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Tribology using homogenization
2009 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Most of physical and engineering problems are described by mathematical models that involves partial differential equations PDE's. Because of the structure of materials involved in this problems, some PDE's presents rapidly oscillating coeffcients that makes them not easy to solve even numerically. Homogenization a technique used to transform this type of problems in ano- ther problems easily solvable and that present a solution which is very close to solution from original problem. Since the fifties a very rapid progress in the development of numerical me- thods has taken place within the engineering sciences in cooperation with numerical analysts and mathematicians. In the light of this, homogeniza- tion theory provides a good example of modern mathematics development by mathematicians aware of recent numerical methods and with an interest in questions in fields where classical mathematical methods have not been successful in formulating problems in a form that suits existing numerical techniques. In this thesis we consider homogenization theory, and the way it can be applied to solve problems from Tribology. This Master thesis is composed by five chapters: in the first chapter we make an brief introduction of homogenization theory. The second chapter we motivate the Reynolds equations by using notions of fluid motion. In the chapter three we present the homogenization procedure for the case where the fluid is incomprehensible considering the presence and absence of surface roughness effect. Numerical methods to compare and show the behavior of our solutions and compare the solutions from real problem with the solu- tions from the homogenized problem are developed in chapter four. In the chapter five we motivate the expression which describe the friction force and we evaluate the effect of hydrodynamic pressure built from lubricant flowing between two thin surfaces into the friction force.

Place, publisher, year, edition, pages
Keyword [en]
Physics Chemistry Maths, Homogenization
Keyword [sv]
Fysik, Kemi, Matematik
URN: urn:nbn:se:ltu:diva-45278ISRN: LTU-PB-EX--09/027--SELocal ID: 2fe2096e-1442-4447-bc22-9d6b02efd9eaOAI: diva2:1018565
Subject / course
Student thesis, at least 30 credits
Educational program
Mathematics, master's level
Validerat; 20101217 (root)Available from: 2016-10-04 Created: 2016-10-04Bibliographically approved

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