AN ABSTRACT OF THE THESIS OF
Steven George Ernst for the degree of Master of Science in
Electrical Engineering and Computer Science presented on May 22, 2009.
Title: A Novel Linear Generator for Wave Energy Applications
Abstract approved:
Ted K. Brekken
With the increasing effort to identify alternative methods of energy generation, extraction
of ocean energy has gathered a large interest. Research and industry have begun
considering wave energy as the next new alternative energy. The unique challenges of
ocean energy requires a wave energy converter to be both robust and efficient. When
looking further into energy extraction via the point absorber technology, a direct drive
linear generator efficiently converts the vertical wave motion into electrical energy. With
considerations of long term reliability in an ocean environment as well as design to
product cost, a longitudinal flux variable reluctance permanent magnet generator is a
promising generator topology. This thesis identifies the reasons behind the selection of
this particular generator topology for a point absorber. It provides a description of the
generator topology and operation before continuing with the details as to the development
of a variable reluctance permanent magnet generator with specifically known design
constraints. The thesis further describes the implementation, testing, and results of such a
device, while touching on considerations to take into account throughout the design
process.
© Copyright by Steven George Ernst
May 22, 2009
All Rights Reserved
A Novel Linear Generator for Wave Energy Applications
by
Steven George Ernst
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Presented May 22, 2009
Commencement June 2009
Master of Science thesis of Steven George Ernst presented on May 22, 2009.
APPROVED:
Major Professor, representing Electrical Engineering and Computer Science
Director of the School of Electrical Engineering and Computer Science
Dean of the Graduate School
I understand that my thesis will become part of the permanent collection of Oregon State
University libraries. My signature below authorizes release of my thesis to any reader
upon request.
Steven George Ernst, Author
ACKNOWLEDGEMENTS
My time at Oregon State has exposed me to a world of opportunities I normally would
not have thought possible. Taking on an active role in the emerging technologies of wave
energy was truly an enjoyable and unforgettable experience. I feel fortunate to have
worked with Dr. Ted Brekken and Dr. Annette von Jouanne for the past years as their
wealth of knowledge and passion has provided me with considerable support and
guidance. Thank you.
My thanks go out to the addition members of my committee, Dr. Huaping Liu and Dr.
Henri Jansen. I would like to express sincere appreciation for the additional support of
such distinguished members of Oregon State’s faculty.
The design of the 100 W linear generator was accomplished due to the collaboration with
an additional research assistant, Zuan (John) Yen. My gratitude goes out to you for your
contributions. Your curiosity throughout the process lead toward innovate solutions.
Finally, my father has been my pillar of encouragement throughout my life. As someone
that I have always looked up to, I am proud to have his support throughout my
accomplishments.
TABLE OF CONTENTS
Page
1
2
3
4
Introduction
1
1.1
Ocean Energy Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Wave Energy Advantages . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Wave Energy Technologies . . . . . . . . . . . . . . . . . . . . . . .
1
3
4
1.2
Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 OSU Wave Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Linear Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
8
10
Generator Overview
11
2.1
Generator Topology Selection . . . . . . . . . . . . . . . . . . . . . . . . . .
12
2.2
Unique VRPM properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
Design
17
3.1
Novel Longitudinal Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
3.2
Identify Design Parameters . . . . . . . . .
3.2.1 Input Variations . . . . . . . . . . .
3.2.2 Mechanical Clearance and Air Gap
3.2.3 Construction Constraints . . . . . .
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22
23
24
25
3.3
Permanent Magnet Selection . . . . . .
3.3.1 Magnetic Material . . . . . . . .
3.3.2 Permanent Magnet Grade . . . .
3.3.3 Defining Magnetic Requirements
3.3.4 Magnet Geometry . . . . . . . .
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27
28
31
32
34
3.4
Additional Magnetic Dimensions . . . . . . . .
