Development of a Hybrid Linear Actuator

Baoping Wen

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Mechanical and Industrial Engineering University of Toronto

©Copyright Baoping Wen 2011

Baoping Wen

Master of Applied Science

Mechanical and Industrial Engineering University of Toronto

2011 Abstract

This thesis focuses on the development of a novel hybrid linear actuator (HLA). The research includes the optimal design, the particular fabrication, and the experimental validation.

The principle of the HLA is based on the integration of the mechanisms of the solenoid actuator and the voice coil actuator. Such integration is achieved by a magnetic circuit consisting of a magnetic flux orientator, a permanent magnet, a composite shell, and a special coil. The HLA is capable of having a high repelling force at one end and a high attractive force at another end. A step-optimization technique is developed and used to determine the key parameters of the HLA, with the aid of sweeping functions in finite element analysis. Moreover, a single-pulse power supply is specially designed and prototyped for driving the HLA. The performance of the HLA is systematically characterized by simulations and experiments.

To my Mom and Dad,

My dear wife, Wendy Wang,

My lovely daughter, Mei, and my son, Marcus

iii

Acknowledgments

I would like to express my gratitude to my advisor, Professor Jean W. Zu, for her full support and guidance throughout my graduate life. Professor Zu’s patience and encouragement bolstered my confidence and fueled my excitement in my work. Under her mentorship, I have grown as a researcher and gradually become much more competent. I am grateful for Professor Zu, as she provided a research platform which helped me integrate my personal interests and social demands.

I would also like to thank Mr. Mats Lipowski and Mr. Anthony Wong, engineers from Vicicog Inc., for providing the design requirement of the actuator and relevant information for the synchronized segmentally interchanging pulley transmission system (SSIPTS) project.

My gratitude belongs to my labmates, Mr.Vahid Mashatan, Ms. Maby Boado, Mr. Wei-Jun Su, Mr. Yang Zhu and Ms.Roshanak Banan, as well. Vahid provided his continuing support in the control design of the experiment set-up. Maby and Wei-Jun gave their sincere suggestions on the format of thesis writing. Yang presented his useful ideas in graphing, and Roshanak offered her valuable proof-reading for the draft version.

I also present my sincere appreciation to Mr. Ryan Mendell, manager of the MIE machine shop in University of Toronto, for providing the convenience and help in the fabrication of the actuator prototyping.

I would like to thank Professor James K. Mills and Professor Yu Sun for serving on my thesis committee and offering their generous comments during their busy academic activities.

Table of Contents

Acknowledgments ...... iv

Table of Contents ...... v

List of Tables ...... ix

List of Figures ...... x

List of Appendices ...... xiv

List of Symbols, Abbreviations and Nomenclature ...... xv

Chapter 1 Introduction ...... 1

1.1 Background and Motivation ...... 1

1.2 Requirements of the New Actuator ...... 3

1.3 Objectives ...... 4

1.4 Thesis Overview ...... 4

Chapter 2 Literature Review ...... 6

2.1 Overview of Actuators ...... 6

2.1.1 Classification of Actuators ...... 6

2.1.2 Characterization of Actuators ...... 7

2.2 Electromagnetic Actuators ...... 9

2.2.1 Nature of Magnetic Interactions ...... 9

2.2.2 Principles of Electromagnetic Actuators ...... 13

2.2.3 Advantages of Electromagnetic Actuators ...... 15

2.3 Improvement of Electromagnetic Actuators ...... 15

2.3.1 Efficient Magnetic Circuit Configurations ...... 16

2.3.2 Improvement of Material Properties ...... 17

2.3.3 Optimal Design of Magnetic Field ...... 20

2.3.4 Inspiration from Electromagnetic Catapult ...... 21

Chapter 3 Conceptual Design ...... 22

3.1 Global Geometric Constraints of Actuators in SSIPTS ...... 22

3.2 Speed Constraints of SSIPTS ...... 24

3.3 Magnetic Circuit Design ...... 28

3.3.1 Concept of Magnetic Circuit ...... 28

3.3.2 Physics of Electromagnetic Actuators ...... 29

3.3.3 Comparison of Magnetized Direction ...... 30

3.4 Structural Design of the Novel Actuator ...... 33

3.4.1 Parameterized Geometry Design ...... 33

3.4.2 Material Selections ...... 36

3.5 Summary ...... 37

Chapter 4 Modeling and Simulation ...... 38

4.1 Basic Electromagnetism ...... 38

4.1.1 Maxwell’s Equations ...... 38

4.1.2 Constitutive Relations ...... 40

4.1.3 Boundary and Interface Conditions ...... 40

4.1.4 Electromagnetic Energy ...... 41

4.1.5 Electromagnetic Forces ...... 42

4.2 Setup of Finite Element Analysis ...... 44

4.2.1 FEA Expression of Electromagnetic Problems ...... 44

4.2.2 Geometrical Modeling of the Actuator in FEA ...... 46

4.2.3 Physics Setting of Model Domains ...... 47

4.2.4 Meshing of the FEA Model ...... 51

4.2.5 Solver Setting ...... 53

4.3 Optimization of the Actuator Design ...... 54

4.3.1 Optimization of Magnet Thickness ...... 54

4.3.2 Optimization of Magnet Length ...... 56

4.3.3 Optimal Combination of Shell Materials ...... 58

4.4 Performance Characterization of the HLA ...... 60

4.4.1 Force Output Distribution vs. Coil Current and Coil Position ...... 60

4.4.2 Predicted Specific Behaviors of the HLA ...... 61

4.5 Reliability Assessment of the Simulation ...... 64

4.5.1 Comparison of Force Calculation in Different Methods ...... 64

4.5.2 Validation of the MotiCont Voice Coil Actuator ...... 66

4.6 Summary ...... 68

Chapter 5 Fabrication ...... 69

5.1 Constructions of the Magnetic Assembly ...... 69

5.1.1 Integrity of the Properties of the Magnetic Materials ...... 69

5.1.2 Integrity of Magnetic Circuits ...... 71

5.2 Coil Winding ...... 73

5.2.1 Filling Factors of Conductors in a Coil Window ...... 73

5.2.2 Coil Calculation ...... 74

5.2.3 Bobbin Machining ...... 75

5.3 Final Prototypes ...... 76

5.4 Summary ...... 77

Chapter 6 Design and Fabrication of the Pulse Power Supply ...... 78

6.1 Requirements in Driving the New Actuator ...... 78

6.2 Design and Construction of the Pulse Power Supply ...... 79

vii

6.3 Summary ...... 82

Chapter 7 Experiment ...... 83

7.1 Experiment Set-up ...... 83

7.1.1 Experiment Jigs and Fixtures ...... 83

7.1.2 Experimental System Configuration ...... 85

7.1.3 Force Sensor Calibration ...... 87

7.2 Data Collection and Analysis ...... 88

7.2.1 Magnetic Force Variations over Coil Current and Coil Position ...... 88

7.2.2 Magnetic Force Variations over Soft Magnetic Materials ...... 93

7.2.3 More Strict Comparisons between Simulation and Experiment ...... 95

7.2.4 Variations of Coil Inductances ...... 98

7.2.5 Actuation Time Prediction ...... 100

7.2.6 Comparison of the New Actuator with Commercial Products ...... 101

7.3 Summary ...... 102

Chapter 8 Conclusions and Future Work ...... 103

8.1 Conclusions ...... 103

8.2 Applications ...... 104

8.3 Future Work ...... 104

Appendices…...... 111

viii

List of Tables

Table 2-1: Actuator Classification by Energy Input ...... 7

Table 2-2: Properties of Different Hard Magnetic Materials ...... 19

Table 3-1 Output Force Demand of the Actuator Regarding Different Rotating Speed ...... 27

Table 3-2: Analogous Comparison of the Magnetic Circuit and the Electrical Circuit ...... 28

Table 3-3: Parameterized Dimensions in SolidWorks Model ...... 34

Table 3-4: Parameterized Dimensions in SolidWorks Model (continued) ...... 35

Table 4-1: Parameter List for Geometric Modeling of the New Actuator ...... 47

Table 4-2: Partial Differential Equations (PDEs) and Constitutive Equations of Domains ...... 48

Table 4-3: Functions of Soft Magnetic Materials (CoNetic AA and Netic S3-6) ...... 50

Table 4-4: Solvers with Corresponding Features ...... 53

Table 4-5: Force Comparison for Different Calculation Means and Different Meshing Sizes .... 64

Table 4-6: Performance Data from Simulation and Datasheet of MotiCont Linear VCA ...... 67

Table 5-1: Numbers of Turns of Coil Calculation ...... 74

Table 5-2: Physical Parameters under Fabrication ...... 76

Table 7-1: Load Cell FC2231 Calibration ...... 87

Table 7-2: Performance Comparison with Commercial Products ...... 101

List of Figures

Figure 1-1: Gear Shift in SSIPTS Transmission System ...... 2

Figure 1-2: The Geometric Constraint of Actuators in SSIPTS Package ...... 3

Figure 2-1: Capacity of Actuators Characterized by Force vs. Stroke ...... 8

Figure 2-2: Agility of Actuators Characterized by Frequency vs. Weight ...... 9

Figure 2-3: Origin of Magnetism at Atomic Level ...... 10

Figure 2-4: Responses of Different Materials to the Same Magnetic Field ...... 11

Figure 2-5: Interaction of Two Magnetic Fields Built Up by Direct Currents ...... 12

Figure 2-6: Principle of Voice Coil Actuator Governed by Lorentz’s Law ...... 13

Figure 2-7: Principle of Solenoid Actuator Governed by Variable Reluctance ...... 14

Figure 2-8: Halbach Cylinders with Different Wavenumbers (k) ...... 16

Figure 2-9: Focus Effect of Magnetic Flux in the New VCA (Courtesy of BEI Kimco) ...... 17

Figure 2-10: Properties of Advanced Soft Magnetic Materials ...... 18

Figure 2-11: Properties of Hard Magnetic Materials ...... 19

Figure 2-12: Thrust Force Improvement by Composite Coil Conductors ...... 20

Figure 2-13: Catapult Force (Strong Field Interaction) ...... 21

Figure 3-1: Geometric Constraints of Actuators in SSIPTS ...... 22

Figure 3-2: Layout of Actuators in SSIPTS ...... 23

Figure 3-3: Space Using Efficiency of Different Cross-Section Shape of Actuators ...... 24

Figure 3-4: Actuation Force Behaviors Required by SSIPTS ...... 25

Figure 3-5: Typical Actuating Strategy ...... 26

Figure 3-6: Relations of Motion Parameters During Actuation Process ...... 27

Figure 3-7: Physics of Electromagnetic Actuators ...... 29

Figure 3-8: Force Behaviors of Electromagnetic Actuators ...... 30

Figure 3-10: Magnetic Field Interaction at Different Magnetic Configurations ...... 31

Figure 3-9: Coils Working in Perpendicular Field ...... 31

Figure 3-11: Magnetic Flux Peripheral Distribution at Different Configurations ...... 32

Figure 3-12: Concept Design of the Proposed Actuator ...... 36

Figure 3-13: Primary Material Selection of the Concept Design of the New Actuator ...... 37

Figure 4-1: Energy Density and Coenergy Density at Work ...... 42

Figure 4-2: Maxwell Stress Tensor at Material Boundaries ...... 43

Figure 4-3: ½ 2D FEA Model of the New Actuator ...... 48

Figure 4-4: BH Curves of Different Permalloys from the Manufacturer ...... 49

Figure 4-5: Working Behavior of Different Magnets at Room Temperature ...... 51

Figure 4-6: Coarser Meshing and Finer Meshing for Different Purposes ...... 52

Figure 4-7: Magnetic Flux Distribution in Optimizing Magnet Thickness ...... 54

Figure 4-8: Optimization of Magnet Thickness ...... 55

Figure 4-10: Energy Integration for a Particular Magnet Length ...... 57

Figure 4-9: Force Distributions over Coil Position and Magnet Length ...... 57

Figure 4-11: Distribution of Energy Integration over Different Magnet Lengths ...... 58

Figure 4-12: Shielding Effects of Different Soft Materials ...... 59

Figure 4-13: Output Force Distribution vs. Coil Current and Coil Position ...... 60

Figure 4-14: Force Behavior over Coil Current at Different Coil Positions ...... 62

Figure 4-15: Force Behavior over Coil Position at Different Coil Currents ...... 63

Figure 4-16: Force Comparison with Meshing Effect ...... 64

Figure 4-17: Modeling and Simulation of MotiCont Actuator ...... 66

Figure 4-18: Performance Validation of MotiCont Actuator ...... 67

Figure 5-1: Operating Point Variance Due to Changing Temperature ...... 70

Figure 5-2: Machining Effect on Magnetic Properties of Permalloy ...... 71

Figure 5-3: Patterns of Sheet Metal Process ...... 72

Figure 5-4: Filling Factors in Different Winding Patterns and Different Magnet Wires ...... 73

Figure 5-5: Coil Winding Calculation ...... 74

Figure 5-6: Bobbin Structure Assembly ...... 75

Figure 6-1: Design of the Variable Voltage and High Current Pulse Power Supply ...... 80

Figure 6-3: Panorama of the Variable Voltage and Variable Current DC Power Supply ...... 81

Figure 6-2: Pulse Generation by IC 555 Connected as the Mono-stable Status ...... 81

Figure 7-1 : Repelling Force Experiment Jigs and Fixtures ...... 84

Figure 7-2: Attracting Force Experiment Jigs and Fixtures ...... 84

Figure 7-3: Experimental System Configuration ...... 85

xii

Figure 7-4: Block Diagram of the System Configuration in LabView ...... 86

Figure 7-5: Integrated Display and Measurement of Force, Current, Voltage, and Signal ...... 86

Figure 7-6: Instron 8511 Testing Machine ...... 87

Figure 7-7: Experiment of Repelling Force over Coil Position and Coil Current ...... 89

Figure 7-8: Variation of Repelling Force Constant over Coil Current and Coil Position ...... 90

Figure 7-9: Experiment of Attracting Force over Coil Current and Coil Position ...... 91

Figure 7-10: Variation of Attracting Force Constant over Coil Current and Coil Position ...... 92

Figure 7-11: Force Comparison over Coil Current for Different Shell Material Combinations .. 93

Figure 7-12: Force Constant Comparison of Different Shell Material Combinations ...... 94

Figure 7-13: Point-Point Force Comparison at the “0” Coil Position ...... 95

Figure 7-14: Force Constant Point-Point Comparison at the“0” Coil Position ...... 96

Figure 7-15: Point-Point Force Comparison at the Middle of Stroke ...... 97

Figure 7-16: Force Constant Point-Point Comparison at the Middle of Stroke ...... 97

Figure 7-17: Solenoid Effect of the Orientator Working as a Core ...... 98

Figure 7-18: Coil Inductance of the New Actuator vs. Coil Position and Frequency ...... 99

Figure 7-19: Agilent E4980A Precision LCR Meter for Inductance Measurement ...... 99

Figure 7-20: Force Variation During the Actuating Movement ...... 100

xiii

List of Appendices

Appendix A Magnetic Unit Conversions ...... 111

Appendix B Permanent Magnet Material Datasheet ...... 112

Appendix C Datasheet of MotiCont Voice Coil Actuator ...... 113

Appendix D BEI Product Performance List ...... 114

Appendix E Sweeping Applied in Magnet Thickness and Magnet Length ...... 115

Appendix F Superposition of Magnetic Fields ...... 116

xiv

List of Symbols, Abbreviations and Nomenclature

A Magnetic Vector Potential R Electric Resistance

A Area R Magnetic Reluctance

B Magnetic Flux Density S Cross-Section Area

Br Remnant Magnetic Flux Density s Stroke of Motion

C Capacitance T Maxwell’s Stress Tensor

D Electric Flux Density T Actuating Duration time

E Electric Field Intensity Tr Rotational Period

F Force V Volume

F Magnetomotive Force (MMF) V Electric Voltage

H Magnetic Field Intensity v Velocity

Hc Coercive Force of Magnetic W General Energy Materials

I Electric Current Wco Coenergy

J Current Density We Electric Energy

L Length of Conductor Wm Magnetic Energy

L Inductance of Coil w Energy Density l Length of Magnetic Path wco Coenergy Density

M Magnetization Vector we Electric Energy Density m Magnetic dipole moment wm Magnetic Energy Density m Mass Wk Kinetic Energy

MMF Magetomotive Force Wme Mechanical Energy

N Number of Coil Turns µ Magnetic Permeability

xv n Unit Normal Vector of Surface µ0 Magnetic Permeability in Vacuum

µ r Relative Magnetic Permeability χm Magnetic Susceptibility

Φ Magnetic Flux ∇× Curl Operator

Ω Domain ∇∙ Divergence Operator

σ Electric Conductivity BHmax Magnetic Energy Product

ε Electric permittivity

xvi

Chapter 1

Introduction

The thesis is focused on the development of a novel actuator with high power output efficiency, characterized by high acceleration and a compact volume. This actuator employs the concept of magnetic field interaction, generated by a solenoid coil and a permanent magnet. Such an energy conversion device mainly supplies a large force and an instantaneous linear motion in the actuation process of segment switching in the synchronized segmentally interchanging pulley transmission system (SSIPTS).

