MAGNETICALLY INDUCED ACTUATION AND OPTIMIZATION OF THE MIURA-ORI STRUCTURE

158 Pages·2015·4.36 MB·English

by  Brett M Cowan

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

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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
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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.
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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
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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 𝐷̅ for each configuration when comparing mountain vs. valley ........ 38
Table 3.4 MATLAB’s Fminsearch results for maximizing the theoretical normalized magnetic work ..... 41
Table 3.5 Preference Sampler results for the symmetry case for the maximum normalized work of ........ 44
Table 3.6 Percent difference comparison between the symmetry cases of Fminsearch and ATSV ........... 45
Table 3.7 Preference Sampler results for independent case for the maximum normalized work of ........... 46
Table 3.8 Actuation, Ideal behavior, and Theoretical Norm. Work from fixed magnetization .................. 47
Table 3.9 Actuation, Ideal behavior, and Theoretical Norm. Work from varying magnetization .............. 48
Table 3.10 Weighted sum model and the respective criterion of Actuation, Ideal behavior, and .............. 57
Table A.1. Excel Statistical Analysis output of panel thickness data and calculation of the upper and ..... 64
Table A.2. Half-thickness model: crease panel thickness data and the selection of suitable ...................... 65
Table A.3. One-third-thickness model: crease panel thickness data and the selection of the suitable ....... 66
Table A.4 Experimental data of the configuration I prototypes ................................................................ 109
Table A.5 Experimental data of the configuration II prototypes .............................................................. 112
Table A.6 Experimental data of the configuration III prototypes ............................................................. 115
Table A.7 Experimental data of the configuration IV prototypes ............................................................. 118
Table A.8 Miura-ori substrate selection data for the configuration I* and configuration I** .................. 138
Table A.9 Experimental data of the configuration I* - Neodymium prototypes ...................................... 140
Table A.10 Experimental data of the configuration I** - Neodymium prototypes .................................. 143
Table A.11 Experimental data of the configuration I** - MAE prototypes ............................................. 146