3.4.1 Stator and Rotor Geometry . . . . . . .
3.4.2 Flux Density and Saturation . . . . . .
3.4.3 Windings . . . . . . . . . . . . . . . . .
3.4.4 Reluctance and Inductance Calculations
3.4.5 Cogging Torque . . . . . . . . . . . . .
3.4.6 Adjustable Frequency . . . . . . . . . .
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41
41
44
45
48
56
60
Modeling and Simulation
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63
TABLE OF CONTENTS (Continued)
Page
5
100 W Hardware Build and Testing Equipment
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70
5.1
Development of Windings . . . .
5.1.1 Winding the Coils . . . .
5.1.2 Coil Tension . . . . . . .
5.1.3 Polyepoxide Application .
5.1.4 Vacuum Sealing Chamber
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70
70
72
73
74
5.2
Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
5.3
Assembly Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
5.4
Integration to the LTB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Stator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
80
87
5.5
Testing Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
6
Experimental Results
96
7
Conclusion
98
7.1
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
Bibliography
100
Appendices
103
LIST OF FIGURES
Figure
Page
1.1
Orbital Pattern of a Wave Particle . . . . . . . . . . . . . . . . . . . . . . .
3
1.2
Seasonal Variation of Wave Potential [1] . . . . . . . . . . . . . . . . . . . .
4
1.3
Wave Energy Converting Technologies . . . . . . . . . . . . . . . . . . . . .
6
1.4
Additional Wave Energy Converting Technologies . . . . . . . . . . . . . . .
7
2.1
Longitudinal Flux Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
3.1
Cylindrical Equivalent of a 1 phase Stator . . . . . . . . . . . . . . . . . . .
18
3.2
Cylindrical Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
3.3
Power Generated for Various Mechanical Clearances . . . . . . . . . . . . .
24
3.4
Real vs. Reactive Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
3.5
Power Factor at Various Mechanical Clearances . . . . . . . . . . . . . . . .
26
3.6
Generic B-H Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
3.7
PM, Stator, and Rotor Dimensions . . . . . . . . . . . . . . . . . . . . . . .
29
3.8
Minimum Shear Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.9
Power Factor and Shear Stress Crossover Point . . . . . . . . . . . . . . . .
38
3.10 Minimal vs. Produced Shear Stress . . . . . . . . . . . . . . . . . . . . . . .
40
3.11 Stator and Rotor Sizing Dimensions . . . . . . . . . . . . . . . . . . . . . .
42
3.12 Sectionally Equivalent Components of a Flux Path . . . . . . . . . . . . . .
53
3.13 Equivalent Magnetic Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.14 Equivalent Electrical Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3.15 Full Period and Half Period Spacing of the Stator Endpoints . . . . . . . .
58
3.16 Typical and Improved Single Phase Cogging Force . . . . . . . . . . . . . .
59
3.17 Absolute and RMS Values of the Single Phase Cogging Force . . . . . . . .
60
3.18 Frequency Modified Stator and Rotor Dimensions . . . . . . . . . . . . . . .
62
LIST OF FIGURES (Continued)
Page
Figure
4.1
Current Generated given Flux and Position . . . . . . . . . . . . . . . . . .
65
4.2
Generated Force given Current and Position . . . . . . . . . . . . . . . . . .
66
4.3
Radial Simulation Represented as Two-Dimensions . . . . . . . . . . . . . .
67
4.4
Three Phase Simulink Schematic . . . . . . . . . . . . . . . . . . . . . . . .
68
5.1
Winding Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
5.2
Windings with High Tension (Left) and Appropriate Tension (Right) . . . .
72
5.3
Epoxy Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
5.4
Typical Windings without a Vacuum Seal Method . . . . . . . . . . . . . .
75
5.5
Windings with a Partial Vacuum Seal Method . . . . . . . . . . . . . . . . .
76
5.6
Visual of Overlapping Laminations . . . . . . . . . . . . . . . . . . . . . . .
