**5. Conclusions**

A semi-analytic contact mechanical model for the fast simulation of fretting wear of axisymmetric contacts has been proposed. The main idea of the model is to neglect the change of the indenter profile during one cycle of the fretting oscillation, which—within the Hertz–Mindlin approximation—allows to analytically calculate the slip-length during one cycle in closed form, and hence gives a zero-order approximation for the time-evolution of the worn profile. This procedure gives the same results as contact mechanically rigorous simulations based on the Hertz–Mindlin approximation, but works significantly faster than those. A comparison of the numerical prediction for the evolution of the worn profile in partial slip torsional fretting of a rubber ball on abrasive paper shows good agreemen<sup>t</sup> with the experimental results from the literature.

**Funding:** This research was funded by the German Research Foundation under the project number PO 810/66-1.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** No additional data (other than stated in the manuscript) were produced or used for the preparation of the manuscript.

**Conflicts of Interest:** The author declares no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
