Development of a Hybrid Linear Actuator
by
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
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Development of a Hybrid Linear Actuator
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.
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To my Mom and Dad,
My dear wife, Wendy Wang,
My lovely daughter, Mei, and my son, Marcus
iv
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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
Materials
W General Energy
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
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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
1
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).
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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
3
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.
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
a) 3D profile b) The actuator locations in sector zones
Figure 1-2: The Geometric Constraint of Actuators in SSIPTS Package
4
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.
5
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.
6
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,
7
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
8
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
9
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
Figure 2-2: Agility of Actuators Characterized by Frequency vs. Weight
(Courtesy of Marc Zupan et al.)
10
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].
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
VM m (2-1)
It defines magnetic field intensity H as
Figure 2-3: Origin of Magnetism at Atomic Level
11
mM H (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
0 0 0( ) (1 )m r B H M H H H (2-3)
where μ0 (as a physical constant, 4π×10-7
Η/m) is the magnetic permeability in free space
(vacuum, air), μr is the relative permeability, and μ is the permeability of a material.
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.
a. Free-space (air) b. Diamagnetic materials c. Ferromagnetic materials
Figure 2-4: Responses of Different Materials to the Same Magnetic Field
12
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
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].
a. Attraction between two conductors b. Repulsion between two conductors
Figure 2-5: Interaction of Two Magnetic Fields Built Up by Direct Currents
13
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].
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.
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
14
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.
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
S R= (2-5)
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
mx
WF
x
, and
2
2m
BW dv
(2-6)
a. Reluctance force on plunger b. Solenoid actuator (Courtesy of Ledex Inc.)
Figure 2-7: Principle of Solenoid Actuator Governed by Variable Reluctance
15
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
16
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 2-9a 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.
Figure 2-8: Halbach Cylinders with Different Wavenumbers (k)
17
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
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)
18
could reach 100,000 to 500,000 after proper heat treatment, and the magnetic flux density could
attain 2.3 teslas.
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
a. Basic B-H hysteresis loop b. BH curves with different materials
Figure 2-10: Properties of Advanced Soft Magnetic Materials
19
magnets, known as Nd2Fe14B, are the most widely used type of rare-earth magnets and currently
are the strongest type of manmade permanent magnet.
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.
Figure 2-11: Properties of Hard Magnetic Materials
20
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
a. Material combination of coil conductors b. Actuators with combined coil materials
Figure 2-12: Thrust Force Improvement by Composite Coil Conductors
21
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)
22
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
23
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.
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.
a. One sector of SSIPTS b. Circular actuators c. Rectangular actuators
Figure 3-2: Layout of Actuators in SSIPTS
24
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.
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
a. Circular b. Rectangular c. Morphing
Figure 3-3: Space Using Efficiency of Different Cross-Section Shape of Actuators
25
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
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
60
n (3-1)
2rT k T k
(3-2)
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
Figure 3-4: Actuation Force Behaviors Required by SSIPTS
26
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.
The relationships among displacement x(t), velocity v(t) or (t), and acceleration a(t) or ( )x t
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
Figure 3-5: Typical Actuating Strategy
27
, (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
(RPM) Angular Velocity
(Rad/sec) Actuation Time
(mS) Acceleration
(g) Max. Force
(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
28
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
Φ
Magnetic Flux
(Weber) I
Electrical Current
(Ampere)
H
Magnetic Field Intensity
(Ampere/meter) E
Electrical Field Intensity
(Volts/meter)
B= Φ
Magnetic Flux Density
(Tesla) J= I/A
Electrical Current Density
(Ampere/square meter)
F =NI=HL
MMF
(Ampere-turn) V
EMF
(Volts)
R =L/( Magnetic Reluctance
( Ampere-turn/Weber) R =L/( σA)
Electrical Resistance
(Ohm)
(H/m)
Magnetic Permeability
( Henry/meter) σ (S/m)
Electrical Conductivity
( Siemens/meter)
F= ΦR Hopkinson’s Law V= I R Ohm’s Law
29
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
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
Figure 3-7: Physics of Electromagnetic Actuators
30
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.
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.
a. Solenoid actuator b. Voice coil actuator c. Hybrid actuator
Figure 3-8: Force Behaviors of Electromagnetic Actuators
31
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.
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
Figure 3-10: Coils Working in Perpendicular Field
a. Outer radial magnet b. Inner radial magnet c. Axial magnet
Figure 3-9: Magnetic Field Interaction at Different Magnetic Configurations
32
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
interactions, shown in Figure 3-11a, while Figure 3-11b creates an even distribution by the
orientator and without the counter effect.
a. Radial magnet combination b. Orientator guided axial magnet
Figure 3-11: Magnetic Flux Peripheral Distribution at Different Configurations
33
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.