1.1 Background and Motivation

An actuator is an energy-converting device that employs one or more energy sources to achieve a mechanical motion. Such a mechanical motion is either linear or rotary, depending on the specific application. The performance of the actuator is mainly represented by the output force, the motion stroke, the mover mass, the power density, and so on. Furthermore, the working mode includes point-to-point position control and continuous coordinate control. The point-to-point mode is sometimes called “bang-bang control” and only pays attention to the start position, the end position, and the total duration, regardless of the process in between, while the continuous mode focuses on the linearity and precision of the motion. There are varieties of actuator driving mechanisms, such as the piezoelectric effect, the shape memory effect, electromagnetic interactions and so on. However, designing an actuator with higher force, longer stroke and more compact geometry is still challenging work in some applications: for instance, the shift actuation in the synchronized segmentally interchanging pulley transmission system (SSIPTS).

The synchronized segmentally interchanging pulley transmission system is a newly designed variable mechanical transmission that combines benefits of existing transmission systems for different industries such as automotive, wind turbine, and HVAC (heating, ventilation, and air conditioning). The working principle of the gear shift in the transmission system is shown in Figure 1-1. The key components in SSIPTS are two morphing pulleys, which change size while connected to a belt. These morphing pulleys are divided into segments called pulley segments. To change drive ratios, pulley segments are rapidly inserted laterally into the position in which they will engage the belt using high-speed actuators. Each morphing pulley is comprised of several sub-pulleys of different sizes, which can take each others’ place by swapping small segments of one pulley for segments of another. When all the segments are swapped, the transition from one pulley size to another is complete. The pulley segments only move while they are not transmitting the load. When SSIPTS is not performing a shift, it operates like normal pulley and belt systems [1] [2].

Figure 1-1: Gear Shift in SSIPTS Transmission System

To ensure high reliability at the high speed and load conditions required for automotive, wind turbine and HVAC applications, SSIPTS needs high speed actuators. A novel bidirectional actuator is required for the individual actuation of the pulley segments. The actuators will be integrated into morphing pulleys and rotate along with the pulley segments. Each pulley segment

2 is required to move axially in a very short time, depending on the rotational speed of the pulleys. The actuator moves the pulley segment into the desired location for both directions. Figure 1-1 depicts the location of actuators.

1.2 Requirements of the New Actuator

The requirements for the new actuator are that it be constructed in a compact size capable of being installed in the transmission package and that it provide enough force to finish the actuation quickly in the transitional area of SSIPTS.

a) 3D profile b) The actuator locations in sector zones Figure 1-2: The Geometric Constraint of Actuators in SSIPTS Package

The basic model of SSIPTS contains three movable segment layers, equally portioned in eight sectors along the circumference. Therefore, the geometrical constraint comes from the space limitation of the sector zones, including the shape and the cross-sectional area, shown in Figure 1-2, where three actuators must be situated in the envelope of the movable segment layers. According to the primary geometric calculation, one of the major requirements for the design is that the new actuator has a thickness of less than 12mm and a width of less than 40mm.

The requirements for the accelerating performance of the new actuator depend on the rotation speed and the moving distance of the pulley segment gear, since the actuation is required to complete in the transition area, shown in Figure 1-1, and the pulley segment must be fully engaged in the belt. The pulley’s different rotation speeds require different actuation times and

3 different accelerations. Therefore, based on Newton’s second law of motion, the necessary actuating force depends on the demanding acceleration and the moving mass. According to the formulae introduced in Chapter 3, the output force of the actuator must be greater than 48 newtons in order to successfully actuate the pulley segment of the SSIPTS system.

1.3 Objectives

The major objectives of this thesis include the parametric design, the FEA (finite element analysis) modeling, the prototyping, and the performance characterization of the novel hybrid linear actuator (HLA). They are described in detail as follows.

1. To design the hybrid linear actuator (HLA) that is able to provide high actuation force and rapid speed in a compact geometry 2. To perform a step optimization process, by which the optimization of the newly designed HLA is simplified 3. To fabricate the HLA by means of proper manufacturing processes, where the designed properties are consistent 4. To design and prototype a pulse-current power supply with wide variable range of voltage and high-current output for effectively driving the HLA 5. To test and characterize the performance of the HLA by experiments

1.4 Thesis Overview

Chapter 2 summarizes the relevant concepts and advancements pertaining to the electromagnetic actuator modeling, the magnetic interaction, the magnetic force calculation, and the optimization techniques.

Chapter 3 introduces the concept design of a hybrid linear actuator (HLA) to satisfy the requirements of the space and the speed in SSIPTS. To achieve high force output and controllability, a hybrid working mode of the linear solenoid actuator and the linear voice coil actuator is proposed. In addition, the parameterized design is used for further improvement.

Chapter 4 reviews the principle of magnetism and the FEA implement in solving electromagnetic problems. The FEA modelling procedures of the HLA are introduced in detail. In the systematic analysis of the HLA, a simplified optimization process called step-optimization is proposed and effectively used to determine the key parameters, magnet thickness and magnet length, with the aid of the parameter-sweeping function embedded in COMSOL Multiphysics. The principle of energy integration combined with the sweeping technique is preferred in the optimization of the magnet’s length.

Chapter 5 discusses the manufacturing process of the HLA. Cautions to keep the extraordinary properties consistent are proposed in dealing with the advanced magnetic materials. Experiences are shared with readers in the fabrication of the new actuator. The stress sensitivity and temperature sensitivity of magnetic materials are reviewed in detail. The coil-winding technique is presented as well.

Chapter 6 presents the specific pulse power supply and control for driving the HLA. The variable voltage DC power supply is designed and assembled, which consists of a 3kw voltage regulator, an isolate transformer, a bridge rectifier and a capacitor bank. The control system is presented, which includes a pulse generator, a set of power MOSFETs, a voltage divider, a current sensor, a force sensor, and a LabView data acquisition and analysis system.

Chapter 7 introduces the experiment setup, data collection procedure, and data analysis method. Further explorations are made in revealing the mechanism of the HLA with superb performance.

Chapter 8 outlines the conclusion drawn from this research, discusses more potential applications of the HLA, and suggests further work for improving the design of the HLA.

Chapter 2 Literature Review

This chapter summarizes the most relevant concepts and advancements pertaining to electromagnetic actuator modeling, magnetic interaction, magnetic force calculation, and optimization techniques.

2.1 Overview of Actuators

2.1.1 Classification of Actuators

As an energy converting device, an actuator transforms energy from one or more external sources into mechanical energy in a controllable way [3]. Since many mechanisms can be involved in an individual or hybrid actuating devices, it is rather difficult to present a clear or complete classification of actuators. According to different operating principles and applications, one can find a wide variety of actuator types. They can be classified as translational actuators (linear actuators) and rotational actuators (angular actuators) based on the motion types. They can also be categorized as active actuators (positive power flow) and semi-active actuators (negative power flow) by the sign of power flow. Furthermore, they can be grouped into soft actuators (pulling force) and hard actuators (push-pull) via the sign of output force as well [4]. Essentially, the actuator input quantities depend on the type of energy used. Among all the quantities involved in the energy conversion from the energy source to the energy output, some of them can be chosen as the input quantities. In general, based on energy domains, researchers categorize actuators as the following types, among others: electromagnetic, electromechanical,

6 fluidic, piezoelectric, smart material [5] [6]. Table 2-1 illustrates such a classification and the corresponding applications.

Table 2-1: Actuator Classification by Energy Input

Class of Actuator Energy Transform Application Electromagnetic Electrical-Magnetic-Mechanical Solenoid, Voice Coil Electromechanical Electrical-Mechanical Linear Drive, MEMS Comb Drives

Fluidic Potentials-Mechanical Hydraulics, Pneumatics Piezoelectric Electrical-Mechanical Ceramic, Polymer

Smart Materials Thermal-Mechanical Shape Memory Alloy, Bimetallic Natural Biological-Mechanical Human Muscle

Electromagnetic actuators include solenoids, moving coil, and linear motors. The magnetic field interaction between coils or permanent magnet generates actuating actions, achieved by a closed magnetic circuit. Piezoelectric actuators create stress and strain by employing the converse effect of piezoelectric materials, where the application of an electrical field generates mechanical deformation in the crystal. The mechanism of actuation in shape memory alloys is a temperature-induced phase change that produces significant shear strain when the material temperature is above the transformation temperature. Hydraulic and pneumatic actuators provide force and displacement via the flow of a pressurized fluid. Muscles as natural actuators exploit the ability of the cross bridges at the heads of the myosin molecules to change shape, detach, and reattach further along the actin fibres.

2.1.2 Characterization of Actuators

The evaluation criteria of actuating performance vary extensively due to the different constructing mechanisms of actuators. The performance index of an actuator is the integrated expression of the actuator’s characteristics and is used to measure the effectiveness of the actuation [7]. In general, the most significant indices are the output force, prescribed displacement, working speed, response time, overall stroke, and power density. In some applications, acceleration and jerk (the acceleration rate) are also important indicators. The range of force, displacement, and stroke predetermine the application situation, on micro or macro

7 scales. The level of work speed, response time, and power density are then used to classify the dynamic behavior, as a high or low level of acceleration.

Figure 2-1: Capacity of Actuators Characterized by Force vs. Stroke (Courtesy of Marc Zupan et al.)

The actuators that are constructed by different mechanisms demonstrate different performances, and hence determine their engineering applications. Figure 2-1 shows the actuating abilities of the maximum output force and maximum stroke with respect to different operating principles. Figure 2-2 exhibits a type of dynamic behaviors of different actuators represented by the relationship of maximum working frequency and actuator weight [8]. For instance, magnetostrictive actuators and piezoelectric actuators could provide a very high actuating force and work at very high frequencies (fast response), but their working stroke is very limited. Hydraulic actuators and electric cylinder actuators could provide rather high forces and a longer

Figure 2-2: Agility of Actuators Characterized by Frequency vs. Weight (Courtesy of Marc Zupan et al.) stroke, but they only work at relatively low frequencies, namely at a slower response. Therefore, in specific engineering applications, experienced designers need to weigh the differences in performance indices, cost and reliability, and then locate a balanced point.

2.2 Electromagnetic Actuators

2.2.1 Nature of Magnetic Interactions

Electromagnetic actuators employ magnetic field interactions to generate magnetic forces and produce mechanical motions. The magnetic field built up by the electric coil or the permanent magnet dates back to the origin of the magnetism, due to the interaction between the two micro- or macro- currents.

The magnetic field generated by the current (i.e., a continual flow of charges), described by the Biot-Savart law, always satisfies Gauss’s law and Ampère's law of magnetism [9]. The magnetic

9 field created by the permanent magnet originates from the microcurrent inside the atomic structure. The magnetism in magnetic materials is contributed by the movement of the electron at the atomic level, as shown in Figure 2-3. It comes from the spin moment and the orbital moment of the electron [10] [11] [12].

Figure 2-3: Origin of Magnetism at Atomic Level

The world's strongest magnetic field (51 Tesla) used for the quantum beam experiment, was created by a team of Japanese researchers at the BL22XU beamline of SPring-8 [13]. The strongest, naturally occurring fields are found on a new kind of neutron star called a magnetar. Its magnetic flux density can exceed 1000 trillion gauss (100 billion tesla) [14]. The strength of the flux density at the Earth’s surface ranges from less than 0.3 gauss in the area including most of South America and southern Africa to over 0.6 gauss around the magnetic poles in northern Canada and south of Australia, and in part of Siberia [15].

The magnetic field of a material depends on its magnetization ability. The magnetization of materials is represented by M, the number (N) of magnetic dipole moments (m) per volume (V), given by

N Mm (2-1) V

It defines magnetic field intensity H as

MH m (2-2)

where χm is called the magnetic susceptibility, the degree of magnetization of a material in response to an applied magnetic field. The relationship between magnetic flux density B and H is described as

BHMHHH0(  )   0 (1  mr )   0    (2-3)

-7 where μ0 (as a physical constant, 4π×10 Η/m) is the magnetic permeability in free space

(vacuum, air), μr is the relative permeability, and μ is the permeability of a material.

a. Free-space (air) b. Diamagnetic materials c. Ferromagnetic materials Figure 2-4: Responses of Different Materials to the Same Magnetic Field

Based on the degree of magnetization of materials in a magnetic field, there are several types of magnetizations, such as diamagnetism, paramagnetism, ferromagnetism and so on. Diamagnetic materials, such as carbon (C), copper (Cu) and plastic, have a relative magnetic permeability of less than 1 (i.e., they have negative magnetic susceptibility). A superconductor acts as an essentially perfect example of diamagnetic materials. When placed in a magnetic field, it excludes the field, and the flux lines avoid passing the conductor region. The relative magnetic permeability of paramagnetic materials, such as platinum (Pt), aluminum (Al), and oxygen (O2), is greater than 1; these materials, therefore, possess a positive magnetic susceptibility. The direction of magnetic moment induced by external magnetic field is the same as the applied field.

The ferromagnetic materials, such as iron (Fe), cobalt (Co), and nickel (Ni) possess very high magnetic susceptibilities and their relative permeability is far greater than 1 [16]. Figure 2-4 illustrates the responses of different materials with different relative permeabilities to one magnetic field.

The magnetic force reactions of two objects come from the interactions between the two magnetic fields. We know that the magnetic field of a magnet bar is equivalent to the field of a solenoid coil. Therefore, other magnetic fields generated by complex magnet structures are legitimately understood as the integrations of magnetic fields caused by electric currents (i.e. the

a. Attraction between two conductors b. Repulsion between two conductors

Figure 2-5: Interaction of Two Magnetic Fields Built Up by Direct Currents movements of electrons inside the magnetic materials). In general, all interactions between magnetic fields can be understood the interactions between the electric currents. The magnetic fields of parallel current-carrying conductors of infinite length are the simplest cases. Each conductor generates a circular magnetic field, the final distribution of which obeys the superposition rule at the linear range. As shown in Figure 2-5, currents of the same direction result in an attractive force and currents of the opposite direction generate a repulsive force. The essence of these interactions originates from the magnetic force on a moving charge in the magnetic field, illustrated by Lorentz’s law [17].

2.2.2 Principles of Electromagnetic Actuators

Electromagnetic actuators convert electrical and/or magnetic energy in the form of voltage and current to mechanical energy in the form of motion (force and displacement). The magnetic force, generating a mechanical motion over a limited range, is the magnetic field interaction built by the current-carrying coil or the permanent magnet [18]. Most often, these actuators can be divided into two different categories, fixed-field actuators and variable-field actuators, based on the distributions of magnetic fields in the actuators [19].

a. Force on current-carrying conductor b. Voice coil actuator (Courtesy of BEI Kimco) Figure 2-6: Principle of Voice Coil Actuator Governed by Lorentz’s Law

Fixed-field actuators, such as voice coil actuators (VCA) or moving coil actuators, are those where the magnetic field distribution does not significantly change during the actuating process. This mechanism, shown in Figure 2-6 [20], is based on the interaction between the two magnetic fields generated by a coil and a permanent magnet respectively. The actuating force F is calculated by Lorentz’s law, via

F = IL× B (2-4) where B is the magnetic flux density, L is the vector along the length of the conductor, and I is the current passing through the conductor.

