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Design and Development of an Actuation
System for the Synchronized Segmentally
Interchanging Pulley Transmission System
(SSIPTS)
By
Vahid Mashatan
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Department of Mechanical and Industrial Engineering
University of Toronto
©Copyright by Vahid Mashatan 2013
ii
Design and Development of an Actuation System for the Synchronized
Segmentally Interchanging Pulley Transmission System (SSIPTS)
Vahid Mashatan
Doctor of philosophy
Department of Mechanical and Industrial Engineering
University of Toronto
2013
Abstract
This Ph.D. thesis presents the design, modeling, optimization, prototyping, and experimental
methodologies for a novel actuation system for the synchronized segmentally interchanging
pulley transmission system (SSIPTS). The SSIPTS is an improved transmission which offers the
combined benefits of existing transmission systems for the automotive, the power generation,
and the heating, ventilation, and air conditioning (HVAC) industries.
As a major subsystem of the SSIPTS, the Pulley Segment Actuation System (PSAS) plays a
critical role in the SSIPTS operation and success. However, the overall design of the SSIPTS and
its operation principle introduce very challenging and conflicting design requirements for PSASs
that the existing actuation technologies cannot meet. To address the lack of actuation
technologies for the PSAS application, this research proposes a unique actuation system that
meets all the challenging design requirements of the PSAS. This new actuation system is based
on the electromagnetic moving coil actuator (MCA) technology. The proposed system is
conceptualized and modeled. The key parameters of the actuation system are defined following
the conceptual design and modeling. Further, the geometry mapping optimization and the FEM
analysis are conducted to determine the optimized values for the key design parameters. From
the simulation results, the optimized actuator is shaped. Moreover, a proper control strategy is
iii
proposed for the motion of the actuator. Experiments are performed to find the empirical
parameters of the actuator, to validate the proposed design, and to test the performance of the
actuator. Experimental results show that the prototype of the actuation system meets the design
requirements and is feasible for implementation in the SSIPTS.
The main contribution of this thesis is to develop a highly efficient and reliable ultra fast bi-
stable actuation system for the PSAS for the SSIPTS. As an ultra fast bistable actuation system,
the designed actuation system has many advantages over other types of actuation systems: higher
load capacity, smaller dimensions, and good controllability. These performance characteristics
make the designed actuation system an excellent candidate in applications requiring fast transient
response, high precision, and high load capacity such as electromagnetic valve actuators for
engines, high speed pick and place, and precise positioning.
iv
To Hossein Mashatan and Fereshteh Izadian
v
Acknowledgments
I would like to express my gratitude to my advisor, Professor Jean W. Zu, for her
delicate support and guidance throughout my graduate career. 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 a competent person. I am
grateful to Professor Zu for giving such a research platform to let me achieve the integration of
my personal interests and the social demands.
I would like to extend my appreciation to my Ph.D. committee, Professor Kamran
Behdinan, Professor Redha Ben Mrad, Professor Goldi Nejat, and Professor Farid Golnaraghi
(Simon Fraser University), for their insight, suggestions, and time in evaluating my research.
I would also like to thank Mr. Mats Lipowski, Mr. Paul Bottero, and Mr. Anthony
Wong, engineers and managers from Vicicog Inc. for providing the design requirement of the
actuation system and background information for the synchronized segmentally interchanging
pulley transmission system (SSIPTS).
My gratitude belongs to Mr. Reza Farshidi and Ms. Roshanak Banan, my lab mates as
well. I also present my sincerely appreciation to Mr. Ryan Mendell, the manager of MIE
machine shop, for providing the convenience and help in the fabrication of the actuation system.
Sincerely,
Vahid Mashatan
June 2013
vi
TABLE OF CONTENT
CHAPTER 1: INTRODUCTION .....................................................................................1
1.1 BACKGROUND ON MECHANICAL TRANSMISSION SYSTEMS .......................1
1.2 OVERVIEW OF THE SSIPTS ......................................................................................6 1.2.1 Introduction .............................................................................................................6 1.2.2 The Design and the Operation Principle of the SSIPTS .........................................7 1.2.3 Technical Benefits of the SSIPTS ........................................................................10
1.2.4 Applications of the SSIPTS ..................................................................................12
1.3 PULLEY SEGMENT ACTUATION SYSTEM (PSAS) IN THE SSIPTS ................14
1.3.1 Introduction ...........................................................................................................14 1.3.2 Design Requirements: Geometric and Volumetric Constraints of the PSAS .......16
1.3.3 Design Requirement: Fast Transient Requirement of the PSAS ..........................19 1.3.4 Design Requirement: Softlanding Requirement of the PSAS ..............................22 1.3.5 Design Requirement: Holding Force ....................................................................23
1.3.6 Design Requirement: Electrical Power Consumption Limitation for the PSAS ..23
1.4 RESEARCH OBJECTIVES ........................................................................................24
1.5 THESIS OUTLINE ......................................................................................................26
CHAPTER 2: LITERATURE REVIEW ......................................................................28
2.1 CLASSIFICATION OF ACTUATION TECHNOLOGIES .......................................28
2.2 CHARACTERIZATION OF ACTUATION TECHNOLOGIES ...............................30
2.3 ACTUATION TECHNOLOGIES USED IN AUTOMOTIVE INDUSTRY .............32
2.4 ELECTROMAGNETIC ACTUATOR TECHNOLOGIES ........................................34 2.4.1 Voice coil actuator ................................................................................................37 2.4.2 Solenoid actuator ..................................................................................................40
CHAPTER 3: DESIGN AND MODELING OF THE ELECTROMAGNETIC
PULLEY SEGMENT ACTUATION SYSTEM ...........................................................42
3.1 ACTUATION TECHNOLOGY SELECTION FOR THE PSAS ...............................42
3.2 DESIGN PRINCIPLE OF THE ELECTROMAGNET PSAS ....................................46
3.3 MATHEMATICAL MODELING OF THE PSAS .....................................................51 3.3.1 Electrical domain modeling and equations ...........................................................53 3.3.2 Magnetic domain modeling and equations ...........................................................55
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3.3.3 Mechanical domain modeling and force equations ..............................................59
3.3.4 Summary of governing equations for the MCA for the PSAS .............................63
3.4 FINITE ELEMENT ANALYSIS AND GEOMETRY MAPPING
OPTIMIZATION ......................................................................................................64
3.4.1 Finite Element Analysis Problem Setup for the PSAS .........................................64 3.4.2 Geometry Mapping Optimization and Parameterization ......................................67 3.4.3 Optimized Design of the PSAS Actuator .............................................................73
3.5 SYSTEM MODELING AND SIMULATION OF THE PSAS ..................................79 3.5.1 System modeling of the mechanical subsystem ...................................................79
3.5.2 System modeling of the electromagnetic actuator subsystem ..............................82 3.5.3 System modeling of the power control subsystem ...............................................88 3.5.4 Position Control Subsystem for the PSAS ............................................................93
3.6 POSITION CONTROL AND SOFTLANDING STRATEGIES ................................94
3.7 SUMMARY .................................................................................................................99
CHAPTER 4: FABRICATION AND EXPERIMENTATION OF THE
ELECTROMAGNETIC PULLEY SEGMENT ACTUATION SYSTEM ..............100
4.1 FABRICATION AND PROTOTYPING OF THE ACTUATOR ............................100
4.1.1 Fabrication of the PSAS Components ................................................................101 4.1.2 Coil Winding for the PSAS ................................................................................106 4.1.3 Final Prototype of the PSAS ...............................................................................108
4.2 DESIGN AND DEVELOPMENT OF EXPERIMENTAL SETUPS .......................109
4.2.1 Static Force Test setup for PSAS ........................................................................109 4.2.2 Dynamic Performance Test Setup for the PSAS ................................................113 4.2.3 Position control Test Setup for PSAS .................................................................118
4.3 DETERMINATION OF THE CHARACTERISTICS OF THE PSAS .....................120
4.4 EXPERIMENTAL RESULTS AND VERIFICATIONS ..........................................131
4.5 SUMMARY ...............................................................................................................136
CHAPTER 5: DESIGN AND DEVELOPMENT OF A SOFTLANDING
MECHANISM FOR THE SSIPTS...............................................................................138
5.1 INTRODUCTION .....................................................................................................138
5.2 DESIGN PRINCIPLE OF THE SOFTLANDING MECHANISM ..........................139
5.3 MATHEMATICAL MODELING OF THE SOFTLANDING MECHANISM .......145
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5.4 FINITE ELEMENT ANALYSIS AND GEOMETRY MAPPING OPTIMIZATION
OF THE MAGNETIC LATCH SYSTEM .............................................................154
5.5 SYSTEM MODELING AND SIMULATION OF THE PSAS ................................164
5.6 FABRICATION AND PROTOTYPING OF THE SOFTLANDING
MECHANISM ........................................................................................................174 5.6.1 Fabrication and Selection of the Softlanding Mechanism Components .............175 5.6.2 Final prototype of the Softlanding Mechanism ..................................................179
5.7 EXPERIMENTATIONS............................................................................................181 5.7.1 Static Force Test Setup for the Springs and the Magnetic Latch Systems .........181
5.7.2 Position control test setup for the PSAS .............................................................185
5.8 SUMMARY ...............................................................................................................188
CHAPTER 6: CONCLUSIONS AND FUTURE WORKS ........................................190
6.1 SUMMARY ...............................................................................................................190
6.2 FUTURE WORK .......................................................................................................194
REFERENCES ................................................................................................................196
Appendix A: Engineering drawings for the electromagnetic ACTUATOR ....................204
Appendix B: Engineering drawings for the Static force test setup ..................................209
Appendix C: Engineering drawings for the softlanding mechanism ...............................215
Appendix D: Data sheet for the analog servo drive .........................................................221
Appendix E: Data sheet for the force sensor ...................................................................224
Appendix F: Data sheet for the LVDT sensor .................................................................226
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LIST OF TABLES
Table 1: Dynamic performance requirement of the PSAS ........................................................... 22
Table 2: Actuation technology classification [40] ........................................................................ 28
Table 3: Dimensional parameters of the PSAS actuator for the FEA model ................................ 66
Table 4: Electromagneic parameters of the PSAS actuator for FEA model ................................. 66
Table 5: Optimized value of geometrical values of the PSAS actuator ........................................ 78
Table 6: Optimized electromagnetic parameters of the PSAS actuator ........................................ 78
Table 7: Actual electromagnetic parameters of teh PSAS actuator ............................................ 130
Table 8: Optimized geometrical values of the magnetic latch for the PSAS.............................. 163
Table 9: Comparison between the performance of the electromagnetic actuator and the
softlanding mechanism for the PSAS for the SSIPTS application ..................................... 193
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LIST OF FIGURES
Figure 1: Morphing pulley assambly .............................................................................................. 8
Figure 2: Different drive ratios of the SSIPTS ............................................................................... 9
Figure 3: Geometrical Constraints of the PSAS in the SSIPTS.................................................... 17
Figure 4: Space utilization of different cross-sections for PSAS [40] .......................................... 17
Figure 5: The integration of a circular actuation system in the SSIPTS ....................................... 18
Figure 6: The integration of a rectangular actuation system in the SSIPTS ................................. 18
Figure 7: Typical stroke profile for position control .................................................................... 21
Figure 8: Required displacement, velocity, and acceleration profiles of the PSAS ..................... 21
Figure 9: Actuation technology matric with respect to output forces and stroke levels [44] ....... 31
Figure 10: Actuation technology matrix with respect to maximum frequency and weight [44] .. 31
Figure 11: Block diagram of the electromagnetic actuator ........................................................... 34
Figure 12 : Lorentz Force Law ..................................................................................................... 36
Figure 13: Voice coil actuator schematic ...................................................................................... 39
Figure 14: The magnetic field lines of a voice coil actuator..................................................... 40
Figure 15: Schematic of solenoid actuator.................................................................................... 41
Figure 16: Force along the stroke for MCA and solenoid actuators ............................................. 45
Figure 17: Force profiles for MCA and solenoid actuators with respect to current direction ...... 45
Figure 18: The three common design configurations for MCAs [40] .......................................... 47
Figure 19: The area of the coil that is in interaction with permanent magnetic flux [40] ............ 48
Figure 20: The electromagnetic PSAS design .............................................................................. 49
Figure 21: Componenets of the electromagnetic PSAS ................................................................ 49
Figure 22: Electrical, magnetic, and mechanical domain of the electromagnetic actuators [58] . 51
Figure 23: The design schematic of the PSAS actuator ................................................................ 52
Figure 24: Assigned parameters for the componenets in the actuators ........................................ 52
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Figure 25: Magnetic flux density, current, and Lorentz force vectors in the actuator .................. 53
Figure 26: Nonlinear relationship between the flux linkage and the current ................................ 61
Figure 27 : 2D FEA model of the PSAS actuator ......................................................................... 65
Figure 28:Magnetic flux lines in the PSAS actuator .................................................................... 69
Figure 29:Effect of permanent magnet on maximum force .......................................................... 69
Figure 30: The saturation of the steel shell due to the decreased thickness of the shell ............... 70
Figure 31: The effect of length of shell on the force along the stroke .......................................... 72
Figure 32:Inductance of the coil along the stroke for different lengths of the magnet ................. 72
Figure 33:Output force along the stroke for different lengths of the magnet ............................... 73
Figure 34:Simulated PSAS force along the stroke for different current values ........................... 75
Figure 35: Force sensitivity parameter along the stroke for different current values ................... 75
Figure 36: Simulated values of the inductance of the coil along the stroke ................................. 76
Figure 37: Simulated values of the change of the inductance per mm ......................................... 76
Figure 38: The magnetic flux density within the actuator ............................................................ 77
Figure 39: SIMULINK simulation model of the PSAS in the SSIPTS ........................................ 79
Figure 40:Model of the mechanical subsystem as an equivalent mass-damper subsystem .......... 80
Figure 41: Simulink model of the mechanical subsystem ............................................................ 82
Figure 42: The block diagram of the PSAS actuator model with look up tables.......................... 83
Figure 43: The block diagram of the voice coil actuator with constant sensitivity parameters .... 84
Figure 44 : Simplified the block diagram of the actuator with constant sensitivity parameters ... 85
Figure 45: Impulse and step responses of the exact and simplified models of the
electromagnetic actuator ....................................................................................................... 86
Figure 46: Pole-zero map of the exact and simplified model ....................................................... 87
Figure 47: The SIMULINK model of the electromagnetic actuator subsystem ........................... 87
Figure 48: Simulink simulation model of the power control subsystem ...................................... 88
Figure 49:Pulse-width modulated signal ...................................................................................... 89
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Figure 50: Schematic of an H-bridge ............................................................................................ 91
Figure 51: Current directions through the load in an H-bridge .................................................... 92
Figure 52: The desired position, velocity, and acceleration trajectories for the PSAS ................ 95
Figure 53: The simulated position trajectories.............................................................................. 97
Figure 54: The velocity profile of the pulley segment .................................................................. 97
Figure 55: Applied PWM voltage ................................................................................................. 98
Figure 56: The closed up of applied PWM voltage during actuation ........................................... 98
Figure 57: The drawn current and the applied PWM voltage ....................................................... 99
Figure 58: Specification of the permanent magnet for the PSAS ............................................... 102
Figure 59: The permanenet Neodymium magnet demagnetization curves for grade N42 [76] . 102
Figure 60: Prototype of the bobbin for the PSAS ....................................................................... 104
Figure 61: The shell assembly with the mount for the PSAS ..................................................... 105
Figure 62: Winding methods with different filling factors [40] ................................................. 107
Figure 63: The coil winding for the PSAS.................................................................................. 107
Figure 64: Components of the MCA for the PSAS .................................................................... 108
Figure 65: The assembled prototype of the PSAS ...................................................................... 108
Figure 66: Flow diagram for the static force test setup for the PSAS ........................................ 110
Figure 67: Mechanical subsyetm of the static force test set up for push force ........................... 111
Figure 68: Mechanical subsyetm of the static force test set up for the pull force ...................... 111
Figure 69: The control circuit for the static force test setup ....................................................... 112
Figure 70: The measurement data in the LABVIEW environment ............................................ 112
Figure 71: The block diagram of the data acquisition system in the LABVIEW environment .. 113
Figure 72: Flow diagram for the dynamic performance test setup for the actuation system ...... 115
Figure 73: Mechanical subsystem of the dynamic performance test setup for the actuation
system ................................................................................................................................. 115
Figure 74: The actuation system and the pulley segment representative.................................... 116
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Figure 75: The block diagram of the data acquisition system in the LABVIEW environment
for the dynamic performance test setup .............................................................................. 116
Figure 76:Measurement data in the LABVIEW environment .................................................... 117
Figure 77: Flow diagram for the position control test setup for the PSAS ................................. 119
Figure 78:Position control test setup for the PSAS .................................................................... 119
Figure 79:Static force generation model ..................................................................................... 121
Figure 80: Current drawn by the coil for different voltage values at 12mm .............................. 123
Figure 81: Generated static force for different voltage values at 12mm .................................... 123
Figure 82: Experimental values of static force at different current values along the stroke
actuator ................................................................................................................................ 124
Figure 83: Experimental force sensitiy parameter along the stroke for different current values 124
Figure 84: RL circuit for the static force test .............................................................................. 125
Figure 85:The current profiles for a constant applied voltage at different positions .................. 126
Figure 86:Simulated and actual current profiles ......................................................................... 127
Figure 87: Experimented position and velocity curves for the drop test using gravity force ..... 128
Figure 88:Fitting modeling to find viscous damping coefficient................................................ 128
Figure 89: Experimental value of the for the back-emf parameter ............................................. 130
Figure 90: Simulated vs Experimented static force curves for different current values along
the stoke of the actuator ...................................................................................................... 132
Figure 91: Simulated vs. experimented position profiles for different current values ............... 133
Figure 92: Simulated vs. experimented velocity profiles for different current values ............... 133
Figure 93: Simulated vs. experimented current profiles ............................................................. 134
Figure 94: Simulated vs. experimented voltage profiles for different current values ................ 134
Figure 95: The experimental results for the position control and softlanding in the
LABVIEW environment ..................................................................................................... 135
Figure 96: The schematic of the softlanding mechanism for the PSAS ..................................... 139
Figure 97: Three states of the softlanding mechanism ............................................................... 140
xiv
Figure 98: The PSAS including the softlanding mechanism in the SSIPTS .............................. 143
Figure 99: The morphing pulley model with the PSASs ............................................................ 144
Figure 100: The softlanding mechanism prototype as a proof of concept .................................. 144
Figure 101: Governing forces in the softlanding mechanism ..................................................... 145
Figure 102: The magnetic field schematic of the magnetic latch ............................................... 147
Figure 103: The magnetic field path and dimensions of the path ............................................... 147
Figure 104: the modeled and fitted magnetic latch forces vs. The airgap (g) ............................ 152
Figure 105: The FEA model and the dimensions of the magnetic latch ..................................... 155
Figure 106: Magnetic flux density lines in the softlanding mechanism ..................................... 157
Figure 107: The magnetic flux contour for the softlanding mechanism ..................................... 157
Figure 108: The magnetic latch force along the stroke for diffrenet thickness of the steel plate 158
Figure 109: The maximum latch force for different thicknesses of the steel plate ..................... 158
Figure 110: The effect of the strength of teh permanenet magnet on the maximum latch force 159
Figure 111:The effect of the length of the latch base on the magnetic latch force ..................... 161
Figure 112: The effect of the diameter of the spring housing on the magnetic latch force ........ 161
Figure 113: The effect of the depth of the spring housing on the magnetic latch force ............. 162
Figure 114: The optimized force curve for the magnetic latch ................................................... 163
Figure 115: The SIMULINK simulation model of the new PSAS in the SSIPTS ..................... 164
Figure 116: The SIMULINK model of the mechanical subsystem for the PSAS ...................... 166
Figure 117: The force subsystem of the PSAS ........................................................................... 166
Figure 118: The modeled and the fitted magnetic latch forces vs. The position of the PSC ...... 169
Figure 119: The simulated magnetic latch force and the simulated spring force ....................... 169
Figure 120: The simulated applied voltage and the current for the electromagnetic actuator .... 170
Figure 121: All the applied forces on the PSC ........................................................................... 171
Figure 122: The simulated applied force with respect to time and postion ................................ 172
xv
Figure 123: The simulated position and velocity trajectories for the PSAS ............................... 173
Figure 124: The model of the prototype for the softlanding mechanism ................................... 174
Figure 125: The moving coil actuator used for the softlanding mechanism for the PSAS ........ 176
Figure 126: The permanent magnet for the softlanding mechanism for the PSAS .................... 176
Figure 127: The permanent neodymium magnet demagnetization curves for grade N52 [76] .. 177
Figure 128: the magnetic latch assemblies for the softlanding mechanism ................................ 178
Figure 129: The assembled prototype of the softlanding mechanism ........................................ 180
Figure 130: The entire PSAS assembly within a guide rail ........................................................ 180
Figure 131: The static force test setup for the softlanding mechanism ...................................... 182
Figure 132: The magnetic latch force along the stroke of the softlanding mechanism .............. 183
Figure 133:The magnetic latch and spring forces along the stroke of the softlaning
mechanism .......................................................................................................................... 183
Figure 134: The spring calibration forces and the compression amount .................................... 184
Figure 135: The mechanical subsystem of the position control test setup for the softlanding
mechanism .......................................................................................................................... 185
Figure 136: The experimental results for the softlanding mechanism in the LABVIEW
environment ........................................................................................................................ 187
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ABBREVIATIONS
SSIPTS Synchronized segmentally interchanging pulley transmission system
HVAC Heating, ventilation, and air conditioning
PSAS Pulley segment actuation system
MT Manual transmission
AT Automatic transmission
CVT Continuously variable transmission
AMT Automated manual transmission
DCT Dual clutch transmission
NREL National renewable energy laboratory
VSD Variable speed drives
ICE Internal combustion engine
VCA Voice coil actuator
MCA Moving coil actuator
PWM Pulse-width modulation
EDM Electrical discharge machining
xvii
LVDT Linear variable differential transformer
PSC Pulley segment composite
xviii
NOMENCLATURE
Angular velocity of the morphing pulley
N Round per minute, RPM
T The permitting actuation duration or time window for the actuation
Tp Rotational period
kt Non-contact zone factor of the belt-pulley pair
S Stroke of the PSAS
t Time
)(tx Position of the pulley segment
)(tx Velocity of the pulley segment
)(tx Acceleration of the pulley segment
maxx Required maximum acceleration
Factutor-max Required maximum force for the actuator
g Gravity
vcontact Contact velocity at softlanding
Fhold Holding force at each end of the stroke
xix
lz Depth of the actuator in z-direction
XO Length of the orientor
XM Length of the magnet
XSB Length of the shell base
XSS Length of the shell side
XC Length of the coil
YO Width of the orientor
YM Width of the magnet
YAG Width of the airgap
YC Width of the coil
YSS Width of the shell side
YSB Width of the shell base
B Magnetic flux density
V Applied voltage
R Resistance of the coil
Moving coil linkage flux
L Inductance of the coil
xx
m Mutual flux between the permanent magnet and the coil flux
l Length of the wire in the coil per turn
n Number of the turns in the coil
Bg Magnetic flux density in the airgap
Vbemf Back electromotive force voltage
kb The back electromotive force sensitivity parameter
Bs Magnetic flux density saturation
NI Ampere-turn
H Magnetic field intensity
mmf Magnetomotive force
mmfmagnet Magnetomotive force of the magnet
Hc Coercive force of the permanent magnet
Br Residual flux density of the permanent magnet
k Permeability of a path segment k
Magnetic flux
Ak Cross-sectional surface area
lk Length of the magnetic path in the path segment k
xxi
Magnetic reluctance
c Damping coefficient
q Electrical charge
kf The force sensitivity parameter
kl Moving coil design factor
Flux linkage
Freluctance Reluctance force
Florentz Lorentz force
W Work done by the magnetic field
Wmag Magnetic energy stored in the magnetic field
Wco Magnetic coenergy
chs Damping coefficient of the hard stop
khs Spring constant for the hard stop
Ffri Friction force
Fhs Force due to the hard stop nonlinearity
elec Electrical time constant
xxii
mech Mechanical time constant
Vmax Maximum voltage given to actuator driver
Tpwm Period of the PWM signal
f Frequency of the PWM signal
d Duty cycle of the PWM signal
Ppwm Power of the PWM signal
ipwm Current from the PWM signal
t1 Duration of the acceleration phase
t2 Duration of the deceleration phase
u(t) Output of PWM signal
e Position error
d(e)Tpwm Pulse width for the PWM signal
Sgn(e) Sign function for the PWM signal
d(e) Duty ratio of the PWM signal
Fspring-up Spring force for the upper springs
Fspring-low Spring force for the lower springs
Fmagnet-up Spring force for the upper magnetic latch
xxiii
Fmagnet-low Spring force for the lower magnetic latch
ksp Spring force constant for the softlanding mechanism
v Unit volume in the magnetic field
Fmagnet-g Magnetic latch force in the direction of the gap
BL Base length in the magnetic latch in the magnetic circuit
ML Magnet length in the magnetic latch in the magnetic circuit
PL Pulley segment length in the magnetic circuit
gap Reluctance of the airgap of the magnetic latch
plate Reluctance of the steel plate of the magnetic latch
gnetpermanetma Reluctance of the permanent magnet of the magnetic latch
base Reluctance of the base of the magnetic latch
c1, c2, and c3 Constants based on the geometry of the magnetic latch
..
