Virtual Test Methods to Analyze Aircraft Structures with Vibration Control Systems Vom Promotionsausschuss der Technischen Universität Hamburg-Harburg zur Erlangung des akademischen Grades Doktor-Ingenieur (Dr.-Ing.) genehmigte Dissertation von Stefan Pleus aus Hamburg 2015
1. Gutachter: Prof. Dr.-Ing. Frank Thielecke Institut für Flugzeug-Systemtechnik Technische Universität Hamburg-Harburg 2. Gutachter: Prof. Dr.-Ing. Dieter Krause Institut für Produktentwicklung und Konstruktionstechnik Technische Universität Hamburg-Harburg Tag der mündlichen Prüfung: 02. Dezember 2015
Schriftenreihe Flugzeug-Systemtechnik Band 4/2015 Stefan Pleus Virtual Test Methods to Analyze Aircraft Structures with Vibration Control Systems Shaker Verlag Aachen 2015
Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. Zugl.: Hamburg-Harburg, Techn. Univ., Diss., 2015 Copyright Shaker Verlag 2015 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publishers. Printed in Germany. ISBN 978-3-8440-4184-2 ISSN 1861-5279 Shaker Verlag GmbH P.O. BOX 101818 D-52018 Aachen Phone: 0049/2407/9596-0 Telefax: 0049/2407/9596-9 Internet: www.shaker.de e-mail: info@shaker.de
Acknowledgments This thesis was performed during my time as scientific engineer at Hamburg University of Technology at the Institute of Aircraft Systems Engineering (Technische Universität Hamburg-Harburg, Institut für Flugzeug-Systemtechnik). First I would like to thank my thesis advisor Prof. Dr.-Ing. Frank Thielecke for his continual guidance, professional support and encouragement throughout the years. I will always remember the trustful working environment, the scientific freedom and the fruitful discussions, which certainly have been the basis for the successful completion of this thesis. I would further like to thank my co-advisor Prof. Dr.-Ing. Dieter Krause and Prof. Dr. Ralf God as the head of my examination board. The research project "Dynamic Barrel - Simulation and Testing" provided great contribution to this thesis. Based on intensive collaboration of university and industrial partners within this project, a unique testing and research platform was realized for developing innovative dynamic testing methods for aircraft structures and components. I am very thankful to Dr.-Ing. Ludger Merz for his professional support and his problem-solving way of thinking. Furthermore, I would like to thank everyone whom I had the chance to work with. Amongst others, I especially like to thank Dr.-Ing. Ulrich Meier-Noe, Prof. Dr.-Ing. Achim Merklinger, Christian Busch and Andreas Grimm. It is a special pleasure to thank the colleagues and friends I met throughout my time at the institute. The technical and scientific discussions with all colleagues and students and also the motivation and support in and out of the office contributed a lot to this work. I owe my deepest gratitude to my family for the continuous support and understanding over all the years. Especially the love, support and encouragement of my wife, Anja Pleus, gave me the supplemental energy and confidence to finish this thesis. iii
iv
Contents Nomenclature viii 1 Introduction 1 1.1 Aircraft Vibration Testing and Modeling... 3 1.1.1 Aircraft Vibration Testing... 4 1.1.2 Aircraft Structural Dynamic Models... 5 1.1.3 Dynamic Loads Component Testing... 7 1.2 Virtual Testing as Part of the Model-based Development... 10 1.2.1 Model-based Development Procedure... 10 1.2.2 Definition of Virtual Testing... 11 1.2.3 Virtual Testing of Vibration Control Systems...... 13 1.3 Objectives, Scope and Structure of this Thesis... 14 2 Simulation Techniques for Structural Dynamic Systems 19 2.1 Structural Dynamic Modeling... 19 2.1.1 Numerical Modal Analysis... 23 2.1.2 Modeling of Damping... 25 2.1.3 Frequency Response Analysis Methods... 30 2.1.4 Model Order Reduction Techniques... 31 2.2 Flexible Multi-Body Simulation... 34 2.2.1 Kinematics of Rigid and Flexible MBS Systems... 35 2.2.2 Dynamics of Flexible MBS Systems... 37 2.2.3 Numerical Methods for Flexible MBS... 39 2.3 Simulation Coupling Methods... 45 2.3.1 Function-Evaluation... 46 2.3.2 External Function Evaluation (XFE)... 48 2.3.3 Co-Simulation (CS)... 48 v
