# Numerical simulation of elastohydrodynamic and hydrodynamic lubrication using the Navier-Stokes and Reynolds equations

Sammanfattning: The work presented in this thesis concerns computer simulations of the lubrication process. The main subject of interest is elastohydrodynamic lubrication (EHL) and, to some extent, hydrodynamic lubrication (HD). The thesis comprises an introductory section and three papers; referred to as A, B and C. Simulation of EHL is an inter-disciplinary task, incorporating the fields of fluid mechanics, solid mechanics, thermodynamics and rheology. In almost all numerical simulations of lubrication performed today, the hydrodynamics are modelled using the Reynolds equation. This equation is derived from the equations of momentum and continuity and using the thin film approximation. However, the assumptions made when deriving this equation limits the size of the computational/spatial domain and the equation cannot predict pressure variations across the lubricating oil film. The subject of papers A and B are numerical simulations using the full equations of momentum and continuity, (Paper B), and the equation of energy (Paper A). The main aim of the work was to investigate the possibilities of carrying out numerical simulations based on the above equations. The rheology was assumed to be Newtonian; the equations are then commonly referred to as the Navier-Stokes equations (N-S). The second aim of the work was to investigate the possibilities of using a commercial software, CFX 4.3 [1], to carry out the numerical simulations. The results in Paper A show that it is possible to simulate thermal EHL line contacts up to pressures of approximately 1 GPa. The limitations of the approach are due to a singularity that can occur in the equation of momentum when a critical shear stress is reached. With a more complete rheological model (non-Newtonian rheology) it should be possible to perform simulations at even higher contact pressures. Paper B presents the results of isothermal simulations comparing the N-S and Reynolds equation approaches. The result show that there may be some discrepancies between the two approaches; although only small discrepancies have been observed in the smooth line contact simulations made. The characteristics of the EHL-contact with a wide range of scales and large gradients in pressure, viscosity and temperature make developing accurate numerical simulations to a difficult task. The computational cost is high due to the small under-relaxations factors that must be used in order to obtain converged numerical solutions. The work to date has shown that is possible to use the extended approach in conjunction with a commercial software, CFX 4.3 [1]. This approach makes it possible to extend the computational domain in future in EHL-simulations, where the Reynolds approach is not valid. Paper C presents the results of simulations of a lubricated pivoted thrust bearing. The objective of this study was to verify a thermo-hydrodynamic (THD) model for this type of bearing. The model developed handles three-dimensional temperature distribution in the oil film and pad, as well as two-dimensional temperature variation in the runner. The viscosity and density are treated as functions of both temperature and pressure. Experiments have been performed in a test rig consisting of two identical equalising pivoted pad thrust bearings. Experimentally measured power loss, runner temperature and pressure profiles as a function of load and rotational speed were compared with the theoretical investigations. The results showed fairly good agreement when the oil inlet temperature and heat transfer coefficients were modified in order to obtain the same runner temperature in both theory and experiment.

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