# How to Create Trusted Tribological Characterization Data of Soft Polymers as Input for FEM Simulations?

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## Abstract

**:**

## 1. Introduction

^{®}) also reveals the gap between the states of the art of both disciplines. The tribological models only consist of the Coulomb friction model and the Archard wear model, lacking specific parameters for individual materials [6].

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Methods

#### 2.2.1. Designing Experimental Tests for Soft Polymers

- the normal load ${\mathrm{F}}_{\mathrm{N}}$;
- the frictional force ${\mathrm{F}}_{\mathrm{fric}}$;
- the relative velocity ${\mathrm{v}}_{\mathrm{rel}}$ between sample and counter body;
- the loss of volume due to wear ${\mathrm{V}}_{\mathrm{w}}$ usually determined by the mass loss assuming constant material density.

- Height of polymer disc $\mathrm{h}$;
- Diameter of polymer disc $\mathrm{d}$;
- Nominal contact pressure ${\mathrm{p}}_{\mathrm{n}}$, given by normal load ${\mathrm{F}}_{\mathrm{N}}$ and the cross-sectional area ${A}_{0}$: ${\mathrm{p}}_{\mathrm{n}}=\frac{{\mathrm{F}}_{\mathrm{n}}}{{\mathrm{A}}_{0}}$;
- Young’s modulus $\mathrm{E}$;
- Poisson’s ratio ν;
- CoF $\mathsf{\mu}$.

#### 2.2.2. Experimental Tribological Model Tests

#### 2.2.3. Verification of Model Test

## 3. Results

#### 3.1. Design Study and Derived Empirical Relationships

#### 3.2. Experimental Results and Friction Model

#### 3.3. Verification

## 4. Discussion

#### 4.1. Numerical Design Study and Verification of the Frictional Model

#### 4.2. Standardization of Tests for Upscaling Material Performance

## 5. Conclusions

- A polymer disc with a height to diameter ratio of less than 1/6 was demonstrated to be most eligible for robust test procedures and uniform contact pressures. This ensures that occurring wear does not change contact pressure;
- The Young’s modulus, which is typically low for soft polyurethane, has little influence on the contact pressure distribution of the newly developed disc-on-plate configuration as long as the ratio of the nominal contact pressure and Young´s modus is below 0.1;
- Poisson’s ratios of the polymer above 0.4 significantly reduce the uniformity of the contact pressure distribution and lead to a maximum in contact pressure in the center of the polymer pin;
- The CoF mainly influences the contact pressure at the leading edge; the higher the CoF, the higher the maximal contact pressure at the leading edge. This effect could be minimized successfully in the disc setup presented in this paper.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Comparison between nominal and true coefficient of friction for arbitrary contact pressure distributions and materials with pressure und velocity dependent frictional behavior.

**Figure 2.**Experimental setup to characterize the tribological behavior of soft polymers with (

**a**) polymer pin-on-plate, (

**b**) crossed-cylinder configuration and (

**c**) a thin polymer disc-on-plate configuration.

**Figure 3.**Comparison between contact pressure distributions for different test setup configurations.

**Figure 4.**Simulation setup for parameter study with 14,115 linear tetrahedral elements: (

**a**) boundary conditions; (

**b**) mesh of the discretized model.

**Figure 5.**Experimental setup to characterize the tribological behavior of soft polymers: Sample holder and polymer sample (upper right); Experimental test stand at AC2T research GmbH for reciprocal tribological experiments.

**Figure 6.**Full 3D model of the test setup including the sample holder and the adapter with (

**a**) applied boundary conditions and (

**b**) numerical mesh with 39,526 elements.

**Figure 7.**(

**a**) Equivalent strain of deformed polymer pin (deformation is scaled by a factor of three); (

**b**) the corresponding normalized contact pressure along the symmetry axis for base parameters.

**Figure 11.**(

**a**) Normalized contact area with contact pressure within ±10% of nominal pressure for different specimen geometries; (

**b**) normalized mean contact.

**Figure 12.**Tribological characterization of HPU premium: (

**a**) wear track after testing procedure; (

**b**) worn sample after test.

**Figure 13.**Coefficient of friction resoved over displacement at different cycle numbers for normal pressure of 1 MPa and 100 mm/s for dry friction.

