# A Dynamic Model and Parameter Identification of High Viscosity Magnetorheological Fluid-Based Energy Absorber with Radial Flow Mode

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## Abstract

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## 1. Introduction

## 2. High-Speed Drop Tower Test

#### 2.1. Constitutive Model of HVLP MRF

#### 2.2. MREA Configuration

#### 2.3. Drop Tower Test Setup

#### 2.4. Test Result Analysis

## 3. MREA Model

#### 3.1. Deformation Force

_{d}represents the impact stiffness of the corrugated tube in the elastic stage. x is the instantaneous impact displacement. η

_{p}is a compensation coefficient. E, G, and n

_{ct}are the elastic modulus, strain-strengthening modulus, and plastic strain-strengthening exponent, respectively.

#### 3.2. Damping Force Based on the E-HBM Model

## 4. Parameter Identification of the E-HBM Model

#### 4.1. Model Parameters in the Non-Controllable Channels

#### 4.1.1. Model Parameters in the Corrugated Tube

#### 4.1.2. Model Parameters in Axial and Annular Channels

#### 4.2. Model Parameters in the Controllable Channel

#### 4.3. Damping Coefficient of Minor Losses

## 5. Evaluation of E-HBM Model

#### 5.1. Peak Force and Mean Force

#### 5.2. Crush Force Efficiency

#### 5.3. Specific Energy Absorption

#### 5.4. Stroke Efficiency

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Sample Availability

## References

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**Figure 1.**Schematic of an HVLP MRF-based MREA with radial flow mode: (

**a**) two-dimensional and (

**b**) three-dimensional models. HVLP: high-viscosity linear polysiloxane; MRF: magnetorheological fluid; MREA: magnetorheological energy absorber.

**Figure 3.**MREA performances at a drop height of 0.4 m: (

**a**) force vs. displacement and (

**b**) time history of the force.

**Figure 4.**MREA performances at a drop height of 0.7 m: (

**a**) force vs. displacement and (

**b**) time history of the force.

**Figure 5.**MREA performances at a drop height of 0.9 m: (

**a**) force vs. displacement and (

**b**) time history of the force.

**Figure 10.**E–HBM model vs. measured data: (

**a**) CFE at 0.4 m, (

**b**) CFE at 0.7 m, (

**c**) CFE at 0.9 m, and (

**d**) relative error of CFE at different drop heights.

**Figure 11.**E–HBM model vs. measured data at different drop heights: (

**a**) SEA, (

**b**) relative error of SEA.

**Figure 12.**E–HBM model vs. measured data at different drop heights: (

**a**) SE, (

**b**) relative error of SE.

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

Inner radius of the inner cylinder, R_{i} | 48 mm |

Radius of the axial channel, R_{x} | 14 mm |

Length of the cylinder, L | 24 mm |

Thickness of the clapboard, L_{c} | 20 mm |

Single-stage radial damping length, L_{r} | 30 mm |

Thickness of the baffle, L_{b} | 25 mm |

Thickness of the outer cylinder, L_{o} | 20 mm |

Length of corrugated tube, L_{ct} | 135 mm |

Corrugated segment length of corrugated tube, L_{cs} | 105 mm |

Effective MR valve gap width of the radial channels, d_{r} | 2 mm |

Number range of overall stages in the MR valve, N | 1 |

Coil turn numbers, Turn | 643 Turn |

Outer radius of straight segment, R_{ct_o} | 34 mm |

Current [A] | Passive Damping Coefficient [kg/s] | Yield Force [N] |
---|---|---|

0 | 35,742 | 2065 |

1 | 47,472 | 2906.3 |

2 | 54,240 | 4293 |

3 | 62,220 | 5637 |

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**MDPI and ACS Style**

Fu, B.; Zhang, X.; Li, Z.; Shu, R.; Liao, C.
A Dynamic Model and Parameter Identification of High Viscosity Magnetorheological Fluid-Based Energy Absorber with Radial Flow Mode. *Molecules* **2021**, *26*, 7059.
https://doi.org/10.3390/molecules26227059

**AMA Style**

Fu B, Zhang X, Li Z, Shu R, Liao C.
A Dynamic Model and Parameter Identification of High Viscosity Magnetorheological Fluid-Based Energy Absorber with Radial Flow Mode. *Molecules*. 2021; 26(22):7059.
https://doi.org/10.3390/molecules26227059

**Chicago/Turabian Style**

Fu, Benyuan, Xianming Zhang, Zhuqiang Li, Ruizhi Shu, and Changrong Liao.
2021. "A Dynamic Model and Parameter Identification of High Viscosity Magnetorheological Fluid-Based Energy Absorber with Radial Flow Mode" *Molecules* 26, no. 22: 7059.
https://doi.org/10.3390/molecules26227059