# Experimental and Numerical Investigation of Tire Tread Wear on Block Level

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup

#### 2.2. Test Procedure

- A
- Sample is set down into contact with the aluminum sheet on track, with no relative motion until all vibrations are stopped. Normal force is applied via a pneumatic bellows cylinder. The resting time before start of motion is approximately $0.5\phantom{\rule{0.166667em}{0ex}}\mathrm{s}$. Then, acceleration with $a=5\phantom{\rule{0.166667em}{0ex}}g=49.05\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}/{\mathrm{s}}^{2}$ to the intended speed still on the aluminum track. The length of the aluminum track is large enough to ensure that the acceleration phase of the sample is finished before coming into contact with the abrasive test surface;
- B
- Leaving the aluminum sheet and coming into contact with the abrasive surface. Short phase of vertical dynamics because of the step down to the track with respective effects in signal of coefficient of friction;
- C
- Overcoming the static friction of the sample on the abrasive counter surface. For the transfer of results to rolling friction, assessment of the static friction coefficient is essential due to the large contribution of the sticking zone to the tangential forces in the tire footprint. Transitioning from sticking to sliding requires some time, in particular steady-state temperatures and block deflection have to be established. In this transition period, the coefficient of friction decreases slightly. The transition time lag constants are specific for the respective frictional contact and affected by materials, surface topographies, and potential third media in contact. Subsequently, a quasi-steady period of sliding friction occurs with a constant level of coefficient of friction, which is evaluated as the steady-state coefficient of friction;
- D
- At the end of the test track, the sample is decelerated and leaves the contact.

#### 2.3. Material Model for Rubber

#### 2.3.1. Identification of Elastic Parameters

#### 2.3.2. Identification of Viscoelastic Parameters

#### 2.4. Wear Model

#### 2.4.1. Post-Processing Re-Meshing Algorithm

#### 2.4.2. Adaptive Meshing Algorithm

#### 2.5. Image Processing and Mesh Generation

#### 2.5.1. Image Processing

#### 2.5.2. Mesh Generation

## 3. Results and Discussion

#### 3.1. Experimental Output

#### 3.2. Wear Parameter Identification

#### 3.3. Wear Simulation and Comparison to Experiments

#### 3.3.1. Wear Simulation

#### 3.3.2. Verification

#### 3.3.3. Validation

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**High-Speed Linear Tester (HiLiTe) for friction and wear measurements. (

**a**) Overall view, (

**b**) Detail lateral view.

**Figure 3.**Test repetitions at $p=0.4\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=50\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$.

**Figure 5.**Fitting of long-term response of rubber compound at $\vartheta =20{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$. (

**a**) Uniaxial tension, (

**b**) Biaxial tension, (

**c**) Pure shear.

**Figure 6.**Master curve of rubber compound at $\vartheta =20{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

**Figure 9.**Image processing at $p=1.2\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=100\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$. (

**a**) Original, (

**b**) Color inversion, (

**c**) Background deletion, (

**d**) Sobel filter, (

**e**) Gaussian filter, (

**f**) Contour identification.

**Figure 10.**Image alignment at $p=\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=100\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$.

**Figure 11.**Contour scaling and edge seed at $p=0.8\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$. (

**a**) Contour scaling, (

**b**) Edge seed.

**Figure 12.**Two-dimensional FEM block models at $p=1.2\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=100\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$. (

**a**) 225 elements, unworn, (

**b**) 256 elements, pre-cond, (

**c**) 1026 elements, pre-cond.

**Figure 13.**Three-dimensional FEM block models at $p=1.2\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=100\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$. (

**a**) 4500 elements, unworn, (

**b**) 5120 elements, pre-cond.

**Figure 17.**Contact pressure ${\sigma}_{N}$ of three-dimensional FEM blocks at $p=1.2\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=100\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$. (

**a**) 4500 elements, unworn, (

**b**) 5120 elements, pre-conditioned.

**Figure 18.**Frictional energy rate distribution $p=1.2\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=100\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$.

**Figure 19.**Comparison of cumulative mass loss. (

**a**) $p=0.8\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$, (

**b**) $p=1.2\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=100\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$.

**Figure 20.**Comparison of rubber block’s contour change. (

**a**) $p=0.8\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=10\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$, (

**b**) $p=1.2\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ and $v=100\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}/\mathrm{s}$.

