# Study on Mechanism Analysis of Skidding Prediction for Electric Vehicle Based on Time-Delay Effect of Force Transmission

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods Analysis for Time-Delay Effect of Force Transmission Based on Single-Wheel Dynamics Model

_{m}is the driving force of the wheel (N); J is the equivalent rotational inertia of the wheel (kg·m

^{2}); ω is the rotational angular velocity of the wheel (rad/s); r is the effective radius of rotation of the wheel [m]; F

_{d}is the wheel ground Inter-friction force (N) (also known as friction force); F

_{dr}is the total resistance of the vehicle movement (N), including wind resistance, rolling resistance; M is the wheel load mass (kg); V is the longitudinal speed of the vehicle (m/s).

_{dr}is the change of wind resistance, which accounts for a small proportion and can be ignored. By Formulas (1)–(5), the dynamic structure block diagram of vehicle force transmission can be drawn, as shown in Figure 3.

_{v}< 0, the friction force feedback is positive feedback, and the wheel-ground contact cannot achieve stable force transmission. In addition, the time constant (τ

_{v}) is proportional to the wheel speed and inversely proportional to the slope (a) of the road surface characteristics. When the working point is close to the maximum attachment point, the delay of force transmission increases sharply, and the friction force change approaches zero. This characteristic provides a theoretical basis for predicting the attachment state of the vehicle.

## 3. Electric Vehicle Skidding Prediction Method Based on Skidding Prediction Factor

#### 3.1. Principles of Electric Vehicle Skidding Prediction Based on Skidding Prediction Factor

#### 3.2. Sliding Window Time

- (1)
- When road surface characteristics are same, the lower speed, the shorter skidding-window-time; the greater traction torque slope, the shorter skidding-window-time.
- (2)
- When vehicle speed and traction torque slope are same, the skidding-window-time varies greatly with different road conditions, and the skidding-window-time on icy roads is shorter.

## 4. Simulation and Experiment of Electric Vehicle Skidding Prediction Method Based on Slip Factor

#### 4.1. Simulation Verification and Analysis

#### 4.2. Experimental Verification of Electric Vehicle Skidding Prediction Based on Slip Factor

#### 4.3. Experimental Waveforms and Analysis

_{d}(simulated friction torque) increased, the wheel speed increased, the vehicle speed increased, and the slip rate increased slowly. As shown in Figure 10a,b, after about 37.926 s, the vehicle speed is about 30 Km/h, the slip factor amplitude starts to increase, and the asynchronous electric torque follows slowly. When the slip factor amplitude is greater than the threshold value of 50, it is determined that the simulated vehicle is about to slip, the control signal (con_sign) is set to 1, the given slip rate (s_ref) is set to 0.83, and then the wheel accelerates and the slip rate increases. It shows that the slip factor can be used to predict the simulated vehicle skidding in advance, and this prediction is about 5 ms ahead of schedule. The road characteristics are constantly changing, although the prediction lead time is not comparable with the simulation results, and the prediction is more difficult.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Simulation waveforms of road recognition under icy roads (high speed). (

**a**) Relevant simulation waveforms in road recognition; (

**b**) local amplified waveforms near the maximum attachment point).

**Figure 7.**Simulation waveforms of road recognition under icy roads (low speed). (

**a**) Relevant simulation waveforms in road recognition; (

**b**) local amplified waveforms near the maximum attachment point).

**Figure 10.**Low-speed slip test waveforms in traction conditions. (

**a**) Experimental waveforms related to skidding prediction; (

**b**) local enlarged waveforms near the maximum attachment point of skidding prediction; (

**c**) simulated road characteristic curve.

**Figure 11.**High-speed slip test waveforms in traction conditions. (

**a**) Experimental waveforms related to skidding prediction; (

**b**) local enlarged waveforms near the maximum attachment point of skidding prediction; (

**c**) simulated road characteristic curve.

Parameter | Values | Unit |
---|---|---|

sprung mass | 1370 | kg |

unsprung mass | 71 | kg |

height | 1535 | mm |

width | 1695 | mm |

mass to front axis | 1040 | mm |

wheel base | 2600 | mm |

to drag hook | 3400 | mm |

face area | 2.2 | m^{2} |

Tire Size | 205/55 R16 |

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**MDPI and ACS Style**

Yang, Y.; Wang, X.; Zhang, Y.
Study on Mechanism Analysis of Skidding Prediction for Electric Vehicle Based on Time-Delay Effect of Force Transmission. *World Electr. Veh. J.* **2021**, *12*, 171.
https://doi.org/10.3390/wevj12040171

**AMA Style**

Yang Y, Wang X, Zhang Y.
Study on Mechanism Analysis of Skidding Prediction for Electric Vehicle Based on Time-Delay Effect of Force Transmission. *World Electric Vehicle Journal*. 2021; 12(4):171.
https://doi.org/10.3390/wevj12040171

**Chicago/Turabian Style**

Yang, Ying, Xiaoyu Wang, and Yangchao Zhang.
2021. "Study on Mechanism Analysis of Skidding Prediction for Electric Vehicle Based on Time-Delay Effect of Force Transmission" *World Electric Vehicle Journal* 12, no. 4: 171.
https://doi.org/10.3390/wevj12040171