# Study on the Stability Control of Vehicle Tire Blowout Based on Run-Flat Tire

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Establishment of Run-Flat Tire Model

#### 2.1. Run-Flat Tire Model before Blowout

_{x}is the longitudinal slip ratio; S

_{y}is the lateral slip ratio; $\Omega $ is the tire rolling angular velocity; R

_{e}is the effective rolling radius; V

_{x}and ${V}_{y}$ are the longitudinal and lateral components, respectively, of the wheel center velocity V.

_{z}is the tire vertical force.

_{x}of the steady semi-empirical model can be expressed as follows:

_{y}is as follows:

_{r}is the longitudinal velocity of wheel center (${V}_{r}=\Omega \cdot {R}_{e}$ ); and ${R}_{l}$ is the load radius of the tire.

#### 2.2. Run-Flat Tire Model after Blowout

#### 2.2.1. Cornering Stiffness and Longitudinal Stiffness after Tire Blowout

^{5}N/rad (4700 N/1.8 deg), which is about 0.90 times the rated tire pressure condition. Similarly, it can be seen from Figure 1b that the longitudinal stiffness becomes about 0.95 times.

#### 2.2.2. Change of Rolling Resistance Coefficient after Tire Blowout

#### 2.2.3. Change of Effective Rolling Radius after Tire Blowout

## 3. Two Degrees of Freedom Model and Control System

#### 3.1. Two Degrees of Freedom Model

_{x}is the velocity of the vehicle along the x-axis; m is the total mass of the vehicle; β is the sideslip angle; r is the yaw rate; δ is the front wheel angle; a and $b$ are the distances from the mass center to the front and rear axles, respectively; I

_{z}is the moment of inertia of the whole vehicle around the z-axis; and C

_{f}and C

_{r}are equivalent cornering stiffness of front axle and rear axle, respectively.

_{d}is the ideal yaw rate; ${r}_{d}*$ is the ideal yaw rate after correction; μ is the adhesion coefficient of pavement; and g is the acceleration of gravity.

#### 3.2. Differential Braking Control System

_{d}is the ideal yaw rate of the vehicle; β is the sideslip angle of mass center; and $\epsilon $ is the weighting coefficient.

## 4. Simulation Results and Test Analysis

#### 4.1. Tire Blowout Dynamic Response

- (1)
- Left front tire blowout

- (2)
- Left rear tire blowout

#### 4.2. Stability Control Analysis

- (1)
- Left front tire control results

- (2)
- Left rear tire control results

## 5. Conclusions

- (1)
- The difference between the left front tire and left rear tire blowout condition of inserts supporting run-flat tire and normal tire was compared. The results show that the characteristic parameters of the two tires are similar. When the front tire blowout occurs, the yaw of the inserts supporting run-flat tire is larger, and when the rear tire blowout occurs, the yaw of the normal tire is larger.
- (2)
- The stability of the inserts supporting run-flat tire after tire blowout is controlled according to the difference between the ideal yaw rate and the sideslip angle and the actual value. The simulation results show that the differential braking control can better maintain the running track of the vehicle, significantly improve the stability of the vehicle, and whether the track adjustment effect of the rear tire of inserts supporting run-flat tire is better.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Curve of inserts supporting run-flat tire test results. (

**a**) Cornering stiffness curve; (

**b**) longitudinal stiffness curve.

**Figure 4.**The simulation curve of left front tire blowout: (

**a**) lateral acceleration curve; (

**b**) lateral displacement curve; (

**c**) yaw rate curve; (

**d**) sideslip angle curve.

**Figure 5.**The simulation curve of left rear tire blowout: (

**a**) lateral acceleration curve; (

**b**) lateral displacement curve; (

**c**) yaw rate curve; (

**d**) sideslip angle curve.

**Figure 6.**The controlled simulation curve of left front tire blowout: (

**a**) lateral acceleration curve; (

**b**) lateral displacement curve; (

**c**) yaw rate curve; (

**d**) sideslip angle curve.

**Figure 7.**The controlled simulation curve of left rear tire blowout: (

**a**) lateral acceleration curve; (

**b**) lateral displacement curve; (

**c**) yaw rate curve; (

**d**) sideslip angle curve.

F/N | W/mm | L/mm | S/mm^{2} | |
---|---|---|---|---|

Whole contact area | 12,250 | 235 | 580 | 136,300 |

Insert contact area | 12,250 | 132 | 258 | 34,056 |

∆r | ∆β | ||||||
---|---|---|---|---|---|---|---|

NB | NM | NS | ZO | PS | PM | PB | |

NB | PB | PB | PB | PB | PM | PS | ZO |

NM | PB | PB | PM | PM | PM | PS | ZO |

NS | PM | PM | PM | PM | PS | ZO | NS |

NO | PM | PS | PS | ZO | NS | NS | NM |

ZO | PM | PM | PS | ZO | NS | NS | NM |

PS | PS | PS | ZO | NM | NM | NM | NM |

PM | ZO | ZO | NM | NM | NB | NB | NB |

PB | ZO | NS | NM | NB | NB | NB | NB |

Parameter/Unit | Parameter Symbol | Parameter Value |
---|---|---|

Sprung mass/kg | Ms | 2290 |

Height of center of mass/mm | h | 810 |

Front axle distance/mm | a | 1180 |

Rear axle distance/mm | b | 1170 |

Wheel base/mm | l | 2950 |

Effective rolling radius/mm | Re | 455 |

Static load radius/mm | R0 | 467 |

Rim diameter/mm | D | 419 |

Width of tire section/mm | B | 317 |

Radial stiffness/N⋅mm^{−1} | Kt | 405 |

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**MDPI and ACS Style**

Wang, X.; Zang, L.; Wang, Z.; Lin, F.; Zhao, Z.
Study on the Stability Control of Vehicle Tire Blowout Based on Run-Flat Tire. *World Electr. Veh. J.* **2021**, *12*, 128.
https://doi.org/10.3390/wevj12030128

**AMA Style**

Wang X, Zang L, Wang Z, Lin F, Zhao Z.
Study on the Stability Control of Vehicle Tire Blowout Based on Run-Flat Tire. *World Electric Vehicle Journal*. 2021; 12(3):128.
https://doi.org/10.3390/wevj12030128

**Chicago/Turabian Style**

Wang, Xingyu, Liguo Zang, Zhi Wang, Fen Lin, and Zhendong Zhao.
2021. "Study on the Stability Control of Vehicle Tire Blowout Based on Run-Flat Tire" *World Electric Vehicle Journal* 12, no. 3: 128.
https://doi.org/10.3390/wevj12030128