Parameter Design of Small Electrostatic Force Driven Mechanisms

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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

Mechanical Engineering

Adewale George Ogbogho

SUMMER 2014

PARAMETER DESIGN OF SMALL ELECTROSTATIC FORCE DRIVEN MECHANISMS

A Thesis

Adewale George Ogbogho

Approved by:

______, Committee Chair Akihiko Kumagai

______, Second Reader Tien I. Liu

______Date

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

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Abstract

PARAMETER DESIGN OF SMALL ELECTROSTATIC FORCE DRIVEN MECHANISMS

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.

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

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.

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.

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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

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

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

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 the location of an ideal

dielectric as well as that of Teflon(dielectric material of choice

for the experiment) ...... 17

9. Figure 4.1 Schematic diagram of the experimental setup ...... 22

10. Figure 4.2 Figures A-D shows pictures of the experimental setup for the

Teflon in its holders and Figures E-G show the pictures of the

connection port labels on the power supply and power controller

as well as the pin numbers and labels on the high voltage

DC converter ...... 23

xii

NOMENCLATURE

SYMBOLS MEANING UNIT

Electrostatic Force N

퐹퐸 표푟 퐹 Relative permittivity of air none

푘 Coulomb’s constant N·m2/C2 (m/F)

푘푒 Charge C

푞 Distance mm or m

푟 표푟 푑 Capacitance F

∁ɛ Permittivity of free space F/m

풐 Area mm2 or m2

퐴 Energy J

퐸 Voltage V

푉 Distance/Displacement mm or m

푥표 표푟 푥 Absolute Permittivity F/m

휀푖 Relative Permittivity None

푘푖 Breakdown Voltage V

푉푏 Dielectric Strength V/m

푆푖 Maximum Force N

퐹푚푎푥

xiii 1

CHAPTER 1

INTRODUCTION

Electrostatic forces operate on the principle of an electric charge (q) which can be either

positive or negative depending on the force it generates. There is always a force of

attraction between opposite charges and repulsion between charges of the same polarity.

The relationship between the electric charge and force can be seen in the Coulombs’ law,

which is expressed mathematically as

| | = (1.1) 푞1푞2 2 퐹퐸 푘푒 푟

Where FE is the electrostatic force that is exerted when each of the two point charges q1

and q2 a distance r apart, acts on each other, and is the Coulomb’s constant. This leads

푒 to the production of a vector field which is dependent푘 on the properties of the charge,

called the electric field, otherwise known as the electrostatic field, when the charges are

static [1].

1.1 Electrostatic Field

Electrostatic field is said to occur when two materials of different electrical charges are in close proximity to each other in which the electric charges are either stationary or moving slowly [1][2]. This is the basis for all small and miniature sized electrostatic mechanisms, and is being widely used in the design and application of Micro-

ElectroMechanical Systems otherwise known as MEMs [3]. 2

Electrostatic fields are used due to the small size of the mechanisms, for example in the

case of small electrostatic suction devices, the device is able to attract electrical charges on the surface of an object by reorienting the electrical dipoles through polarization while in small grippers, it causes a force of attraction between the capacitor plates. Electrostatic fields even though similar to electromagnetic fields should not be mistaken for it.

Electrostatic fields occur as a result of the potential difference due to static electrons.

Unlike electromagnetic fields, electrostatic fields are blocked by metals but can pass

through some other materials [4]. This leads to the question, what materials are good

conductors or carriers of electrostatic fields? Such materials are called dielectric

materials; they are usually poor conductors of electricity but strong conductors of

electrostatic fields [5].

Figure 1.1: Electrostatic Field showing the force of attraction between two terminals of opposite charges

(Electrostatic fields are electric fields which do not change with time, which happens when the charges are stationary) [17]

1.2 Dielectrics

As earlier said, dielectrics can also be referred to as insulators because they allow only

very minimal to no electric charge to pass through them. They allow electrostatic fields to

pass through them while at the same time expending minimal energy in the form of heat.

These materials are used to increase the capacitance of the capacitor plates between them.