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List of Figures

Figure 1.1 Two approaches for rigid-foldable origami with thickness from Tachi [9], (a) the axis ............. 3
Figure 1.2 The Bi-axial shortening of a plane into Miura’s developable double corrugation (DDC) .......... 4
Figure 1.3 Loci of two thumbs in unfolding a map from Miura [12] of (a) orthogonal folding ................... 5
Figure 1.4 Unit cell geometry of a folded Miura-ori sheet from Schenk [15]. The parallelogram ............... 6
Figure 1.5 Designations of (a) soft magnetic particles and (b) hard magnetic particles. (c) Four ................ 8
Figure 1.6 Magnetic work as a function of magnetic field strength for each class of sample from ............. 9
Figure 1.7 (a) Displacement change and (b) block force change of H – MREs with different particle ...... 10
Figure 1.8 (a) The mountain (solid lines) and valley (dotted lines) crease pattern for the Miura-ori ......... 12
Figure 1.9 Schematic of the optimal orientation of magnetic material for (a) the waterbomb base ........... 13
Figure 2.1 Miura-ori design with mountain folds being the dashed red lines and the valley folds ............ 15
Figure 2.2 Top (left) and Isometric (right) views of the first Miura-ori design modeled in SolidWorks ... 16
Figure 2.3 Top (left) and Isometric (right) views of the second Miura-ori design modeled in .................. 17
Figure 2.4 2D Miura-ori panel dimensions for both designs, with the creases centered on the orange ...... 17
Figure 2.5 An arbitrary Miura-ori panel divided into four regions with example torque vector and ......... 18
Figure 2.6 Magnet configuration I and the magnetic field direction, H ..................................................... 20
Figure 2.7 Magnet configuration II and the magnetic field direction, H .................................................... 20
Figure 2.8 Magnet configuration III and the magnetic field direction, H ................................................... 21
Figure 2.9 Magnet configuration IV and the magnetic field direction, H .................................................. 21
Figure 2.10 Representative bottom (left) and top lattice (right) mold for Miura substrate casting ............ 22
Figure 2.11 End-product of Miura substrate fabrication with attached Delrin sheets cut to fit each .......... 23
Figure 2.12 Acrylic test stand suspending the Teflon sheet. The circular base of the stand allows it to .... 24
Figure 2.13 Experimental setup within the big magnet. The Gaussmeter probe extends underneath ........ 25
Figure 2.14 Designated crease numbering of the Miura-ori. The creases highlighted in green ................. 25
Figure 2.15 Image capture of the folding crease 1 of a configuration IV prototype. The black ................. 26
Figure 2.16 Representation of the crease vector 𝐶. The points 𝑝 and 𝑝 are located at adjacent ............27
𝑖 𝑟 𝑞
Figure 2.17 Panel movements during the folding process with the blue lines representing the ................. 28
Figure 2.18 Folded cellular metamaterial of individual Miura-ori sheets with alternating unit cell ........... 29
Figure 2.19 Directionality of the magnetic field H (bisector of crease 6’s fold angle) throughout ............ 30
Figure 3.1 configuration II prototype within the Walker Scientific 7H electromagnetic subjected to ....... 32
Figure 3.2 Average Fold Angle vs. Applied Field Strength results for all prototypes of ........................... 34
Figure 3.3 Bar chart representation of the maximum average fold angles for each crease and .................. 35
Figure 3.4 Vertical Crease Averages and Horizontal Crease Averages compared to the ideal behavior ... 37
Figure 3.5 Magnetic work done per total magnetic energy potential as a function of Horizontal angle .... 40
Figure 3.6 Panel and magnetization orientation numbering for the Miura-ori. Simplification by .............. 41
Figure 3.7 Trade spaces for (a) configuration I, (b) configuration II, (c) configuration III, and (d) .......... 43
Figure 3.8 Preference Sampler trade space results for (a) configuration I, (b) configuration II, (c) .......... 44
Figure 3.9 Weighted sum performance values for the fixed magnetization orientations............................ 48
Figure 3.10 Weighted sum performance values for each case of the varied magnetization orientations ... 49
Figure 3.11 Magnetization orientation directions and corresponding initial magnetic torque directions ... 50
Figure 3.12 3-layer MAE patch mold for Panel 4. The acrylic layers are connected by plastic screws ..... 51
Figure 3.13 MAE patch layer dimensions of (a) Panels 2 and 8, (b) Panel 4, and (c) Panel 6. All ............ 51
Figure 3.14 An embedded MAE prototype of configuration I** ................................................................ 52
Figure 3.15 Neodymium configuration I* prototype within the Walker Scientific 7H .............................. 53
Figure 3.16 Average Fold Angle vs. Applied Field Strength results for all prototypes of configuration ... 54
Figure 3.17 (a) Normalized actuation and (b) idealness factor as a function of field strength for all ........ 55
Figure 3.18 Weighted sum performance values for all configurations and theoretical normalized ............ 57
Figure 4.1 Miura-ori design with mountain folds being the dashed red lines and the valley folds being .. 59
Figure A.1 Configuration I prototype within the Walker Scientific 7H electromagnet subjected to ........ 107
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Figure A.2 Configuration III prototype within the Walker Scientific 7H electromagnet subjected to ..... 108
Figure A.3 Configuration IV prototype within the Walker Scientific 7H electromagnet subjected to ..... 108
Figure A.4 Neodymium configuration I** prototype within the Walker Scientific 7H electromagnet .... 139
Figure A.5 MAE configuration I** prototype within the Walker Scientific 7H electromagnet ............... 139

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Nomenclature

MRE ............................................................................................................... Magnetorheological Elastomer
MAE ..................................................................................................................... Magneto-Active Elastomer
HTC ............................................................................................................................. Half-thickness Crease
OTTC .................................................................................................................. One-third Thickness Crease
ROF ............................................................................................................................... Rigid Origami Folder

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Acknowledgements

I would like to thank my advisor Dr. Paris von Lockette for his academic and life guidance
throughout my graduate studies. I would like to thank my thesis reader, Dr. Zoubeida Ounaies, and Dr.
Mary Frecker for their valuable comments and criticisms during my weekly updates of my research
progress.
There are several other people who aided in my completion of my graduate studies. First, I would
like to thank Zhonghua Xi at George Mason University for generating a 3 x 3 Miura-ori pattern within the
Rigid Origami Folder model that I could base calculations on. I would like to thank Landen Bowen for
helping me extract the necessary information from the Rigid Origami Folder model and teaching me how
to use the ARL Trade Space Visualizer (ATSV). I would also like to thank my fellow MACS lab mates
for their constant support and assistance.
Lastly, thank you to my family and friends for believing in me and encouraging me throughout
my time as a graduate student.
We gratefully acknowledge the support of the National Science Foundation grant number
1240459 and the Air Force Office of Scientific Research. Any opinions, findings, and conclusions or
recommendations expressed in this material are those of the author and do not necessarily reflect the
views of the National Science Foundation.

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