Variable-field actuators, such as solenoid actuators or variable reluctance actuators, are those where the magnetic field distribution changes in the actuating process. These actuators usually include a combination of current-carrying coils, soft magnetic materials, and/or permanent magnets. The principle of this type of actuators, shown in Figure 2-7, takes advantage of the fact that an electromagnetic system always tries to move toward a state of minimum reluctance.

a. Reluctance force on plunger b. Solenoid actuator (Courtesy of Ledex Inc.) Figure 2-7: Principle of Solenoid Actuator Governed by Variable Reluctance

Reluctance, R, is a concept in a magnetic circuit analogous to that of resistance in an electrical circuit. It depends on the geometry and material properties of the magnetic path and is given by

l MMF R=  (2-5) S where l is the length of the magnetic path, µ is the permeability of the material, S is the cross- section area of the path, MMF is the magnetomotive force, and Φ is the magnetic flux. The magnetic force in x component Fx that acts on the plunger is given by

W B2 F  m , and W dv (2-6) x x m  2

14 where Wm is the magnetic energy, B is the magnetic flux density, µ is the material permeability, x is the air gap and v is the volume.

2.2.3 Advantages of Electromagnetic Actuators

Due to the rapid behavior of the build-up and disappearance of magnetic fields, electromagnetic actuators demonstrate very fast operation speeds. Compared with other actuators, the electromagnetic actuators are simpler, cheaper, easily repaired, robust, and more manufacturable [21].

Voice coil actuators generally have low armature mass and can therefore generate high accelerations. These actuators can also be designed to be eddy-current-free in reducing energy loss and with sensor-less control. They therefore demonstrate higher efficiency in the energy conversion and fast response in the dynamic performance. Solenoid actuators exhibit very high force capacity because of their small air gap. At the same time, they offer improved heat dissipation and wire connection, and thus are the simplest and generally the least expensive ones to manufacture.

In general, the merits of electromagnetic actuators are as follows: 1. High actuation force and longer stroke (displacement) 2. Fast response 3. Contactless remote actuation 4. Low voltage control 5. Bidirectional motion 6. Design flexibility 7. Potential for high energy density

2.3 Improvement of Electromagnetic Actuators

Due to the unique advantages described in the previous section, many of electromagnetic actuators have already been commercialized and are used for a wide variety of applications in engineering designs and academic research. However, achieving superb performance from a specific actuator in a particular application is still an imperative and a challenging task for engineers and researchers. To get satisfying solutions, people employ different means for

15 different applications. The most common interests are in the new configuration of magnetic circuits, where new materials and advanced analytical tools must be taken into account.

2.3.1 Efficient Magnetic Circuit Configurations

In improving the performance of electromagnetic actuators, specifically in increasing their magnetic force, more effort is put into intensifying the magnetic flux density in the interested region. Some strong fields are built by researchers [22] through the adoption of the Halbach array principle [23]. Figure 2-8 shows the different Halbach cylinders with an intensified magnetic field inside the cylinders for the different wavenumbers (k) of the Halbach arrangement.

Figure 2-8: Halbach Cylinders with Different Wavenumbers (k)

Figure 2-9a shows a flux-focus technique developed by BEI Kimco [20], which enables the structure of actuators with air gap flux densities equal to or even greater than the magnet’s residual value. This design uses the concept of the compression of magnetic fields and forces the magnetic flux orientating to a specific direction at a particular region. It is magnetically efficient, incurring few leakage paths. Nearly all the magnetic flux emanating from the surface of the magnets passes through the air gap. The air gap flux densities are on the order of 11kG near the coil area. Such an actuator exhibits a very short electrical time constant, very high force-to-mass ratio, and very small armature reaction. Figure 2-9b shows the validation of the focus effect of the magnetic field from the FEA simulation by COMSOL Multiphysics. This design presents a useful clue for the development of the hybrid linear actuator in this project.

a. Focused field VCA design b. FEA analysis of focused field Figure 2-9: Focus Effect of Magnetic Flux in the New VCA (Courtesy of BEI Kimco)

2.3.2 Improvement of Material Properties

The previous section discusses the importance of magnetic circuit configuration, and this section will focus on the advancement of the actuator design by employing new soft magnetic materials, new hard magnetic materials, and new conductors.

Besides magnetic circuit design, material properties have significant contributions to the improvement of the actuator performance as well. The high permeability and high saturation level of soft magnetic materials will significantly increase the concentration of the magnetic flux and largely reduce the flux leakage. They efficiently shrink the size and weight of the device. The objectives of the new material development start with improving the shape of BH curves [24] [25], shown in Figure 2-10. For soft magnetic materials, the improvement targets are always on the high permeability μ and the saturation level Bs, the low coercive force Hc and the low remanence Br. Some soft magnetic materials with extraordinary behaviors are currently available for material manufacturers [26] [27]. The relative magnetic permeability of some new materials

17 could reach 100,000 to 500,000 after proper heat treatment, and the magnetic flux density could attain 2.3 teslas.

a. Basic B-H hysteresis loop b. BH curves with different materials Figure 2-10: Properties of Advanced Soft Magnetic Materials

In contrast to those of soft magnetic materials, the goals for improving of hard magnetic materials are to develop the high coercivity Hc and the high saturation level (i.e. the large hysteresis loop) [28]. Figure 2-11 shows the demagnetization curve of a permanent magnet and the corresponding energy product curve. The values of the maximum energy product (BH)max, the remanence Br, and the coercivity Hc determine the working condition of the magnet. The load line is the straight line drawn from the origin of coordinates to the working point on the demagnetizing curve, and the best load line will be achieved when it passes through the (BH)max point.

With the advancement of the manufacturing process, the magnet materials with high performance are available and cost-effective in smart design. Table 2-2 shows different properties of magnetic materials with different chemical compositions [29] [30]. Neodymium

18 magnets, known as Nd2Fe14B, are the most widely used type of rare-earth magnets and currently are the strongest type of manmade permanent magnet.

Figure 2-11: Properties of Hard Magnetic Materials

Table 2-2: Properties of Different Hard Magnetic Materials

Material Grade Br (Gauss) Hc (Oesterd) (BH)max (MGOe)

Nd2Fe14B N52 14500 11200 52

SmCo5 26 10500 9200 26

Alnico 5 12500 640 5.5

Ferrite 8 3900 3200 3.5

Flexible 1 1600 1370 0.6

Along with the benefits of the magnetic circuit improvement and the advancement of magnetic materials, the newly designed conductors also contribute to the efficiency enhancement of the energy conversion for actuators, shown in Figure 2-12. Recent research shows that the thrust force of newly designed actuators can be significantly boosted by increasing the permeability of the coil wires [31]. For a coil with a 36% iron sheath combined with copper wire, the thrust force is improved by 20%, compared with pure copper coil.

a. Material combination of coil conductors b. Actuators with combined coil materials

Figure 2-12: Thrust Force Improvement by Composite Coil Conductors

2.3.3 Optimal Design of Magnetic Field

Since the electromagnetic actuator is a complex electro-magnetic-mechanical system, it is impractical to obtain accurate analysis and assessment by analytical approaches or empirical formulae. Fortunately, the development of computers and computing technologies offers us an effective and convenient way to optimize the parameters of the actuator’s design. The output force is the most important index in nearly all applications. A large number of design problems, such as mover mass reduction, force linearization, stroke extension, and geometry miniaturization, become no longer formidable.

In solving the complex problems of electromagnetic design, some researchers [32] [33] [34] are determined to develop a space-mapping technique, transform a complex model into a simplified one, and construct the relationship (mapping function) between the two models. Such a technique acquired a successful application in optimizing the cylindrical voice coil actuators.

Furthermore, in order to attain the design objectives, such as the maximal electromagnetic force and the minimal mass of the actuators, some researchers [35] have proposed a poly-optimization concept that uses the genetic algorithm operating together with the COMSOL Multiphysics

20 software package to deal with the maximal electromagnetic force and the minimal mass of multi- coil solenoid actuator systems.

Moreover, some researchers [36] have proposed a two-level modeling technique in dealing with the phenomena, such as magnetic demagnetization by combining the analytical description level and the numerical solver level. In the concept design of geometrical structures, researchers [37] [38] suggest a novel design methodology for magnetic actuators by using a level-set-based topology optimization method to obtain the optimal configurations that maximize the magnetic energy of actuators under the minimum bound of the total volume.

2.3.4 Inspiration from Electromagnetic Catapult

The devices with the high magnetic energy output such as the coil-gun and the electromagnetic launcher [39] [40] work at a high current level and demonstrate a high nonlinearity. Such devices need specially designed pulsed power supplies.

Researchers [41] suggest that industrial-purpose, ultrafast actuators can benefit from electromagnetic launcher technology, employing the concepts of magnetic flux compression and magnetic flux expansion. In the fast actuation process, the actuators require very large amounts of energy in pulsed mode in both the acceleration and deceleration stages. The magnetic flux expansion works at the acceleration stage and the magnetic flux compression works at the deceleration stage. Figure 2-13 shows the concept of strong field interactions. This provides a clue to the powerful actuator design with the high magnetic field.

Figure 2-13: Catapult Force (Strong Field Interaction)

Chapter 3 Conceptual Design

This chapter presents the conceptual design of the hybrid linear actuator which integrates the advantages of the solenoid actuator and the voice coil actuator under the constraints of the geometry and speed required by SSIPTS.

3.1 Global Geometric Constraints of Actuators in SSIPTS

According to the design of SSIPTS packages (shown in Figure 1-2 in Chapter 1), the movable morphing pulley segments are arranged in three layers and distributed in eight identical sector zones, as shown in Figure3-1a. The dimension control of the center for different layers is

a. Configuration of actuator in SSIPTS b. Spaces between segment layers Figure 3-1: Geometric Constraints of Actuators in SSIPTS

22 shown in Figure 3-1b. The innermost and the outermost circular lines signify the package housing walls (i.e. maximum available ring-area). The three lines between the two housing walls are the centerlines of the three movable segment layers. The purpose of such a configuration is to pursue a balanced actuation force for each actuator.

Each sector zone accommodates three actuators, shown in Figure 3-2a. In the ideal design, these three actuators equally and maximally share the sector area to obtain a uniform and maximal force. However, such a scheme is difficult to implement because of the manufacturability and availability of the corresponding materials. More practical designs are the circular and rectangular shapes, shown in Figures 3-2b and 3-2c, respectively. The circular shape is available from commercial products, but space usage is very low.

a. One sector of SSIPTS b. Circular actuators c. Rectangular actuators

Figure 3-2: Layout of Actuators in SSIPTS

In a common sense, the magnetic force generated by the actuator depends on its geometric size. For a particular design, the more volume it uses, the higher the force it can provide. Therefore, the major objective at this stage of the conceptual design is to make use of the available space as much as possible. An approximate estimation with respect to the three alternatives of the actuator shape design shows that the circular shape actuator only shares around 35% available space, the rectangular shape actuator takes advantage of above 78% available space, and the volume usage of the morphing design could reach over 92%, shown in Figures 3-3a, 3-3b, and 3-3c, respectively.

As discussed above, if the circular actuators are employed, the maximum available diameter is about 14mm, which is confined by the center distance of the adjacent segment layers. There is 35% volume utilizing rate for this type of actuator, fundamentally limiting its force output. The best commercially available tubular linear actuator is the model LA05-05-000A from BEI Kimco [42], but its peak force is only 0.7N at rating condition, and less than 6N at pulsed current 10A. Such a capacity is far below the requirements of the SSIPTS system.

a. Circular b. Rectangular c. Morphing Figure 3-3: Space Using Efficiency of Different Cross-Section Shape of Actuators

Figure 3-3c shows the ideal morphing pattern of the actuators in the sector zone, where the service efficiency of the space volume reaches over 92%. However, its poor manufacturability greatly limits its use at current manufacturing conditions because of the high cost. Therefore, the most feasible geometric choice is the rectangular profile, shown in Figure 3-3b. The typical geometric parameter in meeting the package constraints is 12mm for the actuator thickness. This research will be conducted in such a scenario.

3.2 Speed Constraints of SSIPTS

As mentioned in Chapter 1, the segment switch must be finished in the transitional area during the unloading condition. The on and off engagements of the pulley segments indicate that the actuation process is a point-to-point control where the actuator moves from Position A to

Position B, or vice versa. Figure 3-4 shows the essential actuating requirement of SSIPTS. A high force is necessary at the beginning for a high acceleration and an opposite high force is also

Figure 3-4: Actuation Force Behaviors Required by SSIPTS indispensible at the end for a deceleration.

The angular velocity of the pulleys dictates the performance of the actuators. The duration of the actuation is a function of the angular speed of the pulleys. Pulley segment shifts must be executed in the transitional area (unloading pulleys), as shown in Figure 1-1. Based on the angular speed of the pulleys and the size of the transitional area, the actuation time is calculated by the following formula:

2 n   (3-1) 60

2 T k T k (3-2) r 

where ω is the angular velocity, n is the rotational speed (rotation per minute [RPM]) , Tr is the rotational period, T is the permitted duration of the actuation or the time window for actuation, k

25 is the non-contact zone factor of the belt-pulley pairs, and k=0.375 for the wrapping angle of 180 degrees and in the eight-segment-partition.

Figure 3-5 illustrates the typical actuating strategy of SSIPTS. The stroke of the actuation system is set to be S=15 mm and has to be reached within the specified time window, T. The weight of the moving mass is assumed as m=80g.

Figure 3-5: Typical Actuating Strategy

The relationships among displacement x(t), velocity v(t) or (t), and acceleration a(t) or xt() within the time interval (0≤ t ≤ T) are given by the following equations, respectively:

(3-3) ,

(3-4) ,

(3-5)

From equation (3-5), the maximum acceleration is determined by

, (3-6)

and by using Newton’s second law of motion, the maximum force is calculated.

(3-7)

Figure 3-6 depicts the actuator motion profiles corresponding to displacement, velocity, and acceleration. Based on the above given parameters and equations, the maximum acceleration, and required force of the actuators are calculated for each angular speed, shown in Table 3-1.

Figure 3-6: Relations of Motion Parameters During Actuation Process

Table 3-1 Output Force Demand of the Actuator Regarding Different Rotating Speed Pulley Speed Angular Velocity Actuation Time Acceleration Max. Force (RPM) (Rad/sec) (mS) (g) (N)

400 41.9 50.0 3.02 2.37 800 83.8 25.0 12.07 9.47 1200 125.7 16.7 27.06 21.21 1800 188.5 11.1 61.24 48.01

3.3 Magnetic Circuit Design

3.3.1 Concept of Magnetic Circuit

As we know, the magnetic circuit analysis is successfully and conveniently applied in the design of transformers, namely, the closed-loop magnetic circuit analysis. However, it also provides an effectively means of implementing the concept design of the electromagnetic actuators, which mostly work in an open-loop magnetic circuit.

In general, the magnetic circuit is analogous to the electrical circuit, where the magnetomotive force (MMF) F, the magnetic flux Φ, and the magnetic reluctance R, followed by Hopkinson’s law in the magnetic circuit, corresponds to the electromotive force (EMF) V, the electric current I, and the electric resistance R, followed by Ohm’s law. Table 3-2 shows the convenient analogous comparison.