**Figure 14.**Model fit for frictional model for (

**a**) sliding velocity and (

**b**) contact pressure vs coefficient of friction.

Model Parameter | Symbol | Value ^{1} | ||||
---|---|---|---|---|---|---|

Polymer sample height | $\mathrm{h}$ (mm) | 0.25 | 0.5 | 1.0 | 1.5 | 2.0 |

Polymer sample diameter | $\mathrm{d}$ (mm) | 4 | 6 | 8 | 12 | 16 |

Nominal contact pressure | ${\mathrm{p}}_{\mathrm{n}}$ (MPa) | 0.5 | 1.0 | 2.0 | 4.0 | |

Young’s modulus of polymer | $\mathrm{E}$ (MPa) | 5 | 10 | 20 | 40 | |

Poisson’s ratio of polymer | $\mathsf{\nu}$ | 0.0 | 0.3 | 0.4 | 0.49 | 0.499 |

CoF between polymer and counter body | $\mathsf{\mu}$ | 0.0 | 0.1 | 0.25 | 0.5 | 0.75 |

^{1}The values in bold indicate the base parameter set.

Dimensionless Parameter | Formula |
---|---|

Normalized x-coordinate | $\text{}\hat{\mathrm{x}}=\frac{2\mathrm{x}}{\mathrm{d}}$ |

Ratio of nominal contact pressure to Young’s modulus | ${\text{}\hat{\mathrm{p}}}_{\mathrm{n}}=\frac{{\mathrm{p}}_{\mathrm{n}}}{\mathrm{E}}$ |

Ratio of height to diameter | $\text{}\hat{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{d}}$ |

Normalized contact pressure | ${\text{}\hat{\mathrm{p}}}_{\mathrm{c}}=\frac{{\mathrm{p}}_{\mathrm{c}}}{{\mathrm{p}}_{\mathrm{n}}}$ |

Normalized contact area | ${\text{}\hat{\mathrm{A}}}_{\mathrm{c}}=\frac{{\mathrm{A}}_{\mathrm{c}}}{{\mathrm{A}}_{0}}$ |

Normalized mean contact pressure | ${\text{}\hat{\mathrm{p}}}_{\mathrm{c},\mathrm{m}}=\frac{1}{{\mathrm{A}}_{\mathrm{c}}}{{\displaystyle \int}}_{{\mathrm{A}}_{\mathrm{c}}}{\text{}\hat{\mathrm{p}}}_{\mathrm{c}}\text{}\mathrm{dA}\text{}$ |

Study No. ^{1} | Loading Parameter | Value |
---|---|---|

1–2 | Nominal contact pressure ${\mathrm{p}}_{\mathrm{N}}$ Average relative velocity ${\mathrm{v}}_{\mathrm{rel}}$ | 1.0 MPa 3.0 MPa 50 mm/s 50 mm/s |

3–4 | Nominal contact pressure ${\mathrm{p}}_{\mathrm{N}}$ Average relative velocity ${\mathrm{v}}_{\mathrm{rel}}$ | 1.0 MPa 3.0 MPa 100 mm/s 100 mm/s |

^{1}Each study was performed with three repetitions.

Model Parameter | Symbol | Value |
---|---|---|

Static CoF | ${\mathsf{\mu}}_{\mathrm{s}}$ | 1.3 |

Dynamic CoF | ${\mathsf{\mu}}_{\mathrm{d}}$ | 0.9 |

Reference sliding velocity | ${\mathrm{v}}_{0}$ | 25 mm/s |

Reference contact pressure | ${\mathrm{p}}_{0}$ | 1 MPa |

Pressure exponent | $\mathrm{n}$ | 0.26 |

**Table 5.**Input table for displacement over time for multilinear approximation of relative movement of counter surface.

Time (s) | Displacement (mm) |
---|---|

0.0 | −27 |

0.03 | −27 |

0.47 | 27 |

0.53 | 27 |

0.97 | −27 |

1.0 | −27 |

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**MDPI and ACS Style**

Herr, M.; Borras, F.X.; Spaltmann, D.; Kröll, M.; Pirker, F.; Cihak-Bayr, U.
How to Create Trusted Tribological Characterization Data of Soft Polymers as Input for FEM Simulations? *Materials* **2023**, *16*, 131.
https://doi.org/10.3390/ma16010131

**AMA Style**

Herr M, Borras FX, Spaltmann D, Kröll M, Pirker F, Cihak-Bayr U.
How to Create Trusted Tribological Characterization Data of Soft Polymers as Input for FEM Simulations? *Materials*. 2023; 16(1):131.
https://doi.org/10.3390/ma16010131

**Chicago/Turabian Style**

Herr, Marin, F. Xavier Borras, Dirk Spaltmann, Mirco Kröll, Franz Pirker, and Ulrike Cihak-Bayr.
2023. "How to Create Trusted Tribological Characterization Data of Soft Polymers as Input for FEM Simulations?" *Materials* 16, no. 1: 131.
https://doi.org/10.3390/ma16010131