In this thesis, a full-system finite element approach to elastohydrodynamic (EHD) lubrication problems is introduced. EHD lubrication is a full-film regime where the pressure generated in the conjunction is high enough to induce a significant elastic deformation of the contacting bodies. Hence, it involves a strong coupling between hydrodynamic and elastic effects. The non-linear system formed by the Reynolds', linear elasticity and load balance equations is solved using a fully-coupled Newton-Raphson procedure. This approach provides outstanding convergence rates when compared with the semi-system one. A penalty method is used to handle the cavitation problem that arises at the outlet of the contact. Appropriate stabilized formulations are used to extend the solution to the case of highly loaded contacts. The resolution process is then extended to account for non-Newtonian behaviour of the lubricant and for thermal effects. The developed model is used to study the behaviour of EHD contacts lubricated with Ultra-Low-Viscosity Fluids. The use of such fluids as lubricants provides two main advantages: first, the frictional energy dissipation in the contact is reduced and second, in machines that work with a low viscosity operational fluid and a lubricant, the former can be used to fulfil both functions and thus the design and maintenance of such machines would become easier and their performance would be improved.

Covers the latest developments in modeling elastohydrodynamic lubrication (EHL) problems using the finite element method (FEM) This comprehensive guide introduces readers to a powerful technology being used today in the modeling of elastohydrodynamic lubrication (EHL) problems. It provides a general framework based on the finite element method (FEM) for dealing with multi-physical problems of complex nature (such as the EHL problem) and is accompanied by a website hosting a user-friendly FEM software for the treatment of EHL problems, based on the methodology described in the book. Finite Element Modeling of Elastohydrodynamic Lubrication Problems begins with an introduction to both the EHL and FEM fields. It then covers Standard FEM modeling of EHL problems, before going over more advanced techniques that employ model order reduction to allow significant savings in computational overhead. Finally, the book looks at applications that show how the developed modeling framework could be used to accurately predict the performance of EHL contacts in terms of lubricant film thickness, pressure build-up and friction coefficients under different configurations. Finite Element Modeling of Elastohydrodynamic Lubrication Problems offers in-depth chapter coverage of Elastohydrodynamic Lubrication and its FEM Modeling, under Isothermal Newtonian and Generalized-Newtonian conditions with the inclusion of Thermal Effects; Standard FEM Modeling; Advanced FEM Modeling, including Model Order Reduction techniques; and Applications, including Pressure, Film Thickness and Friction Predictions, and Coated EHL. This book: Comprehensively covers the latest technology in modeling EHL problems Focuses on the FEM modeling of EHL problems Incorporates advanced techniques based on model order reduction Covers applications of the method to complex EHL problems Accompanied by a website hosting a user-friendly FEM-based EHL software Finite Element Modeling of Elastohydrodynamic Lubrication Problems is an ideal book for researchers and graduate students in the field of Tribology.

This thesis is concerned with the efficient numerical solution of problems of elastohydrodynamic lubrication (EHL). Our approach is to consider fully-coupled models in which the governing equations for the lubricating film, the elastic deformation and the force balance are each discretized and solved as a single monolithic nonlinear system of algebraic equations. The main contributions of this work are to propose, implement and analyse a novel, optimal, preconditioner for the Newton linearization of this algebraic system, and to assess the development of efficient finite element meshes through both manual tuning and the use of adaptive mesh refinement based upon a posteriori error estimation and control. Throughout this work, we employ first order finite element discretizations for both the Reynolds equation (for the lubricant) and for the linear elasticity model on a finite domain. The resulting nonlinear algebraic equations are then solved using a quasi-Newton algorithm. For each linear solve a Krylov subspace method is used and a new blockwise preconditioner is presented which is designed to exploit the specific structure that is present in this class of problem. This preconditioner combines the use of multigrid preconditioning for the elasticity block and a separate, efficient, approximation to precondition the Reynolds block. The solver developed in this work can be distinguished into two variants based upon the use of algebraic and geometric multigrid preconditioning of the elasticity block. Numerical results are presented both for line and point contact problems to validate the implementations and to allow a comparison of the performance and efficiency of the proposed solution strategies compared to the use of a state-of-the-art sparse direct solver at each Newton step. These results demonstrate that the preconditioned iterative approach is both computationally and memory superior to the sparse direct solver. Most importantly, both the computational and memory costs are seen to grow linearly with the number of unknowns. A locally adaptive solution scheme is also developed for fully-coupled EHL point contact problems. This automates the refinement process to the regions of the domain which exhibit large error in their solutions. Numerical results are presented which demonstrate the performance and effectiveness of the proposed procedure.

Covers the latest developments in modeling elastohydrodynamic lubrication (EHL) problems using the finite element method (FEM) This comprehensive guide introduces readers to a powerful technology being used today in the modeling of elastohydrodynamic lubrication (EHL) problems. It provides a general framework based on the finite element method (FEM) for dealing with multi-physical problems of complex nature (such as the EHL problem) and is accompanied by a website hosting a user-friendly FEM software for the treatment of EHL problems, based on the methodology described in the book. Finite Element Modeling of Elastohydrodynamic Lubrication Problems begins with an introduction to both the EHL and FEM fields. It then covers Standard FEM modeling of EHL problems, before going over more advanced techniques that employ model order reduction to allow significant savings in computational overhead. Finally, the book looks at applications that show how the developed modeling framework could be used to accurately predict the performance of EHL contacts in terms of lubricant film thickness, pressure build-up and friction coefficients under different configurations. Finite Element Modeling of Elastohydrodynamic Lubrication Problems offers in-depth chapter coverage of Elastohydrodynamic Lubrication and its FEM Modeling, under Isothermal Newtonian and Generalized-Newtonian conditions with the inclusion of Thermal Effects; Standard FEM Modeling; Advanced FEM Modeling, including Model Order Reduction techniques; and Applications, including Pressure, Film Thickness and Friction Predictions, and Coated EHL. This book: Comprehensively covers the latest technology in modeling EHL problems Focuses on the FEM modeling of EHL problems Incorporates advanced techniques based on model order reduction Covers applications of the method to complex EHL problems Accompanied by a website hosting a user-friendly FEM-based EHL software Finite Element Modeling of Elastohydrodynamic Lubrication Problems is an ideal book for researchers and graduate students in the field of Tribology.