TECHNISCHE UNIVERSITÄT MÜNCHEN Lehrstuhl für Angewandte Mechanik Permanent Magnet Reluctance Actuators for Vibration Testing Daniel Wiedemann Vollständiger Abdruck der von der Fakultät für Maschinenwesen der Technischen Universität München zur Erlangung des akademischen Grades eines Doktor-Ingenieurs genehmigten Dissertation. Vorsitzender: Univ.-Prof. dr. ir. Daniel J. Rixen Prüfer der Dissertation: 1. Univ.-Prof. Dr.-Ing. habil. Heinz Ulbrich (i.R.) 2. Univ.-Prof. Dr.-Ing. Horst Baier Die Dissertation wurde am 15.10.2012 bei der Technischen Universität München eingereicht und durch die Fakultät für Maschinenwesen am 07.03.2013 angenommen. Abstract The analysis of vehicles and automotive components for disturbing noise requires actuators with high force density, robustness and energy efficiency. This thesis covers the mechatronic design and simulation of magnetic reluctance actuators for vibration excitation. A comparison with hydraulic and electrodynamic actuation concepts shows the application potential of reluctance force actuators in automotive vibration test rigs. For the magnetic design, reluctance circuits and the finite element analysis are used. The developed topology is characterized by a fully laminated armature and a core with surface mounted permanent magnets. The resulting negative magnetic stiffness is completely compensated by mechanical springs which enable a robust and stable operation. For dynamic simulations of the electromagnetic energy conversion a co-energy based model is developed. It features low computational cost and enables an accurate description of the nonlinear actuator characteristics. The presented methods are verified by experiments with two prototype actuators. Zusammenfassung Die Störgeräuschanalyse von Fahrzeugen und Fahrzeugkomponenten erfordert Aktoren mit einer hohen Kraftdichte, Robustheit und Energieeffizienz. Diese Arbeit beschreibt den mechatronischen Entwurf und die Simulation von magnetischen Reluktanzaktoren für die Schwingungsanregung. Der Vergleich mit hydraulischen und elektrodynami- schen Antriebskonzepten zeigt das Anwendungspotential von Reluktanzaktoren in Vibrationsprüfständen bei der Fahrzeugentwicklung. Für den Magnetkreisentwurf wer- den Netzwerkmodelle und die Finite-Elemente-Methode verwendet. Die entwickelte Topologie zeichnet sich durch einen vollständig geblechten Anker und einen mit Perma- nentmagneten bestückten Kern aus. Die negative magnetische Steifigkeit wird durch mechanische Federn voll kompensiert, so dass ein robuster und stabiler Betrieb möglich wird. Für dynamische Simulationen der elektromagnetischen Energiewandlung wird ein Modell unter Verwendung der Co-Energie entwickelt, welches einen geringen Rechenaufwand erfordert und die genaue Beschreibung der nichtlinearen Aktorcharak- teristik ermöglicht. Die vorgeschlagenen Methoden werden durch Experimente mit zwei Prototypen verifiziert. iii Acknowledgments This thesis summarizes a large part of my research carried out at the Institute of Applied Mechanics, Technische Universität München. Without the help of numerous people who supported me over the the course of the previous years the completion of this work would not have been possible. First and foremost, I would like to express my deep gratitude to my advisor Professor Heinz Ulbrich for providing an excellent research environment, stimulating discussions and helpful advice during my time as his PhD student. He gave me the freedom to pursue my own ideas and support when it was needed. I would also like to warmly thank the second advisor Professor Horst Baier and chairman Professor Daniel Rixen for serving on my dissertation committee and for their interest in my work. For managing the project resources and his support in all administrative manners I owe thanks to Dr. Thomas Thümmel. I very much enjoyed working with great colleagues at the institute. Here, I am particularly grateful to Dr. Marcus Herrmann, not only for triggering my interest in magnetic actuators, but also for encouraging me to take a research