79
5.7
Isometric View of the 3-Phase 100 W Generator
. . . . . . . . . . . . . . .
80
5.8
Front and Top Views of the 3-Phase 100 W Generator . . . . . . . . . . . .
81
5.9
Isometric and Front Views of a 1-Phase 100 W Stator . . . . . . . . . . . .
82
5.10 Top and Side Views of a 1-Phase 100 W Stator . . . . . . . . . . . . . . . .
84
5.11 Isometric View of the 3-Phase 100 W Stator . . . . . . . . . . . . . . . . . .
85
5.12 Front View of the 3-Phase 100 W Stator . . . . . . . . . . . . . . . . . . . .
85
5.13 Top View of the 3-Phase 100 W Stator . . . . . . . . . . . . . . . . . . . . .
86
5.14 Side View of the 3-Phase 100 W Stator
. . . . . . . . . . . . . . . . . . . .
86
5.15 Phase Separation and Permanent Magnet Orientation . . . . . . . . . . . .
88
5.16 Isometric and Front Views of the 3-Phase 100 W Rotor . . . . . . . . . . .
89
5.17 Top and Side Views of the 3-Phase 100 W Rotor . . . . . . . . . . . . . . .
90
5.18 Three-phase Converter for Power Generation . . . . . . . . . . . . . . . . .
91
5.19 Sectional Equivalent of a 3-Phase 100 W Linear Generator . . . . . . . . . .
92
LIST OF FIGURES (Continued)
Figure
Page
5.20 Rotor Lamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
5.21 Linear Test Bed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
5.22 CAD viewing of the LTB . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
LIST OF TABLES
Table
Page
1.1
100 W Hardware Prototype Parameters . . . . . . . . . . . . . . . . . . . .
10
1.2
100 kW Hardware Prototype Parameters . . . . . . . . . . . . . . . . . . . .
10
3.1
Flux Path Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
3.2
Magnetic Symbols Classification . . . . . . . . . . . . . . . . . . . . . . . .
28
3.3
Typical Magnet Material Properties [2]
. . . . . . . . . . . . . . . . . . . .
30
3.4
Typical NdFeB Grade Properties [2] . . . . . . . . . . . . . . . . . . . . . .
31
3.5
Design Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
3.6
Design Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
3.7
AWG Copper Wire Table [3] . . . . . . . . . . . . . . . . . . . . . . . . . .
46
3.8
Flux Path Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
6.1
VRPM Machine 100 W Active Loading . . . . . . . . . . . . . . . . . . . .
97
LIST OF APPENDIX FIGURES
Figure
Page
1
Back Plate
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
114
2
BarStock 075x075
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
115
3
Magnet Clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
116
4
Magnet Clamp 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
117
5
Phase Arm Clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
118
6
Phase Back Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
119
7
Phase Clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
120
8
Phase Spacer 2.5 Inch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
121
9
Phase Bottom PVC Spacer . . . . . . . . . . . . . . . . . . . . . . . . . . .
122
10
Lamination Part B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
123
11
Lamination Part C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
124
12
Translator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
125
13
Translator Spacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
126
14
Tubing 2x1x337mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
127
15
Tubing 2x1x800mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
128
16
Angle Tubing 2x1x894mm
. . . . . . . . . . . . . . . . . . . . . . . . . . .
129
17
Tubing 2x1x1500mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
130
18
Tubing 35x35x1200mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
131
Chapter 1 – Introduction
The energy challenges of today require us to explore new avenues that have yet to be
considered. Alternative energies which are clean and renewable diversify our energy source
with hopes of offsetting or even eventually replacing all carbon fuels. While wind energy
was a novelty twenty years ago, the industry has expanded dramatically to the point where
Europe has produced as much as 142 TWh of wind energy in 2008 [4]. However, ocean
energy may hold greater promise. While ocean energy has just begun to emerge to the
commercial market of alternative energies, ocean energy is on the verge of playing a big
role in the near future. Interest in ocean wave energy began as early as 1799 with the
world’s first wave power patent by Monsieur Girard of Paris [5]. Since then, technologies
such as point absorption, attenuation, overtopping, and oscillating water columns have
been developing in different environmental scenarios [6]. Each technology comprises of a
unique method to convert the vertical motion of the waves into electrical energy. The
design and implementation of generator topologies specific to an ocean environment, such
as the one discussed in this thesis, will aid in the progression of the above mentioned energy
technologies for wave energy.