34
Table 3-3: Parameterized Dimensions in SolidWorks Model
35
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
Table 3-4: Parameterized Dimensions in SolidWorks Model (continued)
36
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.
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 3-12: Concept Design of the Proposed Actuator
37
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.
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.
Figure 3-13: Primary Material Selection of the Concept Design of the New Actuator
38
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].
39
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:
t
DH J (4-1)
t
BE (4-2)
D (4-3)
0 B (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
t
J (4-5)
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:
B A (4-6)
Vt
AE (4-7)
In static magnetic field, Maxwell-Ampère’s law reduces to
1( ( ))red ext ext A B J (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.
40
4.1.2 Constitutive Relations
The macroscopic properties of the field medium are described by constitutive relations, given by
0 D E P (4-9)
0( ) B H M (4-10)
( ) J H M (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·10H/m.
A generalized form of the constitutive relation for the magnetic field is
0 r r B H B (4-12)
( )fB H (4-13)
ext J E J (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:
2 1 2( ) 0 n E E (4-15)
2 1 2( ) s n D D (4-16)
2 1 2( ) s n H H J (4-17)
2 1 2( ) 0 n B B (4-18)
41
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
0 0( ) ( )
D T
eV V
W d dV dt dVt
D
E D E (4-19)
0 0( ) ( )
B T
mV V
W d dV dt dVt
B
H B H (4-20)
respectively. For linear and isotropic material, the total electromagnetic energy density is
expressed as
1 1
2 2e mw w w
E E B B (4-21)
The energy density for material with constant permeability is described as
2 1
2 2m
Bw BH
(4-22)
For materials with nonlinear B-H curves, the energy density can be shown to be
mw H dB (4-23)
The coenergy density is described as
cow B dH (4-24)
42
The sum of the coenergy density and the energy density abide by
m cow w 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.
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
0extT f (4-26)
Figure 4-1: Energy Density and Coenergy Density at Work
Point A for a Typical Nonlinear B-H Curve
43
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
1 2 1( ) 0T T n (4-27)
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
1
1 2T dS
F n (4-28)
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
mW F (4-29)
Figure 4-2: Maxwell Stress Tensor at Material Boundaries
44
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:
L dv F J B (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
2inputW dv J A (4-31)
and
2
2stored
BW dv
(4-32)
respectively. And the energy functional is defined as the difference between stored energy and
input energy:
2 1
2 2stored input
BF W W dv
J A (4-33)
45
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
2
2
Bdv Jdv
A
(4-34)
The first-order shape function for a simple triangular element is
, ,
( , ) [ ( )]k k k k
k L M N
A x y A a b x c y
(4-35)
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
2 10
2 2k
BJA dv
A
(4-36)
where B is the curl of A, and for triangle element gives,
22
2 A AB
x y
(4-37)
Analogous to structure mechanics, the matrix equation for a magetostatic filed is
[ ]K A J (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.
46
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.
47
Table 4-1: Parameter List for Geometric Modeling of the New Actuator
Parameter Expressions Name
agx 0.2:0.4 [mm] Air gap
btx 0.2:0.4 [mm] Bobbin thickness
stx 0.1:0.74 [mm] Shell thickness
alx 30:50 [mm] Actuator length
atx 10:14 [mm] Actuator thickness
mlx 10:35 [mm] Magnet length
mtx 2:6 [mm] Magnet thickness
ctx / 2 / 2x x x x xat mt ag stbt Coil thickness
clx x x xag stal Coil length
crlx x x xstal ml Orientator length
crtx mlx Orientator thickness
astx 2 atx Air shell thickness
aslx 2 alx Air shell length
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.
48
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
Ω1 1 1( ) 00 Ar
( )B f H eB
Orientator (iron)
Ω2 1 1( )0 A Jr ext
0
B Hr
Coil (copper)
Ω3
( )B f H eB
Shell 1(permalloy1)
Ω4
( )B f H eB
Shell 2(permalloy2)
Ω5 1 1( ) 00 A Hr c
0B H B
r r
Magnet (Nb2Fe14B)
Ω6
0
B Hr
air
1 1( ) 00 Ar
1 1( ) 00 Ar
1 1( ) 00 Ar
Figure 4-3: ½ 2D FEA Model of the New Actuator
49
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 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),
Figure 4-4: BH Curves of Different Permalloys from the Manufacturer
50
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
51
Hci, the magnet will lose its magnetism permanently. In this design, the external field is provided
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
Figure 4-5: Working Behavior of Different Magnets at Room Temperature
52
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 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.
Figure 4-6: Coarser Meshing and Finer Meshing for Different Purposes
53
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
(UMFPACK)
A highly efficient direct
solver for nonsymmetrical
systems
GMRES An iterative solver for
nonsymmetrical problems
Direct
(SPOOLES)
An efficient direct solver for
symmetric and
nonsymmetrical systems. It
uses less memory than
UMFPACK.