Most of these materials include dry air, ceramics, plastics, glass, polymers and oxides of

metals, vacuum, amongst others [5]. They basically have these major functions;

I. They keep the capacitor plates from coming in contact with each other.

II. To improve capacitance by reducing the electric field strength

III. To limit the effect of a dielectric breakdown when high voltage is being

passed through the system [6].

The important factors in knowing the characteristics of a dielectric material are as follows:

a. Dielectric loss, which is also known as the dielectric loss rate is how much of

energy a material looses when alternating current is applied to it and how

effective the material can prevent energy loss in the form of heat.

b. Relative Permittivity or Dielectric constant is the measure of electrostatic energy

stored within the material and is also how well a material can accommodate or

concentrate the electrostatic lines of flux. 4

c. Dielectric Strength is the ability of a material to withstand continuous increasing

voltage before it breaks down. This voltage is referred to as the breakdown

voltage [7].

1.3 Capacitors

A capacitor is a device that stores electric charge, with one end connected to a positive electrode and the other end to a negative electrode. The charges on a capacitor are usually equal and opposite [8]. Capacitors have a wide range of applications and can be

applicable to a lot of engineering applications such as being used to store potential

energy, frequency filtration, delaying voltage change and used as independent voltage

dividers when combined with resistors and in other various applications [8].

The major types of capacitors can be divided into three categories;

1. Parallel Plate Capacitors

2. Cylindrical capacitors

3. Spherical Capacitors [8]

Figure 1.2: (a) parallel plate capacitor. (b) The electric field between the parallel plates. [18]

1.4 Aim & Objectives

Electrostatics is a widely used and understood concept but its use has been limited to the

design of big mechanisms due to its consumption of very high voltage such as the Van de

Graff generator which is used mainly for research purposes, Copying machines which use

xerography, laser printers, ink jet printers, robotics applications [9], amongst others and

also limited to the design of MEMs. Not much research has been done in the design of

small millimeter sized mechanisms which operate on the electrostatic force principle for

use in various small applications.

The aim of this thesis is to set design parameters in the form of in-depth analyses in the design of small (millimeter sized) electrostatic force driven mechanisms taking into consideration the effects of;

1. Force generated in small mechanisms as well as the maximum force that can be

generated or exerted by these small millimeter sized devices. 6

2. Dielectric materials, taking into consideration factors such as the material type

(that is, the best dielectric material suitable for the design of such small

mechanisms), dielectric constant, the dielectric strength and the effect of

multilayered dielectrics on the overall productivity of this type of mechanism.

3. Size, in terms of the surface area of the capacitor plates, the thickness of the

dielectric material and the separation distance between the two plates.

4. Breakdown voltage and how the design of these small mechanisms can be

optimized by limiting the effect of breakdown voltage.

CHAPTER 2

LITERATURE REVIEW

As aforementioned, the use of electrostatics in various applications has been limited to some use in some big applications such as xerography in the photocopying process and majorly used in micro-engineering applications.

One of the most common use of electrostatics in the modern age is in xerography also known as ‘dry writing’ is the combination of electrostatic printing coupled with photography which is used in photocopy machines in which the copying powder or toner which is negatively charged, sticks to parts of the surface of the drum where the image is taken and then attracts the positive charges from the paper to be printed on, thereby copying the image to the paper [9][10].

Figure 2.1: Xerographic photocopying process. [10] 8

In this era where ‘smaller’ seems to be ‘better’, the demand for smaller devices and

machines is very high. This has led to rapid research in the use of electrostatic forces in

the design of MEMs which has been the foundation for the rapid development of micro

and nanotechnologies as well as micro tools. The need for very small electrostatic

devices has made design of MEMs and nanotechnology applications very complex, using techniques such as the conversion of metals to liquid or gaseous states in order to use them, wire explosion laser ablation, pyrolysis and other very complex methods [11][12].

Although there is the use of simple applications such as the use of parallel plate

capacitors in the design of microgrippers fabricated using standard surface

micromachining technology [12], not much research has been done in the area of

electrostatic forces in the design of millimeter-sized mechanisms which have a much

broader range of applications ranging from medicine to robotics.

