# Study of Brake Disc Friction Characteristics Effect on Low Frequency Brake Induced Vibration of Aircraft Landing Gear

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## Abstract

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## 1. Introduction

## 2. The Model of Gear Walk System

#### 2.1. The Rigid–Flexible Coupling Dynamics Model of Landing Gear

#### 2.1.1. Model of Buffer

#### 2.1.2. Flexible Processing and Constraint Relations

#### 2.2. Variable Friction Model of the Brake Disc

#### 2.2.1. Temperature Variation Model

#### 2.2.2. Temperature–Friction Coefficient Model

#### 2.3. Hydraulic Brake System Model

#### 2.4. Co-Simulation Method

## 3. Analysis of the Brake Disc Friction Characteristics Effect on Gear Walk

#### 3.1. C/SiC Brake Disc Variable Friction Characteristics Effect on Gear Walk

#### 3.2. Brake Disc Friction Characteristics Effect on Gear Walk under Different Ambient Temperatures

#### 3.3. Brake Disc Material Effect on Gear Walk

## 4. Conclusions

- 1.
- In the time domain simulation analysis of gear walk, there is a “negative slope” phenomenon between the C/SiC brake disc friction coefficient and the wheel speed. The friction coefficient changes greatly when the temperature is below 600 °C. This phenomenon has a great effect on the gear walk characteristics and the control effect of the slip rate PID brake control law. The friction coefficient of the C/C disc has little change, and the variable friction characteristic is stable. Attention should be paid to the effect of the friction characteristics of the brake disc on the accuracy of simulation results;
- 2.
- The variable friction characteristics of C/SiC are easily affected by ambient temperature. The occurrence time of the “negative slope” phenomenon will be affected by different ambient temperatures. The change of ambient temperature has a great influence on the displacement and load of gear walk;
- 3.
- A C/SiC brake disc can solve the defect of a C/C brake disc’s low friction coefficient to a certain extent, which requires less brake pressure to be provided by the hydraulic system in the braking process and saves on energy consumption. However, the problem of large braking torque fluctuation caused by the “negative slope” phenomenon will also exacerbate gear walk and affect the braking efficiency of aircraft.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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

The rigid–flexible coupling dynamics model of landing gear | Vertical stiffness of tire | 3.4 × 10^{6} $\mathrm{N}/\mathrm{m}$ |

Vertical damping of tire | 5.5 × 10^{5} $\mathrm{N}\cdot \mathrm{s}/\mathrm{m}$ | |

Cornering stiffness of tire | 3000 $\mathrm{N}/\xb0$ | |

Radius of tire | 0.625 $\mathrm{m}$ | |

Inertia of tire | 10.473 $\mathrm{Kg}\cdot {\mathrm{m}}^{2}$ | |

Mass of fuselage | 77,600 $\mathrm{Kg}$ | |

Inertia of fuselage roll | 1.493 × 10^{6} $\mathrm{Kg}\cdot {\mathrm{m}}^{2}$ | |

Inertia of fuselage yaw | 4.68 × 10^{6} $\mathrm{Kg}\cdot {\mathrm{m}}^{2}$ | |

Inertia of fuselage pitch | 3.317 × 10^{6} $\mathrm{Kg}\cdot {\mathrm{m}}^{2}$ | |

Density | 7.83 × 10^{3} ${\mathrm{Kg}/\mathrm{m}}^{3}$ | |

Elastic Modulus | 2 × 10^{5} $\mathrm{MPa}$ | |

Poisson’s ratio | 0.3 | |

Variable friction model of the brake disc | Reference viscosity of air | 17.5 × 10^{-6} $\mathrm{Pa}\cdot \mathrm{s}$ |

Volume expansion coefficient | 0.0033 | |

Mass of the brake disc | 36 $\mathrm{Kg}$ | |

Radius of rotating disc | 0.141 $\mathrm{m}$ | |

Radius of static disc | 0.209 $\mathrm{m}$ | |

Density of air | 1.225 ${\mathrm{Kg}/\mathrm{m}}^{3}$ | |

Thickness of the interlayer | 0.05 $\mathrm{m}$ | |

Hydraulic brake system model | Anti-skid current amplification factor | 50 |

Proportional coefficient | 200 | |

Integral coefficient | 150 | |

Derivative coefficient | 60 |

Brake Disc Material | $\mathbf{The}\mathbf{Temperature}\mathbf{Change}(\xb0\mathbf{C})$ | $\mathbf{Amplitude}\mathbf{of}\mathbf{Gear}\mathbf{Walk}\mathbf{Displacement}\left(\mathbf{m}\right)$ | $\mathbf{Amplitude}\mathbf{of}\mathbf{Gear}\mathbf{Walk}\mathbf{Load}\left(\mathbf{N}\right)$ | $\mathbf{Amplitude}\mathbf{of}\mathbf{Gear}\mathbf{Walk}\mathbf{Acceleration}\left({\mathbf{m}/\mathbf{s}}^{2}\right)$ |
---|---|---|---|---|

C/C | 676.62 | 1.36 × 10^{-3} | 8.96 × 10^{3} | 0.25 |

C/SiC | 666.70 | 2.77 × 10^{-3} | 21.91 × 10^{3} | 39.98 |

Effect comparison of brake discs of different materials | −1.49% | +51.08% | +59.11% | +99.37% |

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**MDPI and ACS Style**

Zhang, S.; Yin, Q.; Wei, X.; Song, J.; Nie, H.
Study of Brake Disc Friction Characteristics Effect on Low Frequency Brake Induced Vibration of Aircraft Landing Gear. *Aerospace* **2022**, *9*, 809.
https://doi.org/10.3390/aerospace9120809

**AMA Style**

Zhang S, Yin Q, Wei X, Song J, Nie H.
Study of Brake Disc Friction Characteristics Effect on Low Frequency Brake Induced Vibration of Aircraft Landing Gear. *Aerospace*. 2022; 9(12):809.
https://doi.org/10.3390/aerospace9120809

**Chicago/Turabian Style**

Zhang, Songyang, Qiaozhi Yin, Xiaohui Wei, Jiayi Song, and Hong Nie.
2022. "Study of Brake Disc Friction Characteristics Effect on Low Frequency Brake Induced Vibration of Aircraft Landing Gear" *Aerospace* 9, no. 12: 809.
https://doi.org/10.3390/aerospace9120809