24th International Colloquium Tribology - January 2024 149 EHL Simulation for the Design Workflow of Contacts with Limited Lubricant Availability Pastor Cesar 1* , Solovyev Sergey 2 1 Robert Bosch GmbH Corporate Research, Fluid Dynamics and Reliability, Renningen, Germany 2 Robert Bosch GmbH Corporate Research, Applied Mathematics, Renningen, Germany * Corresponding author: cesar.pastor@de.bosch.com 1. Introduction The importance of a reliable component design process for the industry is undeniable and at the same time a great challenge. For decades, limited computational resources forced engineers to develop costly experimental infrastructure to evaluate and design contacts. In the last years, the increasing computational capabilities opened new scenarios in which costly experiments can not only be simulated but also a great number of operating parameters, manufacturing tolerances, materials etc. can be numerically replicated before even having physical samples or prototypes. This creates great possibilities for the optimization and predictability of contacts in all kinds of situations, which offers a great potential for faster development cycles but also requires time-efficient and robust simulation software. 2. Grease lubrication Grease lubricated contacts are very well established in a wide range of industrial applications. The end-user benefits from one-in-a-lifetime greased systems because of their needless maintenance, making them suitable to be positioned in the most inaccessible machine parts. However, even considering the highest quality standards, a failure cannot always be avoided. The contact can run into starved to boundary lubricating conditions leading to a system failure. Moreover, the lifetime of line and elliptical contact surfaces is reduced due to the wiping effect on the lubricant displacing it away from the inlet region (figure 1). Therefore, a macroscopic system consideration is needed since (1) the lubricant film thickness depends on the inlet conditions and (2) the lubricant presence close to the inlet area depends on its availability. Figure 1. Initial grease distribution in gearbox (left). Grease distribution (wiping effect) after short operation without replenishment measures (right). 3. Component design 3.1 Methodological approach In this study a multiscale approach for systems with risk of limited lubricant availability, specifically greased contacts, is proposed. Lubricant availability affects the lubricant presence, but both phenomena have different causes and effects. Furthermore, starved conditions don’t necessarily mean a risk of failure but just a reduction of the inlet and central film thickness. Therefore, a consideration of starvation and its relevance at different operation points is very valuable in early design phases. In [1] a gear-specific simulation toolchain was presented in which an in-house developed EHL software is used. Insights into the software can be found in [2], [3] and [4]. The differences between full flow and starved conditions have been numerically in CFD simulations [5], [6], experimentally demonstrated [7], [8] and integrated in the EHL simulations at Bosch Corporate Research. 3.2 Simulation challenges: convergence methods By these means, the effect of multiple contact design variables and operation conditions may be evaluated simulatively. The main challenge for numerically solving the Reynolds equation when coupled with a fluid model and the contact deformation is its convergence. The solution is achieved by coupling several non-linear equations, the resulting system being highly non-linear. These equations are individually iteratively solved through a “weak”-coupling. Since the equation system is non-linear, damping coefficients (relaxation factors) need to be considered in the solution strategy. For the selection of these coefficients a method based on Bayesian Optimization is proposed and successfully implemented. The Gaussian process associated to the BO algorithm minimizes a predefined objective function in a minimum number of iterations. For that purpose a suitable acquisition function considering exploitation and exploration margins is needed (figure 2). 150 24th International Colloquium Tribology - January 2024 EHL Simulation for the Design Workflow of Contacts with Limited Lubricant Availability Figure 2. An example of Bayesian optimization on a 1D design problem from [9]. 4. Results Using the described methodological approach and convergence methods, a tribological system can be designed attending to certain requirements as minimum permissible film gap or maximum permissible solid contact pressure or surface stress. Figure 3. Fluid level and saturation from the starvation calculation of a 100Cr6 ball vs. sapphire disc with a (a) 0.05mm³/ s, (b) 0.108 mm³/ s and (c) 0.208mm³/ s meniscus volume. Table 1: Evaluation of simulation results for a point contact with different starvation levels. Meniscus volume [mm³/ s] h min [nm] h 0 [μm] Max elastic deformation [μm] 0.05 82.97 86.58 1.93 0.108 86.53 86.86 1.84 0.208 270.9 355.0 1.89 The results show that, due to the different contact deformation at different starvation levels, there is not always a direct relationship between meniscus volume and deformation (see Table 1 and figures 3 and 4) Figure 4. Contact deformation of a 100Cr6 ball vs. sapphire disc for a 0.208mm³/ s meniscus volume. 5. Conclusion The presented results using the proposed multiscale design workflow, EHL simulations and Bayesian Optimization methods demonstrate the value of the approach and the significant advantages of numerical simulation in the design process. References [1] Uhlig M., Pastor C., Simulation Tool-Chain For Plastic Gear Design. In: International Conference on Gears 2019, VDI-Society for Product and Process Design, 2019, 1453-1459 [2] Solovyev S., Reibungs- und Temperaturberechnungen an Festkörper- und Mischreibungskontakten, PhD- Thesis, University of Magdeburg, 2006 [3] Redlich A.C. et al., A Deterministic EHL Model for Point Contacts in Mixed Lubrication Regime. In: 26th Leeds-Lyon Symposium on Tribology, Tribology Series 38. Amsterdam : Elsevier, 2000, 85-93 [4] Solovyev S. et al., Temperaturberechnung in konzentrierten Kontakten. In: Tribologie-Fachtagung GfT. Göttingen, 2004 [5] Cen H., Lugt P.M., Film thickness in a grease lubricated ball bearing. Tribology International, 2019 [6] Zhang S. et al., Prediction of film thickness in starved EHL point contacts using two-phase flow CFD model, Tribology International, 2023, 178 [7] Nogi T., Film thickness and rolling resistance in starved elastohydrodynamic lubrication of point contacts with reflow, Journal of Tribology, 2015, 137 [8] Kochi T. et al., Experimental Study on the Physics of Thick EHL Film Formation with Grease at Low Speeds, Tribology Letters, 2019, 67 [9] Brochu E. et al., A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning, arXiv: 1012.2599, 2010