In this thesis, the design analyses of small electrostatic mechanisms using the parallel

plate capacitor will be discussed.

2.1 Parallel Plate Capacitors

A parallel plate actuator is simply a set of two conductive plates of opposite sides with each connected to different polarities/electrodes. One end can either be fixed with the other end moving towards or away from the fixed plate [13]. When the voltage across the electrode is zero, the electrostatic force between the electrodes is also zero which produces a distance xo called the rest gap or separation distance. Fig. 2.2 (b) below,

shows the schematics of this kind of actuator, where one end of the spring is connected to 9

the positive end of the voltage source and the other end to the moveable electrode while

the fixed electrode is connected to the negative end. The spring force Fs pulls the

moveable electrode towards the spring in opposite direction to that of the electrostatic

force Fe. Dean [13] made us understand that as the voltage between the two electrodes is

increased from zero, the resulting electrostatic force between the two electrodes pulls

them together until the electrostatic force equals the spring force. However, taking a

gripper as an example, a good gripper must be able to hold the object within its grasp

firmly with a force that is sufficiently high enough to keep it within grips yet not too high

enough to damage the material, therefore as the input voltage is increased, the parallel

plates get closer until they reach a point where the electrostatic force is too large and the

dielectric between the plates collapse by allowing voltage to pass through it and conduct,

which is referred to as break down voltage. How to limit the effect of break down

voltage is one the focuses of this thesis work. Fig 2.2 (a) and (b) shows the design of a

parallel plate capacitor and a parallel plate actuator.

Figure 2.2: (a) Parallel Plate Capacitor, (b) An Illustration of a parallel plate actuator [13] 10

If the material between the two plates is considered to be uniform, a parallel plate

capacitor such as the model above can be described by this equation:

ɛ = (2.1) 풐풌푨 ∁ 풅 Where C is the capacitance between the parallel plates, A is the area of the plates, d is the

distance separating both electrodes from each other while ɛ and are the permittivities

표 of free space and air respectively. 푘

Energy stored in a capacitor is given as

= [13] (2.2) 1 2 퐸 2 퐶푉 Where E is the energy, C is the capacitance and V is the applied Voltage

Substituting the capacitance C from equation (2.1) into equation (2.2) will give

ɛ = (2.3) 표푘퐴 2 퐸 2푑 푉 In the application of a parallel plate actuator according to Fig 2.1 (b),

= + (2.4)

푑 푥표 푥 Where is the separation distance between the fixed electrode and the movable electrode, and

표 is the displacement푥 of the spring.

푥 Therefore, substituting the value of from equation (2.4) into equation (2.3) will yield

푑 = ɛ ( ) (2.5) 표푘퐴 2 퐸 2 푥표+푥 푉 11

Equation (2.5) is the Energy stored in a parallel plate actuator in terms of the separation distance

between the plates, permittivity of the dielectric, area of the parallel plates and applied voltage.

The electrostatic force in a parallel plate capacitor according to Dean [13] is given as

= (2.6) 퐶 2 퐹 2푑 푉 Where F is the force generated by applying a Voltage to the Capacitor plates having a

separation distance d between the plates.

Substituting the value of Capacitance from equation (2.1) into equation (2.6) will yield

ɛ = (2.7) 표푘퐴 2 2 퐹 2푑 푉 Equation (2.7) is the general equation showing the amount of force generated in a parallel

plate capacitor having one dielectric material.

