# Improvement of the Vehicle Seat Suspension System Incorporating the Mechatronic Inerter Element

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Half Vehicle Model

_{s}is the vehicle seat mass, z

_{s}is the seat’s vertical displacement, m

_{a}is the vehicle’s sprung mass, z

_{a}is the vertical displacement of the body centroid, F

_{s}is the seat’s suspension force, F

_{f}and F

_{r}are the forces of the front and rear suspensions, l

_{s}is the horizontal distance from the seat to the centroid, l

_{f}and l

_{r}are the distances from the front and rear axles to the body centroid, φ is the body pitch angle, I

_{φ}is the body pitch moment of inertia, k

_{f}and c

_{f}are the spring’s stiffness and the damping coefficient of the front suspension, k

_{r}and c

_{r}are the spring’s stiffness and the damping coefficient of the rear suspension, m

_{uf}and m

_{ur}are the front and rear unsprung mass, z

_{uf}and z

_{ur}are the vertical displacements of the front and rear unsprung mass, k

_{tf}and k

_{tr}are the equivalent stiffness of the front and rear tires, z

_{rf}and z

_{rr}are the displacement inputs of the front and rear wheels, z

_{af}and z

_{ar}are the vertical displacements of the front corner and rear corner of the vehicle’s body. This study was carried out on the basis of a passenger car model in order to achieve an effective increase in ride comfort in passenger cars; the model for this study was built on a mature, commercially available model. Table 1 shows the parameters of the half vehicle model.

## 3. Seat Suspension Layout

#### 3.1. The Ball-Screw Mechatronic Inerter

_{e}and L

_{e}are the coil resistance and inductance. In this paper, the coil factor is not considered in the optimization. The external electrical load can be adopted to simulate the corresponding mechanical network in the optimization process.

#### 3.2. The Seat Suspension Layout

_{s}and b

_{s}are mechanical structures and T(s) is the impedance expression to be solved; the double primary impedance transfer function is as follows:

## 4. Optimal Design of the Mechatronic Seat Suspension

_{1pas}and J

_{2pas}are the root-mean-square (RMS) values of the seat vertical acceleration and the pitch motion acceleration of traditional passive suspension. Here, J

_{1pas}= 0.9913 m/s

^{2}and J

_{2pas}= 1.2852 rad/s

^{2}. J

_{1}and J

_{2}are the RMS values of the seat vertical acceleration and the pitch motion acceleration of the designed suspension system. The mechanical inertance b and the T(s) transfer function as the optimization variables. Particle swarm optimization was used to find the global optimum by following the current search. This algorithm has attracted academic attention for its ease of implementation, high accuracy and fast convergence. Equations (13) and (14) are the updated formulas for the particle velocity and position properties.

_{1}and d

_{2}are non-negative constants. The random numbers r

_{1}and r

_{2}usually have a value between 0 and 1, while P

_{id}and P

_{gd}are the individual extremum and global extremum. Figure 4 shows the optimization process of the algorithm.

## 5. Performance Evaluation

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Electrical network. (

**a**) Bivariate transfer function electrical network; (

**b**) Biquadratic transfer function electrical network; (

**c**) Bicubic transfer function electrical network.

Name | Value |
---|---|

Seat mass m_{s} (kg) | 48 |

Body centroid mass m_{a} (kg) | 928.2 |

Unsprung mass of front wheels m_{uf} (kg) | 26.5 |

Unsprung mass of rear wheels m_{ur} (kg) | 24.4 |

Distance from seat to centroid l_{s} (m) | 0.324 |

Distance from front axle to centroid l_{f} (m) | 0.968 |

Distance from rear axle to centroid l_{r} (m) | 1.392 |

Moment of inertia aound the Y axis I_{φ} (kg·m^{2}) | 1058 |

Front suspension stiffness k_{f} (kN·m^{−1}) | 25 |

Rear suspension stiffness k_{r} (kN·m^{−1}) | 22 |

Front suspension damping c_{f} (Ns/m) | 1500 |

Rear suspension damping c_{r} (Ns/m) | 1300 |

Tire stiffness k_{t} (kN·m^{−1}) | 192 |

Name | Value |
---|---|

Resistor R_{11} (Ω) | 4877 |

Resistor R_{12} (Ω) | 654 |

Capacitor C_{11} (F) | 0.0047 |

Resistor R_{21} (Ω) | 98,754 |

Resistor R_{22} (Ω) | 35,789 |

Resistor R_{23} (Ω) | 5711 |

Capacitor C_{21} (F) | 0.0079 |

Inductor L_{21} (H) | 0.34 |

Resistor R_{31} (Ω) | 81 |

Resistor R_{32} (Ω) | 6998 |

Resistor R_{33} (Ω) | 74,223 |

Resistor R_{34} (Ω) | 158 |

Capacitor C_{31} (F) | 0.0024 |

Capacitor C_{32} (F) | 0.0017 |

Inductor L_{31} (H) | 0.76 |

RMS of Seat Acceleration | Improvement | RMS of Pitch Acceleration | Improvement | |
---|---|---|---|---|

Passive suspension | 0.9913 | / | 1.2852 | / |

Layout S1 | 0.9664 | 2.51% | 1.2638 | 1.67% |

Layout S2 | 0.9459 | 4.58% | 1.2414 | 3.41% |

Layout S3 | 0.8866 | 10.56% | 1.1879 | 7.57% |

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**MDPI and ACS Style**

Qiu, C.; Liu, X.; Shen, Y.
Improvement of the Vehicle Seat Suspension System Incorporating the Mechatronic Inerter Element. *World Electr. Veh. J.* **2023**, *14*, 29.
https://doi.org/10.3390/wevj14020029

**AMA Style**

Qiu C, Liu X, Shen Y.
Improvement of the Vehicle Seat Suspension System Incorporating the Mechatronic Inerter Element. *World Electric Vehicle Journal*. 2023; 14(2):29.
https://doi.org/10.3390/wevj14020029

**Chicago/Turabian Style**

Qiu, Chengqun, Xiaofu Liu, and Yujie Shen.
2023. "Improvement of the Vehicle Seat Suspension System Incorporating the Mechatronic Inerter Element" *World Electric Vehicle Journal* 14, no. 2: 29.
https://doi.org/10.3390/wevj14020029