Table 3-2: Analogous Comparison of the Magnetic Circuit and the Electrical Circuit

Magnetic Circuit Electrical Circuit

Magnetic Flux Electrical Current Φ I (Weber) (Ampere) Magnetic Field Intensity Electrical Field Intensity H E (Ampere/meter) (Volts/meter) Magnetic Flux Density Electrical Current Density B= Φ J= I/A (Tesla) (Ampere/square meter) MMF EMF =NI=HL V F (Ampere-turn) (Volts) Magnetic Reluctance Electrical Resistance R =L/( R =L/( σA) ( Ampere-turn/Weber) (Ohm) Magnetic Permeability Electrical Conductivity (H/m) σ (S/m) ( Henry/meter) ( Siemens/meter)

F= ΦR Hopkinson’s Law V= I R Ohm’s Law

3.3.2 Physics of Electromagnetic Actuators

For the complexity of the interaction of the magnetic fields generated by the coil current and the permanent magnet, the magnetic circuit analysis can present a clear view and guide before the detailed design of a new actuator. Figure 3-7 shows the general physics of the electromagnetic

Figure 3-7: Physics of Electromagnetic Actuators actuators [43]. It contains the electrical circuit, the magnetic circuit, and the mechanical circuit, where energy is converted by means of electro-magnetic coupling and magneto-mechanical coupling. Magnetic circuit analysis plays a significant role in the conceptual design stage of such an electromechanical device.

From the discussion in the previous chapter we know that both the solenoid actuator and the voice coil actuator offer compact size, fast response, and moderate power density. However, the fatal flaw of the solenoid, shown in Figure 3-8a, is that its output force is highly plunger-position dependent: the larger the air gap, the weaker the force. This ultimately means that the solenoid cannot satisfy the specific requirement of SSIPTS, where higher force is imperative to producing a very high acceleration at the starting point and lower force at the end point. In contrast, the voice coil actuator can provide a relatively linear force throughout the stroke, shown in Figure 3- 8b, but it does not match the required behavior, either, shown in Figure 3-4.

Therefore, this thesis intends to develop a hybrid actuator with a new configuration of the magnetic circuit, running a VCA as a solenoid actuator, shown in Figure 3-8c. Although this

29 configuration is still classified as a VCA, its behavior is significantly different from the VCA at high current level, which will be discussed in detail later. In addition, the coil will be held as the stationary part (stator) rather than moving in a VCA and the magnetic material assembly (mover) will execute the required movement. But the actuation force still comes from the inter-reactions between the stator and the mover.

a. Solenoid actuator b. Voice coil actuator c. Hybrid actuator Figure 3-8: Force Behaviors of Electromagnetic Actuators

In contrast to the traditional mode (moving coil mode), such a configuration (stationary coil, moving magnet assembly) will substantially increase the efficiency of coil heat dissipation and avoid the fatigue failure of the wire leads due to the repeated movement of coil. Furthermore, the force between the stator and the mover will be intensified by the mutual reinforcement of the Lorentz interaction and the magnetic reluctance interaction.

3.3.3 Comparison of Magnetized Direction

This section will discuss the hybrid actuator in more detail. Based on Lorentz’s law, a coil in a magnet’s field will work well as long as the magnetic field is perpendicular to the current- carrying conductor and has nothing to do with the cross-sectional shape of the coil and the magnet, shown in Figure 3-9. There is no significant distinction, either, between the outer magnet configuration and the inner magnet configuration when the coil works on lower-level current; namely, no significant disturbance between the coil magnetic field and permanent magnetic field.

Figure 3-10: Coils Working in Perpendicular Field

However, the severe mutual interference occurs between the current-magnetic field and permanent magnet field when the coil works at a higher current level due to the superposition (mostly nonlinear) of the two fields. Not only does the coil conductor in the magnetic field act by the Lorentz force, but it also acts by the reaction force between the two fields, since the coil also functions as an electromagnet at the same time, as shown in Figure 3-10. Furthermore, among the three configurations, only the axial magnet arrangement, Figure 3-10c, functions as a hybrid actuator.

a. Outer radial magnet b. Inner radial magnet c. Axial magnet Figure 3-9: Magnetic Field Interaction at Different Magnetic Configurations

First, for the traditional configuration, as in Figures 3-10a and 3-10b, the permanent magnetic field is directly perpendicular to the coil surface. The uniformity of the field near the coil depends on the uniformity of the magnetization inside the permanent magnet. Therefore, the

31 linear force is achieved in this situation. Nevertheless, the coupling effects between the current magnetic field and the permanent magnet field is insignificant at a high current level, since the two magnetic fields are orthogonal. However, the two magnetic fields in Figure 3-10c are parallel, so the coupling effect is very strong (i.e., the magnetic force produced by the interactions will be strong).

Second, since the magnetic strength of the permanent magnet depends on its thickness in the magnetizing direction, a stronger magnetic field certainly needs a thicker magnet. As a result, a compact design for the radial magnet configuration is very difficult. In contrast, it is easier to get a compact design for the axial magnet configuration by simply employing a magnetic flux orientating member, called a flux-orientator, to guide the magnetic flux pointing to the coil surface.

Thirdly, the orientator also functions as a plunger, like the plunger in the solenoid actuator. Under the action of the coil magnetic field, it has a strong tendency to move toward the coil center. Last but not least important, the axial configuration for a rectangular cross-section design is more imperative, as the flux near the corner is in the reverse direction compared with the flux at the normal area. This will generate a counter effect and significantly reduce the magnetic

a. Radial magnet combination b. Orientator guided axial magnet Figure 3-11: Magnetic Flux Peripheral Distribution at Different Configurations interactions, shown in Figure 3-11a, while Figure 3-11b creates an even distribution by the orientator and without the counter effect.

All in all, the axial magnetized magnet configuration, working in a hybrid mechanism combining the solenoid actuator with the voice coil actuator, is a feasible design for the application of SSIPTS.

3.4 Structural Design of the Novel Actuator

As discussed in previous sections, a novel actuator based on the voice-coil principle running in a hybrid mechanism is designed here. The mover is the magnetic material assembly rather than the coil, and the stator is the coil assembly instead of the magnetic housing assembly in the moving coil situation. The output force of the actuator comes from the overall magnetic interaction between the coil and the permanent magnet systems, not only controlled by Lorentz’s law but also by the changes in magnetic reluctance. This configuration potentially has the advantages of compact size, high power output, good heat dissipation, and feasible manufacturability. These features will be illustrated and validated in later chapters corresponding to the computer simulation, experiment analysis, and fabrication techniques.

The tasks here are focused on the parameterized geometric design and the material and selections.

3.4.1 Parameterized Geometry Design

In order to achieve the continuous improvement of the actuator performance at the concept stage, the parameterized design of the actuator is suggested which can be accomplished by setting up the equation tables in SolidWorks version 2010. The major variables are the magnet thickness and magnet length. The thickness, width, and length of the coil, together with the thickness, width and length of the orientator and others are all dependent variables. The constraints are the actuator thickness and actuator length. The pre-setting variables or constants are the air gap, shell thickness, bobbin thickness, and magnet width. All the variables are listed in Tables 3-3 and 3-4.

Table 3-3: Parameterized Dimensions in SolidWorks Model

Table 3-4: Parameterized Dimensions in SolidWorks Model (continued)

Figure 3-12 shows the one quarter section view of the actuator design, consisting of the mover and stator. The mover assembly is composed of the permanent magnet working as one energy source, the flux orientator playing multiple roles, and the shell materials constraining the magnetic flux in the designed paths. The stator assembly is made up of the coil working as another energy source, and the bobbin functioning as a mechanical supporting structure made of a non-ferromagnetic material. The longitudinal section profile will be defined by optimizing the thickness and length of the permanent magnet in the next chapter and here is just given a

35 reasonable setting. The design parameters of the permanent magnet function as the fundamental variables in determining other structural geometries, namely the coil, the core, and the shell.

Figure 3-12: Concept Design of the Proposed Actuator

3.4.2 Material Selections

The performance of the actuator has close links with the advancement of its structural materials. The selections of the related materials is primarily based on the power capacity (force), the miniaturization (overall size), and the lightening (mover mass). As discussed in Section 2.3.2, the progress in the magnetic materials or the conductive materials probably revolutionizes the performance of the actuator. The interactive forces of the mover and stator of a magnetic actuator largely depend on the magnetic field strength, magnetic flux leakage, and electric current density. Therefore, the advancement in the permanent magnets (the higher remnant flux density, the higher energy product, the higher coercive force, and the higher working temperature), the improvement in the soft magnetic materials (the high permeability, the high flux saturation level, and the narrow hysteresis shape), together with the innovation in the conductors (the conductivity and the permeability), all contribute to the performance improvement of the new actuators.

Figure 26 provides a basic choice of materials for the structure of the conceptual design: the permanent magnet, made of rare-earth Nb2Fe14B for its high remnance, high coercive force, and high energy product; the coil, made of copper for its better conductivity; the flux orientator, made of soft iron for its relatively high permeability and off-the-shelf availability; the shell, made of permalloy or supermalloy for its high permeability and high flux saturation level, and the bobbin made of aluminum for its low magnetic permeability, high thermal conductivity, and structural strength. Cost-effectiveness and manufacturability are also important decision-making factors.

Figure 3-13: Primary Material Selection of the Concept Design of the New Actuator

3.5 Summary

This chapter proposes a novel actuator featuring a rectangular cross-section, based on the requirements corresponding to the constraints of geometrical space confined by the package envelope of the new SSIPTS transmission system and the response time determined by the rotating speed and the geometric feature of the system. The design deploys the configuration of a hybrid actuator by running the voice coil actuator as a solenoid that maximally exploits the advantages of the electromagnetic actuators. The materials selections are rare-earth Nb2Fe14B for the magnet, permalloy for the shell, soft iron for the orientator, copper wires for the coil, and aluminum for the bobbin, as a compromise between cost and performance.

Chapter 4 Modeling and Simulation

The magnetic circuit analysis mentioned in the previous chapter primarily applies to the simple magnetic structure and provides a basic clue in the stage of the conceptual design. To get more accurate and reliable design parameters, some advanced analysis tools must be employed. This chapter will focus on the application of the finite element method (FEM) in solving complex electromagnetic problems. A step optimization approach is proposed and the optimal parameters of the HLA design are achieved.

4.1 Basic Electromagnetism

4.1.1 Maxwell’s Equations

In general, the properties of an electromagnetic field are under the control of Maxwell’s equations. The electromagnetic analysis on a macroscopic level is to solve Maxwell’s equations, subject to certain boundary conditions. Maxwell’s equations are a set of equations, written in a differential or integral form, that describe the relationships between the fundamental electromagnetic quantities. These quantities are the electric field intensity E, the electric displacement or electric flux density D, the magnetic field intensity H, the magnetic flux density B, the current density J, and the electric charge density ρ [44] [45].

The equations can be formulated in differential or integral form. The differential form is introduced here, since partial differential equations (PDEs) are the most suitable form for FEM to handle. For general time-varying fields, Maxwell’s equations can be written as: D HJ   (4-1) t B E   (4-2) t D   (4-3)

B  0 (4-4)

Equation (4-1) and (4-2) are called Maxwell-Ampère’s law and Faraday’s law, respectively. Equation (4-3) and (4-4) are the two forms of the Gauss’s law, in the electric form and magnetic form, respectively.

The equation of continuity as another fundamental equation is given by

 J   (4-5) t

Only three of the above five equations are independent. An independent system is formed either by the first two equations combined with Gauss’ law, or the equation of continuity.

By introducing the quantity of magnetic vector potential A, the filed variables B and E are calculated thus:

BA  (4-6) A E  V  (4-7) t

In static magnetic field, Maxwell-Ampère’s law reduces to

1 ( ( ABJred  ext ))  ext (4-8) where Ared is reduced potential, A=Ared+Aext, Bext is a known external magnetic flux density, and

Jext is an externally generated current density.

4.1.2 Constitutive Relations

The macroscopic properties of the field medium are described by constitutive relations, given by

DEP0 (4-9)

BHM0 () (4-10) JHM() (4-11) where P is the electric polarization vector, ε0 is the permittivity of vacuum, μ0 is the permeability of vacuum, σ is the electrical conductivity, and M is the magnetization vector described in chapter 2. In the SI system, the permeability of vacuum is chosen to be 4π·10H/m.

A generalized form of the constitutive relation for the magnetic field is

BHB0 rr (4-12)

BH f () (4-13)

JEJ ext (4-14)

where µr is the relative permeability, χm is the magnetic susceptibility, and Br is the remnant magnetic flux density.

4.1.3 Boundary and Interface Conditions

In solving the PDEs of an electromagnetic problem, one needs to specify the boundary conditions at the material interfaces and physical boundaries. At interfaces between two media, the boundary conditions can be expressed as follows:

n2( E 1  E 2 )  0 (4-15)

n2() D 1  D 2  s (4-16)

n2() H 1  H 2  Js (4-17)

n2( B 1  B 2 )  0 (4-18)

40 where ρs and Js signify the surface charge density and surface current density, respectively, and n2 is the outward normal from medium 2. Of these four conditions, only two are independent. One of the equations (4-14) and (4-17), together with one of the equations (4-15) and (4-16), form a set of two independent conditions. The above boundary conditions show that the tangential component of E and the normal component of B always continue, and the tangential component of H and normal component of D discontinue at general scenario.

4.1.4 Electromagnetic Energy

The general definitions of the electric and magnetic energies are

DTD W()()EDE  d dV   dt dV (4-19) e VV 00   t

BTB W()()HBH  d dV   dt dV (4-20) m VV 00   t respectively. For linear and isotropic material, the total electromagnetic energy density is expressed as

11 w w  w EEBB    (4-21) em22

The energy density for material with constant permeability is described as

B2 1 w BH (4-22) m 22

For materials with nonlinear B-H curves, the energy density can be shown to be

w H dB m  (4-23)

The coenergy density is described as

w B dH co  (4-24)

The sum of the coenergy density and the energy density abide by

wm w co HB (4-25)

In Figure 4-1, at the working point A, the dark-shaded area represents the energy density and the light-shaded area denotes the coenergy density. At linear working point C, the energy density equals the coenergy density.

Figure 4-1: Energy Density and Coenergy Density at Work

Point A for a Typical Nonlinear B-H Curve

4.1.5 Electromagnetic Forces

Electromagnetic forces originate from the interaction between magnetic fields discussed in preceding chapters. There are several means to calculate them.

The first way introduced by COMSOL Multiphysics is the Maxwell stress tensor method, where the calculation involves the computation of surface forces acting on the boundaries. The surface forces are derived from a general stress tensor that includes electromagnetic terms. Considering the stationary situation of a system, the balanced equation is expressed as

T fext  0 (4-26)

42 where T is the stress tensor and fext is an external volume force. The stress tensor must be continuous at the boundary between two materials, shown in Figure 28, and follows the equation

n1(TT 2  1 )  0 (4-27)

Figure 4-2: Maxwell Stress Tensor at Material Boundaries

where T1 and T2 represent the stress tensor in Materials 1 and 2, respectively, and n1 is the normal pointing out from the domain containing Material 1. By derivation, the magnetic force on Material 1 is expressed as

Fn T dS  12 (4-28) 1

The second approach for computing the magnetic forces is the principle of virtual work, where an energy change of an electromagnetic system is calculated in correspondence to a small virtual displacement. The force under constant magnetic flux is given by

F  Wm (4-29)

The third method of calculating force is the Lorentz force formula, which was introduced in previous chapter in a simple condition. Here is the general form:

FJBdv L  (4-30)

Lorentz force can also be computed by the approaches of the Maxwell stress tensor and virtual work, but equation (4-30) is easier and more accurate. However, this equation can only be used for the force calculation on current-carrying conductors and will be useless for computing the force on non-current domains.

4.2 Setup of Finite Element Analysis

4.2.1 FEA Expression of Electromagnetic Problems

The finite element method applied in electromagnetic problems is derived from the basic principle of energy conservation and functional minimization. The energy input and energy stored in the magnetic system are

1 WJA dv (4-31) input 2  and

B2 W dv (4-32) stored  2 respectively. And the energy functional is defined as the difference between stored energy and input energy:

B2 1 F W  W  JA  dv stored input   (4-33) 22

According to the law of energy conservation, the problem solved by the finite element method becomes the problem of extremum of energy functional (i.e., the partial derivative of energy functional equal to zero). The basis of FEA for linear magnetostatic (DC magnetic) fields is

 B2 dv Jdv (4-34) A 2

The first-order shape function for a simple triangular element is

A( x , y ) [ Ak ( a k  b k x  c k y )] (4-35) k L,, M N where L, M, and N are the vertices of the triangle element, Ak is the vector potential A on z direction at the vertex k, and ak, bk, and ck are polynomial constants. Substituting equation (4-35) into equation (4-34), we have

 B2 1  JA dv 0 (4-36) Ak 22 where B is the curl of A, and for triangle element gives,

2 2 2 AA B  (4-37) xy

Analogous to structure mechanics, the matrix equation for a magetostatic filed is

[]KAJ     (4-38) where K is called the stiffness matrix from its origin in structural FEA, J is the column vector of the current density, and A is the unknown column vector to be solved.