FGMRES An iterative solver for
nonsymmetrical problems. It
can handle more general
preconditioners but also uses
more memory than GMRES.
Direct
(PARDISO)
A highly efficient direct
solver for symmetric and
nonsymmetrical systems. It
often uses less memory than
UMFPACK.
BiCGStab An iterative solver for
nonsymmetrical problems. It
uses a fixed amount of
memory independent of the
number of iterations. It
therefore typically uses less
memory than GMRES.
Direct
(PARDISO out
of core)
An out-of-core version of
PARDISO that stores the
LU-factors on disk.
Conjugate
gradients
An iterative solver for
symmetric positive definite
problems
Direct
Cholesky
(TAUCS)
An efficient direct solver for
symmetric, positive-definite
systems
Geometric
multi-grid
An iterative solver for elliptic
or parabolic problems
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
54
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
55
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.
Figure 4-8: Optimization of Magnet Thickness
60
80
100
120
140
160
180
200
2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
Fo
rce
Ou
tpu
t P
er U
nit
Wid
th (
N/m
)
Magnet Thickness (mm)
Force Capacity vs. Magnet Thickness
L_magnet=15.9mm
L_magnet=12.7mm
L_magnet=19.0mm
L_magnet=22.0mm
L_magnet=25.4mm
Maximum Force at
Magnet Thickness
56
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.
21
2kW mv (4-39)
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).
( )me
s
W f x dx (4-40)
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)
57
10
1
( )2
nn
me i
i
F FW x F
, (4-41)
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.
Figure 4-10: Energy Integration for a Particular Magnet Length
6.28 5.54
4.52
1.78
0
1
2
3
4
5
6
7
0 5 10 15
Mag
net
ic F
orc
e fi
(x)
(N)
Coil position X (mm)
Figure 4-9: Force Distributions over Coil Position and Magnet Length
58
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).
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;
13.5
14
14.5
15
15.5
16
16.5
17
17.5
13 16 19 22 25 28 31
Norm
aliz
ed E
ner
gy O
utp
ut(
5x
10
-3J)
Magnet Length (mm)
Energy Output vs Magnet Length
59
and Figure 4-12d is the composite structure, consisting of the inner layer with NetiS3-6, and the
outer layer with CoNeticAA.
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.
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
60
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
61
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
62
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.
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
Figure 4-14: Force Behavior over Coil Current at Different Coil Positions
63
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
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.
Figure 4-15: Force Behavior over Coil Position at Different Coil Currents
64
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:
542401
FMaxwell
(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:
33637
FMaxwell
(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
Figure 4-16: Force Comparison with Meshing Effect
0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12 14 16 18
Forc
e O
utp
ut
Per
Uin
it W
idth
(N
/M)
Coil Current (A)
Meshing Effect on Force Calculation
Maxwell Force at DoFs 542401
Lorentz Force at DoFs 542401
Maxwell Force at DoFs 33637
Lorentz Force at DoFs 33637
65
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.
66
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.
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
Figure 4-17: Modeling and Simulation of MotiCont Actuator
67
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)
(published)
4.45 4.90 5.15 5.25 5.15 4.66 3.50
Pull F (N)
(simulated)
4.55 5.27 5.50 5.51 5.30 4.65 3.28
Push F (N)
(Simulated)
4.56 5.29 5.49 5.46 5.20 4.47 3.05
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.
Figure 4-18: Performance Validation of MotiCont Actuator
0
1
2
3
4
5
6
0 5 10 15 20
Outp
ut
Pull
ing F
orc
e (N
)
Coil Position (mm)
Comsol Simulation Data
Moticon Parameter Data
Correlation Coefficient r=0.9953
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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.
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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
70
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
71
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.
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
Figure 5-2: Machining Effect on Magnetic Properties of Permalloy
72
strength for steel is 2800 psi and for aluminum 1600 psi.), a short setting time (240-280 sec. for
steel and 260300 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.
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.
a. Axial direction folding b. Circumferential direction folding
Figure 5-3: Patterns of Sheet Metal Process
73
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.
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.
a. Square winding b. Hexagonal winding c. Square wire
Figure 5-4: Filling Factors in Different Winding Patterns and Different Magnet Wires
74
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.
0 02 [ 1]coilwire T coil
T W TL n L
d d
(5-1)
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.
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
Figure 5-5: Coil Winding Calculation
75
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.
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 adhesivefor instance, two-component epoxy.
Figure 5-6: Bobbin Structure Assembly
76
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
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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.
78
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,
2
heat
VP
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
heat heatW P T (6-2)
79
where T is the actuating duration time. The mechanical net work done by actuator is
mechanicalW F S (6-3)
where F is the actuating force and S is the moving distance. The total energy release from the
power supply is
heat mechanical lossW W W W (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
2
2WC
V (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 (0250V), variable current (020A), and
variable pulse control (120mS). 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
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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.
