KARLSRUHER INSTITUT FÜR TECHNOLOGIE (KIT) SCHRIFTENREIHE DES INSTITUTS FÜR TECHNISCHE MECHANIK BAND 27 DANIEL MAIER On the Use of Model Order Reduction Techniques for the Elastohydrodynamic Contact Problem On the Use of Model Order Reduction Techniques for the Elastohydrodynamic Contact Problem Contact Elastohydrodynamic the for On Model Use the of Order Reduction Techniques Daniel Maier Daniel Maier On the Use of Model Order Reduction Techniques for the Elastohydrodynamic Contact Problem Karlsruher Institut für Technologie Schriftenreihe des Instituts für Technische Mechanik Band 27 Eine Übersicht aller bisher in dieser Schriftenreihe erschienenen Bände finden Sie am Ende des Buchs. On the Use of Model Order Reduction Techniques for the Elastohydrodynamic Contact Problem by Daniel Maier Dissertation, Karlsruher Institut für Technologie (KIT) Fakultät für Maschinenbau Tag der mündlichen Prüfung: 6. Februar 2015 Impressum Karlsruher Institut für Technologie (KIT) KIT Scientific Publishing Straße am Forum 2 D-76131 Karlsruhe KIT Scientific Publishing is a registered trademark of Karlsruhe Institute of Technology. Reprint using the book cover is not allowed. www.ksp.kit.edu This document – excluding the cover – is licensed under the Creative Commons Attribution-Share Alike 3.0 DE License (CC BY-SA 3.0 DE): http://creativecommons.org/licenses/by-sa/3.0/de/ The cover page is licensed under the Creative Commons Attribution-No Derivatives 3.0 DE License (CC BY-ND 3.0 DE): http://creativecommons.org/licenses/by-nd/3.0/de/ Print on Demand 2015 ISSN 1614-3914 ISBN 978-3-7315-0369-9 DOI 10.5445/KSP/1000046871 On the Use of Model Order Reduction Techniques for the Elastohydrodynamic Contact Problem Zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften der Fakult¨at fur¨ Maschinenbau Karlsruher Institut fur¨ Technologie (KIT) genehmigte Dissertation von Dipl.-Ing. Daniel Maier aus Karlsruhe Tag der mundlichen¨ Prufung:¨ 6. Februar 2015 Hauptreferent: Prof. Dr.-Ing. Wolfgang Seemann Korreferent: Prof. Francisco Chinesta N° d'ordre 2015-ISAL-0010 2015 Th`ese On the Use of Model Order Reduction Techniques for the Elastohydrodynamic Contact Problem Pr´esent´ee devant L'Institut National des Sciences Appliqu´eesde Lyon et le Karlsruher Institut f¨urTechnologie (KIT) Pour obtenir Le grade de Docteur Formation doctorale : M´ecanique Ecole doctorale : M´ecanique,Energ´etique,G´eniecivil, Acoustique (MEGA) par Daniel MAIER (Ing´enieur) Soutenance le 6 fevrier 2015 devant la commission d'examen Jury Rapporteur F. Chinesta Professeur (Ecole Centrale de Nantes) Examinateur M. Gabi Professeur (Karlsruher Institut f¨urTechnologie) Directeur P. Vergne Directeur de recherche (CNRS - INSA de Lyon) Rapporteur W. Seemann Professeur (Karlsruher Institut f¨ur Technologie) Examinateur H. Hetzler Professeur (Universit¨atKassel) Examinateur D. Dureisseix Professeur (CNRS - INSA de Lyon) Examinateur N. Fillot Ma^ıtrede Conf´erences,HdR (INSA de Lyon) Laboratoire de recherche : Laboratoire de M´ecaniquedes Contacts et des Structures (LaMCoS, INSA de Lyon, CNRS UMR5259) INSA Direction de la Recherche - Ecoles Doctorales – Quinquennal 2011-2015 SIGLE ECOLE DOCTORALE NOM ET COORDONNEES DU RESPONSABLE CHIMIE DE LYON M. Jean Marc LANCELIN CHIMIE http://www.edchimie-lyon.fr Université de Lyon – Collège Doctoral Sec : Renée EL MELHEM Bât ESCPE e Bat Blaise Pascal 3 etage 43 bd du 11 novembre 1918 04 72 43 80 46 69622 VILLEURBANNE Cedex Insa : R. GOURDON Tél : 04.72.43 13 95 [email protected] [email protected] ELECTRONIQUE, M. Gérard SCORLETTI E.E.A. ELECTROTECHNIQUE, AUTOMATIQUE Ecole Centrale de Lyon http://edeea.ec-lyon.fr 36 avenue Guy de Collongue 69134 ECULLY Sec : M.C. HAVGOUDOUKIAN Tél : 04.72.18 60.97 Fax : 04 78 43 37 17 [email protected] [email protected] EVOLUTION, ECOSYSTEME, Mme Gudrun BORNETTE E2M2 MICROBIOLOGIE, MODELISATION CNRS UMR 5023 LEHNA http://e2m2.universite-lyon.fr Université Claude Bernard Lyon 1 Bât Forel Sec : Safia AIT CHALAL 43 bd du 11 novembre 1918 Bat Atrium- UCB Lyon 1 69622 VILLEURBANNE Cédex 04.72.44.83.62 Tél : 06.07.53.89.13 Insa : S. REVERCHON e2m2@ univ-lyon1.fr [email protected] INTERDISCIPLINAIRE SCIENCES- Mme Emmanuelle CANET-SOULAS EDISS SANTE INSERM U1060, CarMeN lab, Univ. Lyon 1 http://www.ediss-lyon.fr Bâtiment IMBL Sec : Safia AIT CHALAL 11 avenue Jean Capelle INSA de Lyon Bat Atrium – UCB Lyon 1 696621 Villeurbanne 04 72 44 83 62 Tél : 04.72.68.49.09 Fax :04 72 68 49 16 Insa : [email protected] [email protected] INFORMATIQUE ET Mme Sylvie CALABRETTO INFOMATHS MATHEMATIQUES LIRIS – INSA de Lyon http://infomaths.univ-lyon1.fr Bat Blaise Pascal 7 avenue Jean Capelle Sec :Renée EL MELHEM 69622 VILLEURBANNE Cedex Bat Blaise Pascal Tél : 04.72. 43. 80. 