The detailed procedure of modeling and simulation in the electromagnetic system is the same as the FEA in other applications. It includes the geometrical modeling, the physics setting (configuration of the material, the boundary condition, and the loading or excitation), the meshing, the solving, and the post-processing.

4.2.2 Geometrical Modeling of the Actuator in FEA

As discussed in the previous chapter, the main purpose of the actuator in SSIPTS is to generate the bidirectional force to achieve a bistable motion in a short time for the shift of the pulley segments. The electromagnetic force is the most important index in characterizing the performance of the new actuator. Therefore, the design and analysis will be focused on magnetic force assessment in the development of the new actuator.

In pursuing the optimal solution of an electromagnetic design, many researchers have tried different approaches, from topology optimization [46] [47] [48] [49] [50] and space mapping [32] [33] [51] to response surface methodology [52] [53]. However, to locate an absolutely optimal resolution is futile because of the complexity of the actual problems. As a result, both academic research and engineering design focus on finding a relatively superior and dependable solution.

The parameter-sweeping function embedded in the commercial software COMSOL Multiphysics, which provides plenty of solvers in dealing with linear and nonlinear electromagnetic problems, makes the above optimization process feasible and convenient. Under this convenience, the key parameters will be taken into account in the modeling of the new actuator. The emphasis of the analysis is still concentrated on the 2-D static magnetic field because of the geometric features of the design, and the simplicity, reliability and cost- effectiveness in 2-D are obvious.

The parameter-sweeping technique is based on the parameterized modeling of the geometric design. For the new actuator, the permanent magnet and the current-carrying coil are the energy sources. The strength of the magnetic field built up by the permanent magnet depends on the magnet volume, and the current magnetic field is determined by the coil size. Under the constraint of the overall actuator thickness and the actuator length, the coil thickness has a direct relationship with the magnet thickness; similarly, the orientator that controls the perpendicular component of the magnetic flux passing through the coil is directly related to the magnet length. Consequently, the magnet thickness and magnet length become the fundamental parameters. Table 4-1 shows the parameters used in the geometric modeling of the new actuator.

Table 4-1: Parameter List for Geometric Modeling of the New Actuator Parameter Expressions Name

0.2:0.4 [mm] Air gap xag 0.2:0.4 [mm] Bobbin thickness xbt 0.1:0.74 [mm] Shell thickness xst 30:50 [mm] Actuator length xal 10:14 [mm] Actuator thickness xat 10:35 [mm] Magnet length xml 2:6 [mm] Magnet thickness xmt

x/ 2 x / 2  x  x  x Coil thickness xct at mt agbt st Coil length x x x xcl al ag st Orientator length xcrl xal x ml xst Orientator thickness xcrt Air shell thickness xast 2xat Air shell length xasl 2xal

4.2.3 Physics Setting of Model Domains

The simplified model shown in Figure 4-3 comes from the conceptual design discussed in the previous chapter. In terms of the characteristics of EMF analysis, the field permeates any medium in the relevant area. Therefore, the actuator geometry is certainly surrounded by air or a vacuum, called free space, seen as domain Ω6. This is a typical feature of the FEA in electromagnetism which is different from the FEA in structural mechanics.

Figure 4-3: ½ 2D FEA Model of the New Actuator

The governing equations (PDEs) and constitutive equations for each domain are listed in Table 4-2.

Table 4-2: Partial Differential Equations (PDEs) and Constitutive Equations of Domains

Domain PDES Constitutive Equations Name

11 Ω1  (  A )  0 B f() H e Orientator (iron) 0 r B

11 Ω2  ()  AJ  BH  Coil (copper) 0 r ext 0 r

Ω3 Shell 1(permalloy1)

Ω4 Shell 2(permalloy2)

Ω5 11 BHB Magnet (Nb2Fe14B)  (  AH  )  0 0 rr 0 rc

Ω6 air

The governing equations in Table 4-2 are the simplified Maxwell’s equations for the 2-D static field, where A is the magnetic potential, μ0 is the permeability of free-space, μr is the relative permeability of the individual soft magnetic materials, Ηc is the coercive force of the permanent magnet, eB is the unit vector of B, Jext is the external current density, and Br is the remanence of the permanent magnet. The nonlinear constitutive relationships between B and H, expressed as f(│H│), are discretized from the BH curves provided by the material manufacturers, assuming the materials are isotropic.

To reduce the magnetic flux leakage of the magnetic circuit, a combined material structure is adopted. The idea is that the inner shell material has a higher magnetic flux saturation level, where a higher field density exists because of the close distance from the magnetic sources, and the outer shell material possesses super magnetic permeability, where the field density remains lower because of the inner shell. Such a configuration is set to take advantages of different soft materials, since currently no materials exists that has both high magnetic permeability and a high magnetic flux saturation level.

Figure 4-4: BH Curves of Different Permalloys from the Manufacturer

Figure 4-4 shows the B-H curves of two different permalloys with different properties provided by the manufacturer. This data sheet cannot be directly used in the FEA software until it is transformed from a CGS (centimetre-gram-second) unit to SI (international system of unit),

49 referred to in Appendix A. The data collected from Figure 4-4 are listed as functions (B=f(︱H︳)) in Table 4-3.

Table 4-3: Functions of Soft Magnetic Materials (CoNetic AA and Netic S3-6) CoNetic AA Netic S3-6

B(T) H(A/m) µr B(T) H(A/m) µr

0.01 0.078 100,000 0.004 15.92 200 0.02 0.120 133,000 0.100 31.83 2,500 0.11 0.318 275,000 0.300 47.75 5,000 0.20 0.398 400,000 0.480 63.66 6,000 0.30 0.531 450,000 0.600 79.58 6,000 0.40 0.796 400,000 1.000 159.2 5,000 0.55 1.590 275,000 1.400 318.3 3,500 0.60 3.180 150,000 1.550 477.5 2,583 0.65 5.180 100,000 1.600 636.6 2,125 0.70 11.15 50,000 1.650 795.8 1,750 0.75 29.90 20,000 1.800 1591 900 0.77 613.0 1,000 1.900 3183 475 0.8 637000 1 2.140 7958 214

The physics setting for the permanent magnet is based on the properties provided by the magnet manufacturer in Appendix B. Figure 30 shows the working behaviours of the different grades of NdFeB magnets [54]. The blue line gives the properties of Grade N42, which was chosen by this research for its market availability. The remanence of this magnet material is 13,000 gauss (1.3T), its coercive force is 12,300 oersteds (979kA/m), and its intrinsic coercive force is 16,000 oersteds (1273kA/m). How the magnet is used (i.e. the magnet shape, the magnetic circuit, and the working temperature), affects the working point of the magnet. The maximum performance is found by keeping the intrinsic working point above the knee and ideally at the (BH) max working point (sees also Figure 2-11). The intrinsic coercive force Hci significantly determines the applicable strength of the reversed external field. If the applied external field H is higher than

Hci, the magnet will lose its magnetism permanently. In this design, the external field is provided

Figure 4-5: Working Behavior of Different Magnets at Room Temperature by the coil current, so the coil current density is under the limitation of Hci.

4.2.4 Meshing of the FEA Model

Since the model contains very narrow air gap areas (0.4mm) and very thin magnetic material (0.1mm), the free meshing technique is preferred. To make sure to get a convergent solution, the resolution of narrow regions should be adjusted according to the solving process. The solving time and accuracy depend on the degree of freedom (DOF) of the model, which is determined by the total number of meshing elements.

The coarser meshing is suggested at the primary optimization stage because time efficiency is very important at this stage, where a large amount of calculations are imperative. Certainly, a trade-off is needed between the solving efficiency and solving accuracy under the conditions of

51 the convergent solution. The finer meshing is employed at the stage of the performance characterization after the key parameters are established, since both the accuracy and the tendency are important to assessing the force output capacity of the new actuator and the validation between the simulation and the experiment.

Figure 4-6: Coarser Meshing and Finer Meshing for Different Purposes

Figure 4-6 shows the different meshing element numbers for different applications, the coarser one for the optimal process where the relative values and the trend of the solution dominate, and the finer one for the assessment of the detailed characterization where the absolute values and accuracy are more important.

4.2.5 Solver Setting

It is rather challenging to solve electromagnetic problems, particularly for the nonlinear situations, where the nonlinearity of the material behaviors is taken into account. This scenario is common when more accurate and more practical solutions are needed. In general, there are several reasons to choose the right solvers for this research. They are the convergence of a solution that includes a narrow region, accuracy where nonlinear B-H relations are better employed, and time efficiency based on the computing capacity of the lab computers. The solvers provided by COMSOL Multiphysics for dealing with the above requirements are listed in Table 4-4.

Table 4-4: Solvers with Corresponding Features

Direct Solvers Iterative Solvers Solver Name Features Solver Name Features Direct A highly efficient direct GMRES An iterative solver for (UMFPACK) solver for nonsymmetrical nonsymmetrical problems systems Direct An efficient direct solver for FGMRES An iterative solver for (SPOOLES) symmetric and nonsymmetrical problems. It nonsymmetrical systems. It can handle more general uses less memory than preconditioners but also uses UMFPACK. more memory than GMRES. Direct A highly efficient direct BiCGStab An iterative solver for (PARDISO) solver for symmetric and nonsymmetrical problems. It nonsymmetrical systems. It uses a fixed amount of often uses less memory than memory independent of the UMFPACK. number of iterations. It therefore typically uses less memory than GMRES. Direct An out-of-core version of Conjugate An iterative solver for (PARDISO out PARDISO that stores the gradients symmetric positive definite of core) LU-factors on disk. problems Direct An efficient direct solver for Geometric An iterative solver for elliptic Cholesky symmetric, positive-definite multi-grid or parabolic problems (TAUCS) systems

In most cases, the solver Direct (PARDISO) provides a fast, memory-saving solution, and FGMRES offers a satisfying solution by tuning the preconditions when Direct (PARDISO) is

53 invalid. FGMRES is a time-consuming solver, and it is recommended for use in situations where Direct PARDISO does not give the convergent solution.

4.3 Optimization of the Actuator Design

4.3.1 Optimization of Magnet Thickness

As discussed in the previous chapter, the magnetic force depends on the magnetic interaction fields generated by the coil current and the permanent magnet. The force amplitude is determined by the energy stored in the magnet and in the coil. The coil current is a controllable parameter, depending on the condition of the insulation grade of coil wire, heat generation and dissipation, the duty cycle, and the control strategy. It is an environment-dependent variable. The magnetic field built up by the permanent magnet is mainly dependent on the magnet volume (i.e., thickness, length, and width).

In the 2-D model, the magnet force is proportional to the magnet width, which is chosen to be as large as possible within the constraints of the transmission package. The magnet thickness and the magnet length are necessarily optimized. However, achieving a complete optimization is difficult, not only because of the complexity of the actuator structure, but because of the feature of the magnetic field. Introduced here is a simplified technique, step optimization, where magnet thickness and magnet length are optimized. Feasibility will be discussed below.

Figure 4-7: Magnetic Flux Distribution in Optimizing Magnet Thickness

By sweeping the parameter of the magnet thickness, shown in Figure 4-7, the force distribution is found and plotted in Figure 4-8. The interesting fact illustrated in Figure 4-8 is that all the magnetic forces corresponding to different magnet lengths tend to reach their own maximum at the same thickness. This implies that the searching paths in finding the extrema of the two variables are orthogonal. Therefore, the optimizing process can be divided into two separate steps. So there is such a prerequisite condition when step optimization is used.

Consequently, the optimal value of magnet thickness is found by such a parameter-sweeping process, as in seen Appendix E. This is a very useful feature in COMSOL Multiphysics and will be an efficient tool in the engineering design. Another advantage of this technique is that by looking at the function distribution in detail, one can see the varying and influencing trends of the variables. For instance, the function value near the maximum point, where the magnet thickness is 4mm, is not sensitive to the variable disturbance, shown in Figure 4-8; namely, this design is highly robust. A small change in magnet thickness does not significantly change the overall performance.

Force Capacity vs. Magnet Thickness

200 Maximum Force at 180 Magnet Thickness

160

140

120 L_magnet=15.9mm L_magnet=12.7mm 100 L_magnet=19.0mm L_magnet=22.0mm 80 L_magnet=25.4mm

60 Force Output Per Unit Width (N/m) Width Unit Per Output Force 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Magnet Thickness (mm)

Figure 4-8: Optimization of Magnet Thickness

4.3.2 Optimization of Magnet Length

The optimization of magnet length is more complex than that of magnet thickness. Since the final objective in actuation is to achieve a high acceleration of the moving parts in the system, the actuation time depends on the average velocity coming from the kinetic energy accumulated during the overall accelerating period. Thus, it is suggested that the energy concept should combine with the sweeping in this step. According to the law of energy conservation, the kinetic energy, Wk, is equal to the electromagnetic energy, Wm, while the friction and heat dissipation are negligible here. Equation (4-39) shows the kinetic energy of the mover with the mass, m, moving at a velocity, v.

1 W mv2 (4-39) k 2

The electromagnetic energy accumulated in the accelerating period is the integration of the function of the electromagnetic force with respect to the total displacement in the total period.

The first step is to find the force function, fi(x) in the simulation, corresponding to the different coil position, x. The second step is to locate the mechanical work done by the magnetic force, expressed as the equation (4-40).

W f() x dx (4-40) me  s

For a particular magnet length, the output force varies with the relative location between the coil and the stationary part. The magnetic force distributions with different magnet lengths at different coil traveling positions are a set of curves shown in Figure 4-9. The shorter magnet demonstrates the higher force at the coil’s start position, but decreases significantly as the coil moves away from its origin. The longer magnet shows the lower force at the beginning, but increases and stabilizes after the mover moves away.

The energy integration of a coil movement for a specific magnet length is the shaded area shown in Figure 4-10. Such integration for a set of discrete data can be calculated by the equation (4-41)

Figure 4-9: Force Distributions over Coil Position and Magnet Length

n1 FF0  n Wme  x()   F i , (4-41) 2 i1 where Fi is the force corresponding to different coil positions, F0 is the force at the start point, and Fn is the force at the finish point of the acceleration. ∆x is the distance between the two observing positions.

7 6 5 4 6.28 3 5.54 2 4.52

1 1.78 Magnetic Force fi(x)(N) Force Magnetic 0 0 5 10 15 Coil position X (mm)

Figure 4-10: Energy Integration for a Particular Magnet Length

Figure 4-11 shows the energy distribution with respect to different magnet length settings. The optimal magnet length can be found in this figure, where the highest kinetic energy is produced during the overall acceleration period of the mover. For this primary design, the optimal magnet length is around 22mm. Similar to the optimal magnet thickness, this optimal value is highly robust (i.e., small changes in the magnet length do not lead to significant changes in the actuator’s performance).