1
CHAPTER 1: INTRODUCTION
This Ph.D. thesis presents the design, modeling, optimization, prototyping, and
experimental methodologies for a novel actuation system for the synchronized segmentally
interchanging pulley transmission system (SSIPTS). It is an improved transmission which offers
the combined benefits of existing transmission systems for the automotive, the power generation,
and the heating, ventilation, and air conditioning (HVAC) industries.
As a major subsystem of the SSIPTS, the Pulley Segment Actuation System (PSAS)
plays a critical role in the SSIPTS operation and success. However, the overall design of the
SSIPTS and its operation principle introduce very challenging and conflicting design
requirements for PSASs which the existing actuation technologies cannot meet. To address the
lack of actuation technologies for the PSAS application, this research proposes a unique
actuation system that meets all the challenging design requirements of the PSAS. This research
program is responsible for the design, modeling, optimization, prototyping, and experimental
methodologies of the PSAS.
1.1 BACKGROUND ON MECHANICAL TRANSMISSION SYSTEMS
In the last decades, a growing attention has been focused on the environmental questions,
global warming, and energy conservation. Governments are continuously forced to define
standards and to adopt actions in order to reduce the energy consumption and the green house
gases. Whether through finding more efficient ways to conserve energy or producing more
power with the same or less inputs, society is intensely focused on energy issues while reluctant
to abandon the productive capacity and consumer demands that have created such strains on our
2
energy supply. This great challenge of the 21st century has become a principle concern of
governments, businesses, institutions, and individuals.
With these growing socioeconomic and environmental concerns, the automotive, the
power generation, and the HVAC industries have become key elements in the current debate on
global warming and energy conservation. Over the past few years, the power generation industry
has been forced to improve the energy production and promote renewable sources of energy such
as wind power. Similarly, the automotive industry has been increasingly facing stringent
performance, emissions, and fuel economy standards to improve energy consumption in order to
address the aforementioned environmental concerns. Further, the HVAC industry has been
forced to improve the efficiency of the motor-driven-systems such as fans, pumps, and
compressors. Therefore, a great deal of research has been devoted to find new technical solutions
that improve power generation, fuel economy of vehicles, and energy conservation. As the power
transmission units, mechanical transmission systems, used in the automotive and power
generation, and HVAC industries, play an important role in energy utilization and conservation
of energy. The efficiency of these mechanical transmission systems must be optimized in order
to conserve energy.
The automotive industry has been commercializing many new technologies to address
energy conservation and emission reduction. A great deal of research has been devoted to
increase the energy efficiency of vehicles by redesigning vehicle components. The fuel economy
and gas emission of a vehicle is a function of many components primarily its powertrain [1]. The
two main components of the powertrain are the engine and the transmission system. As the
power transmission units, transmissions play an important role in vehicle performance and fuel
economy [2]. It has been proved that in order to increase the energy efficiency of the powertrain,
3
it is twice as cost effective to develop the transmission, rather than the engine, for the same
benefit in fuel economy [3-4]. It is therefore beneficial, both in terms of development costs and
manufacturing costs, to first seek a fuel economy improvement by more efficient transmission
systems. Existing transmission technologies are either inefficient, perform poorly, or both,
regardless of price. There are currently several types of transmissions that offer different
performance priorities when fit into a vehicle. Manual transmissions (MT) have an overall
efficiency of 96.2% which is the highest efficiency value for any type of mechanical
transmission [5]. Automatic transmissions (AT) have an efficiency of not more than 86.3% due
to parasitic losses for the operation of the hydraulic pump and the large amounts of slip in the
torque converter [1-2]. Continuously variable transmissions (CVT) have an overall efficiency of
84.6%. The efficiency of a CVT is comparatively lower than the efficiency of MT due to friction
and hydraulic losses [6]. However, the major advantage of CVT is that it allows the engine to
operate in the most fuel-efficient manner [7]. Automated manual transmissions (AMT) have the
same efficiency as manual transmissions. However, one of the limitations of the AMT is the
driving comfort reduction, caused by the lack of traction during gear shift actuation [8]. Similar
to MTs there is an interruption of torque transmission at a gear change since the engine is cut off
by the clutch during shift [9]. Dual clutch transmissions (DCT) also have the same efficiency as
manual transmissions [10] and have shift characteristic that are typical of clutch-to-clutch shifts,
commonly seen in conventional automatic transmissions [10]. However, controlling DCTs is
extremely complex [11].
The power generation industry has been forced to improve the energy generation and
promote renewable sources of energy. Wind energy is an attractive alternative to fossil fuels as it
is plentiful, renewable, widely distributed, clean, and produces no greenhouse gas emissions.
4
Wind power is non-dispatchable, meaning that for economic operation, all of the available output
must be taken when it is available. Therefore, load management and transmission technologies
must be used to match the supply with the demand. A substantial amount of development has
gone into the production of variable speed wind turbines. This is due to the improved energy
production realized by adapting the rotor speed to match the wind speed [12], thus maintaining
the maximum power coefficient regardless of wind speed [13]. Variable speed turbines also have
greater operational flexibility and can benefit from a high rated speed, but still operate at a
reduced speed in noise sensitive areas. Higher rotor speed also has the advantage that, for a given
output power, the torque on the drivetrain is reduced and, therefore, the drivetrain mass and
manufacturing costs also decrease [14]. The use of a technologically advanced transmission
system in wind turbines will provide variable speed and match supply with demand, adding a
significant energy production and a greater energy capture. All current technologies for
providing variable speed are less efficient, which offset some of the energy capture benefits of
the renewable energy [15]. The ideal wind turbine would offer variable rotor speed with
maximum energy capture and efficiency at all wind speeds. There are currently three major
transmission technologies in wind turbines. Fixed speed wind turbines generate power at only
one particular rotor speed, and usually use a fixed-speed gearbox connected to a fixed-speed
generator. These offer a reduced energy capture, and the gearboxes suffer high failure rates [16].
Wind turbines with variable speed power electronics usually connect the rotor to a fixed-speed
gearbox, which connects to a variable speed generator. The power electronics change the
frequency of AC current back to the fixed 60 Hz frequency. While offering increased energy
capture due to variable rotor speed, this configuration is costly, not optimally efficient at all
speeds, and suffers frequent gearbox failures [17]. Only a few wind turbine designs use variable
5
speed transmissions in order to allow variable rotor speed and a fixed speed generator. All
variable speed transmission wind turbines on the market are either unreliable [18-19] or
inefficient [20]. A study was recently conducted on possible uses of advanced variable
transmission technologies for wind turbines by the U.S. National Renewable Energy Laboratory
(NREL) in 2005. The NREL’s study on the use of a CVT in wind turbine design found that only
a 1% energy production benefit could be achieved in extremely high wind conditions due to the
low efficiency of the CVT [21]. Other alternative transmission technologies, AMT and DCT,
offer high efficiency while in gear. However, these designs necessitate a load interruption during
the shift between ratios due to the use of clutches.
Electric motor-driven-systems in commercial HVAC applications consume 9% of global
electricity and make up one of the largest sets of electricity consumers in the world. Their proper
application and operation is essential for decreased capital costs, operational efficiencies, and
green house gas reductions to satisfy policy requirements. It has been shown that optimizing
industrial motor systems by implementing cost-effective energy-saving technologies can reduce
U.S. industrial energy costs by up to $5.8 billion per year [22]. Much of these savings will come
from making motor-driven systems more efficient within the industrial sector – motors that drive
fans and pumps, conveyers, blowers, mixers, compressors, etc. This is $50 Billion/year in
expenses and one of the main drivers for variable speed. Utilizing a mechanical variable speed
drive brings substantial efficiency and performance benefits to electrical motor-driven systems
by dynamically optimizing speed ratios under changing conditions and demands. Most electrical
motor-driven systems are designed to be constant drives, meaning they only operate at 0 or 100%
speed. Electrical motor-driven systems that move a variable load do not need to operate at full
speed at all times. Implementing a mechanical variable speed drive allows the motor to operate at
6
the appropriate speeds for the relevant load requirement at all times. This allows the most
efficient operation and hence the least amount of energy consumption.
In summary, each mechanical variable speed drives and transmission systems used in the
automotive, the power generation, and the HVAC industries has its own advantages and
disadvantages. Some are more efficient than others and some are more users friendly and provide
more controllability. There is still no transmission technology that satisfies all the performance
priorities, provides comfort, and costs relatively low so that it can be mass produced. Such
technology will revolutionize the above-mentioned industries. To address the lack of
transmission technology for above applications, the synchronized segmentally interchanging
pulley transmission system (SSIPTS) is introduced. The SSIPTS is a novel variable mechanical
transmission that offers the most valuable characteristics of all other transmission systems for
above applications.
1.2 OVERVIEW OF THE SSIPTS
1.2.1 Introduction
Developed jointly by Vicicog Inc. and the University of Toronto, the synchronized
segmentally interchanging pulley transmission system (SSIPTS) is a whole new innovation to the
world of mechanical transmission systems and variable speed drives. Variable speed drives
(VSD) are a class of electromechanical technology that varies the speed and torque of the load in
response to the demand placed on it by the output. A VSD allows its driven load to operate at the
appropriate speeds for the relevant load requirement at all times. This allows the most efficient
operation of the transmission system and so the least amount of energy consumption. The
7
SSIPTS accomplishes variable speed mechatronically (the combination of mechanical, computer,
electrical and control engineering).
The SSIPTS offers a better combination of overall system efficiency and price to
performance than any other transmission system or variable speed drive on the market. The
SSIPTS is the first transmission system to combine the high efficiency of a fully toothed driving
mechanism and the continuity of a morphing pulley without gears and clutches reliably.
The SSIPTS spans across multitudes of potential applications from the HVAC, wind
power and automotive industries to the general industrial processes such as motor-driven
systems. It is an improved transmission which offers the combined benefits of existing
transmission systems for above mentioned industries. Further, the SSIPTS can improve the
efficiency of any system with a motor, engine, or generator that can benefit from increased
starting torque or variable speed.
1.2.2 The Design and the Operation Principle of the SSIPTS
The key components in the SSIPTS are two morphing pulleys, which change their sizes
while connected with a belt. The two morphing pulleys are comprised of several toothed
sprockets of a wide range of sizes, which are each divided into segments. Figure 1 illustrates the
morphing pulleys and pulley segments. Further, Figure 2 shows different drive ratios for the
SSIPTS using different sprockets in each morphing pulleys. The belt is transitioned from one
sprocket to another sprocket of a different size (essentially changing a gear) by selectively
moving individual pulley segments along an axis in or out of the path of the belt. This is done
when the segments are in the area where the belt does not engage with the sprockets – the
transition area shown in Figure 1. The transition area is the area of the sprocket where the belt or
8
chain is not engaged with the teeth. When all the segments of the destination sprocket are in
position to complete the whole sprocket and engage the belt, the transition from one size to
another is complete.
Figure 1: Morphing pulley assambly
During transitions the maximum number of teeth on the belt and sprocket remain
engaged from both the original sprocket and the destination sprocket. This is achieved by
designing a "key pulley segment" for each sprocket size. This segment will be the first to engage
the belt when changing from a smaller sprocket to a larger one, or vice-versa. When the key
pulley segment engages the belt, its particular angular position in relation to the teeth of the
smaller sprocket is engineered so that the teeth of the key sprocket segment will seamlessly
engage the teeth of the belt. Once it is in position, all other segments of the same sprocket follow
and engage the belt. A similar key sprocket segment is used for the shift from a larger to smaller
sprocket and performs the same function, though it is the last segment of its sprocket to engage
9
the belt. This process ensures the belt never moves from side to side, maintaining its position
through changing gears either up or down. In addition to this, the intricate tensioner guarantees
that the belt keeps its tension no matter what gear it is engaged with.
Figure 2: Different drive ratios of the SSIPTS
10
The pulley segment actuation system (PSAS) is required for moving individual pulley
segments along an axis in or out of the path of the belt. To ensure high reliability at the high
speed and load conditions, required for both the SSIPTS applications, the PSAS has special
design requirements. The PSASs are integrated in two morphing pulleys and rotate along with
the pulley segments. Each pulley segment is required to move axially in a very short time,
depending on the rotational speed of the pulleys. The PSAS moves the pulley segment into the
desired location for both directions. Figure 1 depicts the location of the PSAS. A computerized
controller and the actuation system dictate the movements of selectable, individual sprocket
segments to ensure that the proper sequence is executed at high speed. The pulley segments only
move while they are not transmitting the load. When SSIPTS is not performing a shift, it
operates like a normal pulley and belt system, which is proven to be the most efficient and the
most reliable form of the mechanical energy transmission. For detailed information on SSIPTS
operation, please refer to [23].
1.2.3 Technical Benefits of the SSIPTS
The SSIPTS is an improved transmission which offers the combined benefits of existing
transmission systems for the automotive, the power generation, and the HVAC industries. The
SSIPTS offers a better combination of overall system efficiency and price to performance than
any other transmission system or variable speed drive on the market [24]. The SSIPTS combines
the high efficiency of a fully toothed driving mechanism and the continuity of a morphing pulley
without gears and clutches reliably. It shifts under load, without relying on friction or fluid
coupling, using toothed pulleys to transmit power. While the SSIPTS is as efficient as a fixed
gear system, it does not impose a power lag or surge during shifting. Closely spaced ratios
produce performance benefits similar to those of the best CVTs, but with maximal efficiency and
11
load handling. The exceptionally high performance of the SSIPTS allows for a greater number of
speed ratios to be implemented, bringing substantial efficiency and performance benefits to
applicable industries equipments by optimizing speed ratios dynamically under changing
conditions and demands. Its robust design is well-suited to high torque applications and utilizes
durable, reliable toothed pulleys to transmit power. The SSIPTS ability to shift under load, its
wide gear range, and clutchless shifting ensures maximum efficiency in operation. To be
specific, the following list outlines the key technical benefits of the SSIPTS:
High Torque Capability: The SSIPTS’s high starting torque capability is
unmatched [24]. With its toothed belt method of power transmission, it has an
excellent torque handling on start-up and torque on demand during normal
operation.
Rapid Shift Capability: The SSIPTS shifts under load, with zero disengagement
time which enables ratios to be spaced closer than what would be practical in a
transmission or drive with lag. The clutchless shifts can be initiated near
instantaneously for rapid shifts and responsive implementation.
High Efficiency: The sprocket and belt-based system is more efficient than
electronic drive systems that generate substantial heat and have inherent internal
systemic inefficiencies [24].
No Harmonics: Unlike competitors the SSIPTS does not create problematic
harmonics - electrical noise, which is damaging to motors and also to equipment
connected to the main power supply.
12
Wide Gear Range: The SSIPTS has no inherent limitation to possible gear ratio
ranges and is equally efficient across the entire range.
Lightweight: the SSIPTS design will be light and of a competitively compact size
[24].
No parasitic loss: The SSIPTS does not rely on friction or fluid coupling, runs
dry.
1.2.4 Applications of the SSIPTS
The SSIPTS spans across multitudes of potential applications from HVAC, wind power
and automotive industries to the general industrial processes such as motor driven systems. The
SSIPTS can improve the efficiency of any system with a motor, engine, or generator that can
benefit from increased starting torque or variable speed. The following list outlines the main
applications of the SSIPTS and its benefits:
Industrial motor-driven systems: The SSIPTS is applicable in a wide variety of
industrial motor-driven systems such as material handling, agricultural, conveyor belts,
extruders, mining operations, drilling and pumping applications. The SSIPTS is able to make
these motor-driven-systems more efficient.
Heating, Ventilation and Air Conditioning (HVAC) systems: The SSIPTS is
applicable in a wide variety of HVAC systems such as fans and pumps applications. The SSIPTS
introduces substantial efficiency and performance benefits to fans and pumps by dynamically
optimizing speed ratios under changing conditions and demands. Virtually all electric motors
driving fans and pumps are designed to run at one speed. The problem is that many applications
13
don’t have to and so waste energy. The motors driving fans are responsible for the majority of
HVAC system energy consumption. Much like with fans, many pump applications are oversized
to handle peak load requirements. Up to 75% of applications are oversized by over 20%. The
SSIPTS introduces substantial efficiency and performance benefits to these applications by
dynamically optimizing speed ratios under changing conditions and demands.
Automotive Industry: The SSIPTS is applicable in pure electric, electric-hybrid, gas and
diesel vehicles. The SSIPTS provides the efficiency benefits of the best manual transmissions
and all the performance benefits of CVT and DCT without their drawbacks. These benefits may
be realized in SSIPTS which operates automatically, handles high torque, and offers closer gear
ratios without imposing energy-wasting friction, while being lightweight and cost effective.
Wind energy and generators: The SSIPTS will provide a number of significant
advantages over current mechanical transmission technologies in wind turbines and generators.
SSIPTS will allow approximately 10% more energy to be produced in wind turbines compared to
other variable speed drive technology, and up to 20% more than fixed wind turbines [25]. This is
due to the fact that the range of rotor speed allowed by the SSIPTS is at least twice as wide as the
range of speeds provided by most variable speed electronics, and the SSIPTS is maximally
efficient at all speed. The SSIPTS will also allow rotor speed to change while maintaining a
constant generator speed which is necessary for synchronization with the public electrical grid,
and hence optimizing power production over a wide range of wind speeds [26].
14
1.3 PULLEY SEGMENT ACTUATION SYSTEM (PSAS) IN THE SSIPTS
1.3.1 Introduction
As it is explained in the operation principle of the SSIPTS, to change drive ratios, pulley
segments are rapidly inserted laterally into the position in which they will engage the belt.
Therefore, a special pulley segment actuation system (PSAS) is required for moving individual
pulley segments along an axis in or out of the path of the belt in the transition area shown in
Figure 1. To ensure high reliability at the high speed and the load conditions required for above-
mentioned applications, the PSAS must be of ultra fast bistable actuation systems. The PSASs
are integrated in two morphing pulleys and rotate along with the pulley segments. Each pulley
segment is required to move axially in a very short time, depending on the rotational speed of the
pulleys. Further, the PSAS must insert and retract the pulley segment into the desired locations
with low seating velocity.
The overall design of the SSIPTS and its operation principle introduce conflicting design
requirements for the PSAS. The PSAS must be very small in size and as light as possible while it
needs to produce a very high force linearly along the stroke. Further, it must be designed to work
for a high frequency actuation and have a high velocity and acceleration, and a linear control
characteristic. Having cog free, hysteresis free, smooth, and fast response characteristics are also
very important. Moreover, due to high number of PSAS needed for the SSIPTS, economical
pricing is very important.
Further, the actuation problem for the SSIPTS introduces a difficult motion control
problem of timing, fast transients, and low seating velocities for soft landing. It is clear that the
pulley segments must be placed in very short period of time, depending on the rotational speed
15
of the SSIPTS. Further, it is necessary for pulley segments to soft land at desired location in
order to achieve low seating velocity for durability and low noise. Failure to soft land at the
desired location leads to fatigue and pulley segment fracture. Therefore, a control strategy is
needed to achieve the conflicting performance requirements of very fast transition times while
simultaneously exhibiting low contract velocities. The detailed analysis of the design
requirements for the PSAS for the SSIPTS is explained in the following sections.
The prior state of the art review and literature survey are conducted on actuation
technologies that have similar design requirements [27]. Based on the surveys and the actuation
system performance requirements, it was concluded that the electromagnetic actuation
technology is the best candidate for the SSIPTS application [28]. Currently, designs of ultra fast
bistable electromagnetic actuators are mainly for hard drive disks [29-31], electromagnetic valve
actuators for engines [32-34], high speed pick and place and precise positioning [35-37], as well
as auto focusing systems for digital cameras applications [38-39]. However, none of above
electromagnetic actuation technologies can meet all the design requirements of the SSIPTS.
First, the actuation systems that can produce the required amount of force are too big for this
application and the actuators that meet the geometrical constraints cannot produce the required
amount of force. Second, force per stroke curves of actuators are not as linear as needed for this
application. Third, commonly used motion control strategies are not able to achieve the
conflicting performance requirements of very fast transition times and softlanding
simultaneously. Last, most of the above actuators are too expensive for this application.
To address the lack of actuation system for the SSIPTS application, this research
proposes a unique ultra fast bistable actuation system that meets all the challenging design
requirements of the PSAS.
16
1.3.2 Design Requirements: Geometric and Volumetric Constraints of the PSAS
According to the overall design of the SSIPTS, shown in Figure 1, each morphing pulley
assembly is divided into two sets of eight identical sector zones. Each sector zone provides
actuation for three movable layers of pulley segments. The geometric and volumetric parameters
of the PSASs are constrained by this sector space. Each sector zone accommodates three PSASs
shown in Figure 3. The ideal design is to utilize the maximum volumetric and geometrical space
within the sector zones since the force generation depends on the volume it possesses
extensively. Therefore, the major objective in this stage of the conceptual design is to make use
of the available space as much as possible. Based on the overall design of the SSIPTS, each
PSAS can have circular, rectangular or racetrack shape cross-sections shown in Figure 4.
If circular actuators are used, shown in Figure 4 A, the maximum viable diameter of the
actuators is 14 mm, which is confined by the center distance of adjacent segment layers. In this
case the volumetric efficiency of the sector zone reaches only 35%. This fundamentally reduces
the generation of the driving force of electromagnetic actuators. Figure 4 C shows the ideal
morphing cross-section of actuators in the sector zone, in which the service area can reach over
95% of the sector zone. However, the manufacturability of the morphing geometry is impractical
due to the extraordinarily high fabrication cost. The feasible geometry is the introduction of
rectangular cross-section, shown in Figure 4 B. For this case the space utilization in the sector
zone reaches above 70%. Based on the design of SSIPTS, volumetric efficiency of the sector
zones, and symmetry and weight distribution requirements, it is concluded that the actuators
must be rectangular in shape. Figure 5 shows the integration of circular actuation system into the
SSIPTS and Figure 6 shows the integration of rectangular actuation system into the SSIPTS.
Based on the geometrical and volumetric analysis it is concluded that the optimized shape for the
17
PSAS is the rectangular cross-section. Therefore, the maximum viable height of the rectangular
actuators is calculated to be 22 mm; the maximum viable width of the rectangular actuators is
calculated to be 12.7 mm. The length of the PSAS is further constrained by the length of the
morphing pulleys assembly. These volumetric constraints provide the design envelope for
designing the actuation system and geometrical mapping optimization of the PSAS.
Figure 3: Geometrical Constraints of the PSAS in the SSIPTS
Figure 4: Space utilization of different cross-sections for PSAS [40]
18
Figure 5: The integration of a circular actuation system in the SSIPTS
Figure 6: The integration of a rectangular actuation system in the SSIPTS
19
1.3.3 Design Requirement: Fast Transient Requirement of the PSAS
The overall design of the SSIPTS and its operation principle introduce conflicting design
requirements for the PSAS. The PSAS must be very small in size and as light as possible while
they need to produce a very high force. Furthermore, they must be designed to work for a high
frequency actuation and have a high velocity and acceleration. Cog free, hysteresis free, smooth,
and fast response characteristics are also very important. It is clear that the pulley segments must
be placed in a very short period of time, depending on the rotational speed of the SSIPTS. The
primary calculations are conducted to determine the fast transient requirement for the PSAS. In
order to design the correct PSAS, it is necessary to calculate the required acceleration and force
that actuators must apply. The angular velocity of the pulleys dictates the performance of the
actuators. The duration of actuation is a function of the angular speed of the pulleys. Pulley
segment shifts must be executed in the transition area (disengaged pulleys), as shown in Figure
1. Based on the angular speed of the pulleys and the size of the transition area, the actuation time
is calculated by using the following formulas:
60
2 N (1)
2tpt KTKT (2)
where ω is the angular velocity, N is the rotational speed (rotation per minute, RPM) , Tp is the
rotational period, T is the permitting actuation duration or time window for actuation, and kt is
the non-contact zone factor of belt-pulley pair (kt=0.375 for the wrapping angle of 180 degrees
and eight segment partition).
