24th International Colloquium Tribology - January 2024 145 Static and Dynamic Friction of Elastomers in Dry Conditions Simulating Commercial Materials and Products Dr.-Ing. Fabian Kaiser 1* , Dr.-Ing. Daniele Savio 1 , Dr.-Ing. Felix Meier 2 , Prof. Michele Scaraggi 3 1 Freudenberg Technology Innovation SE & Co. KG, Tribology, Weinheim, Germany 2 EagleBurgmann Germany GmbH & Co. KG, Research & Development, Wolfratshausen, Germany 3 Istituto Italiano di Technologia, Center for Biomolecular Nanotechnologies, Arnesano (Lecce), Italy * fabian.kaiser@freudenberg.com 1. Introduction Understanding the tribological behavior of elastomers in dry conditions is essential not only for tires but also for sealing applications. One example are the secondary seals in mechanical seals for gases, where rubber O-rings are often used. To ensure the stable function of the whole system, the auxiliary sealing elements need to have smooth and predictable friction properties. 2. Current State of Research In the last decades, Persson, Scaraggi and co-authors have developed a comprehensive theory for rubber contact mechanics [1], adhesion [2], static leakage and dry [3] and lubricated friction [4]. This theory has been thoroughly tested and validated in the literature, e.g., during the “Contact Mechanics Challenge” [5]. 3. Theory According to Tiwari et al. [3], rubber friction without lubricant is due to the viscoelastic losses F visc in the bulk elastomer, and the contribution of the local shear stresses τ f acting in the real contact area A con of the sliding surfaces. The friction force thus is F f = F visc + τ f A con A con is calculated using contact mechanics [1]. The main contributions to τ f are [3]: a. Adhesive bonding-stretching-debonding of rubber molecules or patches at the sliding interface. b. Opening crack propagation at the exit of the contact patches [7]. c. Energy dissipation in wear processes: Hard fillers in the rubber scratching the counter surface or being torn out of the rubber matrix. d. Shearing of thin (nm) transfer film, occurring at temperatures below glass transition [3]. In the present work, the dynamic dry friction model from [3] was implemented with two main modifications: 1. In our experiments with rubber sliding against steel, a transfer film can be observed under all conditions: the corresponding contribution is thus applied at all temperatures. 2. The shear stress τ f for the bonding-stretching-debonding contribution is estimated from the material properties of each elastomer. Furthermore, the model was extended to static friction based on the elastomer relaxation and subsequent increase in contact area with standstill times. The shear stress contribution τ f in the contact spots was described based on the bond-population model of Juvekar et al. [6]. This allows to estimate the lifetime of elastomer-metal bonds during the initial surface motion, thus relating the break-loose friction stresses to the speed at the onset of sliding. 4. Experiments and Validation Validation experiments were performed in a reciprocating tribometer over a wide range of temperatures (-40 - 100-°C), sliding speeds (1 - 300-mm/ s) and waiting times (1 - 5,000-s). The counterface was made of hardened steel ground to a surface roughness of Ra-0.3-µm. The elastomer sample was cut from a 2-mm thick test sheet and installed in a pin to form a curved surface with a radius of approximately 22-mm. The results for many different elastomers are in line with the expected behavior: The general shape of the dynamic friction curves in [3] is reproduced well and the static friction increases with time and break-loose speed. The comparison between experiment and simulation shows a very good agreement: For the tested fully formulated materials (FKM, EPDM and NBR) and under all experimental conditions, the dynamic and static friction can be predicted with an average deviation of only 10% using our parametrization for τ f . Figure 1: Comparison of calculated and measured friction for a 90 ShA FKM material 146 24th International Colloquium Tribology - January 2024 Static and Dynamic Friction of Elastomers in Dry Conditions The analysis of the friction simulation shows that, for the given setup, the contribution from crack propagation is negligibly small and the viscoelastic friction contributes only up to 15% to the total friction. This is considerably less compared to [3] and can be attributed to our smooth steel surface, which significantly lowers the amplitude of oscillations and viscous damping inside the material compared to the road surface used in [3]. Hence, the main contributions to the friction are the shearing of the transfer film and the adhesive bonding-stretching-debonding. Figure 2: Static friction at two different break-loose speeds vs. standstill time 5. Application In mechanical seals, secondary seals (e.g., O-rings) are required to seal alternate leakage paths. To ensure that the main seal rings are exactly parallel, the secondary seals are usually designed to slide some millimeters depending on the conditions (temperature, pressure, etc.). In combination with large standstill times, that lead to increased contact area and breakaway forces, the O-ring may not be able to slide leading to increased leakage and even failure of the whole system. The model was used to explore the relationships between loading conditions, interfacial and material properties and static friction depending on standstill times for a given secondary seal. This allowed to optimize its friction behavior and ultimately improve the function and reliability of the product. 6. Conclusion A comprehensive dry friction model for elastomers was developed and validated to be used for a broad range of applications. No model of similar predictive capabilities is known to the authors. Furthermore, the dry friction model might also be highly relevant for lubricated cases: due to local dewetting some contact patches can slide in dry conditions, even if plenty of liquid is available near the contact zone. References [1] Yang, C., Persson, B.N.J., “Contact mechanics: contact area and interfacial separation from small contact to full contact”, J. Phys.: Condens. Mat-ter, 2008 (20). [2] Persson, B. N. J., Scaraggi, M., “Theory of Adhesion: Role of Surface Roughness”, The Journal of Chemical Physics 141, 124701 (2014) [3] Tiwari, A. et al., “Rubber contact mechanics: adhesion, friction and leakage of seals”, Soft Matter, 2017,13, 9103-9121 [4] Persson, B. N. J., Scaraggi, M., “Lubricated sliding dynamics: Flow factors and Stribeck curve”, Eur. Phys. J. E (2011) 34: 113 [5] Müser, M. H. et al., “Meeting the Contact-Mechanics Challenge”, Tribology Letters, 2017. [6] Juvekar, V. A.; Singh, A. K., “Rate and aging time dependent static friction of a soft and hard solid interface”, arXiv 2016, arXiv: 1602.00973. [7] Persson, B. N. J., “Crack propagation in finite-sized viscoelastic solids with application to adhesion”, 2017 EPL 119 18002.