Energy Output vs Magnet Length

17.5

3J) - 17

16.5

15.5

14.5

14 Normalized Energy Output(5x10 Energy Normalized 13.5 13 16 19 22 25 28 31 Magnet Length (mm)

Figure 4-11: Distribution of Energy Integration over Different Magnet Lengths

4.3.3 Optimal Combination of Shell Materials

The purpose of the optimization of the shell materials is to constrain the leakage of magnetic flux and achieve the higher magnetic force without the significant increase of the mass of the mover assembly. Figure 4-12 depicts the shielding effect for different magnetic fields with different shielding materials. Figure 4-12a is the CoNetic AA foil with the thickness of 0.1mm; Figure 4- 12b is the CoNeticAA sheet with the thickness of 0.74mm; Figure 4-12c is the NecticS3-6 sheet;

58 and Figure 4-12d is the composite structure, consisting of the inner layer with NetiS3-6, and the outer layer with CoNeticAA.

a. Al+CoNeticAA b. CoNeticAA c. NeticS3-6 d. CoNeticAA+S3-6 F=4.51N(4.7A) F=6.02N(4.7A) F=9.45N(4.7A) F=9.51N(4.7A) Figure 4-12: Shielding Effects of Different Soft Materials

The simulation shows the trend of magnetic flux leakage with respect to different material configurations. The flux leakage in Figures 4-12a and4-12b is very high since CoNeticAA has the lower saturation level (0.8tesla), even though it possesses an extraordinaryly high relative permeability (over 450,000). Figure 4-12c shows less flux leakage because of the higher saturation level (2.4tesla) and the moderately high relative permeability (μrmax8000) of NeticS3- 6. Figure 4-12d is the best configuration since the combined structure integrates the benefits of Figures 4-12a and 4-12c, where the material with the higher saturation level and moderate permeability is situated near the strong magnetic field to convey higher magnetic flux density, and the material with the lower saturation level but higher permeability is put in the weaker field to shield the rest of the leaking flux from the inner layer. Such a configuration effectively exploits the benefits of the super-permeability and the high saturation level of different super- magnetic alloys. As a result, a compact design is achieved, especially for this project where the magnet assembly is set up as the mover. The lighter moving mass definitely helps increase acceleration.

4.4 Performance Characterization of the HLA

Based on the geometrical constraints of the SSIPTS package, the optimized geometry of the new actuator is found in the previous section. The structural components of the actuator depend on the optimized thickness and length of the permanent magnet, which is designed to be 4mm thick and 22mm long. This section will continue the simulation by the software to characterize the overall performance of the new actuator.

4.4.1 Force Output Distribution vs. Coil Current and Coil Position

As discussed in the preceding section, the force output of the actuator depends on the actuator’s geometry and the external driving current. The driving current, together with the moving condition (moving position), determines the final behavior of the actuator. A thorough investigation of the actuator’s force over the current of the coil and the coil’s position is studied here. Figure 4-13 shows the global view of the magnetic force over the current of the coil and the coil’s position.

Figure 4-13: Output Force Distribution vs. Coil Current and Coil Position

Figure 4-13 is plotted on the basis of calculations over 252 (12 by 21) points, where the coil is under the excitation of the current from negative 10 ampere to positive 10 ampere at the 1ampere step, and the coil position is from the start point to the end point of the stroke along 22 millimetres. Such calculations systematically characterize the overall performance of the actuator. More calculations will be initiated later in the experiment chapter for results comparisons between the simulation and the experiment. This section basically provides a general assessment of the newly designed actuator.

The overview from Figure 4-13 is that the maximum repelling force occurs at the highest positive current excitation near the stroke origin, and the maximum attractive force takes place at the highest negative current excitation around the stroke end. The nonlinearity increases with the augmentation of the current excitation, and with the coil position moving towards both the stroke starting point and the stroke end point.

4.4.2 Predicted Specific Behaviors of the HLA

From the performance investigation in the preceding section, one can have a general image of the HLA. This section focuses on the study of the specific behaviors corresponding to the HLA. Figures 4-14 and 4-15 show the force-current relationship and the force-position relationship, respectively.

Figure 4-14 depicts the varying trends of the actuator’s force over the current level of the coil for different coil positions. Each line represents a particular distribution of the magnetic interactions between the two fields over the current variations at a specific position. For instance, at the stroke starting point, s=0mm in the figure, the force response demonstrates that with the increment of positive current, the force increases dramatically and follows an exponential trend. The force constant, which is defined by industrial engineers as the ratio of magnetic force over the excitation current, is increasing gradually as the current rises, rather than remaining constant. In contrast, the attractive force under the negative current excitation increases slowly with the rise of the current at this position.

In the other case, at the stroke end point, s=22 mm in the figure, the force response shows that with the increment of negative current, the attracting force increases amazingly following the

61 exponential trend, where the distribution is very different, at s=0mm. The force constant also increases significantly with the rising of the current and no longer remains constant. Similarly, the repulsive force increases slowly at this position, which is very different from the behavior at the stroke start position.

Figure 4-14: Force Behavior over Coil Current at Different Coil Positions

The above special feature makes the HLA superior compared to general commercial products. This performance comes from the integration of the solenoid effect and the voice coil effect. Although it does not fully display in the normal running mode, it does meet the requirements of the SSIPTS project, where the high current pulse is applied and fast point-to-point control is suggested.

Figure 4-15 illustrates the changing tendencies of the magnetic force of the HLA over the coil position. Every curve stands for a specific magnetic force distribution over the coil positions at a particular current level. For example, at the lower current excitation (I=1A in the figure), the

62 force behaves in perfect linearity. The force almost remains constant over the whole stroke range, from the starting point to the end point. This is why people use the term “constant” to characterize the force capability of the actuator running at the normal mode. However, when the

Figure 4-15: Force Behavior over Coil Position at Different Coil Currents excitation current becomes higher and higher, the force behavior over the whole stroke range is highly nonlinear near the stroke start position and stroke end position. For higher coil currents, the repelling force starts from high values at the beginning of the movement, remains stable in the middle stroke position, and then drops at the end of the stroke. In contrast, the attracting force is very high at the stroke end position, where it is necessary for the actuator to return. The above feature perfectly matches the force behavior needed by SSIPTS, discussed in Figure 3-4.

4.5 Reliability Assessment of the Simulation

4.5.1 Comparison of Force Calculation in Different Methods

As discussed in Section 4.1.5, there are several possibilities for calculating electromagnetic forces. Here is a simple comparison of the Maxwell stress tensor method and the Lorentz force method in the magnetic force calculation of HLA. Table 4-5 and Figure 4-16 demonstrates that there is no significant difference between the two force calculations at finer meshing conditions. The difference increases a bit as the current rises, but stays under the range of 5%.

Table 4-5: Force Comparison for Different Calculation Means and Different Meshing Sizes Current (A) 2 4 6 8 10 12 14 16 DoFs: FMaxwell 542401 (N/M) 119.42 252.65 399.79 559.73 725.87 899.27 1079.2 1262.9 FLorentz (N/M) 119.38 252.61 399.85 559.98 726.34 899.99 1080.2 1264.2 DoFs: FMaxwell 33637 (N/M) 115.10 243.32 382.77 532.64 688.10 850.00 1017.8 1189.6 FLorentz (N/M) 119.35 252.47 399.50 559.36 725.45 898.81 1078.7 1262.6

Meshing Effect on Force Calculation

1400

1200

1000

800

600 Maxwell Force at DoFs 542401 400 Lorentz Force at DoFs 542401 Maxwell Force at DoFs 33637 200

Lorentz Force at DoFs 33637 Force Output Per Uinit Width (N/M) Width Per Uinit Output Force 0 0 2 4 6 8 10 12 14 16 18 Coil Current (A)

Figure 4-16: Force Comparison with Meshing Effect

From Table 4-5, one can see that the size of the meshing element determines the accuracy of the solution; the finer the meshing, the more accurate the final calculated result. However, finer meshing means more elements and more degrees of freedom (DOFs), which require more computing capacity in the computer hardware and software. This significantly increases the cost and restricts the amount of computable cases possible within the limitations of the project budget and deadline. However, coarser meshing does not significantly affect the trend assessment (i.e., no remarkable change on the design results).

Table 4-5 and Figure 4-16 also show that the result from the Lorentz force calculation will be more reliable than the Maxwell stress tensor method. The Lorentz force is not sensitive to the meshing element size in this case, because the conductor geometries are simpler than the magnetic circuit assembly. Therefore, the Lorentz force will be preferred in most simulations.

4.5.2 Validation of the MotiCont Voice Coil Actuator

The purpose of this section is to verify the reliability of the FEA modeling procedure. In the course of the development of the HLA required by the project of SSIPTS, a circular voice coil linear actuator from MotiCont is used as a reference for modeling and prototyping, although it does not work well in SSIPTS because of its shape and size. But it is well developed for industrial purpose and acquired a wide range of applications, and its performance is reliable.

The geometric model of the MotiCont linear actuator, from Appendix C, shown in Figure 4-17, shares a comparable topological structure with HLA in the magnetic circuit.

Figure 4-17: Modeling and Simulation of MotiCont Actuator

The structure parameters of the model for the MotiCont linear voice coil actuator come from the manufacturer datasheet and are calibrated by actual measurement. Following the same procedure

66 in the HLA modeling, the calculated data from the simulations and the data collected from the manufacturer datasheet are listed in Table 4-6.

Table 4-6: Performance Data from Simulation and Datasheet of MotiCont Linear VCA Coil Position(mm) 0 3 6 9 12 15 18

Pull F(N) 4.45 4.90 5.15 5.25 5.15 4.66 3.50 (published) Pull F (N) 4.55 5.27 5.50 5.51 5.30 4.65 3.28 (simulated) Push F (N) 4.56 5.29 5.49 5.46 5.20 4.47 3.05 (Simulated)

Carrying out the statistics analysis for the data from Table 4-6, and plotting it in Figure 4-18, the correlation coefficient between the two sets of data is close to 99.53%. This result indicates that the simulation procedure is relatively robust and reliable.

Correlation Coefficient r=0.9953 3

Comsol Simulation Data Output Pulling Force (N) Force Pulling Output Moticon Parameter Data 1

0 0 5 10 15 20 Coil Position (mm)

Figure 4-18: Performance Validation of MotiCont Actuator

4.6 Summary

This chapter first reviewed the basis of electromagnetism, including Maxwell’s equations, constitutive relations, and boundary conditions, and then introduced the concept of electromagnetic energy, approaches to calculating magnetic forces, and the setup procedure of COMSOL Multiphysics. Second, it presented the modeling process on the HLA in detail, consisting of geometric modeling, the physics setting, meshing, and the solver setting. Third, it proposed the concept of step optimization, which is used to optimize the key parameters of the HLA, the magnet thickness and magnet length. The optimal combination of the soft magnetic materials is achieved by a set of comparisons. Fourth, it systematically characterized the performance of the HLA and predicted its very useful advantages for the applications of the project of SSIPTS. Finally, it assessed the reliability of the simulation by comparing different force calculation means at different element meshing sizes and provided more reliable validation by comparing the simulation of the Moticont linear voice coil actuator with the datasheet provided by the manufacturer.

In short, the HLA design offers higher performance and reliability, and it can be carried out to the next step: prototyping.

Chapter 5 Fabrication

This chapter describes the fabrication process and the techniques of the newly modeled and designed HLA, shown in Figure 3-12. The actuator consists of two major components: the magnetic assembly (mover) for creating one of the two magnetic interaction fields, and the coil assembly (stator) for the other magnetic field. The mover contains the hard magnetic material (permanent magnet), the flux orientator (soft magnetic material), and the shell (soft magnetic material). The stator comprises the coil (conductor) and the bobbin (non-magnetic material). Each part has its own special fabrication process.

5.1 Constructions of the Magnetic Assembly

5.1.1 Integrity of the Properties of the Magnetic Materials

The predominate mission for the magnetic assembly is to create the strongest magnetic field in the air-gap area where the coil stays and to minimize magnetic flux leakage by selecting the right materials with high permeability and high flux saturation levels in order to reduce the total mass. Besides the optimal design of this objective, the manufacturing process at the prototyping level is another task that cannot be ignored. A careless manufacturing process could cause a loss of integrity for the properties of the magnetic materials, which means that the material properties would change a lot during the manufacturing process. For instance, the inevitable temperature rise in machining is harmful to both hard and soft magnetic materials. The high stress and strain accompanied of machining should also be avoided because high stress could lead to micro-cracks

69 in the hard magnetic materials, and high strain could cause the microstructure to change in the soft magnetic materials.

Figure 5-1 shows the temperature sensitivity of the strong permanent magnetic material

(Nd2Fe14B) in Grade N42 from K&J Magnetics Inc. As the temperature rises, the working point moves down significantly. The higher the temperature, the lower the coercive force of the magnet. A lower coercive force means that the magnet can only work in a weaker magnetic field.

Figure 5-1: Operating Point Variance Due to Changing Temperature

The properties of the soft magnetic materials (i.e., high magnetic permeability, low coercive force [Hc] and low residual induction [Br]), which are mainly shown in the magnetic hysteresis loop, depend not only on the alloy chemistry (particularly impurities such as carbon, sulfur and nonmetallic inclusions), but also on the stresses and strains caused by the machining processes. Figure 5-2 shows magnetic property changes based on the BH curves. These changes originate from the microstructure (domain walls for magnetism) changes inside in the materials under the stress and strain. Therefore, the advanced soft magnetic materials working under severe stress

70 such as mechanical milling, mechanical turning, and mechanical pressing, should undergo a strict heat treatment process, called annealing in the hydrogen or vacuum environment.

To avoid the occurrence of such a situation and minimize stress and heat in machining, an electro-discharge machining (EDM) operation is suggested for use in this research. It could save the very expensive heat treatment process for the small-scale production, particularly for prototyping, including several pieces.

Figure 5-2: Machining Effect on Magnetic Properties of Permalloy

5.1.2 Integrity of Magnetic Circuits

The integrity of magnetic circuits is defined as the consistence of the properties of the actual magnetic circuit compared with the circuit in theoretical or simulated situations. It is coherently corresponding to the boundary-connecting status of the parts of the magnetic circuit. Any disconnection or improper connection will apparently influence the integrity of the magnetic circuits. For the magnetic assembly in this research, the connections among the orientator, permanent magnet, and shell, are suggested using the Cyanoacrylate super-glue. This adhesive has the great mechanical strength (the tensile strength for steel is about 4000 psi; the shear

71 strength for steel is 2800 psi and for aluminum 1600 psi.), a short setting time (240-280 sec. for steel and 260─300 sec. for aluminum), and the thinnest interface thickness.

The patterns in shell material fabrications also play an important role for the magnetic circuit integrity. There are two types of sheet-metal patterns in the shell fabrication for the magnetic materials: axial direction folding and circumferential direction folding, as seen in Figure 5-3.

a. Axial direction folding b. Circumferential direction folding Figure 5-3: Patterns of Sheet Metal Process

From Figures 3-10, 4-7, 4-12, and 4-17, one can see that the magnetic flux’s return path passes axially from the top-side shell to the bottom shell and then changes direction at the bottom corner along the bottom shell, returning to the magnet source. Any interruption in this magnetic path will significantly increase the magnetic reluctance (i.e., boost the flux leakage). Therefore, the pattern in Figure 5-3a possesses better for the magnetic circuit integrity than the pattern in Figure 5-3b.

5.2 Coil Winding

5.2.1 Filling Factors of Conductors in a Coil Window

Filling factors in a conductor coil means the true area of the conductors in a specified coil area, which reflects the coil winding efficiency. The higher the filling factors, the higher the current density it can provide. Figure 5-4 shows different winding patterns with different winding efficiencies.

a. Square winding b. Hexagonal winding c. Square wire Figure 5-4: Filling Factors in Different Winding Patterns and Different Magnet Wires

The standard circular magnetic wire wound in a square pattern has 78.5% efficiency, shown in Figure 5-4a. Circular wire wound in a hexagonal pattern has 90.7% efficiency, shown in Figure 5-4b, but this pattern is impractical for larger numbers of turns [55]. Figure 5-4c has the highest overall efficiency, but the magnet wire is more expensive and tangling during winding is hard to control. As a prototype, this research uses the hexagonal pattern with the round magnetic wires and is wound as shown in pattern b. In the future, it is suggested to try pattern c in order to get higher current density.

5.2.2 Coil Calculation

Coil winding involves calculating the total turns (N), the total length of wire (Lwire), the layers of coil (nT), and the turns per layer (nL). For a given coil thickness (Tcoil), a coil inner-wall width

(W0), a coil inner-wall thickness (T0), and a coil length (Lcoil), seen in Figure 5-5, the total wire length is calculated by Equation (5-1), based on a specific wire diameter.

TWT00 coil L2 n L [   1] (5-1) wire T coil dd

The wire diameter is expressed in the AWG (American wire gages) number in standard. The calculated values for the coil geometry in Lcoil =38mm, W0=27mm, T0=4.8mm, and Tcoil =2.4mm, are listed in Table 5-1.