Contents 3 Vibration Control Systems 51 3.1 Classification of Vibration Control Systems... 51 3.1.1 Overview of Actuators and Semi-Active Devices... 54 3.2 The Linear Single-Degree-Of-Freedom (SDOF) System... 56 3.2.1 Vibration Isolation versus Damping... 60 3.2.2 Ideal Sky-Hook Damper... 61 3.2.3 Active and Semi-Active SDOF Systems... 62 3.3 FRFs for Nonlinear Systems... 67 3.3.1 The Swept-Sine Signal.... 68 3.3.2 Transformation to Frequency Domain... 71 3.4 Design and Modeling of Passive Shock-Mounts... 76 3.4.1 Properties of Elastomeric Shock-Mounts... 76 3.4.2 Nonlinear Dynamic Modeling of Shock-Mounts... 78 3.4.3 Experimental Identification of Shock-Mount Dynamics. 85 3.5 Semi-Active Vibration Control Systems... 91 3.5.1 Smart Fluid Dampers... 91 3.5.2 Modeling of Smart Fluid Dampers... 96 3.5.3 Control Strategies...102 3.5.4 Numerical Analysis of Semi-Active Damping Systems. 106 3.6 Intermediate Summary...123 4 FEM Model Quality Assessment 125 4.1 Procedure of the FEM Model Quality Assessment...127 4.1.1 Software and Numerical Checks...128 4.1.2 Engineering Checks...129 4.1.3 Correlation Quantities...130 4.1.4 Sensitivity Analysis...131 4.2 FEM Modeling Idealization..... 134 4.2.1 Modeling Idealizations of a Fuselage Frame...135 4.2.2 Local and Global Modeling Imperfections...141 4.3 Uncertainty Analysis...145 4.3.1 Correlation Quantities for the Uncertainty Analysis.. 148 4.3.2 Realization of Monte-Carlo Method with MATLAB and MSC.NASTRAN...150 vi
Contents 4.4 Application to a Fuselage FEM Model...151 5 FEM Model Validation based on Vibration Test Data 159 5.1 Experimental Modal Analysis (EMA)..... 160 5.1.1 EMA Techniques...161 5.1.2 Local and Global SDOF Methods.... 162 5.2 Vibration Test Setups...164 5.2.1 Attachment of the Test Specimen.... 164 5.2.2 Influence of Excitation Systems...166 5.2.3 Versatility of Vibration Test Setups...167 5.2.4 Sensor Placement Optimization...167 5.3 Experimental Modal Analysis for Base Excitation Testing... 168 5.3.1 Relative Kinematics...168 5.3.2 Determination of Base Excitation.... 172 5.3.3 MIMO FRF Methods...173 5.4 Application of Vibration Test Techniques...177 5.4.1 Feasibility Check of Linear Relations...177 5.4.2 Definition of System Boundaries...178 5.4.3 Linearity Check of Structural Dynamic Behavior.... 182 5.4.4 Comparison of FRF Methods...184 5.4.5 Mode-Shape Visualization GUI..... 186 5.4.6 FEM Model Updating...188 6 Virtual Testing of Vibration Control Systems 195 6.1 Setup of Virtual Test Configurations...197 6.1.1 Shaker Table Excitation for Virtual Testing...198 6.1.2 Integration of Semi-Active Systems into MBS Software. 199 6.1.3 Virtual Test Configurations...201 6.2 Verification of Model Reduction and Simulation Techniques.. 205 6.2.1 Integration of FEM Models into Flexible Multi-Body Environment...205 6.2.2 Analysis of Passive Configurations...209 6.2.3 Simulation Coupling...214 vii
6.3 Assessment of Semi-Active Systems based on Virtual Tests.. 218 6.3.1 The Hybrid Sky-Hook-Ground-Hook Control...218 6.3.2 Assessment of OSC Configurations...222 6.3.3 Assessment of Configuration Galley (G2)...228 7 Conclusion and Outlook 231 A Appendix 235 A.1 Model-based Verification of MIMO Identification Techniques. 235 A.2 Semi-Active ER Devices....237 A.2.1 Semi-Active SDOF Time Domain Results...238 A.3 Virtual Test Results...245 Bibliography 249 viii