20
The typical stroke profile, depicted in Figure 7, is assumed for the PSAS. The stroke of
the PSAS is set to be S=20 mm and has to be reached within the specified duration of actuation,
T. The lumped mass M is assumed to be 50 grams. Based on these parameters and the actuation
time, the maximum acceleration, and the required force for the actuators are calculated for each
angular velocities. Figure 8 depicts required displacement, velocity, and acceleration profiles of
the PSAS. Assuming the profiles in Figure 8, the equations for the displacement, the velocity,
and the acceleration within the time interval 0 ≤ t ≤ T are given by following equations
respectively:
)cos(1
2)( t
T
StX
(3)
)sin(2
)( tTT
S
dt
dXtX
(4)
)cos()(2
)( 2 tTT
S
dt
XdtX
(5)
From (5) the maximum acceleration is determined by
2
max )(2 T
SX
(6)
and using the following formula, the maximum force is calculated. For simplicity only the
inertial load is assumed.
2
maxmax)(
2 T
SMXMFact
(7)
21
Figure 7: Typical stroke profile for position control
Figure 8: Required displacement, velocity, and acceleration profiles of the PSAS
Table 1 shows the fast transient requirements. The required acceleration and force are
employed to design the actuators using Maxwell Finite Element Analysis package
(electromagnetic). Moreover, in order to meet above mentioned dynamic performance and high
controllability requirements, the linearity of output force along its stroke is very important.
22
Table 1: Dynamic performance requirement of the PSAS
Angular speed of the
sprocket (RPM)
Angular velocity
(Rad/Sec)
Actuation time
(mSec) Acceleration (g)
Max. Force (N)
required
400 41.9 50.0 4.02 1.97
600 62.8 33.0 9.23 4.53
1200 125.7 16.7 36.07 17.69
1500 157 12.0 69.79 34.23
1.3.4 Design Requirement: Softlanding Requirement of the PSAS
The PSAS introduces the difficult motion control problem of timing, fast transients, and
low seating velocities for softlanding. One of the main problems in such bi-stable ultra fast
actuation systems is the noise and wear associated with high contact velocities during the landing
at the end of the stroke. It is necessary for pulley segments to softland at the desired location in
order to achieve a low seating velocity for durability and low noise. Failure to softland at the
desired location leads to fatigue and a pulley segment fracture. Therefore, a control strategy is
needed to achieve the conflicting performance requirements of a very fast transition time while
simultaneously exhibiting low contract velocities.
The control objective is then to ensure accurate pulley segment insertion and retraction
with small contact velocity of all the moving parts. Further, the pulley segment placement and
retraction must be achieved within a very small time travel interval (ms), otherwise the SSIPTS
operation at high speed will deteriorate. These two requirements are obviously conflicting. The
difficulty in achieving softlanding stems from several factors:
Requirements for softlanding velocity (vcontact < 0.2 m/sec at 1500 rpm)
Requirements for fast transition times (T<12 ms)
23
Unavailability of affordable sensors for robust feedback control
Limited range of actuator technology authority
Thus, position control of the pulley segments and softlanding are outstanding design
challenges for the SSIPTS.
1.3.5 Design Requirement: Holding Force
In order to achieve stability at each ends of the stroke, the pulley segments must be
latched to the end positions. To achieve this, a holding force must be generated to hold the pulley
segments in place before engaging the belt. The holding force of minimum five Newtons is
specified for this application. Further, this holding force compensates for the errors and
disturbances in positioning of the pulley segments. It is clear that the design requirement of
holding force further complicates the position control of the PSAS as it conflicts the softlanding
requirements of the PSAS and increases the actuation force.
1.3.6 Design Requirement: Electrical Power Consumption Limitation for the PSAS
There is further a limitation for electrical power consumption for the PSAS. The
electrical power supply used for the SSIPTS has the following limitations:
Maximum voltage drawn: 200 volt
Maximum Current drawn: 10 amp
24
1.4 RESEARCH OBJECTIVES
The overall design of the SSIPTS and its operation principle introduce very challenging
and conflicting design requirements for the PSAS that the existing actuation technologies cannot
meet. To address the lack of actuation technologies for the PSAS application, this research
proposes a unique actuation system that meets all challenging design requirements of the PSAS.
The following list outlines the design requirements of the PSAS for the SSIPTS application:
Bi-directional actuation
Stroke: S=20 mm
Geometry: very small in size and as light as possible
Very high linear force, Fact-max ≈ 34 N
High velocity and acceleration capabilities, T< 12 ms
Softlanding, vcontact < 0.2 m/sec
Simple control characteristics
Holding force, Fhold > 5 N
Economical pricing, Price < $300 per PSAS
This research program is responsible for the design, modeling, optimization, prototyping,
and experimental methodologies of the new actuation system. The main contribution of this
thesis is to develop a highly efficient and reliable ultra fast bi-stable actuation system for the
PSAS for the SSIPTS. In the proposed Ph.D. research, prototypes of the PSAS along with the
SSIPTS technology will be designed and developed. Further, the prototypes will be tested for
25
applications. Significant level of design, modeling, and considerable experimentation will be
required to develop the prototypes. The specific objectives of this research are as follows:
To perform analysis to determine the overall design and operation principle of the
SSIPTS
To find and analyse all the design requirements for the PSAS.
To propose a novel actuation technology for the PSAS
To perform conceptual design and build a simulation model for the PSAS.
To conduct a geometry mapping optimization of the PSAS.
To design and develop position control and softlanding strategies.
To fabricate and prototype the PSAS, design experimental setups, and perform
experiments on the PSAS.
26
1.5 THESIS OUTLINE
The following is a brief overview of each chapter of this thesis, which illustrates the
sequence of tasks required to design and developing the new actuation system for the PSAS for
the SSIPTS:
Chapter 1 presents background information on mechanical transmission technologies,
and gives an intensive introduction on the SSIPTS, its technical benefits, and applications. Next,
the pulley segment actuation system (PSAS) is introduced, and its design requirements are
analysed in details. This will lead into the motivation behind this research, and the major
objectives that are accomplished. Lastly, the thesis outline is illustrated in this chapter.
Chapter 2 gives a detailed literature review on the actuation technologies, and more
specifically, discusses the classifications and characterization of the actuation technologies.
Further, the chapter gives an extensive literature review on the actuation technologies used
specifically in the automotive industry. Lastly, the chapter introduces two main types of
electromagnetic actuator technologies.
Chapter 3 fully describes the newly proposed electromagnetic actuation system. It
explains the most relevant concepts and advancements pertaining to the actuation technology,
mathematical modeling, simulation methods, and position control strategies.
Chapter 4 explains the most relevant concepts and advancements pertaining to the
prototyping, fabrication, and experimentation of the PSAS. This chapter ends with the summary
of the performance for the proposed electromagnetic actuator.
Chapter 5 introduces the softlanding mechanism for the PSAS. It explains the most
relevant concepts and advancements pertaining to the softlanding mechanism, its benefits,
27
mathematical modeling, simulation, position control strategies, fabrication, and experimentation
methods. This chapter ends with the summary of the performance for the proposed softlanding
mechanism.
Chapter 6 concludes this thesis, and summarizes the objectives and accomplishments of
this research work. Furthermore, it proposes additional ideas for future research on the similar
grounds.
28
CHAPTER 2: LITERATURE REVIEW
This chapter gives a detailed literature review on the actuation technologies, and more
specifically, discusses the classifications and characterization of the actuation technologies.
Next, the chapter gives an extensive literature review on the actuation technologies used
specifically in the automotive industry. Lastly, the chapter introduces two main types of
electromagnetic actuator technologies.
2.1 CLASSIFICATION OF ACTUATION TECHNOLOGIES
An actuator is an energy converting device which transforms energy from one or more
external sources into mechanical energy in a controllable way [41]. It is very difficult to present
a clear or complete classification on actuators due to the complex physical interactions and
energy conversions among the types of actuators. Generally one can find a wide variety of types
of actuators based on different governing principles and applications. Most commonly, actuators
are categorized by energy domains such as electromagnetic, electromechanical, fluidic,
piezoelectric, smart material, and so on [42-43]. Table 2 illustrates this categorization.
Table 2: Actuation technology classification [40]
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
29
The following list explains the classes of the actuators:
Electromagnetic actuators use the magnetic field interaction between conducting
coils or permanent magnet which leads to generating force and motion. Solenoids,
moving coil actuators, and linear motors are all electromagnetic actuators.
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 which produces a significant shear strain on heating above the
transformation temperature.
Hydraulic and pneumatic actuators provide force and displacement via the flow of
a pressurized fluid and compressed air.
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.
30
2.2 CHARACTERIZATION OF ACTUATION TECHNOLOGIES
Actuation technologies are characterized based on the following indices: output force,
prescribed displacement, speed, response time, overall stroke, and power density. In some
applications, acceleration and jerk (acceleration rate) are also important indicators. Usually, the
required force, displacement, and stroke predetermine the type of actuation for applications.
The operation principles of the actuators govern their performances and applications.
Figure 9 shows different actuation technologies with respect of the maximum output force and
the maximum stroke. Also, Figure 10 different types of actuation technology with respect to the
maximum working frequency and actuator weight [44]. For instance, magnetostrictive and
piezoelectric actuators could yield very high actuating force and work at very high frequency
(fast response), but their working stroke is very limited. Hydraulic and electric cylinder actuators
could provide pretty high force and longer stroke, but they only work at relatively low frequency,
namely slower response. Therefore, for specific applications, experienced designers need trade
off the performance indices, and locate the balanced point among performance, cost, size, and
reliability.
31
Figure 9: Actuation technology matrix with respect to output forces and stroke levels [44]
Figure 10: Actuation technology matrix with respect to maximum frequency and weight [44]
32
2.3 ACTUATION TECHNOLOGIES USED IN AUTOMOTIVE INDUSTRY
Currently, the actuation systems employed in automotive transmissions are either pure
hydraulic, electrohydraulic, electromechanical, or piezoelectric.
Traditionally, automatic transmissions (ATs) have employed pure hydraulic actuation
technology due to its high force density [45]. Currently, hydraulic actuation technology is still
the preferred technology for control of gears in transmissions due to high force density, the
readily available source of hydraulic power, and the ability to mount motor and pump away from
the point of actuation, where space is less of a premium, and the maturity of hydraulic
technology in the automotive industry. However, pure hydraulic systems are inefficient and
relatively complex, due to the number of solenoid valves which are required to deliver the high
pressure hydraulic fluid to the point of actuation [46]. Moreover, pure hydraulic systems
represent the same potential parasitic losses as in ATs due to the permanent power-take-off from
the internal combustion engine (ICE) [47]. In addition, hydraulic fluid is prone to leakage.
Electrohydraulic actuation systems in automotive transmissions present an advantage
over pure hydraulic actuation systems in that a single electric machine can be used to drive a
pump to charge a hydraulic accumulator. Therefore, energy is only periodically consumed when
the accumulator pressure falls to a predetermined threshold, and the accumulator needs
recharging [48]. Electrohydraulic actuation systems have high force and power density and are
highly reliable and mature technology in the automotive industry [49]. However,
electrohydraulic systems are complex, having many electrically controlled solenoids valves and
high-pressure hydraulic lines, which can occupy a large volume, and are relatively expensive
[50]. Moreover, most of the prevailing electrohydraulic systems require high precision and high-
cost proportional valves, position sensors, and closed-loop control [51]. An efficient
33
electrohydraulic system implies larger hydraulic flow rates, which in turn demands larger pump,
larger flow passages, larger valves, and deteriorated dynamic responses [52].
Electromechanical actuation systems are becoming competitive against existing actuation
technologies, particularly for control of shifts with in AMTs and DCTs. This is a result of recent
advances in permanent magnet materials, power electronics, and control techniques [53]. Since
they are potentially more efficient and simpler in construction, as well as being easier to
integrate, electromechanical actuation systems are being considered as an alternative to hydraulic
systems for controlling clutches and gearshifts in vehicle transmissions [47]. They require much
smaller space and are less sensitive to temperature, compared to other actuation technologies
[51].
Direct-drive electromechanical actuation systems have been developed which act directly
on the shift rails of either an AMT or a DCT to facilitate gear selection [47]. They offer
advantages such as simplified construction, the elimination of mechanical gearing, which
reduces mechanical hysteresis and backlash, a lower component count, improved dynamic
response, and the potential for zero off-state power consumption. As the actuation system is
direct-drive and does not employ any gearbox, as used in motor driven systems, it does not suffer
from significant mechanical compliance, hysteresis, and backlash [53].
For a comprehensive prior state of the art and literature surveys on actuation technologies
in automotive industry, please refer to [27].
34
2.4 ELECTROMAGNETIC ACTUATOR TECHNOLOGIES
Of a various electromechanical linear actuators, electromagnetic actuators have drawn
special attention. Electromagnetic actuators use magnetic fields to generate forces which lead to
motion. In an electromagnetic actuation system, the input electrical energy in the form of a
voltage and a current is converted to magnetic energy. The magnetic energy creates a magnetic
force which produces mechanical motion over a limited range. Typically, the magnetic force is
generated due to the magnetic field interaction built by the current-carrying coil or the permanent
magnet. Thus, magnetic actuators convert input electrical energy into output mechanical energy
as shown in Figure 11. Further, electromagnetic actuators typically offer strokes in the range of 1
to 20 mm. Moreover, due to the rapid development and disappearance of magnetic energy in the
magnetic fields, electromagnetic actuators demonstrate very fast operation speeds.
Figure 11: Block diagram of the electromagnetic actuator
Compared with pure hydraulic, electrohydraulic, electromechanical, and piezoelectric
actuation technologies, electromagnetic actuation technology is simpler, cheaper, more
repairable, robust, and more manufacturable. Particularly, advantages of electromagnetic
actuation technology are as follows:
High actuation force
Long stroke (displacement)
35
Fast response
Contactless remote actuation
Low voltage actuation
Bi-directional actuation
Design flexibility
Potentially high energy density
In order to analyze the electromagnetic actuators it is important to understand the
governing principle for these actuators. The electromechanical conversion mechanisms in
electromagnetic actuators are governed by the Lorentz force law, Reluctance force law, or
combination of both.
Lorentz Force Law states that if a current-carrying conductor is placed in a magnetic
field, a force will act upon it. The magnitude of this force is determined by the magnetic flux
density, the current, and the length of the conductor placed in the magnetic field. The Lorentz
force is proportional to the product of the magnetic field and the current, in a direction
perpendicular to both of them as shown in Figure 12. By reversing the polarity of the voltage in
the conductor, the direction of the force will change.
Reluctance force Law states that for a current carrying conductor in a stationary coil, the
electromagnetic system always tries to move toward the status of minimum reluctance in its
magnetic circuits. Therefore, if any part of the magnetic circuit is free to move like a plunger in a
solenoid, a force is generated which causes the plunger to move in order to minimize the
36
magnetic reluctance of the magnetic circuits. The generated pulling force is proportional to
the square of the current in the windings and inversely proportional to the square of the
length of the airgap.
Figure 12 : Lorentz Force Law
Currently electromagnetic actuation technology can be divided in three different types
based on the distributions of magnetic fields and moveability of the parts:
Moving coil actuator: Placed in static magnetic field, a moving coil driven by a current
is submitted to the Lorentz force. This force is proportional to the applied current. Thus these
actuators are controllable. Since first applications were in loud-speakers, they are also called
voice-coils. Moving coil actuators are fixed-field actuators since the magnetic field distribution
does not significantly change during actuating process.
Moving iron actuator: A soft magnetic part placed into a coil system naturally moves in
a way that minimises the system magnetic energy. In this case the reluctance force is larger than
37
the Laplace force but it is only attractive and not controllable. Solenoid actuators are the main
type of moving iron electromagnetic actuators. Moving iron actuators are variable-field actuator
or variable reluctance actuators as the magnetic field distribution does change in the process of
actuation. The principle of this type of actuators takes the advantage from the fact that an
electromagnetic system always tries to move toward the status of minimum reluctance.
Moving magnet actuator: Placed between two magnet poles, a mobile permanent
magnet can be switched from one pole to the other using coils. Such moving magnet actuators
are bi-stable. They present high forces but are not very controllable.
Of above electromagnetic actuators, voice coil actuators and solenoid actuators are used
extensively for applications that have similar design requirements as the SSIPTS. The operation
principles of voice coil actuation technology and solenoid technology are explained in details in
the following sections:
2.4.1 Voice coil actuator
Voice-coil actuator (VCA) is a direct drive electromagnetic actuator. The voice-coil
provides a non-commuted limited motion servo-actuation with linear control characteristics.
Its motion capability is of high precision position sensitivity, limited only by the feedback sensor
used to close the control loop. It has very low electrical and mechanical time constants and a
high power to weight ratio. VCAs are ideal electromagnetic actuators for applications that
require high frequency actuation, high velocity and acceleration, and linear control
characteristics. Cog free, hysteresis free, smooth and fast response characteristics make it
an ideal servomotor [55].
38
A voice coil employs a permanent magnet field assembly in conjunction with a coil
winding to produce a force proportional to the current applied to the coil. The principle of
operation of these actuators is the same as the working principle of the permanent magnet DC
motors. When voltage is applied to the core, it will be magnetized. This in turn causes an
interaction between the magnetized core and the permanent magnet surrounding it. As a result of
this interaction, a motion or a force can be generated. The electromechanical conversion
mechanism of a voice coil actuator is governed by Lorentz force principle [55]. The voice coil
works because of the force between a static magnetic field and an electric current perpendicular
to the field as governed by Lorentz force law. If the magnetic field strength is constant, the
magnitude of the force it exerts on the wire is proportional to the magnitude of the current
through it. Figure 12 shows the schematic diagram of a current carrying wire in the magnetic
field.
Voice coils designs come in two shapes: cylindrical and rectangular cross-section. A
conventional design of a voice coil actuator is depicted in Figure 13. The voice coil actuator
consists of a coil that is free to move axially in the airgap. The airgap is formed between a center
pole and a permanent magnet that surrounds it. A soft iron shell houses both the magnet and the
pole. To help focus the magnetic field the permanent magnet is surrounded and held by “keeper”
material – soft iron – capped at one end and penetrating the middle of the coil. It helps complete
the magnetic flux path. The coil is wrapped about a non-conducting bobbin or coil holder. As
shown in Figure 13, the magnet pushes the coil (which in turn pushes the coil holder) to the right
and left. Figure 14 presents the magnetic field lines of a voice coil actuator. The magnetic flux
density vector comes from the north pole (the inner side of the permanent magnet), passes
through the moving coil and soft iron core and comes back to the south pole to complete a
39
continuous closed field line. From this figure it is very clear that the force is produced in the
same direction at every point on the moving coil and only depends on the current direction. If the
current flows in the reverse direction the force will be produced in the opposite direction.
Figure 13: Voice coil actuator schematic
40
Figure 14: The magnetic field lines of a voice coil actuator
2.4.2 Solenoid actuator
A solenoid actuator is an electromagnetic device for creating a short pushing or pulling
force. A simple schematic of a solenoid is shown in Figure 15. The solenoid usually consists of a
stationary current carrying coil, a magnetic steel housing core, and a movable iron core called the
plunger or armature. In a solenoid, the pulling or pushing force is created by energizing the coil
of wire. The operation principle of solenoid actuator is based on reluctance force law, which
states that an electromagnetic system always tries to move toward the status of minimum
reluctance. In the case of solenoid, the current carrying coil creates a magnetic field, which
produces a reluctance force on the magnetized plunger to minimize the magnetic flux leakage in
the airgap. Thus, the reluctance force pulls the plunger inside to reduce the airgap.
41
Figure 15: Schematic of solenoid actuator
In solenoid actuator, when current flows through the coil, a strong magnetic field is
developed around the coil and through its center. Consider the coil of the solenoid is energized
with current flowing in a direction such that the magnetic field creates a north pole on the
plunger and a south pole on the static iron core at the facing ends. These opposite poles then
create a magnetic pulling force to attract each other; hence the plunger moves towards the
static core and reduces the airgap between the cores. The generated pulling force is proportional
to the square of the current in the windings and inversely proportional to the square of the length
of the airgap [57].
Conversely, when the coil current is reversed, the South Pole is created on the plunger
and the North Pole is created on the static iron core. Again the resulting magnetic force attracts
the plunger towards the iron core. This means that the force developed in a solenoid always has
the same direction, even if the direction of the current in the coil is reversed.
42
CHAPTER 3: DESIGN AND MODELING OF THE
ELECTROMAGNETIC PULLEY SEGMENT ACTUATION
SYSTEM
This chapter summarizes the most relevant concepts and advancements pertaining to the
actuation technology, mathematical modeling, simulation methods, and position control strategies.
This chapter ends with the summary of the performance for the proposed electromagnetic actuator.
3.1 ACTUATION TECHNOLOGY SELECTION FOR THE PSAS
The prior state of the art and literature surveys on actuator technologies, primarily used in
the automotive, wind turbine, and HVAC industries, have been conducted; Hydraulic, electro-
hydraulic, electromagnetic, and piezoelectric actuators are dominant technologies [27]. Based on
the surveys and the PSAS performance requirements, it has been concluded that the
electromagnetic actuation technology is the best candidate [28]. Currently, designs of ultra fast
bistable electromagnetic actuators are mainly for hard drive disks [29-31], electromagnetic valve
actuators for engines [32-34], high speed pick and place and precise positioning [35-37], as well
as auto focusing systems for digital cameras applications [38-39]. However, none of above
electromagnetic actuation technologies can meet all the design requirements of the PSAS. First,
the actuation systems that can produce the required amount of force are too big for this
application and the actuators that meet the geometrical constraints cannot produce required
amount of force. Second, force per stroke curves for actuators are not as linear as needed for this
application. Third, commonly used motion control strategies are not able to achieve the
conflicting performance requirements of very fast transition times and softlanding
simultaneously. Last, most of the above actuators are too expensive for this application. To
43
address the lack of actuation system for the PSAS application, this research proposes unique
ultra fast bistable electromagnetic actuation systems that meet all the challenging design
requirements of the PSAS. Of possible electromagnetic actuators designs, moving coil actuators
(MCA) and solenoid actuators are used extensively for applications that have similar design
requirements as the PSAS. These two electromagnetic actuators are further analysed and
compared in this section.
Moving coil actuators generally have low armature mass and can therefore generate high
accelerations. This leads to higher efficiency in energy conversion and higher dynamic behaviour
in the assessment of time response. On the other hand, solenoid actuators permit smaller airgap
and thereafter increase the efficiency and force capacity. At the same time, they possess
improved heat dissipation and wire connection, and therefore are the simplest, and generally the
least expensive ones to manufacture. The force versus displacement characteristics for a MCA
and a solenoid are of a more critical concern. Figure 16 shows the generated force for both
actuation technologies. The force versus stroke curve of a MCA is almost flat, which is a very
useful characteristic for high precision control applications. In a MCA, the degradation of the
force at the two travel extremes with respect to the mid-stroke force might be below 5% [55-56].
In contrast, for a solenoid the developed force varies inversely with the distance between the core
and the pole face. The maximum force occurs when the core is attached to the pole. The
generated pulling force is proportional to the square of the current in the windings and inversely
proportional to the square of the length of the airgap [57].
Furthermore, for a MCA the direction of the force changes with the polarity of the
voltage or the current direction, whereas in a solenoid the force is developed only in one
direction and does not depend on the polarity of the voltage or the current direction as shown in
44
Figure 17. This means that the force developed in a solenoid always has the same direction, even
if the direction of the current in the coil is reversed. Therefore, a spring is usually used to allow
the plunger to retract when the current is switched off. Due to an additional spring, the solenoid
needs a large space that must be accounted for when the system is designed. Also, the position of
the solenoid plunger with a spring is less controllable because the return stroke in a solenoid is
done by the spring force. In addition a spring is used to develop a return force in a
solenoid that makes it complicated to control. Moreover, hysteresis in solenoid devices can be
as great as 10% or more of the developed force, whereas in moving coil actuators it is typically
much smaller than 1% of the developed force [56]. Low hysteresis enables precise and
repeatable position control to be realized. From the above discussion it is clear that both solenoid
actuator and moving coil actuator provide compact size, fast response, and moderate power
density. However, the nonlinearity of the output force and its highly plunger-position
dependence, along with unidirectional force of the solenoid actuator definitely determine that the
solenoid cannot satisfy the specific requirement of the SSIPTS. In contrast, the moving coil
actuator can provide higher force at the very beginning of the actuation. The special requirement
of the linearity of output force for the PSAS determines that the moving coil actuator technology
has more potential advantages than the solenoid actuator. Therefore, among electromagnetic
actuator technologies, moving coil actuator technology is selected for the PSAS. In MCAs the
force between the stator and the mover is the combination of Lorentz and magnetic reluctance
forces. A moving coil actuator employs a permanent magnet field assembly in conjunction with a
coil winding to produce a force proportional to the current applied to the coil. The direction of
the force depends on the polarity of the voltage applied to the terminals of the coil.