${\mathit{C}}_{10}$ | ${\mathit{C}}_{20}$ | ${\mathit{C}}_{30}$ |
---|---|---|

$0.57935\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ | $-0.04953\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ | $0.02483\phantom{\rule{3.33333pt}{0ex}}\mathrm{N}/{\mathrm{mm}}^{2}$ |

Branch k | ${\mathit{\gamma}}_{\mathit{k}}$ | ${\mathit{\tau}}_{\mathit{k}}$ |
---|---|---|

1 | $0.02301$ | $8.01352\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{+2}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

2 | $0.01429$ | $9.67013\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{+1}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

3 | $0.01326$ | $1.97988\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{+1}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

4 | $0.01520$ | $4.05365\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{+0}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

5 | $0.01613$ | $7.76879\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-1}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

6 | $0.01923$ | $1.59060\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-1}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

7 | $0.02194$ | $2.67096\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-2}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

8 | $0.02132$ | $5.84217\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-3}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

9 | $0.02575$ | $1.04805\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-3}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

10 | $0.03220$ | $2.00858\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-4}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

11 | $0.03083$ | $3.15716\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

12 | $0.04522$ | $9.60953\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

13 | $0.08282$ | $1.23883\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-6}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

14 | $0.06142$ | $3.77065\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-7}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

15 | $0.55373$ | $3.73187\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-8}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ |

Parameter | Linear (abs. Error) | Linear (rel. Error) | Non-Linear (abs. Error) | Non-Linear (rel. Error) |
---|---|---|---|---|

${k}_{w}$ in $\mathrm{m}{\mathrm{m}}^{2}\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}N$ | $5.951\times {10}^{-4}$ | $3.857\times {10}^{-4}$ | $2.083\times {10}^{-5}$ | $1.452\times {10}^{-4}$ |

${a}_{w}$ | 1 | 1 | 1.234 | 1.089 |

${R}^{2}$ | 0.978 | 0.808 | 0.988 | 0.961 |

Number | Name | Description | Boundary Conditions |
---|---|---|---|

1 | Contact | Counter surface is lifted to ensure contact between rubber block and bottom rigid surface | $\Delta t={10}^{-2}\phantom{\rule{0.166667em}{0ex}}s$${u}_{v}=1\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\mathrm{m}$ |

2 | Loading | Counter surface is pressed against rubber block | $\Delta t=1\phantom{\rule{0.166667em}{0ex}}s$${F}_{v}={p}_{N}\phantom{\rule{0.166667em}{0ex}}A$ |

3 | Ramping | Counter surface is accelerated while friction is continuously increased | $\Delta t=\frac{v}{a}$${v}_{x}=a\phantom{\rule{0.166667em}{0ex}}t$$\mu ={\mu}_{\mathrm{alu}}\phantom{\rule{0.166667em}{0ex}}t$ |

4 | Sliding-on-aluminum | Counter surface is moving with constant speed and aluminum based friction | $\Delta t=\frac{{L}_{\mathrm{alu}}-\frac{{v}^{2}}{2a}}{v}$${v}_{x}=v$$\mu ={\mu}_{\mathrm{alu}}$ |

5 | Sliding-on-sandpaper | Counter surface is moving with constant speed and sandpaper based friction | $\Delta t=\frac{{L}_{\mathrm{sp}}}{v}$${v}_{x}=v$$\mu ={\mu}_{\mathrm{sp}}$ |

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## Share and Cite

**MDPI and ACS Style**

Hartung, F.; Garcia, M.A.; Berger, T.; Hindemith, M.; Wangenheim, M.; Kaliske, M.
Experimental and Numerical Investigation of Tire Tread Wear on Block Level. *Lubricants* **2021**, *9*, 113.
https://doi.org/10.3390/lubricants9120113

**AMA Style**

Hartung F, Garcia MA, Berger T, Hindemith M, Wangenheim M, Kaliske M.
Experimental and Numerical Investigation of Tire Tread Wear on Block Level. *Lubricants*. 2021; 9(12):113.
https://doi.org/10.3390/lubricants9120113

**Chicago/Turabian Style**

Hartung, Felix, Mario Alejandro Garcia, Thomas Berger, Michael Hindemith, Matthias Wangenheim, and Michael Kaliske.
2021. "Experimental and Numerical Investigation of Tire Tread Wear on Block Level" *Lubricants* 9, no. 12: 113.
https://doi.org/10.3390/lubricants9120113