PARAMETER DESIGN OF SMALL ELECTROSTATIC FORCE DRIVEN MECHANISMS A Thesis Presented to the faculty of the Department of Mechanical Engineering California State University, Sacramento Submitted in partial satisfaction of the requirements for the degree of MASTER OF SCIENCE in Mechanical Engineering by Adewale George Ogbogho SUMMER 2014 PARAMETER DESIGN OF SMALL ELECTROSTATIC FORCE DRIVEN MECHANISMS A Thesis by Adewale George Ogbogho Approved by: __________________________________, Committee Chair Akihiko Kumagai __________________________________, Second Reader Tien I. Liu ____________________________ Date ii Student: Adewale George Ogbogho I certify that this student has met the requirements for format contained in the University format manual, and that this thesis is suitable for shelving in the Library and credit is to be awarded for the thesis. __________________________, Graduate Coordinator ___________________ Akihiko Kumagai Date Department of Mechanical Engineering iii Abstract of PARAMETER DESIGN OF SMALL ELECTROSTATIC FORCE DRIVEN MECHANISMS by Adewale George Ogbogho The millimeter or insect scale sized electrostatic force driven mechanisms using a parallel plate actuation with multilayered dielectric considering air gap as a dielectric has not been delved into so much. This thesis is directed towards design parameters of small mechanisms taking into consideration, the dielectric material, which in this study, Teflon was the material of choice due to its excellent dielectric properties, the size, area and thickness of the capacitor plates and breakdown voltage and its effects on a small scale mechanism operating on the principle of electrostatic actuation having a size such as that of an insect. These parameters were determined using detailed theoretical and practical analyses showing how these parameters relate to ensure an excellent design taking into consideration the effect of breakdown voltage and its effect on the maximum force exerted by the mechanism and on the overall dielectric properties of the dielectrics in- between the capacitor plates. iv The maximum force was determined experimentally by connecting a parallel plate actuator with Teflon and air as the dielectrics to a triple output DC power supply which was connected to a power controller and DC high voltage power converter which amplifies the input voltage by 4310 times. The resulting maximum forces and breakdown voltage for different Teflon thicknesses and air gap distances were measured to determine how to optimize the design of these mechanisms considering the effect of dielectric constant and dielectric strength of the material on the force generated and to aid in material selection for a mechanism as such. _______________________, Committee Chair Akihiko Kumagai _______________________ Date v DEDICATION This Thesis is dedicated to The Lord God Almighty, Jesus Christ my savior for seeing me through all the easy and tough times and giving me the grace to pull through with my masters degree program successfully. I give all thanks and praise to you Lord. vi ACKNOWLEDGEMENTS Firstly, I thank the Lord God Almighty, Jesus Christ my savior for His unending love, care and protection over me during my entire time at California State University, Sacramento. I also want to express my sincere gratitude to my thesis supervisor and graduate coordinator of the mechanical engineering department, Professor Akihiko Kumagai for his unconditional assistance in ensuring that I complete this thesis on time and with the much expected quality by providing his positive criticism, advices and assistance all through the duration of this thesis. God will continue to bless you sir. I’m also expressing my gratitude to all the professors who took their time to teach and lecture me in various courses all through the entire time of my studies. I also appreciate my wonderful parents, Engr. Mike and Pastor (Barr.) Mrs. Adeola Ogbogho, for their support financially, morally and spiritually and for their constant communications to check up on me from a distant land even when it was inconvenient. To my wonderful gift from God and Fiancée, Shanae K. Theall for her sweet words of encouragement, time and assistance to ensure that I had the easiest time going through my thesis and my degree. Also this isn’t complete without expressing my thanks to my siblings, Mr. Olusola Ogbogho, Mrs. Omotola Bolarinwa, Mrs. Temitayo Akinnola and Mrs. Omolola Ajasa for their prayers and care all through my entire program. God Bless you all. vii I also want to appreciate the effort of Mr. Mike Newton at the ECS Tech Shop for the assistance he rendered toward the modification of the base plates. And to the Ogbeide Family, especially Daddy and Mummy Ogbeide for taking me into their house upon my arrival from Nigeria. To my friends Anthony Ogbeide, Kio, Anji and Ibim Amachree, Joy Ndem for being there as brothers and sisters to me, to the pastorate, Pastor Toks and Toyin Adewunmi and entire members of the Redeemed Christian Church of God (Peace Assembly), Sacramento and to all who contributed in one way or the other to my life during this entire time. I can’t thank you all enough but God bless you all richly. viii TABLE OF CONTENTS Page Dedication ................................................................................................................... vi Acknowledgements .................................................................................................... vii List of Tables .............................................................................................................. xi List of Figures ............................................................................................................ xii Nomenclature ............................................................................................................. xiii Chapter 1. INTRODUCTION……………………………………………………….. ...............1 1.1 Electrostatic Field ............................................................................................ 1 1.2 Dielectrics ....................................................................................................... 3 1.3 Capacitors ....................................................................................................... 4 1.4 Aim & Objectives ........................................................................................... 5 2. LITERATURE REVIEW ........................................................................................ 7 2.1 Parallel Plate Capacitors .................................................................................. 8 3. THEORETICAL ANALYSIS .......................................................................... 12 3.1 Force equation of a parallel plate capacitor with more than one dielectric .. 12 3.2 Dielectric and Material Selection ................................................................. 15 3.3 Expression of dielectric strength of combined materials ................................18 4. EXPERIMENTAL SETUP, DATA AND RESULTS.............................................21 4.1 Setup ..............................................................................................................21 ix 4.2 Data and Test ..................................................................................................24 4.3 Results.............................................................................................................24 5. CHALLENGES, RECOMMENDATIONS AND CONCLUSION .......................27 5.1 Challenges .......................................................................................................27 5.2 Recommendations ...........................................................................................27 5.3 Conclusion ......................................................................................................27 Appendix A MATLAB program showing the force equation 3.8 ............................29 Appendix B Table showing the experimental data indicating the breakdown voltage of Teflon for different separation distances and dielectric thicknesses ...........................................................................................30 References ..............................................................................................................31 x LIST OF TABLES Tables Page 1. Table 3.1 Table of dielectric materials showing relative permittivity and Force …………………………… ........................ .……………16 2. Table 4.1 Table showing the Maximum Forces (Fmax) at a range of Fmax (Low)< Fmax (Average)< Fmax (High), for each range of air gap distance d1 at the range of (1mm to 4mm) for each Teflon thickness d2 of 0.5mm, 1mm, 1.5mm and 2mm… ......................... 25 xi LIST OF FIGURES Figures Page 1. Figure 1.1 Electrostatic Field showing the force of attraction between two terminals of opposite charges ……………… . .……………………2 2. Figure 1.2 (a) Parallel Plate Capacitor………………………… ....................... 5 3. Figure 1.2 (b) The Electric field between the parallel plates………………… .. 5 4. Figure 2.1 Xerographic photocopying process……………… .. ………………7 5. Figure 2.2 (a) Parallel Plate Capacitor ................................................................ 9 6. Figure 2.2 (b) An Illustration of a parallel plate actuator ................................... 9 7. Figure 3.1 Parallel plate capacitor with two dielectrics ................................... 12 8. Figure 3.2 Graph Showing the relationship between Force and dielectric constant from table 3.1 showing