**5. Conclusions**

Within the scope of this paper, a pin-on-disc tribometer was used to measure dynamic friction in the contact of surface textured rubber specimens that were manufactured by texturing during moulding (TDM). The operating conditions, defined by relative velocity (*vr* ranging from 6 to 251 mm/s) and contact pressure level (*pc*,*max* ranging from 0.5 to 0.9 MPa), were chosen to correspond to the operating conditions of pneumatic seals. Based on the different experimentally tested texture dimensions, a maximum friction reduction of 70% was determined compared to the untextured reference, with a dimple diameter of 100 μm, a dimple depth of 10 μm and an area density of 9%.

However, since no global surface texture optimum could be found experimentally that exhibits the lowest friction under all operating conditions, it is concluded that a surface texture needs always to be determined individually, based on the prevailing operating conditions, in order to achieve maximum friction reduction. For this purpose, a novel methodology was applied, combining friction measurements with Reduced Order Modelling (ROM). The objective of the ROM was the computation of optimal surface texture parameters that provide the highest friction reduction within the given parameter space of textures and operating conditions. By feeding the ROM with microscope-based texture measurements, it also takes into account deviations of the real dimple dimensions from the nominal dimple values for the output friction value. In summary, friction measurements are suitable as input parameters for the ROM so that the use of ROM for friction prediction has been proven successful. For demonstration, exemplary use cases were defined, from which it can be concluded that ROM enables the identification of optimal surface texture parameters that were not available for experiments, obtaining friction reductions from 63% to 81%, which are significantly higher than the experimentally tested surface textures for the same operating conditions. In addition, the value of ROM was further highlighted, as it is also able to freely interpolate between tested operating conditions to determine optimal textures for each operating condition within the range considered, resulting in a predicted friction reduction of 79%.

Moreover, ROM applicability has been extended further, showing that the method can be also used for statistical analysis, to evaluate the impact of manufacturing uncertainties, observed on surface texture nominal values, on friction measurements. Thus, ROM is not only an extremely powerful technique for scientific users to compute the friction reduction

of surface textured components but also for industrial manufacturers of rubber components, to design rubber surfaces and evaluate the impact of manufacturing deviations on dynamic friction.

**Author Contributions:** Conceptualization, B.H.-G., M.B. and V.Z.; methodology, B.H.-G. and V.Z.; software, V.Z.; validation, B.H.-G., J.R.V., L.A.G., M.B., M.W. and V.Z.; formal analysis, M.B. and V.Z.; investigation, M.B. and V.Z.; resources, I.V., L.A.G., M.W. and S.I.; data curation, M.B. and V.Z.; writing—original draft preparation, M.B. and V.Z.; writing—review and editing, B.H.-G., J.R.V., L.A.G., M.B., M.W., S.I. and V.Z.; visualization, B.H.-G., J.R.V., L.A.G., M.B., M.W., S.I. and V.Z.; supervision, L.A.G., M.W. and S.I.; project administration, B.H.-G., J.R.V. and L.A.G.; funding acquisition, J.R.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work has been funded by the European Union's research program Horizon2020, under grant agreement No. 768705.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Publicly available datasets were analysed in this study. This data can be found here: http://devex.ita.es/mouldtex/optimizer/Data.zip (accessed on 22 March 2021).

**Acknowledgments:** We would like to thank ORP Stampi srl and SKM Aeronautics Ltd for providing the rubber specimens and ML Engraving srl for the surface texturing. We would also like to thank Carmen Alfaro, Rafael Rodríguez, and Susana Calvo for useful discussions.

**Conflicts of Interest:** The authors declare no conflicts of interest.
