# Combining Structural Optimization and Process Assurance in Implicit Modelling for Casting Parts

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## Abstract

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## 1. Introduction

#### 1.1. Structural Optimization of Casting Parts

#### 1.2. Process Simulation

#### 1.3. Combining Structural Optimization and Process Assurance

## 2. Materials and Methods

#### 2.1. Topology Optimization Setup

#### 2.2. Process Simulation and Evaluation

#### 2.2.1. High Pressure Die Casting

#### 2.2.2. Low Pressure Die Casting

_{0}of 1.013 bar at t = 0 s and rising to a maximum pressure of 1.060 bar at t = 5 s. The maximum pressure was estimated using the formula for hydrostatic pressure for a fully filled cavity:

#### 2.3. Post-Processing

#### 2.4. Evaluation and Metric of the Results

## 3. Results

#### 3.1. One Step Optimization

#### 3.2. Iterative Optimization

#### 3.3. Comparison of the Approaches

#### 3.3.1. Manufacturability Evaluation

#### 3.3.2. Structural Analysis

## 4. Discussion

## 5. Summary and Outlook

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Proposed workflow of the optimization for the combination of topology optimization and process assurance. Starting from the initial design space, a TO with a volume target volume ${V}_{t}$ and a parallel process simulation. The One-Step Optimization ends after the first iteration. In the iterative optimization, the design space ${V}_{DS}$ is modified for every new iteration with a step-length of $\lambda $ on the basis of previous results.

**Figure 3.**Results of the initial TO with $\lambda $ = 0.2 and ${x}_{lim}$ = 0.6: (

**a**) Implicit geometry of the optimized structure; (

**b**) Cross-section of the implicit geometry of the TO-margin.

**Figure 4.**Simulation setup for HPDC, exemplarily shown for iteration t = 2. The surrounding die is not shown in the figure.

**Figure 5.**Evaluation of the filling simulation of the HPDC process. The simulation results are shown for a cross section for a part (HPDC simulation, iteration t = 2) during the iterative optimization process. A low quotient indicates cells with a good filling capacity. (

**a**) Time of first fluid arrival, tffa; (

**b**) Time for shortest path length, tsp; (

**c**) Quotient of tffa and tsp, $QuotHPDC$; For better clarity, the maximum legend is set to 12, although there are a few cells with a value of $QuotHPDC$ up to 35.

**Figure 6.**Simulation setup for LPDC, exemplarily shown for iteration t = 4. The pressure boundary is defined by a linear pressure increase on the bottom of the riser tube.

**Figure 8.**Exemplary point map for the QuotHPDC in iterative high-pressure die casting simulation, iteration t = 2.

**Figure 9.**Creation of adapted meshes of the TO-margin by example of iterative HPDC optimization, iteration t = 5. In the adapted tetrahedral mesh, the edge lengths are controlled by the corresponding QuotHPDC ramp function.

**Figure 10.**Implicit volume mesh of the TO-margin before smoothing by example of iterative high-pressure casting optimization, iteration t = 5. The strut thickness of the volume lattice is controlled by QuotHPDC.

**Figure 11.**Final result of the postprocessing workflow by example of iterative high-pressure casting optimization, iteration t = 5. The modified TO-margin (red) and the modified TO-part (blue) are merged into one body which represents the new design proposal. For a better understanding of the result, the boundary conditions of TO and filling simulation are in auxiliary shown.

**Figure 12.**Result of the HPDC-OS Optimization, with a volume of 50% compared to the initial design space.

**Figure 13.**Result of the LPDC-OS Optimization, with a volume of 49% compared to the initial design space.

**Figure 14.**Result of each iteration of the Iterative Optimization of HPDC parts for$\lambda $ = 0.2; the volume of the design proposals is given in brackets: (

**a**) HPDC-IT_1 (90%); (

**b**) HPDC-IT_2 (85%); (

**c**) HPDC-IT_3 (76%); (

**d**) HPDC-IT_4 (68%); (

**e**) HPDC-IT_5 (60%); (

**f**) HPDC-IT_6 (50%).

**Figure 15.**Result of each iteration of the Iterative Optimization of LPDC parts for$\lambda $ = 0.2; the volume of the design proposals is given in brackets: (

**a**) LPDC-IT_1 (93%); (

**b**) LPDC-IT_2 (72%); (

**c**) LPDC-IT_3 (60%); (

**d**) LPDC-IT_4 (47%).

**Figure 16.**Comparison of all HPDC and TO design proposals: (

**a**) HPDC-IT_6; (

**b**) HPDC-OS; (

**c**) HPDC-50; (

**d**) HPDC-30; (

**e**) TO-50; (

**f**) TO-30.

**Figure 17.**Evaluation of the median of QuotHPDC for all optimized geometries. The evaluation indicates that the iterative approach gets trapped in a local minimum.