Figure 5-5: Coil Winding Calculation

Table 5-1: Numbers of Turns of Coil Calculation

AWG# d(mm) nT nL R1000 N Lwire(ft) R(Ω)

26 0.4318 5 88 41.02 440 103.45 4.24

27 0.3886 6 97 51.43 582 127.56 6.56

28 0.3480 6 109 65.33 654 158.86 10.38

29 0.3124 7 121 81.22 847 196.91 15.99

5.2.3 Bobbin Machining

The bobbin is the mechanical structure on which the coil is wound. To ensure a high percentage of use of the conductor in the coil area, the thinner bobbin wall is better. However, the mechanical strength has to be taken into account when decreasing the bobbin wall. A good design is always a trade-off between the air gap and the bobbin wall thickness. The bobbin wall in this research was designed to be 0.4mm by considering the machining ability of the machine shop and comparing it with some commercial products that are designed based on empirical data.

Figure 5-6: Bobbin Structure Assembly

For such a thin-walled structure, traditional machining processes are not available. Therefore, electro-discharge machining (EDM) is suggested. Figure 5-5 shows the mechanical structure of the bobbin.

After EDM machining, the main body of the bobbin is assembled with the bobbin flanges by a strong adhesive─for instance, two-component epoxy.

5.3 Final Prototypes

The parameters of the prototyped actuators are listed in Table 5-1 and shown in Figure 5-6. In total, there have been three shells and two coils made, which can provide six combinations. Shell 1 is composed of NeticS3-6 (inner layer) and CoNeticAA (outer layer), which possesses the best performance in the simulation. Shell 2 is a combination of CoNeticAA (inner layer) and aluminum (outer layer). Since the inner CoNeticAA layer is very thin (0.1mm), very similar to the coating thickness by electroplating, it is used to verify whether the coating technology is feasible or not in producing a light structure with a high magnetic permeability. Shell 3 is made with one single NecticS3-6, just for the comparison.

Coil 1 is potentially a better choice because of its wire gauge and electrical impedance. Coil 2 with the thinner wires, is to test whether it is possible to increase the coil turn and then increase the current density.

Table 5-2: Physical Parameters under Fabrication

Actuator Component Number of Turns DC Resistance (Ω) Mass (gram)

Coil 1 622 9.9 40.2

Coil 2 723 13.2 39.5

Shell 1(CoNeticAA+NeticS3_6) N/A N/A 54.9

Shell 2 (CoNeticAA+Al) N/A N/A 47.5

Shell 3 (NeticS3_6) N/A N/A 37.7

5.4 Summary

This chapter discussed the actuator fabrication process, which includes permanent magnet machining, soft material machining, bobbin machining, and coil winding. The heat and the stress and strain generated during the machining process have a significant effect on the magnetic properties of both hard and soft magnetic materials. The coil’s current density is coherent to the pattern of the coil winding. The bobbin fabrication also needs a unique manufacturing process, for which EDM is suggested.

Chapter 6 Design and Fabrication of the Pulse Power Supply

To investigate the overall performance of the actuator from low current to high current, a wide range of current-variable and voltage-variable power supplies with pulse control are imperative. This chapter will discuss the design and fabrication of such a pulse power supply source.

6.1 Requirements in Driving the New Actuator

From the simulation shown in Figure 4-14, we know that the force constant at high current level is about 3 N/A. Therefore, to achieve a force around 60N, the coil-exciting current should be 20 amperes or so. From Table 5-1, the DC resistance of the new actuator is around at 10 to13 ohms. For a 20-ampere current on a 10-ohm coil, according to Ohm’s law, the DC voltage will be 200V.

The instantaneous power for the Ohm heat generating of the coil is calculated by,

V 2 P  heat R (6-1)

where Pheat is the power loss, V is the voltage on the coil, and R is the DC resistance of the coil. The Joule work is

WPTheat heat (6-2)

78 where T is the actuating duration time. The mechanical net work done by actuator is

WFSmechanical  (6-3) where F is the actuating force and S is the moving distance. The total energy release from the power supply is

WWWWheat  mechanical  loss (6-4)

where Wloss is the energy consumption by other factors. To reduce the capacity requirement for the transformer, the capacitor bank is introduced as an energy reservoir in the pulse power source. The corresponding capacitance is calculated by

2W C  V 2 (6-5)

6.2 Design and Construction of the Pulse Power Supply

As discussed in the previous section, to provide the necessary conditions for the experimental investigation of the performance of the HLA, the power supply must provide the properties of medium power capacity (3000W), variable voltage (0─250V), variable current (0─20A), and variable pulse control (1─20mS). With the development of modern power electronics, implementing such a design is not difficult [56] [57]. The primary electric circuit designed for this specific purpose is shown in Figure 6-1. It is mainly composed of a variable-voltage DC supply, a pulse current generator, and the actuator.

The variable-voltage DC supply is achieved by the autotransformer, the isolation transformer, the rectifier, and the capacitor bank. The autotransformer is an electrical transformer with only one winding, which acts as both the primary and secondary [58]. It is a simple, reliable voltage- adjusting device widely used in the research lab and on industrial sites, and it provides continuous voltage adjustment. It can be connected in two modes: step-down and step-up. Since the autotransformer only has one winding, it does not provide electrical isolation between the primary and the secondary. Therefore, a critical device for safety, the isolation transformer, is

79 imperative to the circuit. An isolation transformer isolates the connections between the two circuits, which are only linked by a magnetic circuit, and its winding ratio is basically set to 1:1. A rectifier is responsible for the conversion from an alternating current (AC) to a direct current (DC), and a bridge rectifier is suggested for conversion efficiency. The capacitor bank plays two important roles. One is to smooth the ripples, working as a filter, and the other is to provide enough energy for the load, working as a reservoir.

Figure 6-1: Design of the Variable Voltage and High Current Pulse Power Supply

The pulse current generator mainly consists of the signal pulse generator and the current switches. The pulse signal is featured as the pulse width and the pulse frequency. Here we only focus on the one-shot pulse, which is used to turn the actuator on and off. This one-shot pulse can be generated by a popular IC 555 device connected as a mono-stable oscillator, shown in Figure 6-2, or by the LabView software as an integration with the force sensor and current sensor signals (to be discussed later). The pulse width in Figure 6-2 is determined by R1 and C1, which are the external resistor and capacitor, respectively. Different pulse duration is achieved by the change in the resistance of R1, or the capacitance C1. The change in the pulse width in LabView is easier than Figure 6-2, but it requires a dedicated computer and special software. The power switches are used to generate a high-current pulse, where the power MOSFET is suggested, based on two reasons. One advantage is that it possesses a very high commutation speed when the fast current switch is needed. Another benefit is that it is easy to drive because of its isolated gate when compared with other power devices, such as SCRs and GTOs.

Figure 6-2: Pulse Generation by IC 555 Connected as the Mono-stable Status

The protection devices include the fast-response circuit breakers, varistor, reverse diode and energy release resistance. Figure 6-3 gives an overview of the variable voltage and variable current DC power supply.

Figure 6-3: Panorama of the Variable Voltage and Variable Current DC Power Supply

6.3 Summary

This chapter introduced the requirements of the pulsed power supply for driving the HLA in the experiment validation. It then proposed the primary design to meet those requirements, which includes the design of variable-voltage DC power supply and the design of the pulse current generator. The variable-voltage DC power supply is composed of the autotransformer, isolate transformer, bridge rectifier, and capacitor bank. The current generator consists of the pulse signal generator and the high-speed power switch device. The pulse signal can be generated by the LabView or by the IC 555. The LabView method is for the purpose of the experiment, and the IC 555 for the future product purposes. The power MOSFET is introduced as a high-current switch device, which is very popular in advanced power electronics. Finally, the power supply is constructed according to the designated objectives.

Chapter 7 Experiment

In this chapter the results achieved from the proposed FEA model in Chapter 4 are validated by the experiment, where the prototype actuators fabricated from Chapter 5 and the pulsed power supply designed and constructed from Chapter 6. The experiment will test the output forces of the prototyped actuators under the different electric current levels and at the different coil positions.

7.1 Experiment Set-up

7.1.1 Experiment Jigs and Fixtures

Since the prototyped actuators are mainly used to the experiment investigation of the performance of the HLA, their installing conditions is not standardized yet. Therefore, the specially designed jigs and fixtures play an important role in the holding of the mover and the stator of the HLA, and the holding of the force sensor. For repelling force experiment, the jigs and fixtures include the housing frame for holding the coil assembly and the force sensor, and the base plate for retaining the housings, shown in Figure 7-1. The requirement for the jigs and fixtures is solid and non-ferromagnetic. The base plate is also machined several parallel slots for the adjustment of the different coil positions and the alignment between the mover and the stator for a free movement in between.

There is only the compress load cell available (Piezoelectric force sensor) in this lab, and purchasing more functional sensors is budget limited and not absolutely necessary. Therefore, for testing the attracting force, a direction-transform device of the force, called the yoke, is

83 suggested, shown in Figure 7-2. The requirements of the yoke design and fabrication are the light weight, the high rigidity, the non-ferromagnetism and the distance adjustable.

Figure 7-1 : Repelling Force Experiment Jigs and Fixtures

Figure 7-2: Attracting Force Experiment Jigs and Fixtures

7.1.2 Experimental System Configuration

For the integrated display and measurement of the triggering signal, the output force, the exciting voltage, and the driving current of the coil, the LabView analytical tool is suggested. Figure 7-3 shows the system configuration. The control flow is that the LabView sends out a width adjustable pulse, this pulse drives the power MOSFET ON and OFF, and then pulse voltage exerts on the coil. By the electromagnetic interaction, a force acts on the mover, and the mover transmits the force to the force sensor. A voltage divider collects the voltage change between two leads of the coil; a current sensor collects the current passing through the coil; a force sensor collects the force varies of the mover exerting on; and all the signals are integrated in a MEGA 2560 prototyping platform board. And then the communication is built up between the computer and MEGA 2560.

Figure 7-3: Experimental System Configuration

Figure 7-4 shows the block diagram of the system configuration in LabView. The Icon of the formula x1 is for the force sensor calibration. The Icon of the formula x2 is for the current sensor calibration. And the Icon of the formula x3 is for the voltage divider calibration. An example of the display on the Manu window shows in Figure 7-5. The actual number in the vertical axis represents the actual value of the corresponding parameter except the voltage value. The voltage number shown in the window needs multiplying by 10, which is the voltage divider coefficient.

Figure 7-4: Block Diagram of the System Configuration in LabView

Figure 7-5: Integrated Display and Measurement of Force, Current, Voltage, and Signal

7.1.3 Force Sensor Calibration

In order to measure the actual force output by the actuator, a load cell OA250121F is selected. Based on preliminary calculations of the maximum force, a 100N force sensor would be adequate to measure the force output from the coil. The output voltage signal of the load cell is linearly proportional to the load applied. The calibration is carried out on Instron 8511 universal material testing machine, shown in Figure 7-6. The calibration results are listed in Table 7-1. By computing, the average force constant of the force sensor is 101.44 N/V.

Table 7-1: Load Cell FC2231 Calibration

Load (N) Output Reading (V)

0 0.554

10 0.652

20 0.752

30 0.848

40 0.947

50 1.046

60 1.145

70 1.247

80 1.346

90 1.445

100 1.542 Figure 7-6: Instron 8511 Testing Machine

7.2 Data Collection and Analysis

The major objectives for initiating the expensive experimentation are to verify the superior simulation results of the HLA achieved from Chapter 4. Possessing such an excellent performance, enables the HLA to become the best candidate for driving the pulley segments in the project of SSIPTS. The successful design together with the reliably physical verification and the cost-effective fabrication process will make it to become a competitive product, potentially applied in other areas. The experiment validation will follow the clues in Chapter 4 and provide the corresponding comparisons, mainly including the force-current-position relationships and comparisons between different material combinations.

7.2.1 Magnetic Force Variations over Coil Current and Coil Position

As repeatedly stressed in this thesis, the magnetic force of the HLA is the most important indicator in evaluating its actuating performance. Static magnetic force measurement is easier and more reliable than the dynamic test where high-cost instrumentation is required. Therefore, all the experiments in this thesis are based on the static test which is more confident under the budget limitation of this research project.

According to the experimental scheme proposed in the preceding section, the magnetic force measurement becomes straightforward, as long as the testing personnel keep adequate patience and meticulousness. It is worth mentioning that the safety issue is the top priority in the operation of the high voltage and current electrical devices. The experiment procedure is summarized as follows.

Firstly, use the test jigs and fixtures as shown in Figure 7-1, and adjust the coil to a specified position by the vernier caliper or gage blocks, and then align it with the force sensor and tight the fastener. Buffering cushion block is suggested to put in between the actuator mover and the force sensor since the possible clearance in between could generate a huge impact where the mover or the sensor could be damaged. Secondly, tune the autotransformer to get a specified DC output voltage read by volt-meter, shown in Figure 6-3, and set the time duration of the pulse from Labview test window, shown in Figure 7-4, and then press the RUN button in the window. A short pulse current passes through the coil and generates a pulse force. The force sensor, the

88 current sensor, and the voltage divider send the signals to the Labview, and the integrated displays in the diagram shows in Figure 7-5. Thirdly, save the diagram-format data for reading and analyzing later and prepare the next voltage setting. Repeat the above steps, and collect a set of data by changing the power voltage and the mover position respectively.

The repelling forces regarding to the coil current changes and the mover position changes are collected and demonstrated in Figure 7-7. The force constants defined as the force divided by the coil current are shown in Figure 7-8. The experiment results exhibit the same pattern with the simulation results in the variation of the magnetic force over the coil current and the coil position. For each current level, the magnetic force is very high at the original position of the mover, where the coil is completely situated in the magnetic assembly, and is very low at the end position, where the coil is maximally move out of the magnetic assembly. At the middle range of the stroke, the magnet force experiences relatively smooth and moderate change in a declining manner.

Repelling Force vs. Coil Position at Different Current 60

1.8A 50 3.4A

5.1A 40 6.8A 8.5A 30 10.2A 11.8A

20 13.5A

Repelling Force (N) Force Repelling 15.0A

10 16.6A

0 0 5 10 15 20 25 Coil Position (mm)

Figure 7-7: Experiment of Repelling Force over Coil Position and Coil Current

Repelling Force Constant vs. Coil Position at Different Current

3.5

3 1.8A 3.4A 2.5 5.1A 6.8A 2 8.5A 10.2A 1.5 11.8A 1 13.5A 15.0A

Repelling Force Constant(N/A) Force Repelling 0.5 16.6A

0 0 5 10 15 20 25 Coil Position (mm)

Figure 7-8: Variation of Repelling Force Constant over Coil Current and Coil Position

Figure 7-7 and Figure 7-8 also show the fact that the magnetic forces almost keep constant at the lower current level such as the current 1.8A and 3.4A, where the most commercial actuators work in. This fact once again proves that the magnetic force calculated by Lorentz force formula, Equation (2-4), is valid under the hypothesis that the permanent magnet field does not severely disturb the magnetic field from the coil current. The magnetic force output along the whole stroke of the actuator presents perfect linearity which is the unique performance that the voice coil or moving coil actuators usually claim.

In the higher current level, the actuator demonstrates an interesting behavior as discussed in Chapter 4. The magnetic force mainly comes from the interactions between the permanent magnet field and the coil-current magnetic field. Such interactions do not obey the simple linear superposition between the two fields, seen in Appendix F. The magnetic flux return paths are changed by the magnetic interactions as well. The magnetic flux leakage may increase or decrease, depending on the magnetic circuit configuration of the actuator geometry, and the material properties.

The magnetic flux orientator also plays a more important role in the intensification of the magnetic interactions between the two fields. Obviously, besides the function of flux direction orientating for the permanent magnet field, the orientator works as a magnet core as well, when the coil is excited. Working as a ferromagnetic core for the coil in this proposed design, endows it two responsibilities in detail. One is constraining the magnetic flux inside in the center of coil and reducing the fringing flux. Another one is the core itself stands a strong magnetic force towards the coil center when the core is at the start position of the coil. All the functions work together provide the HLA a high force output at the start point of stroke.

