# A Novel Digital Design Approach for Metal Additive Manufacturing to Address Local Thermal Effects

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Design Approach Overview

#### 2.1. Digital Design Approach for Metal AM That Addresses Thermal Effects

#### 2.2. Design Optimization and Analysis Steps

^{6}Pa and 0.4, respectively. TFor the current study, a 3D density-based topology optimization formulation, native to the TOSCA module, was used. This gradient-based formulation uses analytic sensitivity approaches similar to most TO methods for computing the derivatives of the objective and constraints. A mesh independent filter is used for filtering the output [44]. For the current study, the objective for the topology optimization problem was to minimize the compliance of the domain. A constraint was applied to limit the volume to 50% of the original. The optimized output was then thresholded to retain only those elements that had a volume fraction of 70% or more. This process was included to reduce any partial density elements and increase the overall solidity of the structure. The thresholding process can lead to jagged surfaces which were smoothed out in this investigation by simplifying the optimized domain. To accomplish this goal, the thresholded domain was exported from Tosca in a compatible mesh format and the optimized domain was recreated using splines in a CAD environment.

#### 2.3. Process Simulation Step

#### 2.4. Lattice Introduction Step

#### 2.5. Lattice Optimization Step

## 3. Results

#### 3.1. Topology Optimization

#### 3.2. Process Simulations

#### 3.3. Lattice Introduction

^{3}and the mass being replaced was 0.19 kg which gave an effective density of the lattice region to be around 0.0041 g/mm

^{3}. The angle of the struts is critical for accurate and supportless manufacturing. Lattice-types considered for this purpose are the ‘X’, ‘W’ and ‘star’ (Table 2) as these lattice unit cells within the Netfabb suite can be modified to be manufactured without any supports.

#### 3.4. Lattice Optimization

#### 3.5. Effect of Lattice on Hotspot

## 4. Discussion

#### 4.1. Topology Optimization and CAD Generation

^{5}mm

^{3}according to the given dimensions. The optimization reduces the volume to 49.9% of the original, resulting to a volume of 3.37 × 10

^{5}mm

^{3}. Thresholding of the optimized geometry further reduces the optimum value of the volume. However, this step is required to reduce the size of the domain and to accurately define a CAD model. For this geometry, it was found that the thresholding value of 0.7 allows for a close approximation of the optimized domain. Another approach to simplify the optimized geometry would have been to use a shape optimization procedure, however, the large number of design variables would lead to a very large computational time in the Tosca environment hence a manual simplification was opted for.

#### 4.2. Lattice Optimization

#### 4.3. Process Simulations

#### 4.4. Advantages and Limitations of Proposed Methodology

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Proposed digital design approach for metal additive manufacturing to address thermal effects.

**Figure 3.**The isometric and planar views of the ‘X’ lattice (

**left**), ‘W’ lattice (

**center**) and the ‘Star’ lattice (

**right**). The overhang angles for the members are ensured to be more than 45 degrees from the horizontal to ensure supportless printing.

**Figure 4.**(

**a**) Evolution of the design domain using topology optimization and (

**b**) the history plot of the compliance and volume for the optimization process.

**Figure 5.**(

**a**) Domain simplification methodology by using the output from topology optimization, thresholding the mesh to a user-specified partial density, designing a simplified CAD geometry using splines for introduction of lattices. (

**bottom**) Static analysis plot shown the von Mises stress for (

**b**) the original design domain and (

**c**) the topology optimized output.

**Figure 6.**Hot spot contour plot from a process simulation of the optimized geometry. The inset shows the region with the highest thermal accumulations in terms of the percentage of finite element volume.

**Figure 7.**Identification of region for lattice introduction by using: (

**a**) the isolines of the hotspot volume in printing, (

**b**) the von Mises stress buildup in the part during printing, (

**c**) the von Mises stress experienced by the optimized cantilever part during static loading and (

**d**) the manufacturing constraints of minimum overhang angle and clearance from the base to create (

**e**) the partitioned domain. The dotted arrows indicate the region to be considered for lattice introduction. Continuous black lines are fixed. Dotted black lines can be adjusted to accommodate the changing parameters for a given setup (e.g., varying hotspot buildup (a) for the same part using different process parameters or different allowable overhang angles for different selective laser melting (SLM) machines (d)).

**Figure 8.**Lattice optimization iterations and the evolution of the lattice thickness in iterations 1, 10 and 49 shown in (

**a**), (

**b**) and (

**c**) respectively; (

**d**) the convergence history of the optimization.

**Figure 9.**Comparing the hotspot observed in (

**a**) the optimized domain and (

**b**) the ‘X’ lattice introduced optimized domain. The inset in (a) shows the regions affected by the hotspot and in (b) the effect of lattice introduction

**Figure 10.**Comparing the hotspot observed in the optimized domain and the lattice introduced optimized domains using the ‘X’, ‘W’ and ‘Star’ lattices. The insets in

**(X)**,

**(W)**and

**(Star)**shows the effect of the different lattices on the hotspots.

Parameters | Value |
---|---|

SLM Printer model | EOS M 290 |

Laser Power (Watts) | 250 |

Heat source absorption efficiency (%) | 40 |

Laser beam diameter (mm) | 0.15 |

Travel speed (mm/s) | 1000 |

Layer thickness (mm) | 0.04 |

Hatch spacing (mm) | 0.15 |

Interlayer rotation angle | 67° |

Lattice Parameters | Value |
---|---|

Unit cell | X/W/Star |

Unit cell dimension (mm) | 15 × 10 × 10 |

Min. beam radius (mm) | 1 |

Max. beam radius (mm) | 4 |

Parameters | Topology Optimized Beam | TO Beam with X Lattice | TO Beam with W Lattice | TO Beam with Star Lattice |
---|---|---|---|---|

Part Volume (cm^{3}) | 307.75 | 267.73 | 272.21 | 269.85 |

Support Volume (cm^{3}) | 8.16 | 8.95 | 8.94 | 8.96 |

Build time (hhh:mm:ss) | 84:21:59 | 76:30:55 | 77:24:51 | 77:47:56 |

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**MDPI and ACS Style**

I. Perumal, V.; R. Najafi, A.; Kontsos, A.
A Novel Digital Design Approach for Metal Additive Manufacturing to Address Local Thermal Effects. *Designs* **2020**, *4*, 41.
https://doi.org/10.3390/designs4040041

**AMA Style**

I. Perumal V, R. Najafi A, Kontsos A.
A Novel Digital Design Approach for Metal Additive Manufacturing to Address Local Thermal Effects. *Designs*. 2020; 4(4):41.
https://doi.org/10.3390/designs4040041

**Chicago/Turabian Style**

I. Perumal, Vignesh, Ahmad R. Najafi, and Antonios Kontsos.
2020. "A Novel Digital Design Approach for Metal Additive Manufacturing to Address Local Thermal Effects" *Designs* 4, no. 4: 41.
https://doi.org/10.3390/designs4040041