Now, considering a parallel plate capacitor with two different dielectrics between it, say

for instance, a gripper having the metal plates attached to the first dielectric which is the

gripper material such as plastic or paper and the second dielectric which is another

dielectric or in the case of this thesis, air. In order to get materials that will work with this kind of small device, only polymers will be suitable dielectrics. Even though having low dielectric constants and low energy densities, they are most suitable because of the size of the device and also because they have excellent electrical and processing/manufacturing properties which includes they being inexpensive, lightweight and easy to produce commercially, having high breakdown strength, high dc resistance and low hysteresis

[14]. 12

CHAPTER 3

THEORETICAL ANALYSIS

3.1 Force Equation of a parallel plate capacitor with more than one dielectric

In most studies, the electrostatic force generated by a parallel plate capacitor could only be described with one dielectric in between the plates. This is not always the case as devices that use electrostatic forces such as grippers and suction cups/plates will most times have one or more dielectric materials. Air is considered to be a dielectric and most times can be referred to as vacuum in most electromagnetic applications but is actually different from a vacuum in some electrostatics applications, especially in small applications such as MEMs or Insect-sized devices.

Having said these, we will be considering a parallel plate capacitor with two or more dielectrics in between.

2 휀 1 2 2 푑

푑 휀1 푑1

1 2 푑2 Figure 3.1: Parallel plate capacitor with two dielectrics, in this case, air is considered a dielectric

The figure above shows two parallel plates embedded in the dielectric material which also parallel to each other. 13

is the total distance between the capacitor plates

푑 Where = + (3.1)

푑 푑1 푑2 and are the air gap or separation distance between the dielectrics and the thickness

1 2 of푑 the dielectric푑 material respectively.

and are the absolute permittivity of air and the dielectric material respectively.

휀1 휀2 Where and is = (3.2)

휀1 휀2 휀푖 푘푖휀0 is the relative permittivity of the ‘ith’ material which in this analysis are the dielectric

푖 material푘 and air while is vacuum permittivity.

휀0 From the previous chapter, the capacitance for a parallel plate capacitor was given as

ɛ = 풌 풐푨 ∁ 풅 In a situation where there is more than one dielectric material which in this case comprises of the first dielectric which houses the capacitor plates, and air as the second dielectric, both dielectrics are parallel to the capacitor plates and in other words can be described as a system of three capacitors connected in series on top each other [15].

For capacitors connected in series, the equation is given as

= + (3.3) 1 1 1 퐶 퐶1 퐶2 Therefore substituting the value of C from equation (2.1) into (3.3), will yield 14

= 1 0 + 2 0 (3.4) 1 1 1 푘 휀1 퐴 푘 휀2 퐴 퐶 푑 푑

Therefore, expanding and solving equation (3.4) will yield the value of C to be

= (3.5) 휀0퐴 푑1 푑2 퐶 푘1+푘2 From equation (3.2), the absolute permittivity was given as =

휀푖 푘푖휀0 Therefore, substituting the value of from equation (3.2) into (3.5) and solving, will

푖 yield 휀

= = = (3.6) 퐴 퐴 휀1휀2퐴 푑1 푑2 푑1휀2+푑2휀1 휀2푑1+휀1푑2 퐶 휀1+휀2 휀1휀2 Equation (3.6) can be said as the capacitance where there is more than one dielectric parallel to the capacitor plates.

The electrostatic force in this mechanism which is a function of the energy stored in the capacitor and the distance moved is given as

= (3.7) 퐸 퐹 푑 The energy stored in a capacitor is given in equation (2.2), therefore, substituting this value of E into the force equation (3.7) will give equation (2.6), now substituting the value of d from equation (3.1) and C obtained from (3.6) into the force equation from

(2.6) will give a simplified version of the electrostatic force between a parallel plate capacitor with more than one dielectric shown below. 15

= (3.8) ( )(ퟐ ) 휺ퟏ휺ퟐ푨푽 푭 ퟐ 휺ퟐ풅ퟏ+휺ퟏ풅ퟐ 풅ퟏ+풅ퟐ The force can be seen as a function of an applied voltage, the area of the capacitor plates,

the absolute permittivities and the separation distance, all of which has an impact on how

much force can be generated depending on the altercation of any of these variables and

what material is used as the dielectric.

3.2 Dielectric and Material Selection

In the design of small mechanisms, selecting the right material is essential as this will

have a strong effect on the overall operation and reliability of the entire mechanism.

