The Pennsylvania State University the Graduate School College of Engineering MAGNETICALLY INDUCED ACTUATION and OPTIMIZATION OF
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The Pennsylvania State University The Graduate School College of Engineering MAGNETICALLY INDUCED ACTUATION AND OPTIMIZATION OF THE MIURA-ORI STRUCTURE A Thesis in Mechanical Engineering by Brett M. Cowan © 2015 Brett M. Cowan Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science December 2015 The thesis of Brett M. Cowan was reviewed and approved* by the following: Paris vonLockette Associate Professor of Mechanical Engineering Thesis Advisor Zoubeida Ounaies Professor of Mechanical Engineering Dorothy Quiggle Career Development Professor Karen Thole Department Head of Mechanical and Nuclear Engineering Professor of Mechanical Engineering *Signatures are on file in the Graduate School ii Abstract Origami engineering is an emerging field that attempts to apply origami principles to engineering applications. One application is the folding/unfolding of origami structures by way of external stimuli, such as thermal fields, electrical fields, and/or magnetic fields, for active systems. This research aims to actuate the Miura-ori pattern from an initial flat state using neodymium magnets on an elastomer substrate within a magnetic field to assess performance characteristics versus magnet placement and orientation. Additionally, proof-of-concept devices using magneto-active elastomers (MAEs) patches will be studied. The MAE material consists of magnetic particles embedded and aligned within a silicon elastomer substrate then cured. In the presence of a magnetic field, both the neodymium magnets and MAE material align with the field, causing a magnetic moment and thus, magnetic work. In this work, the Miura-ori pattern was fabricated from a silicone elastomer substrate with prescribed, reduced-thickness creases and removed material at crease vertex points. Four magnetization orientation configurations of the Miura-ori pattern were generated and fabricated by attaching neodymium magnets to the Miura-ori substrates. The prototypes were tested within a magnetic field ranging from 0 – 240 mT and selected crease fold angles were measured at each field strength. Theoretical magnetic work for each configuration was calculated based on an origami folding model from the Miura-ori’s initial flat state to its completely folded state. These calculations were applied to a design space visualization program to determine the magnetization orientation for each configuration that resulted in the maximum possible theoretical work achieved. Each configuration was analyzed and compared in relation to its experimentally determined overall actuation, experimentally determined ability to follow the ideal folding behavior of the Miura-ori pattern, and the theoretical normalized work for fixed and varied magnetization orientations. The configuration with the highest overall rating of the aforementioned criteria was selected to be tested with the magnetization orientations that resulted in its maximum possible theoretical work. The configuration with the maximum theoretical normalized work was fabricated with attached neodymium magnets. A similar configuration with slightly different magnetization orientations resulting in an offset theoretical normalized work was also tested, and was fabricated using two methods: attached neodymium magnets and embedded MAE patches. The MAE patches were created using a 30% volume fraction of 325 mesh barium hexaferrite particles mixed with Dow Sylgard 184 silicone rubber compound at a 10:1 base to catalyst ratio and cured within a uniform (0.7 T) magnetic field in a prescribed alignment. Both sets of prototypes were tested using the same experimental setup as was used for the original four configurations and were compared using the same criterion. Configuration I*, which had magnetization orientations that maximized the theoretical normalized work, outperformed all other configurations in a iii weighted sum model that additionally accounted for idealness and actuation. The method used to determine favorable magnetization orientations could potentially be applied to other origami structures investigated for magnetic actuation. In addition, the model used to calculate theoretical normalized work can be the basis of more comprehensive model that could include concepts such as crease and panel stiffness and magnetic saturation. iv Table of Contents List of Tables ....................................................................................................................................................... vi List of Figures ..................................................................................................................................................... vii Nomenclature ....................................................................................................................................................... ix Acknowledgements ............................................................................................................................................... x Chapter 1. Introduction ......................................................................................................................................... 1 1.1 Problem statement ...................................................................................................................................... 1 1.2 Literature review ......................................................................................................................................... 1 1.2.1 Origami engineering ............................................................................................................................ 1 1.2.2 Properties and research of the Miura-ori ............................................................................................. 3 1.2.3 Magnetorheological/Magneto-active elastomers ................................................................................. 7 1.2.4 Neodymium magnets ......................................................................................................................... 10 1.2.5 Actuation of origami structures ......................................................................................................... 11 1.3 Research objectives .................................................................................................................................. 14 Chapter 2. Methodology ..................................................................................................................................... 15 2.1 Miura-ori substrate design ........................................................................................................................ 15 2.2 Magnet orientation determination ............................................................................................................. 17 2.3 Substrate fabrication ................................................................................................................................. 21 2.4 Experimental setup ................................................................................................................................... 23 2.5 Magnetic work analysis ............................................................................................................................ 26 Chapter 3. Results and discussion ....................................................................................................................... 32 3.1 Experimental data analysis ....................................................................................................................... 32 3.2 Design space exploration .......................................................................................................................... 40 3.3 Configuration optimization ....................................................................................................................... 46 3.4 Maximum work configuration fabrication and analysis ........................................................................... 49 Chapter 4. Conclusions ....................................................................................................................................... 58 References ........................................................................................................................................................... 61 Appendix A: Prototype selection data for initial four configurations ................................................................. 64 Appendix B: MATLAB code for experimental theoretical normalized work .................................................... 67 Appendix C: Experimental data of initial four configurations .......................................................................... 107 Appendix D: Fminsearch/ATSV MATLAB code ............................................................................................ 121 Appendix E: Configuration I* and I** prototype selection and experimental data .......................................... 138 v List of Tables Table 2.1. Results of the thought-experiment. Region ii has all creases folding in the correct direction ... 19 Table 3.1 List of prototypes and their respective batch within each configuration .................................... 33 Table 3.2 Table 3.1 Maximum average fold angles (240 mT external field strength) in degrees for ......... 35 Table 3.3 Average deviation values 퐷̅ for each configuration when comparing mountain vs. valley ........ 38 Table 3.4 MATLAB’s Fminsearch results for