1.1 Ocean Energy Potential
Ocean energy is a new and exciting field of alternative energy that has been receiving
attention. According to the US Department of Energy, the amount of energy contained
within the ocean waves are believed to provide up to two trillion watts of electricity [7]. So
2
it is no wonder why various emerging energy capture technologies have been targeting wave
energy. Within the vast span of ocean energy conversion technologies, the US Department
of Energy has classified ocean energy into three energy conversion categories; tidal energy,
thermal energy, and wave energy conversion. For a period of a little over twenty four hours,
tidal energy consistently experiences two highs and lows [7]. This cyclic nature can be used
to extract energy. There are not many tidal power plants in the United States; however,
conditions are good for tidal power generation in the Pacific Northwest and the Atlantic
Northeast regions [7]. Thermal energy conversion uses the difference in temperature between
different ocean depths to generate energy. The natural ocean thermal gradient necessary
is between latitudes 20 degrees north and south [7]. For this reason, thermal energy is
an attractive alternative for 29 territories and 66 developing nations [8]. Hawaii has begun
looking into this option since the successful operation of the world’s first closed-cycle OTEC
in 1979 [7].
Devices designed to extract ocean energy via waves extract energy directly from the
surface waves or from pressure fluctuations formed below the surface [7]. If one were to
observe the effect of waves upon the movement of a water particle at the surface, one
would notice a generally circular pattern that occurs. As one were to look below the ocean
surface, the circular pattern continues. As shown in Figure 1.1, the deeper the water
particle the smaller the radius of the circular pattern. Below the ocean surface, a device
can be developed to utilize this rotational pattern as a method of harvesting wave energy.
Alternatively, a device can be constructed to utilize the same rotational pattern at the
surface of the ocean rather than as the sea floor. A wave energy capturing device can utilize
the vertical movement of the waves occurring at the surface to harness energy.
3
Figure 1.1: Orbital Pattern of a Wave Particle
1.1.1 Wave Energy Advantages
Due to the advantages wave energy, it can emerge as the next promising alternative energy.
The potential in the United States alone appears to be substantial. The National Renewable
Energy Laboratory estimates suggest that harnessing 20% of the wave energy potential from
coastal United States with 50% efficiency would be equivalent to all of the hydrogeneration
throughout the United States in 2003, equating to nearly 24,000 MW [8].
The density of the medium to which energy is transferred directly effects the amount
of capable energy. The larger density of water in comparison to air strongly favors the
progression of wave energy. The density of air is around 1.2 kg per cubic meter where,
according to the University Corporation for Atmospheric Research, the density of ocean
water is 1027 kg per cubic meter [9]. As a result, the amount of potential energy in a
particular volume of water is around 855 times greater than the same volume of air. The
capability of a smaller, more cost effective, and aesthetically appealing design increases
when immersed in an environment with such an energy rich potential.
A predictable energy source allows for better integration with other energy producing
sources. The variations in the wave have shown to take on a seasonal dependence. Figure 1.2
displays how the wave height and period consistently vary throughout the year. The annual
4
trend of electric utility usages of the northwest mirrors that of the seasonal wave potential.