The attracting force is validated by using the experiment jigs and fixtures shown in Figure 7-2. The experiment data with respect to the coil current changes and the mover position changes are gathered and displayed in Figure 7-9 and the force constant variation shows in Figure 7-10. In contrast to the repelling force, the attracting force exhibits higher values at the higher current level at the point where the coil comes out further from the magnetic assembly.

Attracting Force vs. Coil Position at Differnet Current 60 1.7A 50 3.5A

5.2A

40 6.9A 8.4A 30 10.1A 11.5A

20 13.2A Attracting Force Force (N) Attracting 15.0A 10 16.1A

0 0 5 10 15 20 25 Coil Position (mm)

Figure 7-9: Experiment of Attracting Force over Coil Current and Coil Position

Attracting Force Constant vs. Coil Positio at Different Current 3.5

3 3.5A

5.2A 2.5 6.9A

8.4A 2 10.1A

1.5 11.5A

13.2A 1 15.0A

Attracting Force Force (N/A) Constant Attracting 16.1A 0.5

0 0 5 10 15 20 25 Coi Position (mm)

Figure 7-10: Variation of Attracting Force Constant over Coil Current and Coil Position

The lower force values occur at the point where the coil is completely situated in the magnetic assembly. At the lower current level, the force behavior is similar to the repelling force, and exhibits relative high linearity along the whole stroke. At the higher current level, the force also changes severely at the position of 20 mm. As discussed before, the significant change of output force at the end point stroke is due to the special design, i.e. the flux orientator plays multiple roles in the magnetic field interactions.

However, the data dispersion in the attracting force experimentation is higher than that of the repelling force test. This is probably because the yoke in the jigs and fixtures needs further improvement. More force transmitting links exist in the jigs and fixtures of attracting experiment, where the friction, the alignment, and the inertia of the yoke may not be ignored. To improve this situation, the tensile load cell is suggested in the future.

7.2.2 Magnetic Force Variations over Soft Magnetic Materials

As calculated and simulated in Chapter 4, the properties of the soft magnetic materials in constructing the designed magnetic circuit plays remarkable roles in improving the performance of magnetic actuator. Experiment results confirmed in this section that changing the material magnetic properties such as the permeability and saturation level leads to the significant change of the efficiency of the magnetic interactions. Figure 7-11 and Figure 7-12 show the significant improvement of force output by the proper combination of the soft magnetic materials in constructing the shell of the HLA. Three types of magnetic assembly are made in this research, the combination #1 of NeticS36 (inner layer) and CoNeticAA(outer layer), the combination #2 of CoNeticAA (inner layer) and Aluminum (outer layer), and the single layer NeticS36 #3. The intent of combination #1 is to integrate the benefits of different materials. The intent of combination #2 is to verify whether it is feasible by coating technique for greatly reduce the mass of mover in order to get a high acceleration. The single layer #3 is just for a comparison.

Force Comparison of Different Shells 50

40 CoNeticAA+S36 Al+CoNeticAA Netic S36 30

Output Pushing Force Force (N) Pushing Output 10

0 1 3 5 7 9 11 13 15 17 Coil Current (A)

Figure 7-11: Force Comparison over Coil Current for Different Shell Material Combinations

Force Constants of Different Shell Materials 3.5

2.5

1.5 CoNeticAA+NeticS36 Al+CoNetic AA

Force (N/A) K Constant Force 1 NeticS36 0.5

0 0 5 10 15 20 Coil Current (A)

Figure 7-12: Force Constant Comparison of Different Shell Material Combinations

From the experiment results shown in Figure 7-11 and Figure 7-12, one can find that the combined structure with CoNeticAA and NeticS36 is the best design in providing the highest force at different coil current levels. This fact confirms that the leaking flux and fringing flux can be effectively restricted by using the combination of different materials with super high permeability and high saturation level. The fact also verifies that such a design and configuration with the combined structure is legitimate and effective. The combination integrates the benefits of the material with higher saturation level and moderate permeability nearby the strong magnetic field for passing on the higher density flux, and the material with lower saturation level but higher permeability situated in the outer weaker field for shielding mostly the rest of the leaking flux. The experiment proves this design is feasible for SSIPTS project in reducing the volume and mass of the actuator.

The experiment indicates that the thin foil material (0.1mm) with high permeability as a lining for light structure (aluminum) is reasonable as well, as long as the output force is adequate for

94 the actuation. For instance, the lightest structure (37 grams) in this thesis can still provide the force over 30N. This fact also implies that the coating technology is a feasible scheme.

7.2.3 More Strict Comparisons between Simulation and Experiment

The force validation discussed in preceding sections mainly focuses on the comparison in the general tendency, since the data from the simulation and the data from the experiment does not strictly obey the correspondence. For instance, the current from the experiment is excited by the voltage, and this may be affected by the dynamic impedance in the electrical circuit. Therefore, the current number from the experiment is measured and with decimals rather than the current data with the neat number in the simulation by setting.

This section redoes the simulation again based on the current number measured by the experiment. An exact comparison of the magnetic force between the simulation and the experiment is possible. Without a doubt, there still exists the model error between the simulation and experiment. The purpose here is to investigate how much the difference is.

Force Variation over Current at "0"mm Position 50 45 40

35 30 25 20

Force (N) Output Force 15 Experiment 10 Simulation 5 0 0 2 4 6 8 10 12 14 16 18 Coil Current (A)

Figure 7-13: Point-Point Force Comparison at the “0” Coil Position

Force Constant Variation over Current at "0" Position 3.1

2.9

2.7

2.5

2.3

2.1

Experiment Force (N/A) Constant Force 1.9 Simulation

1.7

1.5 0 2 4 6 8 10 12 14 16 18 Coil Current (A)

Figure 7-14: Force Constant Point-Point Comparison at the“0” Coil Position

Figure 7-13 and Figure 7-14 show the trends and the differences of the forces and the force constants between the experimentation and the simulation respectively. The data is based on “0”mm position, i.e., the coil is completely situated in the magnetic assembly. The trends indicate that the magnetic force and the force constant are significantly increasing with the coil current increase, and this matches the conclusion discussed previously. The differences between the experiment and the simulation are possibly due to the model difference. For instance, the air gap between the coil and the magnet assembly is set as 0.2 to 0.4mm, while in the actual case it may approaches to zero. However, gap close to zero in the simulation will cause a huge amount of calculations or the divergence of solution. Another reason that may create the above differences is the deviation of the material properties. The material properties used in the simulation such as the permeability and the BH curves are based on the material datasheet provided by manufacturer. The deviation certainly exists between different batches of products.

And the material machining, even though under careful treatment, is definitely cause some degree of changes.

Force Variation over Current at "10"mm Position 35

15 Experiment

Force (N) Output Force 10 Simulation 5

0 0 2 4 6 8 10 12 14 16 18 Coil Current (A)

Figure 7-15: Point-Point Force Comparison at the Middle of Stroke

Force Constant over Current at "10"mm Postion 3.1

2.9

2.7 Experiment Simulation 2.5

2.3

2.1

1.9 Force (N/A) Constant Force 1.7

1.5 0 2 4 6 8 10 12 14 16 18 Coil Current (A)

Figure 7-16: Force Constant Point-Point Comparison at the Middle of Stroke

Figure 7-15 and Figure 7-16 present the comparison of the force and the force constant at the middle stroke of coil position. The results show that the magnetic force is proportional to the coil current, namely, the force variation follows the Lorentz formula. At the same time, the difference between the experiment and the simulation is rather small. The disturbance effect between the permanent magnet field and coil-current magnetic field is insignificant. Another more reasonable interpretation is that the orientor as a core is located near the center of the coil at present (“10”mm coil position), and the solenoid effect is surely the least, seen in Figure 7-17 b). Figure 7-17 a) shows the coil position at “0”mm, and gives an explanation the case in Figure 7-13 and Figure 7-14.

a) Largest Force Position b) Least Force Position Figure 7-17: Solenoid Effect of the Orientator Working as a Core

7.2.4 Variations of Coil Inductances

To provide more characteristics of the HLA for the customer reference in future dynamic test, the static DC inductance is investigated. The inductance of the actuator is complicated to measure due to the complexity of the core materials in the HLA. The core in the general concept is composed of the orientator (soft magnetic material), the magnet (hard magnetic material), and the shell (combined soft magnetic materials with high permeability). With the variation of the coil position, the inductance of the actuator is variable and highly nonlinear. The inductance of the actuator here is measured by Agilent E4980A precision LCR meter, shown in Figure7-18. The test results are plotted in Figure 7-19. The inductance of naked coil (without core) is about 2mH and the inductance at “0” position is 6.2 at 20Hz, and the maximum value is 6.7mH at “12”mm.

Figure 7-19: Agilent E4980A Precision LCR Meter for Inductance Measurement

Figure 7-18: Coil Inductance of the New Actuator vs. Coil Position and Frequency

7.2.5 Actuation Time Prediction

Since the dynamic experimentation is under construction, a reasonable prediction is suggested here. As we know that the magnetic force is variable in the actuation process, the moving part experiences a motion with a variable acceleration. The actual variation of the force can be drawn from the experiment results, shown in Figure 7-20.

Linear Regression of Force over Coil Position 50

35 F=47.35-1.14x r=-0.9609

30 I=16.6A Force Output(N) Force 25

20 0 2 4 6 8 10 12 14 16 Coil Position (mm)

Figure 7-20: Force Variation During the Actuating Movement

Assuming the force varied in linear relation with the coil position, by the linear regression of the force distribution, a force formula is given as,

F( x ) 47.35 1.14 x (7-1)

For a moving mass as 100 grams, the motion equation can be derived by putting the equation (7- 1) into Newton’s second law,

x( t ) 14100 x ( t )  473.5  0 (7-2)

For specific strokes of 0.015m and 0.02m, the actuation time is 8.29ms and 9.72 ms respectively, and the maximum velocity is 1.885m/s and 2.177m/s correspondingly.

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7.2.6 Comparison of the New Actuator with Commercial Products

Table 7-2 shows the comprehensive evaluation compared with the two models from Moticont Inc. and the two models from BEI. The comparable indicators listed in the table are just for reference, since lots of technical details are unknown for customers.

Table 7-2: Performance Comparison with Commercial Products

Manufacturer CoNeticAA+ CoNetic AA Moticont Moticont BEI BEI NeticS36 +AL (1) (2) (1) (2)

Outer Size (mm) 12x33.4 12x33.4 25.4 12.7 24.1 12.7

Section Area (mm^2) 400.8 400.8 506.5 126.6 455.9 126.6

Volume (cm^3) 16.03 16.03 19.30 5.63 6.29 1.14

Force at 16.6A (Ν) 49.3 38.0 64.7 13.9 59.8 10.0

Force Constant (N/A) 3.0 2.3 3.9 0.8 3.6 0.6

Stroke (mm) 20.0 20.0 25.0 36.0 2.5 0.5

Total Weight (g) 95.1 77.9 137 39.6 39.9 9.4

Mover Weight (g) 54.9 37.7 35 14.6 7 0.9

DC Resistance (Ω) 9.9 9.9 7.4 8.5 9.9 4.0

Coil Inductance 1KHz (mH) 3.5 3.2 3.4 1.4 1.2 1.0

Peak Power (W) 2755 2755 2039 2342 2728 1102

Force/Power (N/W^(1/2)) 0.94 0.72 1.43 0.29 1.15 0.29

Force/Weight (N/Kg) 518 484 472 351 1499 1064

Force/Volume (N/cm^3) 3.08 2.37 3.35 2.47 9.51 8.77

Force/ Section Area (N/cm^2) 12.33 9.5 12.76 10.94 13.11 7.87

Acceleration 50g load 470 433 761 215 1049 196 (N/m^2)

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However, from the comparison, one can see that the new actuator possesses some irreplaceable functions for its special design in the shape and in the magnetic circuit. The commercial actuators listed in the table, are either the geometries do not fit the space requirement of SSIPTS or the forces are not strong enough or the strokes are not long enough.

7.3 Summary

This chapter mainly introduces the experiment set-up, the experiment data acquisition and the data analysis. The experiment set-up consists of the manufacturing and the assembly of the experiment jigs and fixtures that is used for the repelling force investigation and the attractive force investigation, the experiment system design and configuration that include the actuator driving, the data acquisition, and the data storage, and the sensor calibration.

The data collection and analysis contains the experiment for validating the relationships of the magnetic force over the coil current and or the coil position. The magnetic force experiment includes the repelling force test and the attractive force test. The results shows that the largest repelling magnetic force generated at the start point of the coil position, and the largest attractive force built up at the end point of the coil position. Accordingly, the repelling force constant occurs at the stroke start point and the attractive force constant comes about at the stroke end point. At the middle range of the stroke, the force constant keeps constant and the force is proportional to the coil current. At the higher current level, the force demonstrates more nonlinear behavior than the force generated at lower current level.

The analysis shows that the nonlinear behavior of the magnetic force at the stroke-start position and the stroke-end position is due to the special designed magnetic circuit where the mechanism of the solenoid actuator and the mechanism of the voice coil actuator work together. The multiple functions of the orientator in the magnetic assembly are discussed in detail in this chapter as well. The predicted actuation time and a general comparison with commercial products are given as well.

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Chapter 8 Conclusions and Future Work

This chapter contains the conclusions regarding the design, the simulation, the fabrication, and the experimentation of the HLA. It includes the discussion of potential application for which the actuator is appropriate. It also includes the suggestions for future work in improving the performance of the HLA.

8.1 Conclusions

In this research, the design, the simulation, the fabrication, and the experimentation of the HLA were discussed. The major contributions of this thesis include the design of the ultra-compact rectangular HLA specifically used for the pulley segment actuation in the SSIPTS project, the step optimization technique used for simplifying the optimal process of a complex electromagnetic problem, and the integration mechanism of the solenoid actuator and the voice coil actuator for generating a high magnetic force. The pulse power supply is a by-product, which provides a large range of variation in the current and in the voltage with the pulse control mode, where it is not available or over expensive in present market.

The actuator’s performance under various current load and moving positions was fully characterized by the computer simulation and validated by the experiment. The actuator possesses a high starting acceleration and high landing deceleration for the repelling and the attracting respectively. 50N force is easily to output in such a compact actuator with a volume of 40mm by 34mm by 12mm. The mover mass 55grams and the unload acceleration could reach 92g at the experiment conditions. Predicted actuation time for SSIPTS is less than 10ms.

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8.2 Applications

Besides the direct application of the HLA in the development of SSIPTS transmission system, its compact size and high power density lends itself to some other spatially-constrained, bi-stable, and rapid actuating applications.

One potentially important application is in the high speed valve control, where the scenario is a fast open or close action for liquid, gas or some other mass media that it is very common in chemical and atomic industries. Another application will be in the manufacturing industry, where a rapid pick-and-place is needed. This actuator will significantly increase the production efficiency by its attributes of the high force and the compact size. Other applications may be the device manipulation in the military equipment where the force, the speed, and the reliability are critical.

8.3 Future Work

Now that the performance of the HLA design has been experimentally validated, and its superior behaviors have been investigated, the next step is to carry out the further assessment on its dynamic performance and the further improvement of the structural design, material processing, and control strategies.

The soft landing for this powerful actuator is a challenging task and need pay more attention to it. The mechanical strength of the bobbin need find some stronger materials, since when the actuator mover undertakes the very high attractive force the coil bobbin stands a very high tensile force. The molded bobbin made by high strength materials may be an alternative.

To improve the performance of the actuator, further actions is suggested to taken in boosting the amplitude of the magnetic field integrations, including the use of the double magnet source, the closed circuit for the magnetic assembly, and the square magnet wires.

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Appendix A Magnetic Unit Conversions

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Appendix B Permanent Magnet Material Datasheet

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Appendix C Datasheet of MotiCont Voice Coil Actuator

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Appendix D BEI Product Performance List

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Appendix E Sweeping Applied in Magnet Thickness and Magnet Length

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Appendix F Superposition of Magnetic Fields

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