Characterization of a Pneumatic Strain Energy Accumulator

164 Pages·2016·4.76 MB·English

Characterization of a Pneumatic Strain Energy Accumulator: Efficiency and First Principles
Models with Uncertainty Analysis

By
Joshua Joseph Cummins

Dissertation Proposal
Submitted to the Faculty of the
Graduate School of Vanderbilt University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
in
Mechanical Engineering
May, 2016
Nashville, Tennessee

Approved:
Douglas E. Adams, Ph.D.
Eric J. Barth, Ph.D.
Sankaran Mahadevan, Ph.D.
Thomas Withrow, Ph.D.
Florence Sanchez, Ph.D.
This work is dedicated to my beautiful bride Kimberly, parents Ed and Joanne, siblings Shaun
and Ryan and has been completed for the glory of God through whom all things are possible!

ii
ACKNOWLEDGEMENTS

I would like to start by thanking the men and women in uniform who protect and serve our
country. It is through your courage and sacrifice that we have the liberty to study and advance
science. I would like to thank the National Science Foundation and the Center for Compact and
Efficient Fluid Power for their financial support of the work herein. I would like to thank my
committee members for their support and guidance along the way to completion of this work. I
would especially like to thank the chair of my committee, Doug Adams for his support, guidance
and encouragement at both Purdue University and Vanderbilt University. I would like to thank
my friends who provide immeasurable emotional support and encouragement on a daily basis.
Specifically I would like to thank the faith communities I have been blessed to be a part of
during my journey thus far. To all of my brothers and sisters in Christ, you have encouraged,
inspired, and strengthened me and those around you by bringing your light and joy to the world.
In a special way I would like to thank those that have dedicated their lives to serving the Lord as
spiritual Fathers and religious Sisters, especially Fr. Patrick Baikauskas, Fr. Brian Doerr, Fr.
Dave Wells, Fr. John O’Neill, and Fr. John Sims Baker. I would like to thank my family: my
loving and faithful parents, Ed and Joanne; my awesome and inspiring siblings Shaun and Ryan;
and especially my beautiful bride Kimberly not only for her support but for her loving sacrifice
to make this possible. Each of you have sacrificed and loved in ways big and small, and I cannot
express how truly grateful and appreciative I am of your unending selflessness. Finally and most
importantly, I would like to thank our Blessed Mother for her constant intercession and love that
only a mother can provide and to God, Father, Son and Holy Spirit, for His grace and strength
that makes all things possible!
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TABLE OF CONTENTS
Page
DEDICATION ................................................................................................................................ ii
ACKNOWLEDGEMENTS ........................................................................................................... iii
LIST OF TABLES ....................................................................................................................... viii
LIST OF FIGURES ....................................................................................................................... ix
Chapter
I. Introduction .............................................................................................................................1

Background .............................................................................................................................1
Existing Accumulator Technology ...................................................................................1
Strain Energy Accumulator Technology ..........................................................................1
Motivation ...............................................................................................................................2
Previous Work ..................................................................................................................2
Objectives and Contributions ..................................................................................................3
Advanced Accumulator Materials Modeling ....................................................................3
Pneumatic Strain Energy Accumulator Model .................................................................3
Component Efficiency with Uncertainty Analysis ...........................................................3
System Efficiency State Models with Energy Savings Projections ..................................4
Carbon Nanotube Reinforced Elastomer Concept ............................................................4

II. Advanced Strain Energy Accumulator: Materials, Modeling and Manufacturing .................6

Introduction .............................................................................................................................6
Current Accumulator Technology ....................................................................................7
Strain Energy Accumulator Technology ..........................................................................7
Applications for Strain Energy Accumulator ...................................................................8
Materials .................................................................................................................................9
iv
Carbon Nanotube Embedded Rubber ...............................................................................9
Advanced CNT Embedded Rubber Strain Energy Accumulator Concept .....................10
Modeling ...............................................................................................................................10
2-D Modeling of Dynamic Performance of Strain Energy Accumulator .......................11
3-D Modeling of Quasi-Static Response of Advanced Strain Energy Accumulator ......12
Multiscale Modeling Homogenization Techniques to Estimate Elastic Modulus of CNT
Embedded Rubber ...........................................................................................................13
Manufacturing .......................................................................................................................15
Conclusions and Future Work ..............................................................................................16