Figure 1.2: Seasonal Variation of Wave Potential [1]
An increased accuracy of a predictable energy source also aids in the grid integration
with other energy producing sources. Wave energy, in comparison to wind energy, is more
favorable when considering the accuracy of energy predictions. Because the density of water
is so much greater than that of air, changes that may occur in the stored energy within the
ocean reacts significantly slower. This is an advantage as slower and heavily energy dense
wave dynamics provide more predictable energy forcasting. Energy forecasting is obtained
by the presence of wave monitoring bouys. These bouys provide data such as the significant
wave height shown in Figure 1.2.
1.1.2 Wave Energy Technologies
Just like wind power at its early stages, various unique technologies of extracting wave
energy is being researched throughout the world. All the technologies have unique charac-
5
teristics which inventors believe would prove to be promising. The Energy Systems research
group at Oregon State University has spent the past years developing point absorber buoys
to capture energy at the surface of the ocean. A point absorber is a vertically extended
device designed to convert energy via the rise and fall of the wave at a single point.
However, other technologies are also in developmental stages. Attenuation, overtopping,
and oscillating water columns are additional emerging technologies [6]. An attenuator is
multiple horizontally elongated structures segmented together which is oriented parallel to
the direction of the wave. As a wave passes through the device, energy is harvested from
the connection points of each segment moving in a manner relative to another. Figure 1.3
displays an attenuator developed by Pelamis Power. Overtopping devices can be either on or
off of the shore. This technology raises the water level above the ocean surface and utilizes
the elevated water level to drive a conversion device, typically a turbine. The operation
of this technology is oriented perpendicular from the direction of the wave. An oscillating
water column is a device with one opening submerged within the water. Within the device
is a trapped chamber of air where the pressure of the air fluctuates as the waves pass by.
The fluctuation in the air pressure is then converted to electrical energy.
6
(a) Point Absorber [10]
(b) Attenuator [11]
Figure 1.3: Wave Energy Converting Technologies
7
(a) Overtopping Device [12]
(b) Oscillating Water Column [12]
Figure 1.4: Additional Wave Energy Converting Technologies
8
1.2 Research Objectives
1.2.1 OSU Wave Energy
1.2.1.1 Wave Energy Progression
Since 1998, the Energy Systems research group at Oregon State University has been an
innovator in of wave energy research in United States. For the past eleven years, Oregon
State has taken the idea of harnessing wave energy and developed the idea into a tangible
task. In order to do this, they have focused on research, design, and optimization of ways
to harness and convert wave energy. In the research phase, members of the Energy Systems
group look into different wave energy converter technologies. Designs that have or are
currently in the stages of being built are good templates for a wave energy converter, or
WEC, but researchers at Oregon State look into what may be missing from these designs and
how to implement improvements. When feasible wave energy converters have been chosen,
the design phase of the WEC begins. With the given design constraints, such as wave
velocity, amplitude, frequency, output voltage, output current, and physical constraints,
novel technologies are proposed and implemented. With the eleven years of experience, the
Energy Systems group has capitalized on the strengths and weaknesses of previous designs
by using them to optimize the subsequent designs. This process allowed the Energy Systems
group to transform wave energy harnessing from just a concept to a feasible and robust
technology that is steadily progressing towards becoming a commercial ready product.
Oregon State has implemented these three concepts by investigating how to appropriately harness the energy as well as how to convert it into electrical energy. Information
from oceanographic data collection centers such as the National Data Buoy Center can aide
9
in deciding the best places to position the point absorbers. OSU has identified an optimal
position to be nearly three miles offshore which equates to being just barely out of sight
when standing on the coastline. The configuration of the buoy, such as the radius of the
float and the vertical length of the spar, and various mooring techniques determine the
hydrodynamic interactions that occur. OSU is investigating various modifications of these
variables to determine the optimal configuration which can be used to harness energy.
The simplification of the energy conversion process can be achieved through the use of
a novel direct drive process. Typical utilization of pneumatic or hydraulic systems incurs
losses and reduces the overall efficiency. A direct drive process directly converts the vertical
motion of the wave into electrical energy. The energy systems research group has spent the
last few years identifying generator topologies which are ideal for this very task.