Choosing the right material depends on the type of application that mechanism is to

perform, for example, a very small mechanism such as a small gripper or suction cup will

require very light weight material with very high strength having the ability to withstand

high voltage without breaking down easily. Table 3.1 shows a table of dielectric materials with their dielectric strength, permittivity and calculated force using the force equation in equation 3.8. A MATLAB program was written to calculate the forces in the table which can be seen in the appendix.

Table 3.1: Table of dielectric materials showing relative permittivity and Force [16]

Dielectric Material Dielectric Force Constant / (N) Permittivity Air 1 0.0492 Paper 3 0.0553

Rubber/Paraffin 2 0.059 Teflon 2.1 0.0596 Waxes/Mineral 2.2 0.0601 Polystyrene 2.6 0.0611 Polyethylene 2.3 0.0615 Polycarbonate 2.9 0.0629 Asbestos Fiber 3.1 0.0635 Epoxy Resin/Nylon 3.4 0.0643 Formica 4.6 0.0648 Porcelain 5.1 0.0672 Graphite 10 0.0703 Ammonia 20 0.072 Methanol 30 0.0726 Glycerol 40 0.0729 50 0.0731 Using this table and the formulas generated earlier on, an analysis showing the general relationship between each of these parameters in graphical form is discussed below.

The parameters and values used for plotting the above table 3.1 and Fig 3.3 were;

= 8.854 10 F/m (Permittivity of free space) −12 휀0 ∗ = Relative permittivity (Dieletric constant) of dieletric materials

푘1 = 1 (Relative permittivity of air)

푘2 = (Absolute permittivity of dielectric materials)

휀1 푘1휀0 = = 1 (Absolute permittivity of air)

휀2 푘2휀0 ∗ 휀0 17

= 0.002 (Separation distance between the dielectric materials)

푑1 푚 = 0.001 (Thickness of dielectric material)

푑2 푚 = 20000 (Applied Voltage)

푉 푉 = 25 10 (Area of the parallel plate capacitors) −5 2 퐴 ∗ 푚 This analysis is very important to help with the design of electrostatic force driven

mechanisms especially with small mechanisms to determine the maximum allowable

force and voltage a mechanism can handle and how to optimize the design by selecting

the right materials and parameters in the design process at low cost.

0.075 Ideal Material 0.07

0.065

Teflon 0.06

0.055 Force (N) Force

0.05

0.045

0.04 0 5 10 15 20 25 30 35 40 45 50 55

Dielectric Constant

Figure 3.2: Graph showing the relationship between Force and Dielectric Constant from table 3.1 above and the location of an Ideal dielectric as well as that of Teflon (dielectric material of choice for the

experiment) 18

From the graph in Fig 3.3 above, the ideal material will be having a dielectric constant of

10 and a force value of about 0.07N since it lies at the saturation point of the graph but dielectric materials at this dielectric constant value and higher cannot be used due to having the chemical and dielectric properties/composition not suitable for an application such as a small parallel plate actuation. Teflon was chosen as a good choice because not only does it have excellent dielectric and chemical properties, it can also exert forces close to that of the ideal material which makes it suitable for this application.

3.3 Expression of dielectric strength of combined materials

This analysis as stated in the first paragraph of this chapter deals with a mechanism with more than one dielectric in-between the capacitor plates, which will have some effect of sort on the dielectric strength of dielectrics combined together, which also has an effect on the overall performance of the mechanism especially with respect to breakdown voltage.

To check for the dielectric strength of multilayered materials, some factors have to be taken into consideration:

i. There is the maximum force at which breakdown voltage occurs.

ii. In order to get the maximum force, an experiment will be set up using a

variable voltage regulator connected to a high DC voltage power source and

the parallel plate actuator in order to determine the voltage at which this force

occurs. This is explained in the next chapter. 19

To find the maximum force when the dielectric strength of the material is known, the following analysis shown below;

Energy stored in a capacitor is given as = from equation (2.2) 1 2 퐸 2 퐶푉 And since = , therefore, = . 퐸 퐶 2 퐹 푑 퐹 2푑 푉 A formula can be derived for finding the maximum force in terms of the dielectric strength, and this maximum force and also the breakdown voltage are going to be achieved experimentally for this analysis.