45
Figure 16: Force along the stroke for MCA and solenoid actuators
Figure 17: Force profiles for MCA and solenoid actuators with respect to current direction
46
3.2 DESIGN PRINCIPLE OF THE ELECTROMAGNET PSAS
The operation principle of the electromagnetic PSAS is based on the magnetic force
interactions, which come from two magnetic sources: electromagnetic and permanent magnet
fields. The generated force is the combination of Lorentz and magnetic reluctance forces.
The PSAS employs a permanent magnet field assembly in conjunction with a coil winding
to produce a force proportional to the current applied to the coil. The direction of the force
depends on the polarity of the voltage applied to the terminals of the coil. When voltage is
applied to the coil, it will be magnetized. This in turn causes an interaction between the
magnetized coil and the permanent magnet. As a result of this interaction, motion or force is
generated. Referring back to Lorentz force law, it states that if a current-carrying conductor is
placed in a magnetic field, a force, will act upon it. The magnitude of this force is determined by
magnetic flux density, the current, and the length of the conductor placed in the magnetic field.
The Lorentz force is proportional to the product of the magnetic field and the current, in a
direction perpendicular to both of them as shown in Figure 14.
Since the PSAS design principle is mainly based on the Lorentz force, the design
configurations for Lorentz force law in the moving coil design must be analyzed. Figure 18
shows the three common configurations: Inner magnet, outer magnet, and axial magnet. Each has
its own advantages and disadvantages. Among three possible magnetic configurations for the
PSAS, the axial magnetized magnet configuration is selected because of the following reasons:
The magnetic strength of permanent magnet depends on the length at the
magnetizing direction. The axial magnetized magnet configuration allows for
47
much longer magnetization direction. This leads to a stronger magnetic field and
consequently stronger actuator.
For the fixed width of the rectangular shape PSAS, it is harder to embody two
permanent magnets as shown in Figure 18 A, and Figure 18 B. The lengths of the
magnetization direction for the two magnets are also very small. This leads to
much weaker magnets and magnetic flux.
In the case of the rectangular cross section, the axial magnetized magnet
configuration provides much more uniform magnetic flux distribution. As shown
in Figure 19 the area of the coil that is in the interaction with permanent magnetic
flux is higher. Therefore, more Lorentz force can be generated.
Figure 18: The three common design configurations for MCAs [40]
A B C
48
Figure 19: The area of the coil that is in interaction with permanent magnetic flux [40]
The axial magnetized magnet configuration is a more feasible design for the PSAS as this
configuration potentially has the advantages of compact size, high power output, good heat
dissipation, and feasible manufacturability. The detailed design of the axial magnetized magnet
configuration for the PSAS will be found by geometry mapping optimization as shown in section
3.4.
Based on the geometrical and volumetric design requirements of the SSIPTS, the novel
rectangular electromagnetic actuation system is proposed for the PSAS. Figure 20 illustrates the
overall design of the PSAS and Figure 21 shows the components of the PSAS. It consists of a
rectangular moving coil, a permanent magnet, an orientor, and a soft iron shell. The coil is free to
move axially in the airgap formed between the permanent magnet and the steel shell. The
permanent magnet is one source of energy in providing magnetic field. The coil is another
source, which generates the reaction force. A flux orientor is for guiding the magnetic field,
generated by the axially magnetized magnet, to more efficient path. Also, a bobbin is used to
support the coil. The air provides the necessary clearance for the relative movement between
moving and stationary parts of the actuator.
49
Figure 20: The electromagnetic PSAS design
Figure 21: Componenets of the electromagnetic PSAS
As shown in Figure 20, the moving coil and the bobbin are directly attached to the pulley
segments for the direct actuation. This mechanical approach is chosen to minimize the
mechanical complexity and the weight of moving parts of the actuation system.
The PSAS dynamic performance is highly depends on the selection of materials used in
construction. This selection is primarily based on the magnetic, electrical, thermal, and
mechanical properties of the PSAS components. The electromagnetic force generation is highly
depended on the magnetic field strength, the flux leakage, and the electrical current density.
Therefore, the electromagnetic properties of the components such as the remnant flux density,
50
the coercive force, the working temperature of permanent magnets, permeability, the flux
saturation level, and the hysteresis shape of soft magnetic materials, as well as the conductivity
and permeability of conductors, play important roles in the development of the new actuators.
Moreover, cost effectiveness and manufacturability are also important decision-making factors.
The following list outlines the material selection for the PSAS as shown in Figure 21:
The permanent magnet is made by rare-earth Nb2Fe14B for its high remnant,
high coercive force, and high energy product.
The current carrying coil is made by copper for its good conductivity.
The flux orientator is made by soft iron for its relatively high permeability and
off-the-shelf availability.
The shell is also made by soft iron for its relatively high permeability and off-the-
shelf availability.
The bobbin is made by aluminum for its low magnetic permeability, high thermal
conductivity, and good structural strength.
The pulley segment and the connecting rod are also made by aluminum for its low
magnetic permeability, light weight, and good structural strength.
51
3.3 MATHEMATICAL MODELING OF THE PSAS
Figure 22 shows the energy conversion of the electromagnetic actuators [58]. It contains
three physical domains: electrical, magnetic, and mechanical. The energy conversion carries out
by means of electro-magnetic coupling and magneto-mechanical coupling. In this section
mathematical modeling of the above-mentioned domains are derived using the couplings. The
two coupling physics must be accurately modeled in order to model the electromagnetic actuator.
Figure 22: Electrical, magnetic, and mechanical domain of the electromagnetic actuators [58]
Figure 23 shows the design schematic of the MCA for the PSAS. Since this design of the
actuator is symmetric, for the sake of simplicity of the calculations, only the right half of the
actuator is considered for modeling. Further, each component in the electromagnetic actuator is
given dimensions as shown in Figure 24. Moreover, it is assumed that the actuator has the
uniform depth of Zl in the z-direction
52
Shell base
Magnet
Shell SideCoil
Orientor
Shell SideCoil
Figure 23: The design schematic of the PSAS actuator
Shell base
Magnet
Shell SideCoil
Orientor
yM= yO yAg ySS
ySB y
xSB
xM
xO
xSS
x
xC
yC
Z
Figure 24: Assigned parameters for the componenets in the actuators
53
Figure 25 illustrates the closed loop magnetic flux of the core as well as magnetic flux
density and current vectors for the coil in the airgap. The closed loop magnetic flux line and the
vectors are used to calculate the magnitudes of the magnetic flux density and the Lorentz force.
B
Bg
B
lglg
FLorentz
Y
X
Z
Air Gap
Figure 25: Magnetic flux density, current, and Lorentz force vectors in the actuator
3.3.1 Electrical Domain Modeling and Equations
The electrical domain of the PSAS is a circuit that has a coil moving through an external
permanent magnetic field density, B as shown in Figure 25. Therefore, a generalized version of
Kirchhoff’s voltage law which takes into account the effects of electromechanical coupling for
such a circuit is derived. The electrical system inputs energy into the actuation system by
applying a voltage across the coil terminals, resulting in a current flow. The differential equation
governing the electrical energy is written as:
54
t
iRV
(8)
where V is the supply voltage, R is the coil resistance, i is the coil current, and is the total
moving coil linkage flux. Faraday’s law of induction relates the voltage induced in the coil and
the flux linkage. Further, the total linkage flux variable, , is expanded into self-inductance and
mutual inductance parts:
),().( iXiXL m (9)
where L is the inductance of the coil and m is the mutual flux between the permanent magnets
and the coil’s flux. Note that for the linear operation of the moving coil actuator the inductance is
constant over a current range but varies with position.
By combining (9) and (8) the following equation is arrived.
dt
dX
dX
iXd
dt
dX
dX
XdLi
dt
diXL
t
m ),()()(
(10)
Therefore, the complete Kirchhoff's voltage law is as follows:
dt
dX
dX
iXd
dt
dX
dX
XdLi
dt
diXLiRV m ),()(
)(
(11)
Further, (11) can be written as
coil
dlBXdt
diXLiRV )()( (12)
where the last term in the equation defines the induced voltage in the coil. In the case of the
PSAS design shown in Figure 24, the induced voltage is as follows:
coil
l
gg XnlBdzBXndlBX0
)( (13)
55
where Bg is the magnitude of the magnetic flux density vector in the airgap, l is the coil
conductor length per turn, and n is the number of turns in the coil in the airgap. This induced
voltage is called the back electromotive-force, Vbemf. Equation (13) can be further reduced by
defining bK as the back electromotive-force sensitivity parameter and is assumed to be constant
with respect to i (but still a function of X). The back electromotive-force sensitivity parameter is
calculated as:
gb nlBXK )( (14)
Therefore, the complete voltage equation of the PSAS is as follows:
XXKXdX
XdLi
dt
diXLiRV b
)()(
)( (15)
3.3.2 Magnetic Domain Modeling and Equations
The reluctance method is used to solve for magnetic fluxes and magnetic fields in the
actuator core as shown in Figure 25. For this method, a magnetic circuit shown in Figure 25 is
assumed. The reluctance method begins with Ampere’s law in integral from:
mmfNIdlH .
(16)
where ampere-turns, NI, or magnetomotive force, mmf, are the input energy source, and magnetic
field intensity H and magnetic flux density B are to be found. In the case of the PSAS, the
magnetomotive force comes from the permanent magnet. When a permanent magnet has a length
of mX and its magnetization direction is along its length, the mmfmagnet of the permanent magnet
is calculated from [59]:
56
mcMagnet XHmmf
(17)
)
Also from the permanent magnet properties, the mmf of the permanent magnet can be
rewritten as:
m
rMagnet X
Bmmf
0 (18)
where HC is the Coercive force of the permanent magnet and Br is the residual flux density of the
permanent magnet.
Back to the Ampere`s Law, the closed-line integral of the Ampere’s law is replaced by a
summation
Magnet
k
kk mmflH (19)
where the closed path consists of line segments of subscript k, corresponding to the shell side, the
shell base, the magnet, the orientor, and the airgap as shown in Figure 24. To account for the
permeability of the closed magnetic path, recall that B is permeability times H, giving
kkk HB
(20)
where k is the permeability of path segment k in Figure 25. Also, the magnetic flux is the
surface integral of the magnetic flux density:
dAB.
(21)
Assuming that each path segment of the magnetic path has a cross-sectional surface area
kA , normal to the segment direction carrying kB , each segment carries the magnetic flux density:
57
kkk HB (22)
Substituting into (19) gives
Magnetk
k
kk
k mmflA
(23)
Moreover, Gauss’s law of magnetism indicates that magnetic flux is continuous (since
the divergence of flux density is zero). Thus, the magnetic flux through all segments of Figure 25
is the same value. Equation (24) states that the algebraic sum of the fluxes entering or leaving a
junction of a magnetic circuit is equal to zero. In other words, the sum of the magnetic fluxes
entering a junction is equal to the sum of the magnetic fluxes leaving a junction.
k....21 (24)
Leavingentering (25)
Therefore, the magnetic flux can be factored out:
Magnetk kk
k mmfA
l
(26)
The term being summed is called reluctance, symbolized by the script letter . Thus,
(26) becomes
Magnet
k
k mmf (27)
Units of reluctance must be amperes per weber. It is defined as:
A
l
(28)
If all path reluctances are known, then (27) can be used to find the unknown flux:
58
k
k
Magnetmmf (29)
With magnetic flux known, individual flux densities can be found:
k
kA
B
(30)
Thus, reluctances can be used in the reluctance method to solve for flux and flux density
everywhere along the closed flux path. The simplest equation for the reluctance method is a
simplification of (27).
NI (31)
In order to find the magnetic flux density in the airgaps, the magnetic flux must be
calculated by
OrientorMagnetbaseShellsideShellgapAir
Magnet
k
k
Magnet mmfmmf
(32)
where gapAir ,
sideShell , baseShell ,
Orientor , and bMagnet are given as:
gapAir
gapAir
gapAirA
l
0
(33)
sideShellsideShell
SideShell
SideShellA
l
(34)
baseShellBaseShell
BaseShell
baseShellA
l
(35)
OrientorOrientor
OrientorOrientor
A
l
(36)
59
MagnetMagnet
Magnet
MagnetA
l
(37)
Therefore, the magnetic flux density in the airgap is as follows:
gap
k
k
mr
gap
k
k
gA
XB
A
mmfB
1.
1. 0
(38)
3.3.3 Mechanical Domain Modeling and Force Equations
The two magneto-mechanical couplings in the PSAS actuator are governed by Lorentz
and magnetic reluctance forces. Therefore, the differential equation, governing the forces within
the moving coil actuator, is as follow:
XCXMFF cereluclorentz tan
(39)
where M is the total mass of the moving portion of the actuator (Masses of the coil, bobbin,
connecting rod, and the pulley segment) and C is the damping coefficient. Both Lorentz force
and magnetic reluctance force are mathematically modeled below.
The Lorentz force relates the force on a current carrying conductor given an external
magnetic field. In particular, when a particle of charge q moves through an external field B it
with velocity X , it experiences a Lorentz force:
)( BXqFLorentz (40)
In the case of current carrying conductor, the (40) becomes
BdliFwire
Lorentz (41)
60
where this line integral is evaluated in the direction of the current flow over the length of the
wire, l. This force on an infinitesimal length of the wire is
BidldF (42)
In the special case of the PSAS actuator, where the wire of length l is perpendicular to Bg
as shown in Figure 25, and there are n number of wires in the airgap, the Lorentz force reduces
to
g
Coil
l
ggLorentz inlBdzBinBdliF 0
(43)
Equation (43) can be further reduced by defining fK as the force sensitivity parameter and is
assumed to be constant with respect to i (but still a function of X). It is calculated by:
nlBKXK glf )( (44)
where lK is a constant depending on the moving coil design, Bg is the magnitude of the magnetic
flux density vector in the airgap, l is the coil conductor length per turn, and n is the number of turns
in the coil in the airgap. Therefore, the Lorentz force equation is as follows:
iXKF florentz )( (45)
The magnetic reluctance force states that in a current carrying coil, the electromagnetic
system always tries to move toward the status of minimum reluctance in its magnetic circuits. In the
case of the PSAS actuator, the coil always attracts the orientor inside the coil in order to minimize the
overall reluctance of the magnetic circuit around the coil. In order to model this attractive force, the
energy method is used. The flux linkage and inductance of the coil is used to model the reluctance
force.
61
Flux linkage, is used to find the magnetic energy, magnetic coenergy, and the reluctance
force. Energy input to any electromagnetic actuator is power (voltage times current) integrated over
time, giving [60]:
idVidtW (46)
where in general i versus is a nonlinear relation shown in Figure 26. This figure is similar to the
nonlinear relation of B–H in any magnetic device. From (46), the energy stored is the area to the left
of the curve:
idWmag (47)
Similarly the coenergy is the area below the curve, which is [60-61]:
diWco (48)
Figure 26: Nonlinear relationship between the flux linkage and the current
62
With the coenergy and energy known, the reluctance force can be obtained using virtual
work techniques.
constiforx
WF co
cereluc
tan
(49)
Further, for the linear region of above curve, the inductance of the coil is defined as:
iL / (50)
In the case of devices with purely linear B–H materials (of constant permeability),
Ampere’s law gives flux and flux linkage proportional to current. Hence, in linear devices,
inductance is a constant, independent of current. Inductance units are henrys (H). All coils have
inductance and can be called inductors. In the linear region of Figure 26, ( i curve), inductance
is not function of i but can be function of the position. The magnetic energy stored in a constant
(linear) inductor is [60]:
2)(2
1iXLLidIdiidWW comag (51)
When inductance is constant over a current range but varies with position, it can be used
to obtain magnetic reluctance force as follows. From (51), we obtain
2)(
2
1ixL
xx
WF co
x
(52)
and
dx
xdLiFreluctnace
)(
2
1 2 (53)
This generated pulling force is proportional to the square of the current in the
windings and proportional to the rate of change of the inductance of the coil
63
Therefore, the Lorentz and the reluctance forces are governed by:
XCXMX
LiiXKFF fcereluclorentz
2
tan2
1)(
(54)
3.3.4 Summary of Governing Equations for the MCA for the PSAS
To summarize, the two governing differential equations for the MCA for the PSAS are
XXKXdX
dLi
dt
diLiRV b
)( (55)
XCXMX
LiiXKFF fcereluclorentz
2
tan2
1)(
(56)
where
gbf nlBXKXK )()( (57)
and
gap
k
k
mr
gap
k
k
gA
XB
A
mmfB
1.
1. 0
(58)
In some moving coil designs, the dX
dL value is quite small and can be assumed as zero. In
the case that this value is not negligible, meaning inductance is changed with respect to position;
the reluctance force is very considerable. In the case that the dX
dL value is quite small, the two
governing differential equations for the PSAS are
XXKdt
diLiRV b
)( (59)
XCXMiXKF florentz )( (60)
64
3.4 FINITE ELEMENT ANALYSIS AND GEOMETRY MAPPING OPTIMIZATION
The purpose of the PSAS is to carry the pulley segment from its disengaged position to
its engaged position within a specified time. Therefore, the design goal of the PSAS is to achieve
the maximum force, produced by magnetic circuit with minimum space and at the same time to
lower its power dissipation. In additional to the energy saving and geometrical requirements, fast
dynamic response and linearity of the force along the stroke are also required for the positioning
control of the PSAS. Therefore, a systematic design procedure is required to optimize the force
output of the PSAS along the stroke with in the design envelope.
Since the analytical methods for the force calculation, mentioned in the previous chapter,
are based on simplifications, they don't provide very accurate values and cannot be used for
optimization purpose. Specifically, the uniform distribution of magnetic flux density in the
magnetic circuits is assumed, which leads to inaccuracy for more complex geometry.
Alternatively, Finite Element Analysis (FEA) method provides more accurate results and is the
more effective approach. In particular, ANSYS Maxwell is the premier electromagnetic field
simulation software for designing and analyzing 3-Dimensional and 2-Dimensional
electromagnetic and electromechanical devices.
3.4.1 Finite Element Analysis Problem Setup for the PSAS
An FEA model is developed for the PSAS actuator. In order to achieve an optimization-
oriented design, an accurate model of the PSAS actuator is necessary. However, the complete
optimization of an actuator, considering all design factors, is a great challenge due to the
complexity of the actual problem. Many researchers have tried different optimization
approaches, from topology optimization [62-66], space mapping [67-68] and [69], to response
65
surface methodology [70-71]. The feasible methodology is to carefully collect several factors as
known parameters, and merely set the key factors as design variables for meeting above-
mentioned requirements. In particular, the electrical power consumption by the winding coil, the
geometry of different components and electromagnetic and thermal properties of the components
are optimized for the actuator design. Table 3 shows the parameters used in the geometric
modeling of the new actuator. Also, Table 4 shows the electromagnetic parameters of the
actuator. To minimize computing time, the 2-D FEA model of the actuator is used, as shown in
Figure 27. It consists of different domains, which correspond to different partial differential
equations (PDE), governing magnetic properties of the components [40]. Moreover, it is
important to note that the volumetric optimization of the moving coil actuator requires trade off
between above mentioned design requirements.
Shell base
Magnet
Shell SideCoil
Orientor
yM= yO yAg ySS
ySBy
xSB
xM
xO
xSS
x
xC
yC
Figure 27 : 2D FEA model of the PSAS actuator
66
Table 3: Dimensional parameters of the PSAS actuator for the FEA model
Name Parameter Expression
Length of the shell base XSB
Length of the magnet XM
Length of the orientor XO
Length of the shell side XSS mmX SS 32
Length of the coil XC
Width of the orientor YO
Width of the magnet YM
Width of the coil YC
Width of the shell side YSS
Width of the shell base YSB mmySB 35.6
Depth of all the component Zact mmZ act 4.25
Table 4: Electromagneic parameters of the PSAS actuator for FEA model
Name Parameter Expression
Current in to the coil i AmpiAmp 1010
Resistance of the coil R 20R
Inductance of the coil L
Number of turns in the coil n
Stroke of the actuator S S=20 mm
Maximum force generated Fmax 34max F
Flux density in the airgap Bairgap
Force sensitivity parameter Kf
Back emf sensitivity parameter Kb
67
A simplified optimization process called step-optimization is effectively used to
determine the key parameters, by the aid of a sweeping technique in the FEA package. 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 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 overall
actuator thickness and actuator length, the coil thickness has direct relationship with the magnet
thickness, similarly the orientator that control the perpendicular component of the magnetic flux
pass through the coil is straightly related to the magnet length. Consequently, the magnet
thickness and the magnet length are the fundamental parameter.
3.4.2 Geometry Mapping Optimization and Parameterization
Geometry mapping optimization involves finding the optimized dimensions for the
components in the PSAS actuator in order to meet the geometrical and performance
requirements. In particular, the lengths and the thicknesses of the steel shell, the magnet, the
orientor, and the coil, shown in Figure 27 must be found. Each of these dimensions will
influence the electromagnetic parameters shown in Table 4. In particular, the dimensions will
influence the Lorentz and the magnetic reluctance forces as shown in (56). This equation shows
the summation of generating forces for the PSAS actuator. From this equation, it is clear that in
order to maximize the Lorentz force for constant input current, the force sensitivity parameter
must be maximized. Equation (57) shows the parameters that define the force sensitivity
parameter. By maximizing all the parameters in the formula, it will be maximized. However, this
is not possible due to the constraints on the length of the actuator and the cross-section of the
actuator.
68
The first part of the geometry mapping optimization is to optimize the width of the
components in the PSAS actuator as shown in Figure 27. Since this FEA problem is symmetric
with respect to z-direction, only half of the width is considered for optimization. Equation (61)
shows the geometrical constraints for the actuator in y-direction.
mmyyyy SBSSAGm 35.6 (61)
Increasing of the winding space, YAG will provide more space for the coils with penalty of
a decreased magnetic flux density. On the other hand, a decrease in the winding space will result
in a higher magnetic flux density but with a lower number of coil winding, which means a higher
exciting current is required to generate the same force. Another design issue resides in how to
arrange a fixed volume of the magnet with properly selected ferromagnetic material within a
restricted volume to achieve the largest force constant.
Figure 28 shows the magnetic flux lines along the PSAS actuator. In particular, (58)
defines the magnetic flux density in the airgap. MMFmagnet is the magnetomotive force generated
from the permanent magnet. Aairgap is the area of the airgap that flux lines passes through. is
the summation of magnetic reluctance along the magnetic circuit. Note that reluctance is the
function of the both X values and the Y values as shown in Figure 27. Optimizing any of these
parameters will lead to optimized flux density. Equation (58) indicates that one way to increase
the flux density is to maximize the MMFmagnet, which is defined by (18). In particular, rB is
defined as residual flux density, which is the property of magnets. Larger the residual flux
density is, stronger the magnet becomes. The strongest commercially available magnet is NdFeB
N52 magnet, which will lead to the highest output force. Figure 29 illustrates the maximum force
that is generated by using different strengths of neodymium magnets. It is clear that NdFeB N52
must be selected.
69
Figure 28:Magnetic flux lines in the PSAS actuator
Figure 29: Effect of permanent magnet on maximum force
Another way to increase the flux density is to minimize the reluctance of the components.
This in turn leads to increase in the thickness of the shell and the orientor. However, decreasing
the winding space will result in higher magnetic flux density but with lower number of coil
winding, which means less force can be generated. Therefore, it is not possible to make the shell
20
25
30
35
40
45
50
N52 N50 N42 N35
Max
imu
m F
orc
e (
N)
Maximum force vs Magnet type
Max. Force (N)
70
thickness and the orientor very large. By increasing of the coil cross section YAG, the length of
the coil in the airgap, l and the number of turns, n, will be increased. From (57) it is clear that
this leads to higher force. However, since the cross section area of the shell and the orientor are
smaller, this leads to the saturation of steel components. The saturated magnetic flux density, Bs
of the selected magnet is about 1.3T [40]. In order to achieve maximum usage of the magnetic
field and at the same time to maintain a safe tolerance for temperature variation, an empirical
value between 90%-95% of its saturated flux density is selected as the designed operating point.
Figure 30 shows the saturation of the steel shell due to the decreased thickness of the shell.
Moreover, the resistance of the coil is going to increase. The thickness of the magnet is mostly
specified by the availability of the magnets from the manufactures.
Figure 30: The saturation of the steel shell due to the decreased thickness of the shell
71
The second part of the geometry mapping optimization is to optimize the length of the
components in the actuator as shown in Figure 27. Equation (62) shows the geometrical
constraints for the actuator in the x-direction.
mmXXXX SBMOSS 32 (62)
From (35) and (38) it is clear that the length of the shell base, XSB, must be increased in
order to achieve higher flux density. However, this will make the actuator longer. XSB cannot be
too small either because it will saturate the steel shell. Figure 31 shows the effect of length of
shell on the force along the stroke. It is clear that as the length of the shell is increased to 3mm
the output force is maximum.