1.2.1.2 Wave Energy Awareness
Another goal for the work done at Oregon State is to educate society about the potentials
of wave energy. Greater progress in wave energy can be expected as the community learns
the advantages that wave energy has to offer. Therefore, Oregon State has been reaching
out to the community to encourage this awareness. OSU has collaborated with the Hatfield
Marine Science Center to provide demonstrations and a wave energy display [10]. They have
been working with Oregon Department of Energy, or ODOE, to establish a demonstration
site near Newport Oregon. Additionally, the faculty members at Oregon State have offered
invaluable courses and research opportunities that allow students to actively engage in wave
energy. These opportunities, such as the development of the novel linear generator described
throughout this thesis, has brought the awareness of ocean energy to a national level.
10
1.2.2 Linear Generator
The fundamental goal of the research is to identify and develop the most promising topology
for commercial wave energy conversion. In order to effectively identify the best topology, a
series of novel direct drive power take off devices were designed to convert wave energy to
electrical energy. The result of each topology includes the design, simulation, construction,
and testing of a 100 W prototype as well as the design and simulation of an equivalent
100 kW wave energy converter. Each of which was constructed with the constraints listed
in Tables 1.1 and 1.2. One of the novel direct drive power take off devices is the linear
generator described in the following chapters.
Table 1.1: 100 W Hardware Prototype Parameters
Mechanical Parameters
Electrical Parameters
Stroke
0.5m
Current Density
3.5A/mm2
Peak Velocity
0.8m/s
Air Gap
1mm
Peak Acceleration
2.6m/s2
Designed Voltage
21V P eak
Peak Force
250N
Voltage
14.8V RM S
Period
1.9sec
Max Current
4ARM S
Average Power
100W
Per Phase Peak Power
118W
Peak Power
200W
Bus Voltage
42V
Factor of Safety
2x
Table 1.2: 100 kW Hardware Prototype Parameters
Mechanical Parameters
Electrical Parameters
Stroke
1.5m
Current Density
3.5A/mm2
Peak Velocity
0.8m/s
Air Gap
3mm
2
Peak Acceleration
0.82m/s
Designed Voltage
560V P eak
Peak Force
2500N
Voltage
395V RM S
Period
8sec
Max Current
126ARM S
Average Power
100kW
Per Phase Peak Power
115kW
Peak Power
200kW
11
Chapter 2 – Generator Overview
Power and torque are two characteristics commonly used to characterize the performance of
a generator. For traditional rotary generators, the power produced is determined by a force,
or torque, and the rotational speed. In the case of a linear generator, the linear equivalent
of torque, or shear stress, and the linear velocity are substitutes. Equation 2.1 identifies the
power of a typical rotary generator where tau represents torque, or angular force, and alpha
represents angular momentum as well as the power of a linear equivalent where F represent
a linear force applied in the direction of movement and v would be the linear velocity.
P ower = (F orce)(velocity) = τ ω = F v
(2.1)
When designing a linear generator specific to wave energy applications, the desired output power of the generator and typical vertical velocity of the waves can be used to determine
the minimum amount of linear force that will be necessary as shown in Equation 2.1. The
appropriate selection of magnets would then be designed to produce the necessary force or
shear stress.
In order to be able to identify which generator topology is best suited for wave energy
application, the characteristics of the wave environment in which the generator will be operating must be considered. Generators are usually designed to run at a constant frequency
and high constant speed in a dry and controlled temperature environment. For an ocean
wave environment, this is not the case. Waves tend to take on anything from a sinusoidal to
fully stochastic waveform. The frequency of the waves and the amplitude are consistently
12
varying as well. The change in vertical wave height occurs and low speeds and the generator has to run in such way that all of these varying conditions are accounted for while
the generator is partially to fully submerged in salt water. Due to these constraints, a fully
enclosed generator that doesn’t require frequent maintenance becomes a must as well as a
generator topology which could reliably operate in the harsh environment.
