigma}_{t,li{m}_{z}}$ | 0.5 kPa |

${\sigma}_{c,li{m}_{z}}$ | −7.0 kPa |

**Table 3.**Maximum tensile and compression stresses ${\sigma}_{t,cma{x}_{i}}$ for each orientation $j$ of the staircase. The safety factor $S$ is written in brackets.

(1) | (2) | (3) | (4) | (5) | (6) | |
---|---|---|---|---|---|---|

${\sigma}_{tma{x}_{x}}$ | 0.361 kPa (16.62) | 85.33 kPa (0.07) | 0.356 kPa (16.85) | 85.50 kPa (0.07) | 1.615 kPa (3.72) | 41.08 kPa (0.15) |

${\sigma}_{cma{x}_{x}}$ | −1.475 kPa (4.75) | −94.05 kPa (0.07) | −0.151 kPa (46.33) | −85.45 kPa (0.08) | −6.331 kPa (1.11) | −82.41 kPa (0.08) |

${\sigma}_{tma{x}_{y}}$ | 0.338 kPa (17.75) | 45.67 kPa (0.13) | 0.392 kPa (15.32) | 36.71 kPa (0.16) | 1.707 kPa (3.51) | 42.81 kPa (0.14) |

${\sigma}_{cma{x}_{y}}$ | −1.483 kPa (4.72) | −62.65 kPa (0.11) | −1.477 kPa (4.74) | −36.60 kPa (0.19) | −6.192 kPa (1.13) | −142.4 kPa (0.05) |

${\sigma}_{tma{x}_{z}}$ | 0.022 kPa (22.73) | 66.18 kPa (0.01) | 0.027 kPa (18.52) | 21.53 kPa (0.02) | 0.641 kPa (0.78) | 75.52 kPa (0.01) |

${\sigma}_{cma{x}_{z}}$ | −2.514 kPa (2.78) | −113.3 kPa (0.06) | −2.518 kPa (2.78) | −55.63 kPa (0.13) | −10.75 kPa (0.65) | −167.4 kPa (0.04) |

**Table 4.**Maximum tensile and compression stresses ${\sigma}_{t,cma{x}_{i}}$ for each orientation $j$ of the gear. The safety factor $\mathrm{S}$ is written in brackets.

(1) | (2) | (3) | (4) | (5) | (6) | |
---|---|---|---|---|---|---|

${\sigma}_{tma{x}_{x}}$ | 5158 kPa (0.00) | 2498 kPa (0.00) | 2511 kPa (0.00) | 2495 kPa (0.00) | 0.524 kPa (11.45) | 26.52 kPa (0.23) |

${\sigma}_{cma{x}_{x}}$ | −3462 kPa (0.00) | −3511 kPa (0.00) | −3573 kPa (0.00) | −3904 kPa (0.00) | −1.974 kPa (3.55) | −48.24 kPa (0.15) |

${\sigma}_{tma{x}_{y}}$ | 5191 kPa (0.00) | 2338 (0.00) | 2436 kPa (0.00) | 2324 kPa (0.00) | 0.438 kPa (13.70) | 30.34 kPa (0.20) |

${\sigma}_{cma{x}_{y}}$ | −3556 kPa (0.00) | −3219 (0.00) | −3042 kPa (0.00) | −3684 kPa (0.00) | −1.933 kPa (3.62) | −43.90 kPa (0.16) |

${\sigma}_{tma{x}_{z}}$ | 8068 kPa (0.00) | 5155 (0.00) | 5427 kPa (0.00) | 5073 kPa (0.00) | 0.350 kPa (1.43) | 11.09 kPa (0.05) |

${\sigma}_{cma{x}_{z}}$ | −8094 kPa (0.00) | −7476 (0.00) | −6472 kPa (0.00) | −7928 kPa (0.00) | −3.287 kPa (2.13) | −43.77 kPa (0.16) |

**Table 5.**Maximum tensile and compression stresses ${\sigma}_{t,cma{x}_{i}}$ for each orientation $j$ of the staircase. The safety factor $S$ is written in brackets.

(1) | (2) | (3) | (4) | (5) | (6) | |
---|---|---|---|---|---|---|

${\sigma}_{tma{x}_{x}}$ | 7.419 kPa (0.81) | 5170 kPa (0.00) | 5.036 kPa (1.19) | 4305 kPa (0.00) | 1240 kPa (0.00) | 12.12 kPa (0.50) |

${\sigma}_{cma{x}_{x}}$ | −5.542 kPa (1.26) | −3859 kPa (0.00) | −8.222 kPa (0.85) | −7013 kPa (0.00) | −1393 kPa (0.01) | −20.19 kPa (0.35) |

${\sigma}_{tma{x}_{y}}$ | 7.726 kPa (0.78) | 5144 kPa (0.00) | 7.61 kPa (0.79) | 4742 kPa (0.00) | 1114 kPa (0.01) | 7.076 kPa (0.85) |

${\sigma}_{cma{x}_{y}}$ | −7.488 kPa (0.93) | −3650 kPa (0.00) | −7.978 kPa (0.88) | −6463 kPa (0.00) | −1736 kPa (0.00) | −27.69 kPa (0.25) |

${\sigma}_{tma{x}_{z}}$ | 6.859 kPa (0.07) | 7921 kPa (0.00) | 4.607 kPa (0.11) | 8662 kPa (0.00) | 2319 kPa (0.00) | 14.75 kPa (0.03) |

${\sigma}_{cma{x}_{z}}$ | −6.616 (1.06) | −6220 kPa (0.00) | −6.352 kPa (1.10) | −9114 kPa (0.00) | −2638 kPa (0.00) | −32.65 kPa (0.21) |

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**MDPI and ACS Style**

Rosnitschek, T.; Glamsch, J.; Lange, C.; Alber-Laukant, B.; Rieg, F.
An Automated Open-Source Approach for Debinding Simulation in Metal Extrusion Additive Manufacturing. *Designs* **2021**, *5*, 2.
https://doi.org/10.3390/designs5010002

**AMA Style**

Rosnitschek T, Glamsch J, Lange C, Alber-Laukant B, Rieg F.
An Automated Open-Source Approach for Debinding Simulation in Metal Extrusion Additive Manufacturing. *Designs*. 2021; 5(1):2.
https://doi.org/10.3390/designs5010002

**Chicago/Turabian Style**

Rosnitschek, Tobias, Johannes Glamsch, Christopher Lange, Bettina Alber-Laukant, and Frank Rieg.
2021. "An Automated Open-Source Approach for Debinding Simulation in Metal Extrusion Additive Manufacturing" *Designs* 5, no. 1: 2.
https://doi.org/10.3390/designs5010002