81
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
Figure 6-2: Pulse Generation by IC 555 Connected as the Mono-stable Status
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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.
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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
84
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
85
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 7-4 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 7-3: Experimental System Configuration
86
Figure 7-4: Block Diagram of the System Configuration in LabView
Figure 7-5: Integrated Display and Measurement of Force, Current, Voltage, and Signal
87
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
Figure 7-6: Instron 8511 Testing Machine
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
88
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
89
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.
Figure 7-7: Experiment of Repelling Force over Coil Position and Coil Current
0
10
20
30
40
50
60
0 5 10 15 20 25
Rep
elli
ng
Fo
rce
(N)
Coil Position (mm)
Repelling Force vs. Coil Position at Different Current
1.8A
3.4A
5.1A
6.8A
8.5A
10.2A
11.8A
13.5A
15.0A
16.6A
90
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.
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25
Rep
elli
ng F
orc
e C
on
stan
t (N
/A)
Coil Position (mm)
Repelling Force Constant vs. Coil Position at Different Current
1.8A
3.4A
5.1A
6.8A
8.5A
10.2A
11.8A
13.5A
15.0A
16.6A
91
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.
Figure 7-9: Experiment of Attracting Force over Coil Current and Coil Position
0
10
20
30
40
50
60
0 5 10 15 20 25
Att
ract
ing F
orc
e (N
)
Coil Position (mm)
Attracting Force vs. Coil Position at Differnet Current
1.7A
3.5A
5.2A
6.9A
8.4A
10.1A
11.5A
13.2A
15.0A
16.1A
92
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.
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25
Att
ract
ing F
orc
e C
onst
ant
(N/A
)
Coi Position (mm)
Attracting Force Constant vs. Coil Positio at Different Current
3.5A
5.2A
6.9A
8.4A
10.1A
11.5A
13.2A
15.0A
16.1A
93
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.
Figure 7-11: Force Comparison over Coil Current for Different Shell Material Combinations
0
10
20
30
40
50
1 3 5 7 9 11 13 15 17
Outp
ut
Push
ing F
orc
e (N
)
Coil Current (A)
Force Comparison of Different Shells
CoNeticAA+S36
Al+CoNeticAA
Netic S36
94
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
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20
Forc
e C
onst
ant
K (
N/A
)
Coil Current (A)
Force Constants of Different Shell Materials
CoNeticAA+NeticS36
Al+CoNetic AA
NeticS36
95
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.
Figure 7-13: Point-Point Force Comparison at the “0” Coil Position
0
5
10
15
20
25
30
35
40
45
50
0 2 4 6 8 10 12 14 16 18
Forc
e O
utp
ut
(N)
Coil Current (A)
Force Variation over Current at "0"mm Position
Experiment
Simulation
96
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.
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
3.1
0 2 4 6 8 10 12 14 16 18
Forc
e C
onst
ant
(N/A
)
Coil Current (A)
Force Constant Variation over Current at "0" Position
Experiment
Simulation
97
And the material machining, even though under careful treatment, is definitely cause some
degree of changes.
Figure 7-15: Point-Point Force Comparison at the Middle of Stroke
Figure 7-16: Force Constant Point-Point Comparison at the Middle of Stroke
0
5
10
15
20
25
30
35
0 2 4 6 8 10 12 14 16 18
Forc
e O
utp
ut
(N)
Coil Current (A)
Force Variation over Current at "10"mm Position
Experiment
Simulation
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
3.1
0 2 4 6 8 10 12 14 16 18
Forc
e C
onst
ant
(N/A
)
Coil Current (A)
Force Constant over Current at "10"mm Postion
Experiment
Simulation
98
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.
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.
a) Largest Force Position b) Least Force Position
Figure 7-17: Solenoid Effect of the Orientator Working as a Core
99
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
100
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.
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,
( ) 47.35 1.14F x 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,
( ) 14100 ( ) 473.5 0x t x t (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.
20
25
30
35
40
45
50
0 2 4 6 8 10 12 14 16
Forc
e O
utp
ut
(N)
Coil Position (mm)
Linear Regression of Force over Coil Position
F=47.35-1.14x r=-0.9609 I=16.6A
101
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+NeticS36
CoNetic AA +AL
Moticont (1)
Moticont (2)
BEI (1)
BEI (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 (N/m^2)
470 433 761 215 1049 196
102
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.
103
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.
104
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.
105
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111
Appendix A Magnetic Unit Conversions
112
Appendix B Permanent Magnet Material Datasheet
113
Appendix C Datasheet of MotiCont Voice Coil Actuator
114
Appendix D BEI Product Performance List
115
Appendix E Sweeping Applied in Magnet Thickness and Magnet Length
116
Appendix F Superposition of Magnetic Fields
