A NURBS-Based Model for Elastohydrodynamically Lubricated Contacts

In the field of tribology, a diverse spectrum of applications, ranging from fundamental scientific research to practical industrial requirements (e.g. journal bearings and wet grinding processes), necessitates comprehensive and robust simulation tools to describe lubricated contacts between solid bodies. This thesis delves into a specific regime of lubricated contacts, namely elastohydrodynamic lubrication (EHL), characterized by minimal solid contacts but significant elastic solid deformations induced by fluid stresses. It represents a complex multi-physical process that encompasses nonlinear deformations, fluid dynamics, and their interactions. The presence of cavitation bubbles within the lubricant flow introduces further complexity to the numerical modeling of the EHL contact, arising from the inherent nonlinearity and discontinuities of the involved physical fields. In this thesis, the applicability of isogeometric analysis (IGA) based on non-uniform rational B-splines (NURBS) for the modeling of EHL contacts is explored. As an advanced alternative to the conventional finite element analysis (FEA) framework, IGA employs NURBS as both geometrical design tools and basis functions for analysis. This approach eliminates the need for an additional meshing process and takes full advantage of NURBS's superior features (such as variation diminishing properties) for physical analysis. Instead of employing the Navier-Stokes equations in typical CFD models, this work utilizes the Reynolds equation, a simplified alternative, to characterize the cavitation flow in the narrow gap between contact surfaces considering the negligible flow in the gap height direction. A novel cavitation algorithm is introduced here to ensure mass conservation of the two-phase flow (lubricants and cavitation bubbles). This algorithm converts the inequality complementarity conditions between fluid pressure and cavitation volume fraction into a weak formulation using the augmented Lagrangian method, enabling efficient solution processes. The primary contribution of this work, however, lies in the fully consistent linearization of all weak formulations pertinent to EHL contacts and their discretizations employing NURBS basis functions. In particular, the mortar method is utilized to discretize the fluid-structure interaction interface, allowing for the non-matching NURBS meshes across solid and fluid domains. Consequently, a comprehensive model is developed within the IGA framework, capable of simulating nonlinear deformations, fluid stresses, and the transient evolution of cavitation volumetric distributions in EHL contacts. The proposed model is examined through several benchmark tests in this work. By comparing the results with those obtained from the commercial software ANSYS or other available models, the superiority of the new EHL model is demonstrated in terms of accuracy, robustness, and low computational costs. Furthermore, this model is applied to investigate the relationship between the coefficient of friction (COF) and the lubricant quantity in EHL contacts involving rough surfaces. The results reveal a significant impact of lubricant quantity on the COF, especially at low lubricant volumes, where the addition of a small amount of lubricant can drastically reduce the COF. This observation is in line with the experimental studies carried out by our research group. These outcomes offer the promising prospect that the numerical model developed in this thesis is not only beneficial for investigating frictional behaviors within the EHL regime but also serves as the groundwork for a general analytical tool in the realm of lubricated contacts. It is envisioned to compute the entire transition from boundary lubrication to hydrodynamic lubrication regimes, offering a robust framework for understanding and predicting the complex multi-physical interactions that influence lubrication performance.