position. He introduced me into the field of electromagnetic devices, being a competent advisor and partner for scientific discussions. Special thanks I wish to offer to Dr. Ulrich Koch who was responsible for the shaker plant and the control system design. The collaboration with him was always very inspiring and productive. Besides for his tireless efforts in the common project, I would like to thank him for sharing good ideas and providing industrial background knowledge to our research. Further, I would like to sincerely thank Dr. Thomas Villgrattner, Valerio Favot, Dr. Markus Schneider and Dr. Thorsten Schindler for their continuous assistance and the many fruitful discussions. I am particularly indebted to Markus Schwienbacher for his valuable advice and helpful suggestions regarding the mechatronic aspects of this thesis. The hardware development would not have been possible without the excellent work of the institute’s mechanical and electrical workshops. For the development of the power electronics and for numerous discussions about sensors and actuators I wish to express my sincere thanks to Georg Mayr. His enthusiasm and broad engineering experience contributed substantially to the experimental research. Working with him was always deeply pleasant and rewarding. Furthermore, I warmly thank Simon Gerer, Philip Schneider and Tobias Schmid for manufacturing the mechanical components and their assistance during the assembly of numerous prototypes. I would like to thank my proofreaders Dr. Marcus Herrmann, Dr. Thomas Villgrattner, Dr. Ulrich Koch and Valerio Favot for their interest and helpful comments. Finally, I would like to express my immense gratitude to my family who has always encouraged and supported me in all my endeavours. Munich, April 2013 Daniel Wiedemann v Contents 1. Introduction 1 1.1. Literature Review . 2 1.2. Contributions and Outline of the Thesis . 6 2. Vibration Testing 9 2.1. Noise, Vibration and Harshness Analysis . 9 2.2. Actuators . 11 2.2.1. Hydraulic Actuators . 12 2.2.2. Electrodynamic Actuators . 14 2.2.3. Magnetic Reluctance Actuators . 18 2.3. Vibration Test Rigs . 19 2.3.1. Components . 19 2.3.2. Cars . 21 2.4. Chapter Summary . 22 3. Magnetic Reluctance Actuators 25 3.1. Magnetic Forces . 25 3.2. Magnetic Induction . 28 3.3. Power Losses . 29 3.3.1. Eddy Currents . 30 3.3.2. Skin Depth . 31 3.3.3. Hysteresis . 32 3.3.4. Coil Windings . 33 3.4. Modeling Methods . 33 3.4.1. Reluctance Circuits . 34 3.4.2. Finite Element Analysis . 36 3.4.3. Reduced Order Model . 37 3.4.4. Comparison . 38 3.5. Chapter Summary . 39 4. Magnetic Design 41 4.1. Design Process . 41 4.2. Design Objectives . 43 4.3. Topology . 48 4.3.1. Polarized Magnetic Circuits . 49 4.3.2. Actuator Concept . 50 4.4. Magnetic Material Selection . 51 4.4.1. Soft Magnetic Materials . 51 4.4.2. Hard Magnetic Materials . 52 4.5. Eddy Current Reduction Strategies . 55 4.6. Laminations . 58 4.7. Magnetic Circuit Dimensioning . 58 4.7.1. Magnetic Equivalent Circuit . 58 4.7.2. Static Parameters . 61 vii viii Contents 4.7.3. Main Geometric Dimensions . 63 4.8. Coil Design . 64 4.8.1. Parameter Calculation . 64 4.8.2. Inductance and Time Constant . 66 4.9. Finite Element Analysis . 67 4.10.Chapter Summary . 70 5. Energy-based Modeling and Simulation 71 5.1. Co-Energy . 71 5.2. Reduced Order Approach . 73 5.3. Approximation Methods . 77 5.4. System Parameters . 79 5.4.1. Single Energized Winding . 79 5.4.2. Two Energized Windings . 80 5.5. Actuator Model . 83 5.5.1. Electric Circuit . 84 5.5.2. Magnetic Force . 84 5.5.3. Eddy Currents . 86 5.5.4. Mechanics . 87 5.5.5. Mechatronic System . 90 5.6. Outlook: Control . 91 5.7. Chapter Summary . 91 6. Mechatronic Design Aspects 93 6.1. Actuator Design . 93 6.2. Mechanical Design Aspects . 95 6.2.1. Core . 95 6.2.2. Armature . 98 6.2.3. Housing . 100 6.2.4. Membrane Springs . 100 6.3. Information Processing . 103 6.3.1. Sensors . 103 6.3.2. Control Unit . 105 6.3.3. Software . 106 6.4. Chapter Summary . 107 7. Experimental Results 109 7.1. Static Performance . ..