# Metamodels Resulting from Two Different Geometry Morphing Approaches Are Suitable to Direct the Modification of Structure-Born Noise Transfer in the Digital Design Phase

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## Abstract

**:**

## 1. Introduction

## 2. Fundamentals and State of the Art

#### 2.1. NVH Optimization in the Digital Design Phase

#### 2.2. Morphing

#### Application of Morphing

#### 2.3. Morphing Alternatives

## 3. Method

#### 3.1. Direct Morphing Approach

#### 3.2. Box Morphing Approach

#### 3.3. Metamodeling

## 4. Application

#### 4.1. Scenario

#### 4.2. Method Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CAD | Computer Aided Design |

CAE | Computer Aided Engineering |

EFFD | Extended-Free-Form-Deformation |

FE | Finite Element |

FEM | Finite Element Method |

FFD | Free-Form-Deformation |

FRF | Frequency Response Function |

NVH | Noise, Vibration and Harshness |

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**Figure 3.**Detailed Direct Morphing process from Figure 2.

**Figure 4.**Detailed Box Morphing process from Figure 2.

**Figure 5.**Visualization of smoothing operation after performing the displacement of one kinematic hard point through Box Morphing. The hard point under investigation is located in the center of the bushing, identified by yellow circles highlighting its nodes. The black outline represents the undeformed geometry in (

**a**). (

**a**) Undeformed. (

**b**) Morphed. (

**c**) 1st smoothing. (

**d**) 2nd smoothing.

**Figure 6.**Showcase of morphing structure necessary for displacement and smoothing operations. (

**a**) Control points for general displacement. (

**b**) Control points for 1st smoothing. (

**c**) Control points for 2nd smoothing.

**Figure 7.**Illustration of the used knuckle. The kinematic hard point P for the connection to the track rod is located in the center of the gray area on the left side. The large gray area on the right represents the connection to the wheel hub.

**Figure 8.**FRF between hard point track rod in ${x}_{2}$-direction and wheel hub in ${x}_{3}$-direction. 777 $\mathrm{Hz}$ in blue.

**Figure 9.**FRF between hard point track rod in ${x}_{2}$-direction and wheel hub in ${x}_{3}$-direction and Skyline of 100 designs. (

**a**) Results using Direct Morphing. (

**b**) Results using Box Morphing.

**Figure 10.**Metamodels for the influence of the ${x}_{1}$-, ${x}_{2}$- and ${x}_{3}$-coordinates derived from 100 design variants by using Direct and Box Morphing. Original design at ${\left(0\text{}\mathrm{m}\mathrm{m},0\text{}\mathrm{m}\mathrm{m},0\text{}\mathrm{m}\mathrm{m}\right)}^{T}$ and an amplitude of $6.68$ $\mathrm{N}$ ${\mathrm{N}}^{-1}$, highlighted by a black dot. Manually optimized design at ${\left(-5.77\text{}\mathrm{m}\mathrm{m},5.77\text{}\mathrm{m}\mathrm{m},5.77\text{}\mathrm{m}\mathrm{m}\right)}^{T}$, highlighted by a black triangle. (

**a**) Direct Morphing, metamodel for ${x}_{1}$- and ${x}_{2}$-coordinates with ${R}^{2}=0.94$, manually chosen optimum at $5.8$ $\mathrm{N}$ ${\mathrm{N}}^{-1}$. (

**b**) Direct Morphing, metamodel for ${x}_{1}$- and ${x}_{3}$-coordinates with ${R}^{2}=0.90$, manually chosen optimum at $4.7$ $\mathrm{N}$ ${\mathrm{N}}^{-1}$. (

**c**) Box Morphing, metamodel for ${x}_{1}$- and ${x}_{2}$-coordinates with ${R}^{2}=0.95$, manually chosen optimum at $5.8$ $\mathrm{N}$ ${\mathrm{N}}^{-1}$. (

**d**) Box Morphing, metamodel for ${x}_{1}$- and ${x}_{3}$-coordinates with ${R}^{2}=0.94$, manually chosen optimum at $4.3$ $\mathrm{N}$ ${\mathrm{N}}^{-1}$.

**Figure 11.**Three different optimization methods and simulation results obtained by different morphing approaches. (

**a**) Manual Optimization via separate metamodels in Figure 10. (

**b**) Optimization via Optislang metamodel resulting from Direct Morphing data. (

**c**) Optimization via Optislang metamodel resulting from Box Morphing data.

Method | ${\mathit{x}}_{1}$ | ${\mathit{x}}_{2}$ | ${\mathit{x}}_{3}$ | Predicted Amplitude |
---|---|---|---|---|

Manually | $-5.77\text{}\mathrm{mm}$ | $5.77\text{}\mathrm{mm}$ | $5.77\text{}\mathrm{mm}$ | $5.15$$\mathrm{N}$${\mathrm{N}}^{-1}$ |

Optimization Direct | $-4.42\text{}\mathrm{mm}$ | $3.36\text{}\mathrm{mm}$ | $8.32\text{}\mathrm{mm}$ | $4.04$$\mathrm{N}$${\mathrm{N}}^{-1}$ |

Optimization Box | $-0.30\text{}\mathrm{mm}$ | $4.83\text{}\mathrm{mm}$ | $8.75\text{}\mathrm{mm}$ | $3.31$$\mathrm{N}$${\mathrm{N}}^{-1}$ |

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**MDPI and ACS Style**

von Wysocki, T.; Leupolz, M.; Gauterin, F. Metamodels Resulting from Two Different Geometry Morphing Approaches Are Suitable to Direct the Modification of Structure-Born Noise Transfer in the Digital Design Phase. *Appl. Syst. Innov.* **2020**, *3*, 47.
https://doi.org/10.3390/asi3040047

**AMA Style**

von Wysocki T, Leupolz M, Gauterin F. Metamodels Resulting from Two Different Geometry Morphing Approaches Are Suitable to Direct the Modification of Structure-Born Noise Transfer in the Digital Design Phase. *Applied System Innovation*. 2020; 3(4):47.
https://doi.org/10.3390/asi3040047

**Chicago/Turabian Style**

von Wysocki, Timo, Michael Leupolz, and Frank Gauterin. 2020. "Metamodels Resulting from Two Different Geometry Morphing Approaches Are Suitable to Direct the Modification of Structure-Born Noise Transfer in the Digital Design Phase" *Applied System Innovation* 3, no. 4: 47.
https://doi.org/10.3390/asi3040047