In order to evaluate the optimized length of the magnet, both lorentz and reluctance
forces must be considered. For Lorentz force, from (18), it is clear that the MMFmagnet will be
increased by increasing the length of the magnet, Xm . This in turn will decrease the length of the
orientor, which leads to decreasing the area of the airgap and number of turns that are in the
magnetic field. However, it is important to consider the effect of reluctance force in this analysis
as well. The second part of the forces in (56) has to do with the change of inductance along the
stroke. Figure 32 illustrates the effect of magnet length on nonlinearity and change of the
inductance. For shorter magnets, as the stroke of the actuator is increased, the inductance drops
dramatically. Therefore, dX
dL is increased negatively. In this case, since it is also multiplied by
square of the current value shown in (56), high amount of negative force is generated, which
works against the Lorentz force. Figure 33 shows the summation of the two forces. For longer
magnets since dX
dL is negligible, the output force is much more linear and negative force is not
72
generated. Since the linearity of the PSAS actuator force is very important for control, the length
of the magnet that generates more linear force must be chosen.
Figure 31: The effect of length of shell on the force along the stroke
Figure 32:Inductance of the coil along the stroke for different lengths of the magnet
30
32
34
36
38
40
42
0 5 10 15 20
Forc
e (
N)
Stroke (mm)
1 mm
2 mm
3 mm
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20
Ind
uct
ance
(m
H)
Stroke (mm)
5 mm
10 mm
15 mm
20 mm
25 mm
73
Figure 33:Output force along the stroke for different lengths of the magnet
3.4.3 Optimized Design of the PSAS Actuator
Geometry mapping optimization is performed to find the optimized actuator for the
application of the SSIPTS. The optimized actuator meets all the geometrical and volumetric
design requirements specified in above. In particular, the optimized actuator is within the design
and meets the force requirements. Figure 34 shows the output force of the actuator. It is clear that
the new actuator demonstrates an excellent linear behaviour along the stroke and generates
enough force for the application of PSAS. Further, this figure shows that the actuator generates
less force at each end of the stroke. Figure 35 shows the simulated force sensitivity parameter
along the stroke for different values of input current. It is clear that the force sensitivity is
relatively constant with respect to the input current and is a function of the position of the coil.
This validates the assumption for position-dependent force sensitivity parameter. The average Kf
line shows the average values of the force sensitivity parameter for each position. This curve is
going to be used to shape K(X) function.
-40
-30
-20
-10
0
10
20
30
40
50
0 5 10 15 20
Forc
e (
N)
Stroke (mm)
5 mm
10 mm
15 mm
20 mm
25 mm
27 mm
74
Further simplification can be made by assuming constant force sensitivity parameter
along the stroke. This simplification does not impact the performance of the actuator since the
variance in for the sensitivity parameter is very low. Therefore, using (45) the force sensitivity
parameter can be assumed to be 3.1 N/Amp and assumed to be constant with respect to both
input current and potion of the coil. This is an important design criterion for controllability of the
PSAS.
Moreover, Figure 36 illustrates the simulated values of the inductance of the coil. Note
that the PSAS actuator is optimized in such a way that the inductance of the winding coil does
not change much with respect to the coil position. Figure 37 illustrates the value of dX
dL along the
stroke. From these two graphs it can be assumed that the inductance of the coil is constant and
the value of dX
dL is negligible.
Lastly, Figure 38 illustrates the magnetic flux density within the actuator. Note that the
maximum flux density is 1.5965 Tesla, which is slightly higher than recommended 1.3 Tesla
limit. However since this is occurred only on a small portion of the shell base, it can be tolerated.
75
Figure 34:Simulated PSAS force along the stroke for different current values
Figure 35: Force sensitivity parameter along the stroke for different current values
-40.00
-35.00
-30.00
-25.00
-20.00
-15.00
-10.00
-5.00
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
0 4 8 12 16 20
Forc
e (
ne
wto
n)
Stroke (mm)
-10 Amp
-8 Amp
-6 Amp
-4 Amp
-2 Amp
0 Amp
2 Amp
4 Amp
6 Amp
8 Amp
10 Amp
2.00
2.20
2.40
2.60
2.80
3.00
3.20
3.40
3.60
0 4 8 12 16 20
Forc
e s
en
siti
vity
par
ame
ter,
ne
wto
n/A
mp
Stroke (mm)
-10 Amp
-8 Amp
-6 Amp
-4 Amp
-2 Amp
2 Amp
4 Amp
6 Amp
8 Amp
10 Amp
Average Kf
76
Figure 36: Simulated values of the inductance of the coil along the stroke
Figure 37: Simulated values of the change of the inductance per mm
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 5 10 15 20
Ind
uct
ance
(m
H)
Stroke (mm)
Inductance
-0.14
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0 4 8 12 16 20
Ch
ange
in In
du
ctan
ce p
er
mm
, (m
H)
Stroke (mm)
Delta inductane
77
Figure 38: The magnetic flux density within the actuator
Table 5 indicates the dimensions of the optimized actuator illustrated in Figure 27.
Moreover, Table 6 shows the electromagnetic properties of the optimized actuator. Further,
empirical characterization and parameterization of the actuator is needed to fully characterize the
actuator as explained in section 4.3.
78
Table 5: Optimized value of geometrical values of the PSAS actuator
Name Parameter Optimized value
Length of the shell base XSB 5 mm
Length of the magnet XM 25.4 mm
Length of the orientor XO 2.6 mm
Length of the shell side XSS 33 mm
Length of the coil XC 25 mm
Width of the orientor YO 3.175 mm
Width of the magnet YM 3.175 mm
Width of the coil YC 3 mm
Width of the shell side YSS 1 mm
Width of the shell base YSB 6.35 mm
Depth of all the component Zact 25.4 mm
Table 6: Optimized electromagnetic parameters of the PSAS actuator
Name Parameter Optimized value
Current in to the coil I AmpiAmp 1010
Resistance of the coil R 21
Inductance of the coil L 5 mH
Number of turns in the coil n 760
Stroke of the actuator S S=20 mm
Maximum force generated Fmax 33 Newtons
Flux density in the airgap Bairgap 0.5 Tesla
Force sensitivity parameter Kf 3.1 N/Amp
Back emf sensitivity parameter Kb 3.1 V/m/sec
79
3.5 SYSTEM MODELING AND SIMULATION OF THE PSAS
The PSAS for the SSIPTS is a complete mechatronics system, consisting of several
subsystems such as mechanical, electromagnetic actuator, power control electronics, and position
controller. Each of these subsystems are modeled and simulated in order to facilitate the design
and development phase. MATLAB and SIMULINK simulation environments are used to model
the PSASs. Figure 39 illustrates the entire PSAS model in SIMULINK environment. Modeling
techniques and simulations for each of these subsystems are explained in details in the following
sections. It is necessary to drive simulation models of the PSAS in order to analysis the
performance of the PSAS and implement the control and softlanding strategies
Figure 39: SIMULINK simulation model of the PSAS in the SSIPTS
3.5.1 System modeling of the mechanical subsystem
The mechanical subsystem of the PSAS is mainly referred to the moving components of
the actuation system. It consists of a pulley segment, a connecting shaft, and the moving coil as
shown in Figure 20. Figure 40 shows a model of the mechanical subsystem as an equivalent
mass-damper subsystem.
Force
V+
V-
VCA
Signal
Generator
v in v out
Power sensor
P_ref
P
Vel
PWM Duty
Rev erse
Position Controler
f orce P
Mechanical Plant
Pos
VelP
Linear position sensor
PWM Duty
Rev erse
V+
V-
PWM & H-Bridge
80
Mass (M)X=0
X
C
Chs Khs
Hard Stop
Hard Stop
Fact
KhsChs
Figure 40:Model of the mechanical subsystem as an equivalent mass-damper subsystem
For a single actuator, the position variable is X and the origin of the X coordinate is
chosen to coincide with the location of the mass at rest as shown in Figure 40. For simplicity, the
moving components are modeled as a lumped mass M, since they constitute a rigid body.
Dynamic dry friction forces, damping force, and hard stop nonlinearity are considered in the
mathematical modeling of this subsystem. Fact is the applied force by the actuator. Ffri is the
force due to coulomb friction and damping is provided by mostly air as viscous friction. Fhs is
the force due to the hard nonlinearity, which is active when the pulley segment strikes the hard
stops. For ease of implementation, it can be approximated as a piecewise linear function. The
impact interaction between the pulley segment and the hard stops is assumed to be elastic. This
means that the hard stop is represented as a spring that comes into contact with the pulley
segment as the gap is cleared and opposes pulley segment penetration into the stop with the force
81
linearly proportional to this penetration. To account for energy dissipation and nonelastic effects,
the damping is also introduced.
max
max
,0
00),(
XXXXCXK
XXXXF
hshs
hs
(63)
Where
0103 hshs CandK (64)
The degree of bounce is adequately modeled by iteratively varying the values of kst and
Cst to match that of the surface. The mechanical subsystem of the PSAS is modeled in
SIMULINK using three built in modules shown in Figure 41. The mass module indicates the
mass and the origin of the movable pieces. The transitional friction module models dynamic dry
friction forces and the damping force. Lastly, transitional hard stop models the impact force due
to hard stop nonlinearity.
82
Figure 41: Simulink model of the mechanical subsystem
3.5.2 System modeling of the electromagnetic actuator subsystem
In the last sections the mathematical governing equations of the PSAS are derived as
shown in (55) and (56). These equations can be used to make a SIMULINK simulation model of
the PSAS. Figure 35 shows the simulated force sensitivity parameter along the stroke for
different values of input current. It is clear that the force sensitivity is relatively constant with
respect to the input current and is a function of the position of the coil. This validates the
assumption for the position-dependent force sensitivity parameter. The force sensitivity
parameter, )(XK f is to be found empirically by a static force characterization method. Knowing
the back electromotive-force parameter, )(XKb , is equal to the force sensitivity parameter,
)(XK f, the empirical function found for )(XK f
can be used for )(XKb . These empirical
functions are then used in a look-up table in SIMULINK.
2
P
1
force
R C
Translational Hard
Stop
R C
Translational
Friction
Mechanical
Translational
Reference2
Mechanical
Translational
Reference1
Mass1
83
Further, Figure 36 illustrates the simulated values of the inductance of the coil. Note that
the PSAS actuator is optimized in such a way that the inductance of the winding coil does not
change much with respect to the coil position. Figure 37 illustrates the value of dX
dL along the
stroke. From these two graphs it can be assumed that the inductance of the coil is constant and
the value of dX
dL is negligible. Figure 42 shows the block diagram of the PSAS actuator model
with look up tables for )(XK fand )(XKb .
Figure 42: The block diagram of the PSAS actuator model with look up tables
Further simplification can be made by assuming constant force sensitivity and the back
electromotive-force parameters along the stroke. This simplification does not impact the
performance of the actuator since the variance in for the sensitivity parameter is very low.
Therefore, using (45) the force sensitivity parameter can be assumed to be 3.1 N/Amp and be
constant with respect to both input current and potion of the coil. This is an important design
criterion for the controllability of the PSAS. The above simplifications lead to use equations (59)
Step Scope
1
m.s+c
Mechanical
subplant
Kf Lookup Table
Kf
Kbmf Lookup Table
Kbmf
1
s
Integrator
1
L.s+R
Electrical subplant
Coulomb &
Viscous Friction
Volt(S) V(S)I(S)F(S)
X(S)
84
and (60), to build the simulation model. The transfer function between the applied voltage V(s)
and the moving coil position X(s), using equations (59) and (60), can be written below. Figure 43
shows the block diagram of the PSAS actuator with constant `fK and bK .
sKKCRsCLRMMLs
K
sV
sXsG
bf
f
)()()(
)()(
23
(65)
Figure 43: The block diagram of the voice coil actuator with constant sensitivity parameters
Moreover, further model simplification is possible without costing the model accuracy.
Since the electrical time constant is much smaller than mechanical time constant, mechelec ,
the order of the transfer function is reduced to second order as shown in the following equation.
Figure 44 shows the block diagram of the simplified voice coil actuator model.
)()(
)()(
bf
f
simplifiedKKCRMRss
K
sV
sXsG
(66)
Step Scope
1
m.s+c
Mechanical
subplant
kf
Kf
1
s
Integrator
1
L.s+R
Electrical subplant
Coulomb &
Viscous Friction
kb
BEMF
Volt(S) V(S)I(S) F(S) X(S)
85
Figure 44 : Simplified the block diagram of the actuator with constant sensitivity parameters
However, it is vital to compare the dynamic performance of the exact and simplified
model to validate the accuracy of the simplified model. The following graphs illustrate the
impulse responses and step responses for both exact and simplified models. It is clear that the
simplified model matches the exact model pretty closely.
Step Scope
1
m.s+c
Mechanical
subplant
kf
Kf
1
s
Integrator
1
R
Electrical subplant
Coulomb &
Viscous Friction
kb
BEMF
Volt(S) V(S)I(S) F(S) X(S)
86
Figure 45: Impulse and step responses of the exact and simplified models of the electromagnetic
actuator
Moreover, it is important to note that model simplification reduces the order of the
transfer function by eliminating the effect of the super-fast pole as shown in below pole-zero
map of the exact model.
87
Figure 46: Pole-zero map of the exact and simplified model
Based on above simplifications, the electromagnetic actuator for the PSAS is modeled
using SIMULINK modules shown in Figure 47. The translational electromechanical converter
module is set to model electromagnetic and magnetomechanical energy conversions. The resistor
and inductor modules model the resistance and inductance of the coil.
Figure 47: The SIMULINK model of the electromagnetic actuator subsystem
3 V-
2 Force
1
V+
+-
RC
Translational
Electromechanical
Converter
+ -
Resistor
Mechanical
Translational
Reference1
+ -
Inductor
88
3.5.3 System modeling of the power control subsystem
The power control subsystem of the PSAS is mainly referred to the high voltage power
electronics for the electromagnetic actuator. It can be perceived as a motor driver for the linear
actuator. It consists of a high voltage power supply, an H-bridge, and a pulse-width modulated
signal generator, PWM. Figure 48 shows the SIMULINK simulation model of the power control
subsystem. The detailed explanations of design and simulation of these components are as
follows:
Figure 48: Simulink simulation model of the power control subsystem
The process of creating rapid electronic switched transitions to convert electrical energy
from an electrical supply into a series of high frequency voltage or current pulses is called pulse-
width modulation (PWM). It is a commonly used technique for controlling power to inertial
electrical devices such as rotary and linear motors. One of the basic reasons for the increasing
interest in PWM systems is their ability to process a large signal power with a very high
frequency [72]. Many electromechanical actuators are controlled using PWM amplifiers, since
the electronic switching leads to amplifiers with reduced size, weight, and power dissipation
[73].
4
Reverse3
V-
2
V+
1
PWM Duty
PWM_Vol
PWM Voltage
PWM
REF
REV
BRK
+
-
H-Bridge
Electrical Reference3
+ref
-ref
PWM
REF
Controlled PWM
Voltage
89
A pulse width modulation signal is defined as a square wave of fixed frequency with
variable width of the ‘ON’ time. The amplitude of the signal is also fixed and is equal to the
maximum voltage Vmax. Therefore, at the ‘ON’ state, the voltage equals Vmax and at the ‘OFF’
state it equals zero volts. As shown in Figure 49, the portion of the time within one period, Tpwm
(where f
Tpwm
1 sec and f is the frequency in Hz), during which the signal has the amplitude
of Vmax is called the ‘ON state’ and the rest of the time during which the amplitude is zero is
called the ‘OFF state’. The radio of the ‘ON state’ over the period Tpwm is called the ‘duty cycle’,
d. The duty cycle is controlled or modulated in order to control the power to the actuators.
Vmax
Time (Sec)Period, T Period, T
ON state OFF state
0 Volt
Figure 49:Pulse-width modulated signal
At a certain voltage V let the current drawn by the plant i. Then the required power input
to the system is P=VI [Watts] to reach the desired performance of the actuator. In the PWM
system, this energy input per second (or power) is fed to the actuator in many packets all at the
90
maximum voltage Vmax. The number of such packets per unit of time equals the frequency of the
signal used. The amount of energy contained in each packet depends on the duty cycle of the
signal. During ‘Off state’ of the PWM, there is no energy input in the system [74]. In the case of
PWM signal, the power input to the actuator system is defined by
][max WattsifdVP PWMPWM
(67)
where Vmax is the maximum supply voltage to the actuator, f is the fixed frequency of the PWM
signal, d is the duty cycle of the PWM signal, and iPWM is the current drawn by the actuator. As
long as PPWM = P, then the PWM can be used as a control method to control the dynamics of the
actuator.
The main advantage of PWM is that the power loss in the switching devices is very low.
When a switch is off there is practically no current, and when it is on, there is almost no voltage
drop across the switch. Power loss, being the product of voltage and current, is thus in both cases
close to zero. By applying the maximum voltage to the system and by turning off the supply for a
certain period of time (as determined by the duty cycle), the control system operates at its
maximum efficiency and the energy loss is minimized [75]. This means the PWM control system
uses almost full power of its duty cycle that is transferred to the load whereas a resistive
analogue controller consumes more current for transferring the same amount of power to the load
as it converts some of the current to heat. Another advantage of PWM is the ability to optimize
the amplitude of the actuating signal according to the actuator saturation magnitude while
achieving a better control system performance. PWM also works well with digital controls,
which, because of their on/off nature, can easily set the needed duty cycle. The PWM signal
generator is modeled in SIMULINK using built in module. The frequency of modulation is pre-
91
set in the module. The SIMULINK module allows the system to dynamically change the duty
cycle of the PWM signal and the Vmax value.
The switching power device shown in Figure 50 is called an H-Bridge. H-Bridges are
often used to control the speed, the position, or the torque of linear and rotary motors. In general
an H-bridge is a rather simple circuit, containing four switching element, with the load at the
center, in an H-like configuration. It takes a DC supply voltage and provides 4-quadrant control
to a load connected between two pairs of power switching transistors. Because the switches
allow current to flow bi-directionally, the voltage across the load and the direction of current
through the load can be either polarity. The switching elements (Q1..Q4) are usually MOSFET
transistors. The diodes (D1..D4) are called catch diodes. In general all four switching elements
can be turned on and off independently, though there are some obvious restrictions.
Figure 50: Schematic of an H-bridge
The basic operating mode of an H-bridge is fairly simple: if Q2 and Q3 are turned on, the
left lead of the actuator will be connected to ground, while the right lead is connected to the
power supply. The current starts flowing through the actuator, which energizes the actuator in the
92
forward direction and the actuator starts to move. If Q1 and Q4 are turned on, the converse will
happen, the actuator gets energized in the reverse direction, and the actuator will start to move in
that way.
Figure 51: Current directions through the load in an H-bridge
In order to achieve the full control of the power to the actuator, two of the switches are
controlled using PWM signal. The average voltage seen by the actuator will be determined by
the ratio between the 'ON' and 'OFF' time of the PWM signal. The average output voltage across
the load of the H-Bridge is continuously controlled by PWM. Both polarity of output voltage can
be obtained and current can flow through the load in either direction as required. Simply
modifying the duty cycle adjusts the average voltage and the current to the load for the speed
control and the position. The voltage of the output terminal of one leg of the H-Bridge is held
stationary while the average voltage of the opposite leg is varied by the duty cycle of a PWM
input signal. The sign or the polarity of the voltage across the load is dictated by which side of
the H-Bridge is held stationary by having one of the transistors constantly ON, and the
93
Magnitude of the average load voltage is determined by the switching duty cycle of the two
switches in the opposite leg.
In application where fast dynamic control of inertial loads (i.e., the rapid reversal of the
direction of rotation of a motor) it is important that the “regeneration” of net average power from
the load back to the supply be able to take place. When the motor (inductive load) is turned off,
there is a large voltage surge. You cannot use a diode to suppress this due to reversing polarity of
the installation. Therefore, use an MOV across the motor.
The H-bridge is modeled in SIMULINK using built in module. The sign or polarity of the
voltage across the load is dictated by control signal called reverse, and the magnitude of the
average load voltage is determined by the PWM signal from the PWM signal generator.
3.5.4 Position Control Subsystem for the PSAS
As shown in Figure 39 the control subsystem receives the command signal along with
position and velocity signals for the actuator. Using these input signals, the position control
subsystem performs the position control and softlanding strategies. The output of the control
subsystem is a modulated PWM signal and the polarity command for the H-bridge. The detailed
explanations of the position control and softlanding strategies can be found in the next section.
94
3.6 POSITION CONTROL AND SOFTLANDING STRATEGIES
This section proposes a closed-loop position control methodology where the objective is
to achieve very low contact velocities while maintaining the fast system transient response. The
control strategy is based on applying PWM voltages for the transient and the steady state
performance. Referring to the performance requirements in section one, it is clear that the pulley
segments must be placed in a very short period of time, depending on the rotational speed of the
SSIPTS. Further, it is necessary for pulley segments to softland at the desired location in order to
achieve a low seating velocity for durability and low noise. The closed loop feedback control
strategy must make sure that the desired position, velocity, and acceleration trajectories, shown
in Figure 52, are achieved. As one can see in Figure 52, the pulley segments must be accelerated
until the maximum velocity is reached, and they must be decelerated once the peak velocity is
reached in order to softland at the desired position. Further, from section one it is clear that the
desired closed loop position controller must achieve the following:
Fast system transient response ( T < 12 ms)
While maintaining soft landing, vcontact < 0.2 m/sec
95
Figure 52: The desired position, velocity, and acceleration trajectories for the PSAS
The control strategy is based on applying PWM voltages for the transient and the steady
state performance. During the transient stage, the actuation system requires a high acceleration to
overcome the inertia and to achieve a very fast pulley segment motion. This is done by applying
a higher voltage than the nominal rated voltage for a very short period of time. This PWM
voltage signal produces a boost current to accelerate the pulley segment. The PWM driver
applies a positive voltage pulse to accelerate the moving coil actuator for the time period, t1.
After this time, the PWM driver switches its voltage polarity and applies a negative voltage pulse
to decelerate the actuator for the time period, t2, to achieve the low contact velocity. Therefore,
the total transition time is as follows:
21 ttt (68)
96
The proposed control strategy falls under the framework of switched control. The width
of the PWM pulse depends on the position error and is determined by a position feedback
controller. The output of the PWM driver is defined by:
PWMPWM
PWMPWM
TktTedkfor
TedktkTforVetu
)1())((0
))(()sgn()(
max (69)
where TPWM is the period of the PWM signal, e is the position error, d(e)TPWM is the pulse width
for (k+1)th
period, Vmax is the PWM amplitude, and sgn(e) is the sign function that is based on
the velocity of the pulley segment. Note that the duty cycle and the sign function are functions of
the position error and the pulley segment velocity. The duty ratio of the PWM pulse is defined
by:
5.00
15.0
1
0
1
))((
e
e
e
for
for
for
eted
(70)
The sign function is defined based on the velocity of the pulley segment. A positive
voltage signal is activated until the pulley segment velocity reaches its peak point. Then the
controller changes the voltage polarity and a negative voltage is applied to decelerate the pulley
segment in order to achieve softlanding.
The above control strategy is simulated and implemented in SIMULINK. The main
purpose of the simulation model is to achieve the performance requirements of the actuation
system and control the position of the pulley segments.
Figure 53 illustrates the simulated position trajectory of the PSAS for both extension and
retraction of the pulley segment. Further, Figure 54 shows the velocity profile of the PSAS at
transients.
97
Figure 53: The simulated position trajectories
Figure 54: The velocity profile of the pulley segment
It is clear that there is a good match between the desired position and velocity trajectories
shown in Figure 52 and those of the simulation. Moreover, it is important to analyse the applied
PWM voltage and corresponding current. Figure 55 shows the applied PWM signal to the
actuator during the transients. In order to see the switching signal at the transient time, the close
98
up of the applied PWM voltage is shown in Figure 56. Lastly, Figure 57 shows the current and
voltage applied to the actuator. It is clear that the current lags the voltage as the load is inductive.
Figure 55: Applied PWM voltage
Figure 56: The closed up of applied PWM voltage during actuation
99
Figure 57: The drawn current and the applied PWM voltage
These simulation results validate the position control and softlanding strategies. Further,
the simulation results indicate that the dynamic performance requirements are met.
3.7 SUMMARY
This chapter presented a new electromagnetic actuation technology for the PSAS for the
SSIPTS. The complex operation principle of the SSIPTS introduces challenging and conflicting
design requirements. Since current actuator technologies cannot meet all the design requirements
of the PSAS, this research proposes a novel actuator based on electromagnetic moving coil
actuator (MCA) technology. The design and modeling of the actuator was performed and
optimization was conducted to achieve optimal actuator. It is shown from simulation results that
the proposed actuation system meets all of the design requirements and is feasible for the
SSIPTS. However, the physical prototype of the PSAS must be developed and significant level
of experimentation is required to characterize the PSAS and verify its performance.