46 Fax 04 72 43 16 87 e 3 etage [email protected] [email protected] MATERIAUX DE LYON M. Jean-Yves BUFFIERE http://ed34.universite-lyon.fr INSA de Lyon Matériaux MATEIS Sec : M. LABOUNE Bâtiment Saint Exupéry PM : 71.70 –Fax : 87.12 7 avenue Jean Capelle Bat. Saint Exupéry 69621 VILLEURBANNE Cedex [email protected] Tél : 04.72.43 71.70 Fax 04 72 43 85 28 [email protected] MECANIQUE, ENERGETIQUE, GENIE M. Philippe BOISSE MEGA CIVIL, ACOUSTIQUE INSA de Lyon http://edmega.universite-lyon.fr/ Laboratoire LAMCOS Bâtiment Jacquard Sec : M. LABOUNE 25 bis avenue Jean Capelle PM : 71.70 –Fax : 87.12 69621 VILLEURBANNE Cedex Bat. Saint Exupéry Tél : 04.72 .43.71.70 Fax : 04 72 43 72 37 [email protected] [email protected] ScSo* Mme Isabelle VON BUELTZINGLOEWEN ScSo http://recherche.univ-lyon2.fr/scso/ Université Lyon 2 86 rue Pasteur Sec : Viviane POLSINELLI 69365 LYON Cedex 07 Brigitte DUBOIS Tél : 04.78.77.23.86 Fax : 04.37.28.04.48 Insa : J.Y. TOUSSAINT [email protected] [email protected] *ScSo : Histoire, Géographie, Aménagement, Urbanisme, Archéologie, Science politique, Sociologie, Anthropologie Acknowledgments The present work was generated during my stay at the department for contact dynamics and tribology at the corporate research center of the Robert Bosch GmbH in Gerlingen-Schillerh¨ohe. First of all, I would like to express my kind gratitude to Prof. Dr.-Ing. Wolfgang Seemann for the adoption of the doctoral advisory, the numerous helpful advices and last but not least for inspiring me with the subject of engineering dynamics through various lectures. Furthermore, I want to thank Prof. Francisco Chinesta for taking over the position as a second reviewer. Outstanding thanks go to Pr. David Dureisseix, Dr. Philippe Vergne and Dr. Nicolas Fillot for the supervision of this work, the very helpful advices, fruitful discussions and for their great hospitality. They lead me to a deeper understanding in the area of EHL and its computation. I also wish to thank Prof. Dr.-Ing. Harmut Hetzler for his excellent supervision. His great comments and suggestions have always pushed my understanding to a higher level. Moreover, I stongly appreciate his trust and encouragement whilst the study and beyond that. Furthermore, I deeply want to thank Dr. rer. nat. Corinna Hager for the excellent supervision of my work at Bosch. Her advices in general and especially on the subject of mathematics were of immense value. Despite numerous other duties and responsibilities, she always found some time for answering questions and giving advice. I would like to thank Prof. Dr.-Ing. habil. Alexander Fidlin for the profound ques- tions and remarks. Special thanks go to Dr.-Ing. Rudy Eid. His expertise in the field of model order reduction helped me to keep the right direction. I am grateful to the whole working group at Bosch for the innumerable scientific and non-scienctific conversations and for their support in general. In particular, I wish to thank Dipl.-Ing. Jan Henrik Schmidt for the various interesting and helpful discussions. Finally, I want to thank my parents without their absolute support I would have never come so far. Abstract In today's product development process, fast and exact simulation models of com- plex physical problems gain in significance. The same holds for the elastohydro- dynamic (EHD) contact problem. Thus, the objective of this work is to generate a compact model for the EHD contact problem by the application of model order re- duction. Thereto, the EHD contact problem, consisting of the nonlinear Reynolds equation, the linear elasticity equation and the load balance, is solved as a mono- lithic system of equations using Newton's method. The reduction takes place by projection onto a low-dimensional subspace, which is based on solutions of the full system. Moreover, a so-called system approximation is executed at which the reduced system matrices are substituted by less complex surrogates. For the sta- tionary EHD contact problem, an algorithm for the automated generation of the compact model is presented. This algorithm provides fast and numerically stable reduced systems on a given parameter range. Additionally, the reduced Newton method is extended to the consideration of Non-Newtonian fluids whereat highly accurate results are obtained requiring a very low computational time. Further- more, a new formulation for the transient EHD contact problem is introduced, at which the computational area is adapted to the current contact size. This kind of morphing enables efficient reduced models in particular for excitations of large amplitude. Besides of the reduced Newton-method with system approximation, the method Trajectory Piecewise Linear (TPWL) is applied to the transient EHD contact problem. Here, further speed-up potential arises. Despite a distinctly lower computational time, the reduced model is in very good accordance with the full system. Kurzfassung Im heutigen Produktentwicklungsprozess nehmen schnelle und exakte Simula- tionsmodelle komplexer physikalischer Probleme eine zunehmend wichtige Rol- le ein. Dies gilt auch fur¨ das elastohydrodynamische (EHD) Kontaktproblem.