III. Modeling of a Pneumatic Strain Energy Accumulator for Variable System Configuration
with Quantified Projections of Energy Efficiency Increases ................................................18

Introduction ...........................................................................................................................18
Pneumatic Strain Energy Accumulator Work.................................................................19
Current Strain Energy Accumulator Focuses .................................................................19
Application of the Strain Energy Accumulator ..............................................................19
Accumulator Model ..............................................................................................................20
Total Energy Stored and Extracted: Component ............................................................20
Efficiency ........................................................................................................................23
System Model .......................................................................................................................24
Total Energy Expended: System .....................................................................................24
System Efficiency ...........................................................................................................27
Sensitivity Analysis ........................................................................................................27
Modeling Discussion ............................................................................................................29
Conclusions and Future Work ..............................................................................................29

IV. Experimental Evaluation of the Efficiency of a Pneumatic Strain Energy Accumulator .....31

Introduction ...........................................................................................................................31
Pneumatic Strain Energy Accumulator ...........................................................................32
Pneumatic and Strain Energy Literature Survey .............................................................32
Accumulator Component Efficiency Model .........................................................................33
v
Efficiency Experiments .........................................................................................................34
Experimental Setup .........................................................................................................34
Experimental Data Collection .........................................................................................36
Results and Discussion .........................................................................................................39
Component Efficiency ....................................................................................................39
Component Efficiency Uncertainty Analysis .................................................................40
Component Key Performance Parameters ......................................................................41
Key Performance Parameters Uncertainty Analysis .......................................................44
Conclusions and Future Work ..............................................................................................45

V. Energy Conservation in Industrial Pneumatics: A State Model for Predicting Energetic
Savings using a Novel Pneumatic Strain Energy Accumulator ............................................48

Introduction ...........................................................................................................................48
Pneumatic System State Efficiency ......................................................................................50
Analytical Model ............................................................................................................51
Applied Model ................................................................................................................53
Pneumatic System Efficiency Experiments ..........................................................................54
Experimental Setup .........................................................................................................54
Experimental Data ..........................................................................................................56
Results and Discussion .........................................................................................................57
Experimental System Efficiency Increases with Uncertainty Analysis ..........................57
Energy Savings Projections ............................................................................................63
Conclusions and Future Work ..............................................................................................63

VI. Elastomeric Evolution: A New Look at Carbon Nanotube Reinforced Elastomers .............66

Introduction ...........................................................................................................................67
Early CNT Elastomer Work ............................................................................................67
Current Measurement Techniques ..................................................................................67
New Measurement Techniques .......................................................................................68
Applications of Sensor Thread........................................................................................68
Carbon Nanotube Elastomers ...............................................................................................69
vi
Carbon Nanotube Embedded Elastomers .......................................................................70
CNT Embedded Elastomer Components ........................................................................71
Dispersion of Carbon Nanotubes in Viscous Substances .....................................................72
Carbon Nanotube Dispersion in Polymers ......................................................................72
Carbon Nanotube Dispersion in Concrete ......................................................................72
Magnetic Nanoparticle Dispersion .................................................................................72
Carbon Nanotube Strain Sensing ..........................................................................................72
Carbon Nanotube Thread Strain Sensing ........................................................................73
Modeling of CNT Elastomers ...............................................................................................73
Homogenization Techniques Estimating the Elastic Modulus of a CNT Embedded
Elastomer ........................................................................................................................73
Summary of Homogenization Methods ..........................................................................74
Preliminary Testing on Metal Rubber...................................................................................74
Conclusions and Future Work ..............................................................................................78