100
CHAPTER 4: FABRICATION AND EXPERIMENTATION OF
THE ELECTROMAGNETIC PULLEY SEGMENT
ACTUATION SYSTEM
This chapter summarizes the most relevant concepts and advancements pertaining to the
fabrication of the pulley segment actuation system, designs of the test setups, the characterization
of the actuator, and the experimentation of the proposed actuation system. This chapter ends with
the summary of the performance for the proposed electromagnetic actuator.
4.1 FABRICATION AND PROTOTYPING OF THE ACTUATOR
The fabrication and prototyping procedures of the actuator are highly dependent on
feasible manufacturability methods and the choice of materials. This includes machining the
permanent magnet, the soft magnetic material, and the bobbin as well as the coil winding. Note
that the heat and mechanical stress and strain, generated during machining process, have
significant effects on the magnetic properties of both hard and soft magnetic materials. Further,
the coil current density is coherent to the pattern of the coil winding. The bobbin fabrication also
needs a unique manufacturing process. Finally, cost effectiveness is an important decision-
making factor. The manufacturing process in prototyping is essential since a careless
manufacturing process results in the loss of the integrity of magnetic properties. For instance, the
inevitable temperature rise in the machining process is harmful to both the hard and soft
magnetic materials. Moreover, the high stress and strain in the machining procedure must be
avoided; the high stress leads to micro-cracks in hard magnetic materials and high strain arouses
the microstructure change in soft magnetic materials [40].
101
4.1.1 Fabrication of the PSAS Components
The permanent magnet, the shell, the orientor, and the bobbin as well as the coil winding
must be prototyped for the PSAS assembly. The permanent magnet is made by rare-earth
Nb2Fe14B for its high permanence, high coercive force, and high energy product. Figure 58
show the specification of the permanent magnet. Note that two of these magnets are stacked in
order to provide 25.4 mm long magnet as designed for the prototype. It is very important to clean
the connecting surface and assure that there is no airgap and dust particles between the magnets.
Further, after alignment, the magnets are glued to each other for integrity.
Moreover, the operating temperature affects the magnetic performance of the permanent
magnet as shown in Figure 59. The temperature sensitivity of the permanent magnetic requires
two important considerations for the actuator. Firstly, it is not recommended to machine and
modify the permanent magnets as the mechanical stress during machining processes leads to
losing the magnetic integrity of the permanent magnet. Secondly, it is important to note that the
heat generated by the coil heats up the magnet and leads to reduction in the magnetic field
generation. Then, the actuator does not operate as designed. Therefore it is important to avoid
excessive heating during the operation of the actuator.
102
Figure 58: Specification of the permanent magnet for the PSAS
Figure 59: The permanenet Neodymium magnet demagnetization curves for grade N42 [76]
103
Further, the bobbin is made from aluminum for its low magnetic permeability, high
thermal conductivity, and good structural strength. To maximize the size of the coil area, the
bobbin wall must be as thin as possible. However, the mechanical strength has to be taken into
account with the decreasing of bobbin wall thickness. A good design is always a compromise
between the airgap and the bobbin wall thickness. The bobbin wall is designed as 0.5 mm in this
research compared with some commercial products which is designed based on empirical data.
For such a thin-wall structure, traditional machining process is not available. Therefore, the
electro-discharge machining (EDM) is suggested. The bobbin is also equipped with a threaded
connection to mount the connecting rod to it. Further, in order to wind the coil around the
bobbin, it is very important to electrically isolate the bobbin from the coil as aluminum is a great
conductor. This is done by painting an epoxy on the outer surface of the bobbin.
104
Figure 60: Prototype of the bobbin for the PSAS
The inner surface of the bobbin is designed to have an interference fit with the permanent
magnet. In this case the permanent magnet provides a good guide and sliding surface for the
bobbin and the airgap between the coil and the magnetic assembly is very small. However, the
imperfections and the misalignment caused during the machining will roughen this interference
fit. Proper sanding procedure is required to smooth the inner surface of the bobbin. Lastly, note
that no lubrication is needed as aluminum-steel interface is reasonably friction free.
Moreover, the flux orientator and the shell are made from soft iron because of a
relatively high permeability and off-the-shelf availability. Figure 61 shows the actuator shell
assembly. Note that as the shell provides the most part of the magnetic path, its integrity and
uniformity is very important. The integrity of magnetic circuits is defined as the rate of consistency
105
of the properties of the actual magnetic circuit compared with the circuit in theoretical or simulated
situations. It is coherently corresponding to the connecting status of the members in the magnetic
circuit. Any disconnection or improper connections will apparently influence the integrity of the
magnetic circuits. Therefore, the shell is made out of one piece. Proper milling machining is used to
produce the cavity inside the shell. However, note that due to the small thickness of the shell, the
process of milling must be done very carefully. Further, the radii of the inner fillets must be selected
very carefully. It is clear that a big radius will cause interference with the coil and the bobbin.
Further, two installation threaded holes are machined at the base of the shell. These holes are used to
secure the shell to the mounting piece as shown in Figure 61.
Figure 61: The shell assembly with the mount for the PSAS
106
4.1.2 Coil Winding for the PSAS
The coil is made from copper and different wire gauges have been used for this
application. The procedure to wind the coil affects the performance of the actuator. In particular,
it influences the number of the turns in the coil and the resistance of the coil.
A filling factor in a conductor coil defines the true area of the conductors with respect to
the specified coil area, which reflects the coil winding efficiency. The higher the filling factors,
the higher the current density it can provide. Figure 62 shows different winding pattern with
different winding efficiency. The standard circular magnetic wire winding as square pattern has
78.5% efficiency; the circular wire winding as hexagonal pattern has 90.7% efficiency, but this
pattern is impractical for large number turns [77]. The rectangular magnetic wire has the highest
efficiency while the regular magnet wire is more expensive and entangling during winding is
hard to control. For this prototype, a standard round magnetic wire is used and the first winding
method is used. At the end of the winding procedure, a special type of epoxy is used to secure
the coil and make it a solid. It is important to test for the conductivity, resistance, and the
inductance of the coil. Figure 63 shows the complete coil winding in the bobbin. The
conductivity of the coil is checked and its resistance is 20.5 ohms, which is a desired value.
107
Figure 62: Winding methods with different filling factors [40]
Figure 63: The coil winding for the PSAS
108
4.1.3 Final Prototype of the PSAS
Figure 64 shows the components of the final prototype and Figure 65 shows the actuation
system assembly with the pulley segment representative. For detailed explanations and drawings
for the PSAS prototype, the reader is referred to see APPENDIX A.
Figure 64: Components of the MCA for the PSAS
Figure 65: The assembled prototype of the PSAS
109
4.2 DESIGN AND DEVELOPMENT OF EXPERIMENTAL SETUPS
This section explains the design and the development of experimental setups used for
characterization methodologies, and the experimental performance of the PSAS.
4.2.1 Static Force Test setup for PSAS
This section explains the design and the development of the static test setup, used to
characterize and to test the static performance of the PSAS. It consists of three subsystems:
mechanical, control circuit, and data acquisition subsystems. The purpose of this test setup is to
characterize the PSAS actuator and measure the followings:
Static actuation force, both pushing and pulling
The force sensitivity parameter, )(XK f
The current drawn by the coil
The applied voltage
The inductance of the coil
In this test set up, the actuator is maintained steady while measuring the force and other
electrical signals. In this case, there is no back-emf force as there is no velocity. The above
parameters are measured at each position within the stroke of the actuator. The flow diagram in
Figure 66 illustrates the components of the test setup and how the measurements are performed.
Figure 67 show the mechanical subsystem, which includes a load cell, an actuator, and fixtures.
Similarly, Figure 68 illustrates the mechanical subsystem in case of pull force. In this case a
reverse fixture is added to the test system to capture the pull force.
110
Figure 69 shows the designed control circuit, which includes a solid state relay, a voltage divider
circuit, current sensors, and input/output ports. For the specifications of the load cell, the solid
state relay and the current sensors, refer to appendix section. Further, Figure 70 shows a sample
measurement data from Labview. These graphs are used to analyse the performance of the
actuator. Lastly, Figure 71 shows the block diagram of the data acquisition in Labview
environment.
Power supply
Solid state Relay
Actuator
Force sensor
Labview Pulse
GeneratorLabview Data
Acquisition
Force
Voltage & current
sensor
Voltage
Pulse Pulse
Current
Figure 66: Flow diagram for the static force test setup for the PSAS
111
Figure 67: Mechanical subsyetm of the static force test set up for push force
Figure 68: Mechanical subsyetm of the static force test set up for the pull force
112
Figure 69: The control circuit for the static force test setup
Figure 70: The measurement data in the LABVIEW environment
113
Figure 71: The block diagram of the data acquisition system in the LABVIEW environment
4.2.2 Dynamic Performance Test Setup for the PSAS
This section explains the design and development of the dynamic performance test setup,
used to characterize and to test the dynamic performance of the PSAS. It consists of three
subsystems: mechanical, control circuit, and data acquisition subsystems. The purpose of this test
setup is to characterize the PSAS actuator and measure the followings:
Position and velocity responses of the actuator
The actuation timing
The acceleration and dynamic force generated by the actuator
The viscous damping coefficient and the coulomb friction
114
The current drawn by the coil
The applied voltage
The back electromotive-force parameter, )(XKb
The impact of hard landing
The flow diagram in Figure 72 illustrates the components of the test setup and how the
measurements are performed. Figure 73 shows the mechanical subsystem, which includes the
actuator, an accelerometer, a LVDT position sensor, a pulley segment representative, and
required fixtures. Figure 74 illustrates the actuator and pulley segment representative and the
connections. Same control circuit and data acquisition methods as in case of static test are used.
For the specifications of the LVDT position sensor, refer to Appendix E.
Further, Figure 75 shows the block diagram of the data acquisition in LABVIEW
environment. Lastly, Figure 76 shows a sample measurement data from LABVIEW. These
graphs are used to analyse the performance of the actuator.
115
Power supply
Solid state Relay
Actuator
Accelerometer
Labview Pulse
GeneratorLabview Data
Acquisition
Acceleration
Voltage & current
sensor
Voltage
Pulse Pulse
Current
LVDT position
sensor
Displacement
Figure 72: Flow diagram for the dynamic performance test setup for the actuation system
Figure 73: Mechanical subsystem of the dynamic performance test setup for the actuation system
116
Figure 74: The actuation system and the pulley segment representative
Figure 75: The block diagram of the data acquisition system in the LABVIEW environment for the
dynamic performance test setup
117
Figure 76:Measurement data in the LABVIEW environment
118
4.2.3 Position control Test Setup for PSAS
This section explains the design and development of the position control test setup, used
to characterize and to test the control strategies for the PSAS. It consists of four subsystems:
mechanical, H-bridge and PWM, microcontroller, and data acquisition subsystems. The purpose
of this test set up is to experiment the performance of the position control and softlanding
strategies. To be specific, the position control for pulley segments and softlanding results from
the simulation are verified experimentally using this test setup.
The flow diagram in Figure 77 illustrates the components of the test set up and how the
measurements are performed. Figure 78 shows the entire system which includes the actuator, an
accelerometer, a LVDT position sensor, a pulley segment, and required fixtures as well as the
microcontroller, customized H-bridge, and the data acquisition card for LABVIEW.
The position control and softlanding strategies, explained in the section 3.6, are
implemented in the microcontroller, which communicates with the PWM generator and the H-
bridge. Further, an LVDT position sensor is used to provide position and velocity feedbacks to
the microcontroller and to the National Instrument data acquisition card.
The actuator draws its power from a 200 volt DC power supply, which is connected to
the H-bridge. The microcontroller provides 5 volt regulated PWM signal to the H-bridge for
amplification. For the specifications of the microcontroller and the actuator driver, please refer to
Appendix D.
119
Power supply
Fast Switching
H-Bridge
Actuator
Accelerometer
Microcontroller
and PWM Signal
Generator
Labview Data
Acquisition
Acceleration
Voltage & current
sensor
Voltage
Control
Signal Control Signal
Current
LVDT position
sensor
Displacement
Pulley Segment
Displacement
Figure 77: Flow diagram for the position control test setup for the PSAS
Figure 78:Position control test setup for the PSAS
120
4.3 DETERMINATION OF THE CHARACTERISTICS OF THE PSAS
Based on the two differential equations, (55) and (56), that govern the electromagnetic
actuator, it is necessary to empirically find the parameter of the actuators. This process is called
parameterization of the electromagnetic actuator. The values of these parameters are further
compared with the simulated and desired values. The methodology of characterization and
parameterization of the actuator and model validation are explained in details in this section. The
list of parameters is as follows:
The force sensitivity parameter, )(XK f
The resistance of the coil
The inductance of the coil
The moving mass
The back electromotive-force parameter, )(XKb
The viscous damping coefficient
The coulomb coefficient
Further, the following assumptions used in the modeling of the electromagnetic actuator
must be also verified:
The effect of position on coil inductance can be neglected i.e . 0dX
dL.
121
The force sensitivity parameter, )(XK f, and the back electromotive-force
parameter, )(XKb , are functions of position and are constant with respect to the
coil current.
Static force test setup is used to determine the force sensitivity parameter, )(XK f. In this
test set up, the PSAS is maintained steady while measuring the generated static force and current
developed in the coil. In this case, there is no back electromotive force since there is no velocity.
The static force and current profiles are measured at each position within the stroke of the
actuator. The first step is to measure the force sensitivity parameter, )(XK f. Since no back
electromotive force exists, the actuator model is simplified to the following:
Figure 79:Static force generation model
which relates the static force to the applied voltage and the developed current. Rearranging (45),
the force sensitivity parameter, )(XK f, is derived:
)(
)()(
si
sFXK f
(71)
Therefore, by measuring the current drawn by the coil and the generated static force at
discrete positions within the stroke of the actuator, )(XK f can be found. Figure 80 and Figure
81 illustrate sample simulated and experimented current and force measurements for different
voltage values at 12 mm stroke. These measurements are collected at each current value and
along the stroke of the actuator to generate Figure 82. As one can see the experimental values
Step Scope
kf
Kf
1
L.s+R
Electrical subplant
Volt(S) I(S) F(S)
122
match those of simulation. Also note that the generated forces are highly linear with respect to
the stroke of the actuator. The actuator is able to generate a maximum force of 33 Newtons.
Figure 83 illustrates the force sensitivity constant, )(XK f, along the stroke of the
actuator for both pushing and pulling actions for different values of current. The average force
sensitivity parameter is defined by the black curve "Average Kf". This curve can be used in a
look up table for the position dependent force sensitivity parameter, )(XK f. Therefore, it is
experimentally verified that the force sensitivity parameter, )(XK f, is indeed function of
position and is relatively constant with respect to the coil current. This validates the assumptions
in the modeling. Further, the force sensitivity parameter can be assumed to be constant
N/Amp 3.1fK . This simplification is possible since for the most of the times the
approximation error is less than five percent.
123
Figure 80: Current drawn by the coil for different voltage values at 12mm
Figure 81: Generated static force for different voltage values at 12mm
124
Figure 82: Experimental values of static force at different current values along the stroke actuator
Figure 83: Experimental force sensitiy parameter along the stroke for different current values
-40.00 -35.00 -30.00 -25.00 -20.00 -15.00 -10.00
-5.00 0.00 5.00
10.00 15.00 20.00 25.00 30.00 35.00 40.00
0 4 8 12 16 20
Forc
e (
ne
wto
n)
Stroke (mm)
Force Vs Stroke
-10 Amp
-8 Amp
-6 Amp
-4 Amp
-2 Amp
0 Amp
2 Amp
4 Amp
6 Amp
8 Amp
10 Amp
2.00
2.20
2.40
2.60
2.80
3.00
3.20
3.40
3.60
0 4 8 12 16 20
Forc
e s
en
siti
vity
par
ame
ter,
ne
wto
n/A
mp
Stroke (mm)
Force sensitivity parameter Vs Strole
-10 Amp
-8 Amp
-6 Amp
-4 Amp
-2 Amp
2 Amp
4 Amp
6 Amp
8 Amp
10 Amp
125
The static force test setup is further used to determine the inductance of the coil and to
verify that the actuator is designed in such a way that the effect of position on coil inductance
can be neglected i.e . 0dX
dL. In this test setup, the PSAS is maintained steady while measuring
the current developed in the coil. In this case, there is no back electromotive force since there is
no velocity. The current profiles are measured at each position within the stroke of the actuator.
In this case (59) reduces to a simple RL circuit, as shown in the following and is simulated in
SIMULINK.
dt
diLiRV
(72)
Figure 84: RL circuit for the static force test
A series of step voltage test of 100 volts at fixed discrete positions has been performed.
Figure 85 shows the experimental data for each position. Note that the current profiles are all
reasonably identical for all positions. Further, these graphs were compared with simulated results
to determine the value of inductance as shown in Figure 86. For all for step tests inductance was
found to be 7 mH. Therefore, it can be concluded that for this particular voice coil actuator there
is no variance in coil inductance with position, i.e. 0dX
dL, and L=7 mH.
Step Scope
1
L.s+R
Electrical subplant
I(S)Volt(S)
126
Figure 85:The current profiles for a constant applied voltage at different positions
127
Figure 86:Simulated and actual current profiles
The dynamic performance test setup is used to determine the viscous damping coefficient
and coulomb friction. Mechanically, the PSAS is modeled as a mass-damper system as shown in
(39). A precise weight scale is used to measure the weight of the moving part, M. It results in a
moving mass of M = 38.2 grams. To determine the viscous damping coefficient and coulomb
friction, data is fit to the solution of (39) for a simple drop test, where the only force acting on
the actuator is gravity. This results in a viscous damping coefficient of 0.7 N/(m/s) and static
coulomb friction of 0.75 Newtons.
Figure 40: Mechanical simulation of the mass and damper model with constant applied force
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10-3
0
1
2
3
4
5
6
7
8
9
10
Time (ms)
Curr
ent
(Am
p)
Current Vs. Time @ 5mm
6.5 mH
7 mH
7.5 mH
8 mH
8.5 mH
9 mH
Experimental
Step Scope
1
M.s +C.s2
Electrical subplant
X(S)F(S)
128
Figure 87: Experimented position and velocity curves for the drop test using gravity force
Figure 88:Fitting modeling to find viscous damping coefficient
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160
5
10
15
20
25
30
Time (ms)
Positio
n (
mm
)
Position Vs. Time
0.65
0.7
0.75
0.8
0.85
0.9
Experimental1
Experimental2
129
Further, the dynamic performance test setup is used to determine the back-emf parameter
of the actuator, )(XKb . For most typical electromagnetic actuators, the back-emf parameter,
)(XKb , is equal to the force sensitivity parameter, )(XK f. This needs to be validated.
Rearranging (59) to solve for )(XKb results in the following:
dt
dX
Vdt
diLiR
XK b
)( (73)
With numerical derivative approximations for dt
di and
dt
dX, (73) is used to establish the
)(XKb . The values of the developed current, applied voltage, the position are measured with
respect to time and are further used to calculate )(XKb for discrete positions in the stroke.
Figure 89 shows the sample experimental value of the back-emf parameter )(XKb . The
calculated back-emf parameter )(XKb is very similar to the force sensitivity parameter, )(XK f
found using the static force test. Therefore, for simplicity, same graph is used for the back-emf
parameter of the actuator as shown in Figure 83. Similarly, it was verified that the back
electromotive-force parameter, )(XKb , is a function of position and is constant with respect to
the coil current.
130
Figure 89: Experimental value of the for the back-emf parameter
Based on the above empirical characterization and parameterization of the actuator, Table
7 shows the actual electromagnetic properties of the actuator prototype. The actuator is fully
characterized and is ready to be used. Further, all the simulation parameters are validated and the
assumption used in the modeling of the electromagnetic actuator were verified.
Table 7: Actual electromagnetic parameters of teh PSAS actuator
Name Parameter Optimized value
Current in to the coil I AmpIAmp 1010
Resistance of the coil R 5.20
Inductance of the coil L 7 mH
Number of turns in the coil n 742
Stroke of the actuator S S=20 mm
Maximum force generated Fmax 33 Newtons
Flux density in the airgap Bairgap 0.5 Tesla
Force sensitivity parameter Kf 3.1 N/Amp
Back emf sensitivity parameter Kb 4.2 Voltage/velocity
131
4.4 EXPERIMENTAL RESULTS AND VERIFICATIONS
This section explains the experimental performance of the PSAS. Figure 90 shows the
simulated and experimented static force curves for different current values along the stroke for
the actuator. It is shown that the experimental values match those of simulation. Also note that
the generated forces are highly linear with respect to the stroke of the actuator. The actuator is
able to generate a maximum force of 33 Newtons.
One of the major performance experiments for the PSAS is called shooting experiment,
where the pulley segment and the moving coil are free to move along the guide rail and constant
voltage is applied to the actuator. Figure 91 shows the simulated and experimented position
profiles for different current values for the shooting experiment. Note that there is a reasonable
match between the simulation and experimental results. Figure 92 shows the simulated and
experimented velocity profiles for different current values for the shooting experiment.
Similarly, there is a reasonable match between the simulation and experimental results. Note that
for both position and velocity profiles, the experimental results lag the simulation results. This
means that there is some sort of latency in the performance of the actuator. Moreover, Figure 93
shows the simulated and experimented current profiles for the shooting experiment. The latency
in developing the current is also clear in this graph. Lastly, Figure 94 shows the simulated and
experimented applied voltage for the shooting experiment. Note that there is no latency in
developing the voltage.
Figure 95 shows the experimental results for the position control and softlanding
measurement in the LABVIEW environment. In particular, it includes the position and the
velocity profiles, the dynamic force, as well as the current and the PWM command to the driver.
By implementing the position control and softlanding strategies, the PSAS was able to place the
132
pulley segment at desired location (S=20 mm) in 17 msec. Moreover, the pulley segment is
softlanded at the desired location with a very smaller landing velocity (Vcontact ≈ 0.3 m/sec). The
pulley segment is further kept secured at desired place by applying a very small holding force.
This force is to make sure that the pulley segment is securely placed at the desired position.
Further, the motion of the pulley segment is reversed to bring the pulley segment back to the
disengaged position. Exact same strategies are applied, and very similar performance is
achieved. This shows that the position control and softlanding strategies work for both direction
of the motion. To sum up, the experimental results show that the performance requirements of
the position control, outlines in section one, are mostly achieved. Moreover, the position and
velocity profiles in Figure 95, follow the desired motion profiles, shown in Figure 8.
Figure 90: Simulated vs Experimented static force curves for different current values along the stoke
of the actuator
0 5 10 15 20
-30
-20
-10
0
10
20
30
Stroke (mm)
Forc
e (
N)
Force Vs. Stroke
-10 Amp
-8 Amp
-6 Amp
-4 Amp
-2 Amp
0 Amp
2 Amp
4 Amp
6 Amp
8 Amp
10 Amp
133
Figure 91: Simulated vs. experimented position profiles for different current values
Figure 92: Simulated vs. experimented velocity profiles for different current values
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020
2
4
6
8
10
12
14
16
18
20
Time (ms)
Positio
n (
mm
)
Position Vs. Time
1amp
2amp
3amp
4amp
5amp
6amp
7amp
8amp
9amp
10amp
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (ms)
Velo
city (
m/s
ec)
Velocity Vs. Time
1amp
2amp
3amp
4amp
5amp
6amp
7amp
8amp
9amp
10amp
134
Figure 93: Simulated vs. experimented current profiles
Figure 94: Simulated vs. experimented voltage profiles for different current values
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020
2
4
6
8
10
12
Time (ms)
Curr
ent
(Am
p)
Current Vs. Time
1amp
2amp
3amp
4amp
5amp
6amp
7amp
8amp
9amp
10amp
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020
20
40
60
80
100
120
140
160
180
200
Time (ms)
Voltage (
Volt)
Voltage Vs. Time
1amp
2amp
3amp
4amp
5amp
6amp
7amp
8amp
9amp
10amp
135
Figure 95: The experimental results for the position control and softlanding in the LABVIEW
environment
136
4.5 SUMMARY
This chapter presents the fabrication, prototyping, and experimentation methodologies for
the PSAS for the SSIPTS. The test setups are designed and developed to characterize the PSAS
and verify the performance of the PSAS. The prototype of the proposed actuator is built and
experiments are conducted for the application of the SSIPTS. It is shown from experimental
results that the prototype of the actuation system meets most of the design requirements and is
feasible for implementation in the SSIPTS. From this chapter the following conclusions are
summarized:
The prototype of the PSAS provides bi-directional actuation for the stroke of
S=20 mm.
The optimized actuator is within the design envelope and meets the geometrical
constraints of the SSIPTS application.
The amount of force generated exceeds the force requirements - the maximum
amount of force reaches 33 Newtons. The force sensitivity parameter is 3.1 N/Amp
and is constant with respect to the position of the coil and the input current.