Breakdown voltage for any given dielectric is given as

= (3.9)

푉푏 푆푖푑 Where is the breakdown voltage;

푉푏 is the dielectric strength of the dielectric material in which in this case Teflon

푖 was the푆 dielectric used in this experiment and

is the total distance between the two capacitor plates (Including the thickness of the dielectrics푑 between the plates).

The maximum force which in this analysis is also called the “break-down” force can be expressed as thus,

= 2 (3.10) 푉푏 퐹 퐶 2푑 20

Which can also be expressed by substituting the value of into equation (3.9) 2 푉푏 = 2 (3.11) 푆푖 푑 퐹 퐶 2 Equation 3.11 can be used to find the maximum force in terms of the dielectric strength of the material.

CHAPTER 4

EXPERIMENTAL SETUP, DATA AND RESULTS

4.1 Setup

For the experimental setup as seen in figures 4.1 and 4.2 below, A Hewlett Packard –

E3630A Triple Output DC power supply set to +/- 20 volt and 4 amps setting was connected from the “com” port to the negative output port of a Kikusui PMC35-1A power controller and to “pin 1” of an Ultravolt 20A12 – P4 DC high voltage power converter. The +20V port of the power supply connected to “pin 2” of the power converter and the positive output port of the PMC35-1A is connected to “pin 6” of the power converter. This converter amplifies the input voltage by approximately 4310 which is then connected from “pin 8” to the negative; and the red high voltage output wire to the positive terminals of the Teflon holders respectively. The terminals are made of thin copper wires connected to the capacitor plates made from Aluminum, the Teflon holders as well as the base on which they rest, are made of Delrin plastic material.

Teflon was the choice of dielectric material because of its excellent dielectric properties such as high dielectric strength and very good dielectric constant. And Delrin was used as the base plate for the setup to ensure proper insulation throughout the process which can be seen in the experimental setup and figures below.

HP-E3630A Power Supply Kikusui PMC35-1A Power Controller

UV 20A12-PA DC power converter

Teflon - +

Figure 4.1: Schematic Diagram of the experimental setup

Figure A Figure B

Figure C Figure D

Figure E Figure F

Figure G

Figure 4.2: Figures A-D shows pictures of the experimental setup for the Teflon in its holders and

Figures E-G shows the pictures of the connection port labels on the power supply and power controller as well as the pin numbers and labels on the high voltage DC converter.

4.2 Data and Test

In the experimental setup, series of tests were taken with different thicknesses (d2) of

Teflon material and air gaps (d1) ranging from 1mm to 4mm to find and determine the

effect of the factors such as material thickness (Teflon thickness of 0.5mm, 1mm, 1.5mm

and 2mm), and air gap in the breakdown of the material. This is achieved by increasing

the voltage across the system using the Kikusui PMC35-1A power controller until the

Teflon material breaks down. Teflon Dielectric strength table showing the breakdown

voltage from the experiment performed can be seen in the index page.

4.3 Results

Using the Experimental table, the maximum force produced at each value of d1 (mm) and d2 (mm) can be determined by applying the force equation 3.8 and substituting the value of Voltage (V) to become the breakdown voltage (Vb) to become

= (4.1) ( )(2 ) 휀1휀2퐴푉푏 퐹푚푎푥 2 휀2푑1+휀1푑2 푑1+푑2 Table 4.1 below shows the values of the maximum force generated by Teflon at each

value of air gap distance (d1) ranging from 1mm to 4mm and each Teflon thickness

(d2) values of 0.5mm, 1mm, 1.5mm and 2mm.