VII. Conclusion ............................................................................................................................81

Appendix

A. Complete Smart Materials and Structures Journal Manuscript ......................................83

Carbon Nanotube Sensor Thread for Distributed Strain and Damage Monitoring on
IM7/977-3 Composites ...................................................................................................83

B. Matlab Codes ................................................................................................................102

Multiscale Modeling Homogenized Modulus ..............................................................102
Analytical System Efficiency Increase .........................................................................105
Component Efficiency Data Acquisition and Analysis ................................................106
System Efficiency Increase Data Acquisition and Analysis .........................................108
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LIST OF TABLES

Table Page
2-1 CNT material properties used in homogenization methods ...............................................10
2-2 Mooney-Rivlin constants ...................................................................................................12
4-1 Component experimental efficiency of pSEA ...................................................................41
4-2 Linear Regression R2 and S x values for expansion and contraction pressures .............44
Y |
5-1 Cylinder dimensions and calibration constants..................................................................55
5-2 Stroke ratio of primary to secondary cylinder ...................................................................56
5-3 Efficiency improvement projections summary ..................................................................62
6-1 Normalized homogenized modulus values ........................................................................74
6-2 Change in resistance with damage .....................................................................................76

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LIST OF FIGURES

Figure Page
2-1 Strain energy accumulator US patent application ................................................................7
2-2 Pneumatic strain energy accumulator proof of concept .......................................................7
2-3 Typical P-V and stress-strain curves of rubber strain energy accumulator .........................8
2-4 Ankle foot orthosis (AFO) and hydraulic hybrid concepts ..................................................8
2-5 Effect of increasing weight percent of CNTs on rubber modulus .......................................9
2-6 CNT embedded rubber accumulator concept in initial and final states .............................10
2-7 2D Abaqus dynamic model of strain energy accumulator .................................................11
2-8 2D Abaqus model with Von Mises stress and P-V curve from simulation .......................11
2-9 Mesh for 3D quasi-static simulation of strain energy accumulator with final stresses .....12
2-10 Elastic modulus homogenization results for CNT embedded rubber ................................15
3-1 Quick disconnect commercially viable pSEA ...................................................................19
3-2 pSEA control volume .........................................................................................................20
3-3 Pressure-volume curve of pSEA fill process .....................................................................20
3-4 Closed system CV with constant mass allowed to expand isothermally ...........................22
3-5 Exhaust pressure-volume curve of pSEA ..........................................................................23
3-6 Pneumatic accumulator demonstrator ................................................................................24
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3-7 Outstroke diagram of pSEA ...............................................................................................25
3-8 Instroke diagram of pSEA .................................................................................................25
3-9 Percent efficiency increase vs accumulator P ................................................................28
exp
3-10 Projected percent efficiency increase for manual accumulator demo ...............................28
4-1 Single inlet/outlet control volume ......................................................................................33
4-2 Component efficiency testing experimental test setup ......................................................35
4-3 Airflow block diagram for automated valve for fill, hold and exhaust positions ..............35
4-4 Pressure vs time .................................................................................................................36
4-5 Volumetric flow vs time and volume vs time ....................................................................37
4-6 Pressure vs volume for cycles at beginning, middle and end of 500 cycle test .................38
4-7 Pressure volume plot showing strain energy in and out of pSEA ......................................39
4-8 Energy efficiency of pSEA component for five 100 cycle trials .......................................40
4-9 Points on P-V curve used to determine expansion, contraction, and max pressures .........42
4-10 Expansion and contraction pressures for five 100 cycle trials ...........................................42
4-11 Energy into pSEA and energy out of pSEA.......................................................................43
4-12 95% confidence interval of expansion and contraction pressures .....................................45
5-1 Empty and filled pSEA with PV Curve .............................................................................49
5-2 Two cylinder system with pSEA test configuration model ...............................................51
5-3 System with accumulator efficiency increase experimental test setup ..............................54
x