The force linearity requirement is well met - the force generated is relatively
constant with respect to position of the coil.
The prototype of the actuation system does not meet the dynamic performance
requirements of the SSIPTS. In particular, the PSAS is able to place the pulley
segment at the desired location in 17 msec, and the pulley segment is softlanded at
137
the desired location with a very small landing velocity of 0.3 m/sec. It is clear that
they duration of the actuation is 5 msec longer than the required time.
The prototype of the PSAS provides a holding force to securely place the pulley
segments at the desired position.
The prototype of the PSAS costs 390$ which is higher than the required
economical pricing.
138
CHAPTER 5: DESIGN AND DEVELOPMENT OF A
SOFTLANDING MECHANISM FOR THE SSIPTS
5.1 INTRODUCTION
This chapter introduces a softlanding mechanism for the Pulley Segment Actuation
System, PSAS. It summarizes the most relevant concepts and advancements pertaining to the
softlanding mechanism, modeling methodologies, control strategies, and the experiments. The
combination of the electromagnetic actuator and the softlanding mechanism provides an ultra
fast bistable actuation system for the PSAS.
Experimental results in Chapter 4 indicate that the proposed the PSAS is able to meet
most of the design requirements and is feasible for implementation in the SSIPTS. To further
improve the performance of the PSAS and to meet all of the design requirements, a softlanding
mechanism is introduced. In particular, the performance of the PSAS with regards to
the fast transient requirement of the PSAS,
the softlanding requirement of the PSAS,
the necessary latching force, and
the electrical power requirement for the PSAS
is improved by adding the softlanding mechanism. The proposed mechanism is an
electromechanical actuation system consisting of two magnetic latches, mechanical springs, the
pulley segment composite, and the electromagnetic actuator from Chapter 3.
139
5.2 DESIGN PRINCIPLE OF THE SOFTLANDING MECHANISM
The proposed mechanism is an electromechanical actuation system. Figure 96 shows a
schematic of the softlanding mechanism. It consists of four subsystems: two magnetic latches,
mechanical springs, the electromagnetic actuator, and the pulley segment composite (PSC). The
mechanism is principally a pendulum that is driven by magnetic latch forces, spring forces, and
the actuator force. In this mechanism the potential energy is transferred between the two springs
and magnetic latches via pulley segment composite.
+
Pulley Segment Composite
Electromagnetic Actuator
Springs
+
Magnet
SteelPlates
Upper magnetic
latch
Lower magnetic
latch
Figure 96: The schematic of the softlanding mechanism for the PSAS
Since the pulley segment itself is made of aluminum for lighter weight, there is a need for
soft magnetic material, like steel, to be coated or attached to the pulley segment. This
combination produces a pulley segment composite, PSC. Each latching mechanisms attracts the
associated steel plate for latching. The actuation system uses two magnetic latches that catch and
hold the PSC that moves with a damped oscillation between two extreme positions under the
140
forcing of two springs and the actuator. The magnetic latch mechanism includes a lower
magnetic latch for the retraction of the PSC and an upper magnetic latch for the insertion of the
PSC. The latching mechanism operates by magnetically generated attractive force built by
inducing a flux in a steel plate in the PSC. The magnitude of this force decreases rapidly over the
distance which the steel plate travels.
The pulley segment composite is latched into the end positions by permanent magnetic
latches against the force of compressed springs. The differential in forces is called the holding
force. The actuator, when activated with a current, provides enough force to cancel the holding
force and allows the compressed springs to move the PSC quickly through a central neutral
position toward the other end position, where upon it is attracted by the other magnetic pole to
compress the other spring and latch into the other position. At neutral position springs are
equally compressed and the pulley segment is centered between the upper and lower magnetic
latches. Figure 97 shows the three states of the softlanding mechanism.
Figure 97: Three states of the softlanding mechanism
141
The electromagnetic actuator plays an important role in the operation of the softlanding
mechanism. The actuator is used for the following purposes: firstly, the actuator provides enough
force to cancel the holding force and allows the compressed springs to move the pulley segments
rapidly. Secondly, the actuator provides large force for rapid acceleration and deceleration of the
pulley segments. Thirdly, the actuator generates catching force to overcome the losses from
friction forces, vibration, and possibly magnetic force losses in the latch. Lastly, the actuator
serves as a control signal to the softlanding mechanism.
The magnetic latch systems provide the magnetic force that is inversely proportional to
the square of the gap between the PSC and the latch. This means that the latch excretes the
maximum attraction force when there is no airgap and the magnitude of this force decreases
rapidly over the distance which the steel plate travels. A permanent magnet latching mechanism
is selected for this application, which has several advantages over conventional (current-driven)
electromagnetic latching mechanism. The fundamental advantage is that they can provide a
relatively strong magnetic field over an extended spatial region for an indefinite period of time
with no expenditure of energy. The field they provide is fixed whereas the field of an
electromagnet can be changed by adjusting the current. Another advantage of permanent
magnets is that they can be fabricated with a wide range of structural properties, geometric
shapes, and magnetization patterns. They are also relatively inexpensive on a per unit basis
depending on the material used. Permanent magnets have an additional advantage over
electromagnets in that their performance scales well with size.
The mechanical springs act as an energy booster and an energy harvester. For the first
half of the travel, the compression force stored in the springs are used to accelerate the PSC
toward the neutral position and since then the springs are used to decelerate the PSC by
142
harvesting the kinetic energy. Note that at each end of the travel, the attraction force of the
magnetic latch becomes higher than the repelling force of the springs. Consequently, the PSC is
latched to the magnetic latch while the potential energy is stored in the compressed springs.
The proposed design of the softlanding mechanism for the PSAS has several advantages
including the followings:
The proposed actuation system retains the advantageous features of a magnetic
latched spring mass oscillating system with reduced energy consumption. The
kinetic energy is stored in compressed springs as a potential energy and is further
converted back to a kinetic energy during the transition. This oscillating system of
the spring-mass type can store a significant amount of energy.
Unlike electromagnetic latching mechanisms, the proposed latching mechanism
does not consume electrical energy while the PSC is latched in either ends.
In terms of the force requirement, the electromagnetic actuator does not need to
produce the high amount of force since the mechanical springs provides most of
the repletion force. In this case, the electrical energy consumption is reduced.
Since the actuator is latched until the actuator force overcomes the holding force,
the rising time and the initial latency for the actuator is not part of the transient
time. This reduction in time can shorten the transient time considerably.
Figure 98 illustrates the PSAS with the electromagnetic actuator and the softlanding
mechanism. The purpose of this modeling is to make sure that the combination of the softlanding
mechanism and the actuators can actually fit the overall design of the SSIPTS. Figure 99 shows
143
the integration of the PSAS in to the morphing pulley. In order to fit the curvature of the
morphing pulley the latching mechanisms must be curved like the pulley segments. Further the
pulley segment is combined with two thin steel plates to provide the pulley segment composite,
PSC.
Figure 98: The PSAS including the softlanding mechanism in the SSIPTS
144
Figure 99: The morphing pulley model with the PSASs
In this PhD thesis, the simpler prototype of the softlanding mechanism and the
electromagnetic actuator is proposed. Figure 100 shows the conceptual design of the PSAS
prototype. Note that the softlanding mechanism has rectangular shape and is not curved.
Figure 100: The softlanding mechanism prototype as a proof of concept
145
5.3 MATHEMATICAL MODELING OF THE SOFTLANDING MECHANISM
This section explains the most relevant concepts and advancements pertaining to
mathematical modeling for the softlanding mechanism for the PSAS. The spring forces, the
magnetic latch forces, and the electromagnetic actuator force largely determine the operation of
the PSAS. As such, an analysis of the complete system must consider interactions among the
actuator, magnetic latches, springs, and mechanical subsystems. Since the pulley segment
insertion and retraction are similar, we will first concentrate on pulley segment insertion and then
extend the analysis to include retraction. Figure 101 shows the schematic of the softlanding
mechanism with all the applied forces on the PSC.
X=0
-X
+X
+
++
F_m1
F_m2 F_spr
F_sprF_spr
F_spr
F_act
Figure 101: Governing forces in the softlanding mechanism
The differential equation, governing the forces within the softlanding mechanism, is as
follow:
146
XCXMFFFFFFF FrictionlowMagnetupMagnetlowSpringupSpringActuator ____
(74)
where the force of the springs are governed by Hook's law as shown in
XkF spSpring
(75)
and the two governing differential equations for the electromagnetic actuator are
XXKdt
diLiRV b
)( (76)
XCXMiXKF florentz )( (77)
where all the parameters of the actuator are known and stated in section 4.3.
However, the magnetic latch force is not known yet. The magnetic circuit analysis and
the virtual work model are used to model the magnetic latch force. The following section
explains the mathematical modeling for the magnetic latch systems for the soft landing
mechanism. In particular, the magnetic latch force must be modeled and found. Figure 102
shows the schematic of magnetic field for the magnetic latch system. Since the geometry of the
magnetic latch is symmetric with respect to the center of the magnetic latch, only half of the
latch is considered for modeling. Consequently, the amount of magnetic force is multiplied by
two to account for the symmetry. Figure 103 illustrates the magnetic flux path and the
corresponding dimensions for the components of the magnetic latch. PL, ML, BL correspond to
the length of the magnetic flux path in the pulley segment steel plate, the magnet, and the base
respectively. g1 and g2 correspond to the length of the airgap or the distance between the steel
plate and the magnetic latch.
147
+
Pulley Segment
Figure 102: The magnetic field schematic of the magnetic latch
BL1
BL2
PL2PL1
g2
PL3
BL3
g1
ML1
Figure 103: The magnetic field path and dimensions of the path
The energy and the virtual work method are used to find the magnetic force in the
magnetic latch. The expression for energy stored in a magnetic field is
dv
BWmag 2
2
(78)
where B is the magnetic flux density in the field and v is the unit volume in the field. Constant
permeability is assumed for the field [61]. Force is related to energy. Indeed, energy is in
148
units of force times distance. One of the most common methods to determine force is to use the
method of virtual work [61]. It states that force in a given direction, equals the partial derivative
of stored energy with respect to that direction as shown in (79).
g
WF gmag
(79)
To determine the magnetic latch force acting in the airgap direction in Figure 103, one
may replace the derivative of (79) by its approximation
g
WF gmag
(80)
Further, assuming the flux density B in the airgap of Figure 103 is uniform, the magnetic
energy magW is
v
BWmag ]
2[
0
2
(81)
Virtual work method states that during a virtual displacement, g , of a steel plate in the
gap direction, the volume of the airgap changes from )( ggA to Ag . Hence, we obtain
g
BAg
BggA
g
WFg
0
2
0
2
22)(
(82)
and thus the magnetic force is
0
2
2
BAF gmag
(83)
149
For the magnetic latches in the softlanding mechanism, everything in (83) is known
except the magnetic flux density in the airgap. The reluctance method is used to find the
magnetic flux density in (83). The reluctance method begins with Ampere’s law in integral form:
mmfNIdlH .
(84)
where ampere-turns NI or magnetomotive force are the input energy source, and magnetic field
intensity H and magnetic flux density B are to be found. In the case of softlanding mechanism,
the magnetomotive force comes from the permanent magnet. When a permanent magnet has a
length of ML1 and its magnetization direction is along its length, the mmf of the permanent
magnet is calculated from this:
1
0
MLB
mmf r
(85)
For the case of the magnetic latch shown in Figure 103, the closed-line integral of the
Ampere’s law is replaced by a summation
mmfNIlHk
kk
(86)
where k relates to the components in the magnetic field path. Since the reluctance of each
component can be calculated, (86) is replaced by
mmfk
k
(87)
The above equation is used to find the unknown magnetic flux.
k
k
mmf
(88)
Therefore the magnetic flux is calculated using
150
PMbasegapplategap
k
k
mmfmmf
2_1_
(89)
where 1_gap ,
plate , 2_gap ,
PM , and base are given as:
gg
gap
gapA
g
A
gl
0
1
0
1_
1_
)(
(90)
gg
gap
gapA
g
A
gl
0
2
0
2_
2_
)(
(91)
pppp
plate
plateA
PLPLPL
A
l
321
(92)
basebasebasebase
base
baseA
BLBLBL
A
l
321
(93)
PMPMPMPM
PMPM
A
ML
A
l
(94)
Therefore, the magnetic flux is calculated in (95). Note that the magnetic flux is a
function of the length of the airgap and the position of the PSC.
PMbaseplategap
k
k g
mmfmmfg
2
(95)
With flux known, magnetic flux density in the airgap can be found using the following
g
g
gA
B
(96)
Substituting (90) to (94) in (95) and (96) and simplifying gives:
151
2
1
cg
cgB
(97)
where 1c and
2c are constants and are defined by:
PMbaseplate
gaprA
candMLB
c 22
0
21
1
(98)
Now that the magnetic flux density in the airgap is found, substituting (97) in the force
equation, (83), gives the magnetic latch force:
2
2
3)(cg
cgF gmag
(99)
where c3 is constants and is defined by:
0
2
13
2
Acc
(100)
Note that the force is inverse proportional to the square of the length of the airgap (g).
This means that the amount of magnetic latch force increases dramatically as the airgap reduces
as shown in Figure 104. Further, a 7th
order polynomial is fitted to the curve for modeling
purposes.
152
Figure 104: the modeled and fitted magnetic latch forces vs. The airgap (g)
0 2 4 6 8 10 12 14 16 18 20 220
20
40
60
80
100
120
140
160
180
200
position (mm)
For
ce (
N)
Magnet Force Vs. Position
Actual force
Fitted force
153
To sum up, the governing differential equations for the softlanding mechanism for the
PSAS are
XCXMFFFFFFF FrictionlowMagnetupMagnetlowSpringupSpringActuator ____
(101)
where the force of the springs are governed by Hook's law as shown in
kXFSpring
(102)
and the force of the actuator is governed by
iXKF factutaor )( (103)
where the current in the electromagnetic actuator is governed by
XXKdt
diLiRV b
)( (104)
and the magnetic latch force is governed by
22
3
cg
cF gmag
(105)
where c2 and c3 are constant defined in (98) and (100).
154
5.4 FINITE ELEMENT ANALYSIS AND GEOMETRY MAPPING OPTIMIZATION OF
THE MAGNETIC LATCH SYSTEM
The purpose of the magnetic latch is to latch the PSC and hold the high compression
force of the springs. It is therefore the design goal to generate the maximum latch force,
produced by magnetic circuit with minimum space. In order to achieve this design goal, a
systematic design procedure is required to optimize the latch force output with in the design
envelope.
Since the analytical methods for the force calculation, mentioned in the previous section,
are based on simplifications, they cannot be used for optimization purpose. Specifically, the
uniform distribution of magnetic flux density in the magnetic circuits is assumed, which leads to
inaccuracy for more complex geometry. Alternatively, Finite Element Analysis (FEA) method
provides more accurate results and is the more effective approach. In particular, ANSYS
Maxwell is the premier magnetic field simulation software for designing and analyzing 3-D and
2-D magnetic and electromechanical devices.
An FEA model is developed for the magnetic latch as shown in Figure 105 in Maxwell.
In order to achieve an optimization-oriented design, an accurate model of the latch is necessary.
However, the complete optimization of a magnetic latch, considering all design factors, is a great
challenge due to the complexity of the actual problem. The feasible methodology is to carefully
collect several factors as known parameters, and merely set the key factors as design variables
for meeting above-mentioned requirements. In particular, the maximum latch force, the profile of
the magnetic force, and the geometry of different components are optimized for the magnetic
latch design.
155
Further, geometry mapping optimization involves finding the optimized dimensions for
the components in the magnetic latch in order to meet the geometrical and performance
requirements. In particular, the thickness of steel plate, the size of the magnet, the diameter of
spring housing, the depth of spring housing, and the length of the base, shown Figure 105 must
be found. Each of these dimensions will influence the magnetic latch force. In particular, the
dimensions will influence c1, c2, and c3 which define the magnitude of the force generation as
shown in (99). This equation shows the amount of magnetic latch force. From this equation, it is
clear that in order to maximize the latch force c3 and c1 must be maximized.
Figure 105: The FEA model and the dimensions of the magnetic latch
156
Some of the dimensions for the magnetic latch and softlanding mechanism are based on
the geometric and volumetric constraints of the PSAS, as explained in section 1.3.2. Base on this
the width of the softlanding mechanism is the same as that of the actuator. Similarly the height of
the softlanding mechanism must be same as that of the actuator. Therefore, the remaining
geometric parameters such as the length of the base, thickness of the steel plate, the size of the
spring holes, and the magnet size must be optimized within the defined design envelope.
Figure 106 shows the closed loop magnetic flux path and vectors. The flux generated by
the magnet is passed through the airgap, the steel plate, and the base of the magnet. The
thickness of the steel plate plays an important role here. With a thick plate, the steel is not
magnetically saturated. It can hold all of the magnetic flux coming from the magnet. However, if
the steel plate is too thick, it won't make the pull force any stronger. When this is the case, there
is a very little magnetic field on the far side of the steel. On the other hand, if a very thin plate is
used, the steel may become magnetically saturated. This means that it can't hold the entire
magnet's flux, and the 100% of the pull force is not achieved. When this is the case, the magnetic
field goes behind the steel plate, because it isn't thick enough to shield it all. Figure 107 shows
the potential areas of the saturation. Base on this analysis, it is important to find the optimized
thickness of the steel plate. Figure 108 shows the magnetic latch force profile along the stroke
for different thicknesses of the steel plate. It is clear that the thickest plate, 3mm thick, produces
the largest amount of the force. Note that the magnetic latch force increases dramatically when
the airgap is very small. Also note that the force is very small as the PSC travels further. The
amount of force reaches zero at the neutral position. This characteristic of the magnetic latch is
much desired as it will work as planned with the compressed springs. Figure 109 illustrates the
maximum latch force when the airgap is zero.
157
Figure 106: Magnetic flux density lines in the softlanding mechanism
Figure 107: The magnetic flux contour for the softlanding mechanism
158
Figure 108: The magnetic latch force along the stroke for diffrenet thickness of the steel plate
Figure 109: The maximum latch force for different thicknesses of the steel plate
0
50
100
150
200
250
1 1.5 2 2.5 3
Max
imu
m la
tch
fo
rce
(N
)
Thickness of the steel plate (mm)
Maximum latch force
159
The strength of the permanent magnet defines the strength of the magnetic flux. It is
desired to select the strongest commercially available magnet for this purpose. The strongest
commercially available magnet is NdFeB N52 magnet, which will lead to the highest output
force. Figure 110 illustrates the maximum force that is generated by using different strengths of
neodymium magnets. It is clear that NdFeB N52 must be selected.
Figure 110: The effect of the strength of teh permanenet magnet on the maximum latch force
The volume of the permanent magnet and its length define the residual flux density of the
permanent magnet and the magnetomotive force as shown in (85). The larger the magnet
becomes the residual flux density increases and consequently the magnetomotive force increases.
Similarly, longer magnets provide more magnetomotive force. Therefore, it is the design goal to
select the largest commercially permanent magnet. However, it is necessary to accommodate the
two spring housing holes in the mating area of the magnetic latch.
110
115
120
125
130
135
140
145
150
N52 N42 N35
Max
imu
m la
tch
fo
rce
(N
)
160
Further, it is clear from Figure 106 that the length of the latch base is critical for the
closed loop magnetic path. If the length of the base is set to be very small, the latch base will be
magnetically saturated and there will be leakage of magnetic flux. Therefore, thick enough base
must be selected. Moreover, this part of the base is used for securing the magnetic latch to the
housing by bolts. Thus, there should be enough space to accommodate holes for the bolts. Figure
111 shows the effect of the length of the base on the force outcome. It is clear that the force does
not change much. Therefore, the length is selected that can fit the bolt holes and avoid saturation.
Moreover, the spring housing must be sized and optimized. As shown in Figure 105, the
spring housing holes must be placed in the contact area between the PSC and the magnetic latch.
Since there is enough space in the base for the magnetic flux lines to path, the size of the circle
does not affect the magnetic force considerably. Figure 112 shows the effect of the diameter of
the spring housing on the generated force. Similarly, it is important to investigate the effect of
the length of the spring housing on the magnetic latch force as shown in Figure 113. Once again
the length of the spring housing does not affect the magnetic force considerably.
161
Figure 111:The effect of the length of the latch base on the magnetic latch force
Figure 112: The effect of the diameter of the spring housing on the magnetic latch force
100
110
120
130
140
150
160
14 16 18 20
Max
imu
m la
tch
fo
rce
(N
)
Length of the magnetic latch base (mm)
Maximum force (N)
120
125
130
135
140
145
150
155
160
0 2 4 6 8 10
Max
imu
m la
tch
fo
rce
(N
)
Diameter of the spring housing
Magnetic latch force
162
Figure 113: The effect of the depth of the spring housing on the magnetic latch force
Table 8 indicates the dimensions of the optimized magnetic latch system, illustrated in
Figure 105. Further, Figure 114 shows the optimized magnetic latch force along the stroke for
the softlanding system. The maximum latch force is 148 Newtons. Further, an experimental
validation is needed to fully characterize of the magnetic latch.
144
146
148
150
152
154
156
158
160
0 2 4 6 8 10 12
Max
imu
m la
tch
fo
rce
(N
)
Depth of the spring housing (mm)
Maximum latch force
163
Table 8: Optimized geometrical values of the magnetic latch for the PSAS
Name Parameter Optimized value
Length of the latch base XLB 22 mm
Length of the latch magnet XLM 12.7 mm
Width of the latch base YLB 35 mm
Width of the latch magnet YLM 12.7 mm
Width of the steel plate YSP 35 mm
Thickness of the steel plate XSP 1.5 mm
Height of the latch base ZLB 12.7 mm
Height of the latch magnet ZLM 12.7 mm
Height of the steel plate ZSP 12.7 mm
Diameter of spring housing SH 8 mm
Depth of spring housing XSH 18 mm
Figure 114: The optimized force curve for the magnetic latch
-150
-100
-50
0
50
100
150
0 5 10 15 20
Latc
hin
g fo
rce
(N
)
Displacement (mm)
Magnetic latching force
164
5.5 SYSTEM MODELING AND SIMULATION OF THE PSAS
The combination of the electromagnetic actuator and the softlanding mechanism for the
PSAS is a complete mechatronics system, consisting of several subsystems such as mechanical
springs, electromagnetic actuator, magnetic latches, power control electronics, and position
controller. Each of these subsystems are modeled and simulated in order to facilitate the design
and development phases. MATLAB and SIMULINK simulation environments are used to model
the PSAS. Figure 115 illustrates the entire PSAS model in SIMULINK environment. Modeling
techniques and simulations for each of these subsystems are explained in details in the following
sections. It is necessary to drive simulation models of the PSAS in order to analysis the
performance of the PSAS and implement the position control and softlanding strategies.
Figure 115: The SIMULINK simulation model of the new PSAS in the SSIPTS
The mechanical subsystem of the PSAS is mainly referred to the moving components of
the actuation system. It consists of a pulley segment composite, a connecting shaft, the
electromagnetic actuator moving coil, and the springs in the softlanding mechanism. The
mechanical subsystem of the PSAS is modeled as an equivalent mass-damper subsystem similar
to Figure 40. The mechanical subsystem of the PSAS is modeled in SIMULINK using four built
in modules shown in Figure 116. The mass module indicates the mass and origin of the movable
pieces. The transitional friction module models dynamic dry friction forces and damping force. The
165
transitional spring module models the springs in the softlanding mechanism. Lastly, transitional hard stop
models the impact force due to hard stop nonlinearity.
The force subsystem of the PSAS defines the forces applied to the pulley segment
composite as shown in Figure 117. The magnetic latch modules govern the force per stroke
characteristic of the magnetic latches. The force function shown in Figure 114 is mapped and
used for this module. The electromagnetic actuator module embodies the entire actuation system
shown in section 3.5. The identical electromagnetic actuator model shown in section 3.5 is
implemented as the actuator in the softlanding mechanism. Further, a very similar system
modeling for the power control subsystem shown in section 3.5 is used. Lastly, the position
control subsystem, including the microcontroller and sensor shown in section 3.5 is used for the
softlanding mechanism. These forces are all added and are fed through an ideal force source
which is used to model the applied force on the mechanical subsystem.
166
Figure 116: The SIMULINK model of the mechanical subsystem for the PSAS
Figure 117: The force subsystem of the PSAS
2
P
1
Force R C
Translational Spring
R C
Translational Hard
Stop
R C
Translational
Friction
Mechanical
Translational
Reference3
Mechanical
Translational
Reference2
Mechanical
Translational
Reference1
Mass1
167
The PSAS model is further used to implement the position control and softlanding
strategies. The aim is to improve the performance of the PSAS. However, meeting the
softlanding requirement is still a very challenging problem for the PSAS. The difficulty in
achieving softlanding stems from several factors:
Requirements for low landing velocity ( vcontact < 0.2 m/sec at 1500 rpm)
Requirements for fast transition times (T < 12 ms)
Highly nonlinear magnetic force characteristics
Limited range of actuator authority
Availability of commercial springs for this application
The modified position control and softlanding strategies are simulated and implemented
in the SIMULINK environment. The main purpose of the simulation model is to achieve the
performance requirements of the PSAS. The simulation results are explained in details below.
