A new paradigm in discovering nonlinear governing equations from the time evolution of tribological phenomena

Tribology has a profound impact on a broad range of engineering areas and daily life. As the nature of tribological interactions is very complex, conventional theoretical and computational approaches are far from being holistic and central in tribology science. This project, therefore, aims at establishing the foundations for a new paradigm in modeling and computation of complex tribological problems. Sparse regression methods are employed to derive governing equations that accurately represent the time evolution of tribological phenomena from given spatiotemporal datasets. Several tribology problems, e.g. dry contact, hydrodynamic lubrication, and elastohydrodynamic lubrication are numerically solved using conventional methods. Thereafter, the acquired time-series datasets will be used to test the correctness of the methodologies developed in this study. Optical fiber sensors are embedded into the metallic and polymeric articulating bodies to be tested by means of a tribological test-rig to measure and collect the internal states of the dynamic system in both space and time. Using the proposed model-discovery techniques, parsimonious models governing the tribological phenomena will be discovered from measurement data. As the resulting models have the capability of interpretability and generalizability, the specific objective of the present study is to infer the Multiphysics of tribology phenomena, i.e. coupled mechanical, metallurgical, thermal and others. Several sizes of bearing components, surface roughness, lubricants, loadings and motion, and material properties will be considered to better understand their contribution to the obtained coefficients appearing in discovered equations. The discovered tribology models are also validated based on not only classical tribology problems but also conservation laws and thermodynamic energy principles.