# Reducing the Structural Mass of Large Direct Drive Wind Turbine Generators through Triply Periodic Minimal Surfaces Enabled by Hybrid Additive Manufacturing

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Implicit Modeling

#### 2.2. Rotor Loading Criteria

^{2}. The 5 MW deflection criteria were determined such that the radial deflection was less than 10% of the air gap diameter (to avoid closing the airgap), the torsional deflection less than 0.05${}^{\xb0}$ angle of twist (to prevent shear failure), and the axial deflection less than 2% the axial length (to prevent transportation damage). For our 5 MW machine this results in a maximum radial, torsional, and axial deformations of 0.65, 2.84, and 32.17 mm, respectively. For FEA analysis, the rotor was assumed to be homogeneous and isotropic and made out of structural steel with an elastic modulus of 200 GPa, Poisson ratio of 0.28, and density of 7850 kg m

^{−3}. The rotor was assumed to be well cooled and thermal effects assumed to be mitigated.

#### 2.3. Lattice Optimization and Simulation

#### 2.4. Hybrid Additive Manufacturing

#### 2.5. Experimental Validation

## 3. Results and Discussion

#### 3.1. Simulation

#### 3.1.1. GA Optimized Minimal Surfaces

#### 3.1.2. Functionally Graded Lattice Optimization

#### 3.2. Manufacturing

#### 3.3. Experimental Validation

## 4. Conclusions

- A 34% max mass reduction with a Schwartz Primitive TPMS design in a 5 MW PMDD generator rotor structural mass coupling implicit modeling, functionally graded lattice optimization, and FEA through a genetic algorithm
- Implementation of functionally graded lattice optimization for further parameter optimization allows customization of the lattice thickness towards the deflection field. This enabled a design catered towards the weakness of each lattice and further improved mass savings while maintaining deflection criteria.
- Successful manufacturing with hybrid additive manufacturing on a scaled rotor TPMS structure suggesting feasibility of scaling to full size using this technique.
- The Schwartz Primitive design depicted increased strength in the torsional deflection than Gyroid or Diamond designs
- Experimental validation of the TPMS structure FEA model through DIC of a 3D printed Schwartz Primitive rotor model in PLA.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

TPMS | Triply Periodic Minimal Surface |

FEA | Finite Element Analysis |

PMDD | Permanent Magnet Direct Drive |

AM | Additive Manufacturing |

FDM | Fused Deposition Modeling |

DMLS | Direct Metal Laser Sintering |

GA | Genetic Algorithm |

DIC | Digital Image Correlation |

PLA | Polylactic Acid |

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**Figure 1.**(

**a**) B-rep representation of a torus (

**b**) Implicit modeling of a torus as a signed distance field where F < 0 indicates part, F = 0 indicates boundary, F > 0 indicates void.

**Figure 4.**(

**a**) Optimization scheme combining FEA and lattice generation with genetic algorithm (

**b**) Visualization of three lattice types used in implicit optimization.

**Figure 5.**(

**a**) Lattice parameters used in minimal surface optimization (

**b**) Parameters used in functionally graded lattice optimization.

**Figure 6.**Results of TPMS parameter optimization (

**a**) Top view of Diamond rotor (

**b**) Side view of Diamond rotor (

**c**) Top view of Schwartz Primitive rotor (

**d**) Side view of Schwartz Primitive rotor (

**e**) Top view of Gyroid rotor (

**f**) Side view of Gyroid rotor (

**g**) Tabulated Results of TPMS parameter optimization.

**Figure 7.**Results of TPMS functionally graded lattice optimization with color map depicting gradient lattice thickness (

**a**) Diamond rotor TPMS design with strain field thickness (

**b**) Schwartz Primitive rotor TPMS design with strain field thickness (

**c**) Gyroid rotor TPMS design with strain field thickness (

**d**) Tabulated results from functionally graded lattice rotor optimization.

**Figure 8.**Functionally graded lattice optimization results with dotted line at critical values (

**a**) Inactive Mass of all designs (

**b**) Radial deformation of all designs (

**c**) Torsional deformation of all designs.

**Figure 9.**(

**a**) Polycast FDM printed Schwartz Primitive rotor (

**b**) Bronze cast Schwartz Primitive rotor.

**Figure 10.**(

**a**) Abaqus simulated DIC loading conditions deflection magnitude (

**b**) DIC deflection magnitude with weighted torque arm.

**Table 1.**Large scale AM techniques and associated printing time and mass for scaled Schwartz Primitive rotors.

AM Method | Possible Part Dimensions (m) | Cost ($) | Part Resolution (m) | Estimated Print Time (hrs) | Schwartz P Scaled Rotor Weight (mT) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

0.03 MW | 1 MW | 3 MW | 5 MW | 0.03 MW | 1 MW | 3 MW | 5 MW | ||||

DMLS [39] | 0–0.5 | $$$ | 100 | 16 | — | — | — | 0.01 | 2.48 | 12.93 | 27.72 |

Investment Casting Wax Printed Part [41] | 0–3 | $$ | 500 | 6 weeks | 6 weeks | — | — | ||||

Powder Binder Jetting Sand Casting [44] | 3–10 | $ | 1000 | — | — | 80.9 | 105 |

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**MDPI and ACS Style**

Hayes, A.C.; Whiting, G.L.
Reducing the Structural Mass of Large Direct Drive Wind Turbine Generators through Triply Periodic Minimal Surfaces Enabled by Hybrid Additive Manufacturing. *Clean Technol.* **2021**, *3*, 227-242.
https://doi.org/10.3390/cleantechnol3010013

**AMA Style**

Hayes AC, Whiting GL.
Reducing the Structural Mass of Large Direct Drive Wind Turbine Generators through Triply Periodic Minimal Surfaces Enabled by Hybrid Additive Manufacturing. *Clean Technologies*. 2021; 3(1):227-242.
https://doi.org/10.3390/cleantechnol3010013

**Chicago/Turabian Style**

Hayes, Austin C., and Gregory L. Whiting.
2021. "Reducing the Structural Mass of Large Direct Drive Wind Turbine Generators through Triply Periodic Minimal Surfaces Enabled by Hybrid Additive Manufacturing" *Clean Technologies* 3, no. 1: 227-242.
https://doi.org/10.3390/cleantechnol3010013