**Figure 18.**Evaluation of the manufacturability of HPDC design proposals; the deviation compared to the Initial DS is given in brackets. The One-Step optimization approach increases the manufacturability of the design proposal by 159%.

**Figure 19.**Comparison of all LPDC and TO design proposals: (

**a**) LPDC-IT_4; (

**b**) LPDC-OS; (

**c**) TO-50; (

**d**) TO-30.

**Figure 20.**Solidification time for a cross section along the mid-plane. In the geometry LPDC-IT_5, a directed solidification was achieved, whereas for TO-30, a hot spot above the void region could not be fed adequately. (

**a**) LPDC-IT_5; (

**b**) TO-30.

**Figure 21.**Evaluation of the median of QuotLPDC for all investigated geometries in the LPDC process. The median hardly changes between the design of the iteration and the One-Step result.

**Figure 22.**Evaluation of the manufacturability of LPDC design proposals; the deviation compared to the Initial DS is given in brackets. The evaluation shows that the TO configurations have a significantly lower number of manufacturable elements for LPDC.

**Figure 23.**Volume-related stiffness for all HPDC configurations; the deviation to the Initial DS is noted in brackets. The One-Step and iterative HPDC configuration show significantly lower stiffness than the TO configurations.

**Figure 24.**Volume-related stiffness for all LPDC configurations; the deviation to the Initial DS is noted in brackets. Both approaches show similar relative-volume-related stiffness to the TO configurations.

${\mathit{x}}_{\mathit{l}\mathit{o}\mathit{w}\mathit{e}\mathit{r}}$ | ${\mathit{x}}_{\mathit{u}\mathit{p}\mathit{p}\mathit{e}\mathit{r}}$ | |
---|---|---|

HPDC | 0.0 | 3.0 |

LPDC | 0.8 | 1.0 |

**Table 2.**Overview of the selected configurations. The optimization approach differs between the workflows for, respectively, One-Step, iterative optimization, TO, and manual part design. The target volume is given as relative volume. For the iterative optimization, the step-length in the TO is additionally given in brackets.

Configuration Name | Optimization Approach | Target Volume (Step-Length) |
---|---|---|

Initial DS | None | 1 |

HPDC-OS | One-Step | 0.5 |

HPDC-IT | Iterative | 0.5 (0.2) |

HPDC-50 | Manual | 0.5 |

HPDC-30 | Manual | 0.3 |

LPDC-OS | One-Step | 0.5 |

LPDC-IT | Iterative | 0.5 (0.2) |

TO-30 | TO | 0.3 |

TO-50 | TO | 0.5 |

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**MDPI and ACS Style**

Rosnitschek, T.; Erber, M.; Hartmann, C.; Volk, W.; Rieg, F.; Tremmel, S.
Combining Structural Optimization and Process Assurance in Implicit Modelling for Casting Parts. *Materials* **2021**, *14*, 3715.
https://doi.org/10.3390/ma14133715

**AMA Style**

Rosnitschek T, Erber M, Hartmann C, Volk W, Rieg F, Tremmel S.
Combining Structural Optimization and Process Assurance in Implicit Modelling for Casting Parts. *Materials*. 2021; 14(13):3715.
https://doi.org/10.3390/ma14133715

**Chicago/Turabian Style**

Rosnitschek, Tobias, Maximilian Erber, Christoph Hartmann, Wolfram Volk, Frank Rieg, and Stephan Tremmel.
2021. "Combining Structural Optimization and Process Assurance in Implicit Modelling for Casting Parts" *Materials* 14, no. 13: 3715.
https://doi.org/10.3390/ma14133715