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! iii 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