# Tire/Road Rolling Resistance Modeling: Discussing the Surface Macrotexture Effect

^{*}

## Abstract

**:**

^{2}exceeding 0.8. A good correlation between the MPD (mean profile depth) of the surfaces and the rolling resistance is also shown. It is also noticed that a random distribution and pointed shape of the summits may also be an inconvenience concerning rolling resistance, thus leading to the conclusion that beyond the macrotexture, the positivity of the texture should also be taken into account. A possible simplification of the model by neglecting the damping part in the constitutive model of the rubber is also noted.

## 1. Introduction

## 2. Modeling

#### 2.1. From DFM to RRM: Adaptation of the Dynamic Friction Model to the Modeling of Rolling Resistance

#### 2.2. Two Steps Calculation

#### 2.3. Calculating the Rolling Resistance Coefficient (Crr)

_{i}$\left(\mathrm{t}\right)$ is the displacement of the tread ith element contacting the ith element on the road. δ$\left(\mathrm{t}\right)$ is the solid displacement of the tire at t. h

_{i}represents the tire geometry. z

_{i}is the height of the ith point of the road profile.

#### 2.4. Calculation Algorithm

## 3. Experiments

#### 3.1. Measuring the Rolling Resistance Coefficient

#### 3.2. Tested Surfaces

## 4. Results

^{2}of 0.8, even though there was a factor close to two between the measured and predicted values. One also notices that only surfaces A and M1 are far from the trend, which has not yet been explained at this level. This good general trend leads us to conclude that our model can capture some of the physics involved in the phenomenon of the generation of rolling resistance forces by the asperities of road surfaces.

^{2}higher than 0.86, but once again the surfaces A and M1 are out of this trend. One can conclude that the contribution to the rolling resistance due to the pavement asperities increases with the macrotexture. This was confirmed by the direct comparison between Crr_WS and MPDs (Figure 7).

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The two calculation steps. The first step determines the apparent contact area assuming the tire static on a smooth road (

**a**). The second step determines the real contact area and thus the rolling resistance with the rolling tire upon the rough road surface (

**b**).

Name | Description | MPD | Surface Texture |
---|---|---|---|

Tile | Smooth | 0.02 | |

E1 | Semi-coarse asphalt concrete | 0.27 | |

E2 | Semi-coarse asphalt concrete | 0.53 | |

A | Porous asphalt concrete | 0.34 | |

M2 | Very thin asphalt concrete | 0.35 | |

F | Hight-friction dressing «COLGRIP©» | 0.69 | |

M1 | Very thin asphalt concrete | 0.69 |

Surfaces | MPD | Crr_RRM | Crr_WS |
---|---|---|---|

Tile | 0.02 | 1.30 × 10^{−3} | 8.75 × 10^{−2} |

E1 | 0.27 | 3.42 × 10^{−2} | 9.34 × 10^{−2} |

E2 | 0.53 | 5.19 × 10^{−2} | 9.56 × 10^{−2} |

A | 0.34 | 5.36 × 10^{−2} | 9.24 × 10^{−2} |

M2 | 0.35 | 4.65 × 10^{−2} | 9.34 × 10^{−2} |

F | 0.69 | 8.15 × 10^{−2} | 9.97 × 10^{−2} |

M1 | 0.69 | 6.27 × 10^{−2} | 1.00 × 10^{−1} |

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**MDPI and ACS Style**

Kane, M.; Riahi, E.; Do, M.-T.
Tire/Road Rolling Resistance Modeling: Discussing the Surface Macrotexture Effect. *Coatings* **2021**, *11*, 538.
https://doi.org/10.3390/coatings11050538

**AMA Style**

Kane M, Riahi E, Do M-T.
Tire/Road Rolling Resistance Modeling: Discussing the Surface Macrotexture Effect. *Coatings*. 2021; 11(5):538.
https://doi.org/10.3390/coatings11050538

**Chicago/Turabian Style**

Kane, Malal, Ebrahim Riahi, and Minh-Tan Do.
2021. "Tire/Road Rolling Resistance Modeling: Discussing the Surface Macrotexture Effect" *Coatings* 11, no. 5: 538.
https://doi.org/10.3390/coatings11050538