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.

d2 d1 Fmax (Low) Vb (Low) Fmax Vb (Average) Fmax Vb (High)

(mm) (mm) (N) (V) (Average) (N) (V) (High) (N) (V)

0.5 1 0.0106 13317.9 0.0113 13796.31 0.0123 14395.4

2 0.0043 14697.1 0.0048 15503.07 0.0053 16291.8

3 0.0029 17153.8 0.0034 18576.1 0.0036 19308.8

4 0.0019 18231.3 0.0022 19623.86 0.0025 20946.6

1.0 1 0.0055 12111.1 0.0066 13292.04 0.0085 15085

2 0.0031 14438.5 0.0035 15300.5 0.0043 16938.3

3 0.0020 15990.1 0.0023 16977.09 0.0028 18619.2

4 0.0018 18877.8 0.0021 20636.28 0.0028 23877.4

1.5 1 0.0042 12714.5 0.0052 14162.66 0.0060 15214.3

2 0.0021 13404.1 0.0027 15218.61 0.0033 16938.3

3 0.0017 16248.7 0.0021 17839.09 0.0029 20989.7

4 0.0014 18058.9 0.0017 20084.6 0.0024 23920.5

2.0 1 0.0026 11723.2 0.0034 13317.9 0.0040 14610.9

2 0.0019 14136.8 0.0021 15089.31 0.0025 16421.1

3 0.0014 15817.7 0.0017 17326.2 0.0022 19696.7

4 0.00099 16334.9 0.0012 18140.79 0.0015 20084.6 26

Where:

Fmax (Low), Fmax (Average), and Fmax (High) are the lowest, average and highest maximum forces that can be exerted by the dielectric material just before is breaks down.

From the data obtained in experimental breakdown voltage table (see Appendix), it can be inferred that the breakdown voltage of Teflon is not dependent on its thickness

(d2) but the maximum force that can be generated are dependent of factors such as the material thickness, the separation distance and the voltage.

From the above tables (4.1) and the index table, it can be seen that: i. At constant separation distance, the maximum force decreases as the thickness

of the dielectric material is increased. This infers that in the design of small

millimeter sized electrostatic devices, in order to get the required or maximum

force the device can exert, for example, the force a gripper of such size will

exert on the object it is gripping, the thickness of the material will have to be

taken into consideration as it is an important factor. ii. At constant dielectric material thickness, the maximum force decreases while

the breakdown voltage increases as the separation distance increases. This

infers that in the case of a small millimeter sized gripper using electrostatic

actuation; it would require a much higher voltage but lesser gripping force to

pick objects as they get bigger.

CHAPTER 5

CHALLENGES, RECOMMENDATIONS AND CONCLUSION

5.1 Challenges

Due to the limited voltage range of the Ultravolt power converter, the experiment could only be conducted for separation distances of 1mm to 4mm, clear and concise readings could not be determined for distances above 4mm.

5.2 Recommendations

More research can be conducted in finding the direct relationship between the dielectric constant and dielectric strength as it can be seen from the experiments and research that a good material for such a design is not only dependent on the dielectric constant of the material or dielectric strength alone but on a combination of these two parameters.

Also, Teflon is a good material of choice but there are other dielectric materials that may yield better results than Teflon. Teflon was chosen for this experiment because of its good dielectric properties such as good dielectric constant, a very high dielectric strength and having low cost and available.

5.3 Conclusion

The design of small electrostatic force driven devices is a large pool with a lot of potentials to be researched and determined. It can be seen from this research that the effect of multilayered dielectrics such as the combination of a dielectric material and air 28

gap (air is considered a dielectric in this kind of situation and its effect is not negligible) has a large effect on the design of very small devices that work on the principle of electrostatic actuation especially the amount of force these combinations can exert.

Also in order to either make a fresh design of a small device that operates on this

principle or if it is optimizing an existing design, the parameters to be considered are the

type of material, the separation distance between the plates, the maximum amount of

force that can be generated or exerted by the device, the effect of breakdown voltage and

the thickness of the material, depending on what action the design is to perform.

This design analysis can be applied to all dielectric materials.

APPENDIX A

MATLAB program showing the force equation 3.8

APPENDIX B

Table showing the experimental data indicating the breakdown voltage of Teflon for different separation distances and dielectric thicknesses.

Dielectric strength -PPM experiment plan

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