Adaptive Finite Element Methods for the Reynolds Thin Film Model with Cavitation

Abstract: The main purpose of this thesis is to use modern goal-oriented adaptivè finite element techniques in order to improve the numerical simúlatiôn of tribology. Two novei adap tive finite element methods for the Re¡'nolds thin film model including cavitation a,re presented and their different strategies are compared. The algorithms are inspired by an analogy with the obstacle problem and the cavitation problem that we consider is written as a variational inequality considering in the formulation the fact that the lubricant can not stand negative stresses induced by sub-atmospheric pressure. A posteri, ori, error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied. The cavitation problem and calculations is introduced and put into historical and modern perspective. Modern thoughts and techniques around the oil-pocket idea in sheet metal forming are presented. The influence of oil pockets on the contact regime is assessed, and in pa,rticular the likely effect of oil-pocket-induced cavitation in order to produce lift, is discussed. The ultimate goal with the numerical simulation is to be able to optimize the surface structure so as to take advantage of cavitation effects in the lubricant.