Figure 118 illustrates the simulated magnetic latch force for one latch. For the simplicity
of the computation, a 7th
order polynomial is also curve fitted to the force. It is clear that the
polynomial represents the magnetic force accurately. Figure 119 shows the two opposing forces:
the magnetic latch force and the spring force. Note that as it is required by the operation principle
of the softlanding mechanism, the magnetic latch force is higher that the compression force of
the spring when the airgap is zero. This validates the fact that the PSC is latched by a holding
force. As the PSC travels farther from the latch position the magnetic latch force drops
considerably while the spring force drops linearly. This fact allows the springs to boost power
168
and speed in the PSC. Further, note that the area between the magnetic latch force and the spring
force represents the energy used to accelerate the PSC.
Figure 120 shows the applied voltage and current to the electromagnetic actuator. The
actuator control strategy is based on applying PWM voltages for the transient and the steady
state performance. During the transient stage, the actuation system requires a high acceleration
force to overcome the holding force and to achieve a very fast PSC motion. This is done by
applying a higher voltage than the nominal rated voltage for a very short period of time. This
PWM voltage signal produces a boost current to accelerate the pulley segment. The PWM driver
applies a positive voltage pulse to accelerate the PSC for the time period ‘t1’. After this time, the
PWM driver switches its voltage polarity and applies a negative voltage pulse to decelerate the
PSC for the time period ‘t2’ to slow down the PSC. For the details of this operation, refer to
section 3.6 as the control strategy is very similar to that of the actuator itself. Note that the
deceleration phase of the electromagnetic actuator is shortened. This is due to the fact that if the
PSC decelerate all the way to the end of the stroke, the PSC will not be latched at the end.
Further, note that due to the inductive nature of the electromagnetic actuator, the current always
lags the voltage and consequently the force lags as well. This fact overcomplicates the control
strategy of the electromagnetic actuator as well.
169
Figure 118: The modeled and the fitted magnetic latch forces vs. The position of the PSC
Figure 119: The simulated magnetic latch force and the simulated spring force
0 2 4 6 8 10 12 14 16 18 20 220
20
40
60
80
100
120
140
160
180
200
position (mm)
Forc
e (
N)
Magnet Force Vs. Position
Actual force
Fitted force
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
140
160
180
position (mm)
For
ce (
N)
Forces Vs. Position
spring force
m1 force
170
Figure 120: The simulated applied voltage and the current for the electromagnetic actuator
Figure 121 shows all the applied forces: the two magnetic latch forces, the spring force,
and electromagnetic actuator force. These forces are applied along the stroke as shown. The
force characteristics are as desired. Note that except the electromagnetic actuator force, all the
forces are symmetric with respect to the middle point of the stroke. This validates the principle
of operation of the softlanding mechanism. Further, Figure 122 show the summation of the
forces applied to the PSC with respect to time and along the stroke. Note that base on the
conservation of energy, in order to softland the area under the force vs position curve must add to
zero. This means that the amount of energy given to the PSC to accelerate is taken away from it
during the deceleration phase. Therefore, it will softland.
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014-300
-200
-100
0
100
200
Time (msec)
Voltage (
Volt)
Voltage Vs. Time
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014-30
-20
-10
0
10
20
Time (msec)
Curr
ent
(Volt)
Current Vs. Time
Voltage
Current
171
Finally, Figure 123 shows the simulated position and velocity trajectories for the PSAS.
The PSC reaches the end of 20 mm stroke in 10.5 msec. This is substantial improvement
compared to actuator only scenario. Further, the PSC is softlanded at the end by very small
contact velocity. Therefore, these simulation results validate the principle of the operation of the
softlanding mechanism and indicate substantial improvement in meeting the design requirements
of the PSAS. Experimental validation is required to test the performance of the softlanding
mechanism and claimed improvements.
Figure 121: All the applied forces on the PSC
-10 -5 0 5 10
-150
-100
-50
0
50
100
150
position (mm)
Forc
e (
N)
Forces Vs. Position
spring force
m1 force
m2 force
actuator force
172
Figure 122: The simulated applied force with respect to time and postion
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014-200
-100
0
100
200
Time (msec)
Forc
e (
N)
Force Vs. Time
-10 -5 0 5 10
-100
-50
0
50
100
Position (mm)
Forc
e (
N)
Force Vs. Position
Force
Position
173
Figure 123: The simulated position and velocity trajectories for the PSAS
174
5.6 FABRICATION AND PROTOTYPING OF THE SOFTLANDING MECHANISM
The fabrication and prototyping procedures of the softlanding mechanism are highly
dependent on feasible manufacturability methods and the choice of materials. This includes
machining the pulley segment composite, the latch base, and the connecting rod, as well as
selecting the proper permanent magnets and springs. Note that the cost effectiveness is an
important decision-making factor since the actuator itself is expensive. The manufacturing
process in prototyping is essential since a careless manufacturing process results in the loss of
the integrity of magnetic properties. For instance, the inevitable temperature rise in the
machining process is harmful to both the hard and soft magnetic materials. Moreover, the high
stress and strain in the machining procedure must be avoided. The high stress leads to micro-
cracks in hard magnetic materials and high strain arouses the microstructure change in soft
magnetic materials [40]. Figure 124 shows the model of the prototype for the softlanding
mechanism.
Figure 124: The model of the prototype for the softlanding mechanism
175
5.6.1 Fabrication and Selection of the Softlanding Mechanism Components
The pulley segment composite (PSC), the latch bases, and the connecting rod must be
prototyped for the softlanding mechanism assembly. The exact moving coil actuator described in
chapter 3 is used for the softlanding mechanism for the PSAS as shown in Figure 125. Further,
the proper permanent magnet and springs must be selected.
The permanent magnet is made by rare-earth Nb2Fe14B for its high permanence, high
coercive force, and high energy product. Figure 126 show the specification of the permanent
magnet selected for the softlanding mechanism. It is very important to clean the connecting
surface and assure that there is no airgap and dust particles between the magnet and the latch
base. Further, after alignment, the magnets and the latch bases are glued to each other for
integrity. Also, note that the magnet has a center hole which provides a guide for the connecting
rod. The diameter of the connecting rod is selected in such a way that there is no substantial
friction between the rod and the hole.
Moreover, the operating temperature affects the magnetic performance of the permanent
magnet as shown in Figure 127. The temperature sensitivity of the permanent magnetic requires
two important considerations for the softlanding mechanism. Firstly, it is not recommended to
machine and modify the permanent magnets as the mechanical stress during machining processes
leads to losing the magnetic integrity of the permanent magnet. Secondly, it is important to note
that the heat generated by the coil heats up the magnet and leads to reduction in the magnetic
field generation. Then, the magnetic latch does not operate as designed. Therefore, it is important
to avoid excessive heating during the operation of the softlanding mechanism.
176
Figure 125: The moving coil actuator used for the softlanding mechanism for the PSAS
Figure 126: The permanent magnet for the softlanding mechanism for the PSAS
177
Figure 127: The permanent neodymium magnet demagnetization curves for grade N52 [76]
The magnetic latch bases are made from soft iron because of a relatively high
permeability and off-the-shelf availability. Figure 128 shows the magnetic latch assemblies for
the softlanding mechanism. Note that as the bases provide the most part of the magnetic paths in
the latch, its integrity and uniformity is very important. The integrity of magnetic circuits is
defined as the rate of consistency of the properties of the actual magnetic circuit compared with
the circuit in theoretical or simulated situations. It is coherently corresponding to the connecting
status of the members in the magnetic circuit. Any disconnection or improper connections will
apparently influence the integrity of the magnetic circuits. Therefore, the magnetic latch base is
made out of one piece. A proper milling machining is used to produce the cavity inside the base
for the magnet. However, note that due to the press fit interference, the process of milling must
178
be done very carefully. Further, the radii of the spring housings must be machined very carefully.
Further, two installation holes are machined at the base of the magnetic latch. These holes are
used to secure the magnetic latch.
Figure 128: the magnetic latch assemblies for the softlanding mechanism
The pulley segment composite is made of aluminum block and two steel plates. A very
special structural adhesive is used to attach the steel plates to the aluminum pulley segment. For
experimentation purpose, three sets of PSC with different thicknesses for the steel plates are
prototyped. Further, a center hole is made in the composite for the connecting rod. Note that
unlike other holes, this hole must be threaded to transfer all forces to the pulley segment
composite. For eliminating backlash and better mechanical integrity, the connecting rod and the
PSC are glued as well.
The selection of proper springs is actually a challenging step. Firstly, the outer diameter
of the spring must be smaller than the spring housing diameter in the magnetic latch. Secondly,
the uncompressed length of the springs must not be longer than the depth of the spring housing
and the engaging length of the spring. Thirdly, it is very important to select a stainless steel
springs as it is not magnetic. Lastly, the springs force constant must be selected in such a way
179
that the spring force curve matches the magnetic latch force as explained in the operational
principle of the softlanding mechanism. In particular, the amount of allowed deflection must
match the magnetic latch force curve.
Moreover, it is very important to calibrate the springs and find the accurate force
constants. Next the springs must be tested for durability and reliability. In particular, it is
possible for a spring to lose its stiffness and decrease its force constant.
5.6.2 Final prototype of the Softlanding Mechanism
Figure 129 shows the assembled softlanding mechanism and Figure 130 shows the entire
PSAS assembly within a guide rail. There are few engineering considerations for assembling the
final prototype of the softlanding mechanism and the PSAS:
It is very important to remove all the dust and metal particles from the magnetic
latches. In particular, if there are dust and metal particles between the magnet and
the latch base it will result in a reduction in the magnetic latch force.
The proper alignment of the connecting rod plays a critical role. The connecting
rod has fittings with the moving coil, magnetic latches, permanent magnets, and
the PSC. It is very important that these components are aligned in such a way that
the PSC and the moving coil can freely travel along the stroke with minimal
friction.
In order to minimize the divergence of the magnetic field, it is critical to use non-
magnetic fasteners. Stainless steels bolts and screws are used for assembling the
softlanding mechanism and the PSAS.
180
Figure 129: The assembled prototype of the softlanding mechanism
Figure 130: The entire PSAS assembly within a guide rail
181
5.7 EXPERIMENTATIONS
This section explains the design and the development of experimental setups, used to
characterize and to test the performance of the softlanding mechanism and the PSAS.
5.7.1 Static Force Test Setup for the Springs and the Magnetic Latch Systems
This section explains the design and development of the static force test setup, used to
characterize and to test the static performance of the magnetic latch system and mechanical
springs for the PSAS. The purpose of this test setup is to characterize the softlanding mechanism
and measure the followings:
Nonlinear magnetic latch force along the stroke of the softlanding mechanism.
Calibrate the mechanical springs
Validate the applied force outcome of the softlanding mechanism
In this test set up, the PSC is maintained steady while measuring the force acting on it.
Figure 131 shows the mechanical subsystem, which includes a force gauge, a connecting rod, a
sliding rail, and a set of softlanding mechanism. This test setup is designed in such a way that the
airgap between the PSC and the magnetic latch can be incrementally change by rotating two
threaded rods. At each discrete position along the stroke of the softlanding mechanism, the
applied force is measured. Figure 132 shows the experimental magnetic latch force with respect
to the airgap. The experiment was conducted two times for repeatability purposes. The overall
shape of the curve is very similar with that of simulation. However, note that the amount of
maximum latch force is decreased considerably. This is due to some experimental errors such as
magnetic leakages and imperfection in the shape of the components. Also, it was not possible to
182
achieve perfect zero airgap due to the dust and contact area imperfection. Figure 133 illustrates
the combination of the magnetic latch force and the compression force of the springs. Each curve
corresponds to a certain compression level of the springs.
Moreover, same test setup is used to characterize the mechanical springs and find the
spring constants. For this procedure the springs are compressed with discrete forces and the
amount of deflections are collected. The linear curve fitting is further used to find the force
constants for the mechanical springs. Figure 134 shows the calibration data for four springs used
in the softlanding mechanism.
Figure 131: The static force test setup for the softlanding mechanism
183
Figure 132: The magnetic latch force along the stroke of the softlanding mechanism
Figure 133:The magnetic latch and spring forces along the stroke of the softlaning mechanism
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6
Att
ract
ion
fo
rce
(N
)
Airgap (mm)
Magnetic latching force
Experiment 1
Experiment 2
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
0 1 2 3 4 5
Spri
ng
forc
e +
latc
hin
g fo
rce
Air gap (mm)
Summation of latching and spring forces
4 mm spring engagement-1
4 mm spring engagement-2
5 mm spring engagement-1
5 mm spring engagement-2
6 mm spring engagement-1
6 mm spring engagement-2
184
Figure 134: The spring calibration forces and the compression amount
y = 0.1462x - 0.1196
y = 0.1457x + 0.4739
y = 0.1114x - 0.265
y = 0.1319x + 0.3557
-2
0
2
4
6
8
10
0 10 20 30 40 50 60
De
form
atio
n (
mm
)
Pushing force (newton)
Spring forces
S1
S2
s3
s4
Linear (S1)
Linear (S2)
Linear (s3)
Linear (s4)
185
5.7.2 Position control test setup for the PSAS
This section explains the design and development of the position control test setup, used
to characterize and to test the control strategies for the softlanding mechanism. It consists of four
subsystems: mechanical, H-bridge and PWM, microcontroller, and data acquisition subsystems.
The purpose of this test set up is to experiment the performance of the position control and
softlanding strategies. To be specific, the position control for PSC and softlanding results from
the simulation are verified experimentally using this test setup. Except the mechanical subsystem
all other subsystems are identical to those of position control test setup for PSAS explained in
section 4.2.
Figure 135 shows the mechanical subsystem of the position control test setup for the
softlanding mechanism. All the components of the softlanding mechanism and the
electromagnetic actuator are connected through rod that is further connected to the LVDT for
sensing the position.
Figure 135: The mechanical subsystem of the position control test setup for the
softlanding mechanism
186
Figure 136 shows the experimental results for the position control and softlanding
measurements in the LABVIEW environment. In particular, it includes the position and the
velocity profiles, the acceleration, as well as the current and the PWM command to the driver.
By implementing the position control and softlanding strategies, the softlanding mechanism was
able to place the pulley segment at desired (S=20 mm) in 14 msec. Moreover, the pulley segment
is softlanded at the desired location with a very smaller landing velocity (Vlanding ≈ 0.24 m/sec).
The PSC is further latched at desired place by the holding force.
The position and velocity profiles in Figure 136 follow the desired motion profiles,
shown in Figure 7 and Figure 8. The experimental results show that the softlanding mechanism
was able to improve the performance of the PSAS. In particular, the performance requirements
of the position control and softlanding are improved compared to those of the electromagnetic
actuator explained in section 4.4. Moreover, the PSC is latched by a force Fhold ≈ 8 newtons,
which exceeds the design requirements. Lastly, the actuator power consumption is reduced
considerably which means that the power requirement of the actuator is reduced. To sum up, the
combination of the electromagnetic actuator and the softlanding mechanism improved the
performance of the PSAS and reduced the power consumption.
187
Figure 136: The experimental results for the softlanding mechanism in the LABVIEW environment
188
5.8 SUMMARY
This chapter presented a new combination of the electromagnetic actuator and the
softlanding mechanism as an ultra fast bistable actuation system for the PSAS. Experimental
results in Chapter 3 indicate that the proposed the electromagnetic actuator was not able to meet
all the design requirements of the PSAS. Therefore, to improve the performance of the PSAS and
to meet all of the design requirements, a softlanding mechanism is introduced. The design and
modeling of the softlanding mechanism was performed and optimization was conducted to
achieve optimal softlanding mechanism and the magnetic latches. Further, the prototype of the
proposed softlanding mechanism was built and experiments were conducted for the application
of the SSIPTS. It is shown from experimental results that the prototype of the softlanding
mechanism for the PSAS meets most of the design requirements and is feasible for
implementation in the SSIPTS. In particular, the performance of the PSAS with regards to
the fast transient requirement of the PSAS,
the softlanding requirement of the PSAS,
the necessary latching force, and
the electrical power requirement for the PSAS
were improved by adding the softlanding mechanism. Therefore, from this chapter the following
conclusions are summarized:
The prototype of the PSAS provides bi-directional actuation for the stroke of
S=20 mm.
189
The optimized softlanding mechanism is within the design envelope and meets
the geometrical constraints of the SSIPTS application.
The prototype of the softlanding mechanism improves the dynamic performance
requirements of the SSIPTS. In particular, the PSAS is able to place the pulley
segment at the desired location in 14 msec, and the pulley segment is softlanded at
the desired location with a very small landing velocity of 0.24 m/sec. It is clear
that they duration of the actuation is 2 msec longer than the required time. These
dynamic performances are considerably more desired compared to those of the
electromagnetic actuator explained in section 4.4.
Since most of the actuation force drives from the springs and kinetic energy is
stored during the operation of the softlanding mechanism, the electromagnetic
actuator does not need to consume large amount of electrical power. This leads to
a reduction in electrical power consumption of the electromagnetic actuator.
The magnetic latches provide a holding force to securely place the pulley
segments at the desired position.
The prototype of the PSAS costs 480$ which is higher than the required
economical pricing.
190
CHAPTER 6: CONCLUSIONS AND FUTURE WORKS
6.1 SUMMARY
This Ph.D. thesis presents the design, modeling, optimization, prototyping, and
experimental methodologies for the novel actuation system for the synchronized segmentally
interchanging pulley transmission system (SSIPTS). As a major subsystem of the SSIPTS, the
Pulley Segment Actuation System (PSAS) plays a critical role in the SSIPTS operation and
success. However, the overall design of the SSIPTS and its operation principle introduce very
challenging and conflicting design requirements for PSASs that the existing actuation
technologies cannot meet. To address the lack of actuation technologies for the PSAS
application, this research proposes a unique actuation system that meets all the challenging
design requirements of the PSAS.
The main contribution of this thesis is to develop highly efficient and reliable ultra fast
bi-stable actuation system for the PSAS for the SSIPTS. In the Ph.D. research, prototypes of the
PSAS were designed and developed. Further, the prototypes were tested for applications.
Significant level of design, modeling, and considerable experimentation were required to
develop the prototypes. The following contributions of this research were made:
A thorough literature review and state of art survey for mechanical variable speed
drives and transmission systems used in the automotive, the power generation,
and the HVAC industries were conducted. These were followed by the
introduction of the SSIPTS and its technical benefits and applications.
191
After introducing the SSIPTS, a thorough analysis was performed to determine
the overall design and operation principle of the SSIPTS. The unique nature of the
SSIPTS requires careful attention. Further, as a major subsystem of the SSIPTS,
the pulley segment actuation system was introduced and its critical role in the
SSIPTS operation was defined.
After assessing the PSAS critical role and its operation, a thorough analyse of all
the design requirements for the PSAS was conducted. It was then vital to conduct
the prior state of the art review and literature survey on actuation technologies
that have similar design requirements as the PSAS in order to realize the viable
options. Based on the surveys and the actuation system performance
requirements, it was concluded that the electromagnetic actuation technology is
the best candidate for the PSAS. However, none of the available electromagnetic
actuation technologies can meet all the design requirements of the SSIPTS.
Thus, a novel electromagnetic actuation technology was proposed for the PSAS.
This was followed by performing conceptual design and building a simulation
model for the PSAS. A geometry mapping optimization of the electromagnetic
actuator was performed to achieve the optimized design of the moving coil
actuator.
The actuation motion for the PSAS is very challenging and conflicting. Proper
position control and softlanding strategies were designed and developed to
achieve the challenging fast transient and softlanding requirements of the PSAS.
192
The prototype of the electromagnetic PSAS was then fabricated. The
experimental setups were further designed to characterize the actuation
technology and to test the performance of the PSAS. It is shown from
experimental results that the prototype of the actuation system meets most of the
design requirements and is feasible for implementation in the SSIPTS.
Experimental results for the prototype of the electromagnetic actuator indicate
that the proposed the electromagnetic actuator was not able to meet all the design
requirements of the PSAS. Therefore, to improve the performance of the PSAS
and to meet all of the design requirements, a softlanding mechanism is introduced.
The design and modeling of the softlanding mechanism was performed and
optimization was conducted to achieve optimal softlanding mechanism and the
magnetic latches. Further, the prototype of the proposed softlanding mechanism
was built and experiments were conducted for the application of the SSIPTS. It is
shown from experimental results that the prototype of the softlanding mechanism
for the PSAS was able to improve the performance of the PSAS substantially.
The following table compares the performances of the electromagnetic actuator and the
softlanding mechanism with respect to the design considerations and the requirements of the
PSAS for the SSIPTS application.
193
Table 9: Comparison between the performance of the electromagnetic actuator and the softlanding
mechanism for the PSAS for the SSIPTS application
Design considerations Electromagnetic actuator Softlanding mechanism
Bi-directional actuation Yes Yes
Stroke of the actuation S=20 mm S=20 mm
Geometrical constraints, length 47 mm 86 mm
Geometrical constraints, width 25.4 mm 25.4 mm
Geometrical constraints, height 12.7 mm 12.7 mm
Maximum applied force Fmax ≈ 33 Newtons Fmax ≈ 69 Newtons
Fast transient requirement T ≈ 17 msec T ≈ 14 msec
Softlanding, vcontact < 0.2 m/sec
vcontact < 0.3 m/sec vcontact < 0.24 m/sec
Holding force
Fhold ≈ 5 Newtons Fhold ≈ 8 Newtons
Economical pricing per PSAS
390$ 480$
Power consumption 2000 W 605 W
Mechanical complexity Not complex Complex
Simple control characteristics
Yes Yes
Reliability High High
Maintenance Low Medium
As an ultra fast bistable actuation system, both the electromagnetic actuator and the
softlanding mechanism have many advantages over other types of actuation systems: higher load
capacity, smaller dimensions, and good controllability. These performance characteristics make
it an excellent candidate in applications requiring fast transient response, high precision, and
high load capacity.
194
6.2 FUTURE WORK
The results of this thesis can be extended and enhanced in the following ways:
Use of a nonlinear spring. Nonlinear springs enhance the performance of many
applications. A nonlinear spring has a nonlinear relationship between force and
displacement. The spring stiffness value varies along the length of the spring.
Therefore, a graph showing force vs. displacement for a nonlinear spring will be
nonlinear with a changing slope. The spring’s load-range, displacement-range,
and nonlinear behavior must be matched with the nonlinear magnetic latch force.
By using a nonlinear spring for the softlanding mechanism, the amount of energy
stored in the compressed spring is higher, which leads to faster acceleration and
deceleration.
Coating of permalloy for the PSC: Permalloy is an alloy of nickel and iron. It is
a soft magnetic alloy with exceptionally high magnetic permeability. Commercial
permalloy alloys typically have relative permeability of around 100,000,
compared to several thousand for ordinary steel. In order to reduce PSC weight
and avoid problem with producing a composite, it is possible to coat permalloy
instead of attaching steel plates. Since the permeability of the permalloy is
substantially higher than the steel, much thinner composite can be made.
Cost reduction for the PSAS: As indicated in the conclusion section of the
softlanding mechanism, the prototype of the PSAS is more expensive that the
budget. Therefore, it is required to investigate methods of reducing costs. In
195
particular, the fabrication cost can be reduced. Moreover, in case of large quantity
order, the price of the permanent magnets will be reduced dramatically.
Applying an anti-rust coating: It is important to protect the soft iron material
such as the orientor, the actuator shell, and the magnetic latch bases. These
components will rust over the time as the humidity in the air can be high. It is
strongly recommended to apply an anti-rust coating on all the soft iron material.
However, note that the coating must not increase the thickness of the components
when there are tight interferences.
Installation of the PSASs in the SSIPTS: It is necessary to integrate the PSAS
prototypes into the SSIPTS prototype and test for applications. The performance
of the proposed PSAS will be further validated in the real application.
196
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APPENDIX A: ENGINEERING DRAWINGS FOR THE
ELECTROMAGNETIC ACTUATOR
205
206
207
208
209
APPENDIX B: ENGINEERING DRAWINGS FOR THE STATIC
FORCE TEST SETUP
210
211
212
213
214
215
APPENDIX C: ENGINEERING DRAWINGS FOR THE
SOFTLANDING MECHANISM
216
217
218
219
220
221
APPENDIX D: DATA SHEET FOR THE ANALOG SERVO
DRIVE
222
223
224
APPENDIX E: DATA SHEET FOR THE FORCE SENSOR
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226
APPENDIX F: DATA SHEET FOR THE LVDT SENSOR
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