Modelling of mixed lubrication using the heterogenous multiscale methods

Surface topography is inherently multiscale. Macroscale topography is covered in microscale surface roughness, which has a substantial, quantifiable impact on overall performance. However, this difference in scales raises modelling challenges. Contemporary mixed lubrication research is dominated by two methods: the accurate but computationally expensive deterministic approach and the more efficient flow factors method that cannot predict local parameters (pressure, contact, etc.) accurately. The principal objective of this work is to develop a framework that will both predict local scale variables accurately and solve in a feasible amount of time. Through the use of the Heterogeneous Multiscale Methods (HMM) the macroscale and microscale surface features can be modelled using separate domains, whilst maintaining the coupling between the scales. This homogenisation approach allows for both accurate predictions of local scale phenomena and computational efficiency. The HMM have been extensively validated for hydrodynamic/elastohydrodynamic lubrication. Within this work, the HMM are extended to model mixed lubrication and are validated against existing models and experimental data. To build further confidence, plots of simulated data are presented for various conditions on the Stribeck curve. Both idealised and measured microscale topographies are applied and their impact quantified. The interaction between asperities in contact and lubricant flow has been fully resolved. This framework represents the first time that this microscale behaviour has informed the solution of a computationally efficient macroscale operating within the mixed lubrication regime. Average solution time is 8 h on a local PC with 16GB of RAM.