# Z-Damper: A New Paradigm for Attenuation of Vibrations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Vibrations: Mechanical Impedance

#### 1.2. Magnetic Harmonic Gear for Matching of Mechanical Impedances and Magnetic Dampers

#### 1.3. Magnetic Dampers

^{3}, even at low frequencies. In addition, these systems can operate up to a maximum temperature of about 310 °C for SmCo magnets, with improved performance at low temperatures, and they are fully passive and do not have contact between the moving parts, minimizing wear and fatigue in the mechanical elements, and have a null time of response.

^{2}times. In addition, non-linear effects are usually present in the system [15].

#### 1.4. Thermal Constrictions

## 2. Design and Method

- Slow stage or input stage: connected directly to the source of the vibration.
- Fast stage: magnetically coupled with the other stages and able to generate dissipative eddy currents.
- Spline: fixed layer provided with a set of permanent magnets.
- A 2-mm-thick copper dissipater fixed to the stator part of the device where the eddy currents are dissipated mainly due to the amplified motion of the fast stage.

- m is the mass of the fast moving stage,
- X
_{fast}is the position of the fast stage, - t is time,
- and ${F}_{mag\to fast}$ is the contribution of all the magnetic forces on the fast stage.

- M is the mass of the input moving stage,
- X
_{input}is the input position, - and ${F}_{mag\to input}$ is the contribution of all the magnetic forces acting on the input stage.

## 3. Results

#### 3.1. Z-Damper: Magnetostatic FEM Simulations

#### 3.2. Z-Damper: Dynamics

^{−8}Ω/m at 250 °C, the frequency is 100 Hz, and μ is the magnetic permeability of the material and equal to 4π·10

^{−7}A/m, and f is the magnetic field variation frequency, in this case coincident with the input motion frequency.

#### 3.3. Z-Damper: Damping and Dissipated Power

_{i}𝑑X

- X is the displacement on the Z-Damper input stage,
- and F
_{i}is the input force.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 8.**Equivalent viscous damping coefficient vs. input oscillation frequency for a 3 mm displacement input amplitude.

Constructive Material | Curie Temperature [°C] | Max. Continuous Service Temperature [°C] |
---|---|---|

NdFeB | 310 | 150 |

Sm2Co17(Tm) | 825 | 350–550 |

FeCrCo 250 | 640 | 500 |

AlNiCo 8–9 | 860 | 550 |

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

Spline permanent magnets | SmCo YXG32 | Br = 1.1 T |

Hcb = 800 kA/m | ||

Fast stage magnets | SmCo YXG32 | Br = 1.1 T |

Hcb = 800 kA/m | ||

Soft magnetic material input stage | FeCo Alloy | Bs = 2.28 T |

μ_{max} = 4500 | ||

Hc = 40 A/m | ||

Copper dissipator | Cu | 99% purity |

Structural material | Ti6Al4V |

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

Input Stroke | ±5 | mm |

Diameter | 108 | mm |

Length | 499 | mm |

Weight | 18.9 | kg |

Maximum Damping Force (250 °C) | 7800 | N |

First Resonant Frequency | 15 | Hz |

Internal Heat Generation RMS (at 15 Hz and 250 °C) | 87 | W |

Maximum Damping Power (F·V) RMS (at 15 Hz and 250 °C) | 1050 | W |

Ventilation Calculated Requirements | Value | Units |

Air Environment Temperature | 200 | °C |

Max. Internal Temperature | 276 | °C |

Max. Surface Temperature | ≃255 | °C |

Air flow requirement | ≃1.42 | kg/s |

Air speed | ≃7 | m/s |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Pérez-Díaz, J.L.; Valiente-Blanco, I.; Cristache, C.
Z-Damper: A New Paradigm for Attenuation of Vibrations. *Machines* **2016**, *4*, 12.
https://doi.org/10.3390/machines4020012

**AMA Style**

Pérez-Díaz JL, Valiente-Blanco I, Cristache C.
Z-Damper: A New Paradigm for Attenuation of Vibrations. *Machines*. 2016; 4(2):12.
https://doi.org/10.3390/machines4020012

**Chicago/Turabian Style**

Pérez-Díaz, José Luis, Ignacio Valiente-Blanco, and Cristian Cristache.
2016. "Z-Damper: A New Paradigm for Attenuation of Vibrations" *Machines* 4, no. 2: 12.
https://doi.org/10.3390/machines4020012