2.1 Generator Topology Selection
When selecting a generator topology, there are many options to take into account; ac or
dc, synchronous or asynchronous, brushed or brushless, linear or rotary, and permanent
magnets or field coils are just a few of the options. Due to the remote locations and harsh
conditions this generator would encounter, maintenance and long term survivability are
critical issues to consider. Machines which utilize brushes are known to require more frequent maintenance. A brushless design provides no brushes or commutators to contend
with. Therefore, brushless designs are known to be more efficient. Induction motors can
also provide the advantage of higher efficiencies at higher speeds. Synchronous machines,
however, are also known to have higher efficiencies at lower operating speeds than other motors. Additionally, the speed at which a synchronous machine operates also is independent
of the load.
A wound field motor has the ability to alter the current through the field which changes
the field strength, but comes at the cost of employing slip rings or brushes. When the
magnetic field is generated via permanent magnets, no power is wasted generating the
field. Furthermore, the permanent magnets a smaller, lighter, and more reliable for long
term applications. With the above conditions in mind, a combination of two topologies
appears to be most advantageous; a variable reluctance machine and a permanent magnet
13
synchronous machine. A hybrid of both topologies, also known as a variable reluctance
permanent magnet machine or VRPM machine, is well suited for direct drive applications.
As a variable reluctance machine, VRPM machines have the advantage of a high torque
density but the disadvantage of a low power factor and a strict requirement of a small air
gap. As an AC synchronous machine, VRPM machines can provide a very large power
density at low speeds and the ability to apply power factor correction techniques.
There are many situations when the ideal generator topology would be a variable reluctance permanent magnet machine, or VRPM machine. A VRPM machine is most suitable
in conditions with low speeds where a linear operation is desired and high power density
must be achieved. They are also appealing when low design and manufacturing costs at
large production volumes are preferred [13]. A VRPM machine can be designed with an
electrical gearing effect that allows it to operate at a higher frequency during low speed
operation. VRPM machines are also known for their high energy density which allows for
the size of all associated components to be less than a typical generator. In order for these
advantages to occur, a relative portion of power generated is stored as reactive power. To
counteract this, power factor correction is required to harness the full potential of the apparent power as real power. Previous research discuss a common trade off of a high power
density resulting in a cogging torque which may affect the performance [13].
Waves oscillate at lower frequencies which would deteriorate the efficiency of several
generator topologies. VRPM machines contain a built in electrical gearing effect. Based
upon the velocity of the waves, the geometry of the magnets and the rotor and stator teeth, a
VRPM machine can move at low speeds while operating the generator at a higher frequency.
Several generator topologies achieve maximum performance from a rotary motion, but the
conversion from linear to rotary motion requires mechanical losses. A significant advantage
of a VRPM machine is the capability of the generator to transform a linear motion directly
14
into electric energy.
The physical size and loss of an electrical machine is related to its torque rather than
its power capabilities [13]. The ability to produce large quantities of power is a result of the
large torque density, or shear stress, formed from the magneto motive force, MMF. This
MMF created by the interaction between the permanent magnets, PM, and the varying
electromagnetic field, EMF, can become quite significant in a VRPM machine. Since the
VRPM machine has a high torque density in comparison to other generator topologies [14],
the physical size of the generator and energy losses incurred would generally be less.
The final topology consideration for a generator in a point absorber would be whether
to have a transverse or longitudinal flux path. In a transverse flux generator, the plane on
which the flux path lies is transverse, or perpendicular to the direction of movement. Similarly, the flux path of a longitudinal flux machine is longitudinal, or parallel to the direction
of movement. In the past few years there has been discussion favoring the transverse flux
because of its capabilities to obtain a high force density [15]. However, there are drawbacks
to a transverse flux design. Transverse machines inherently take on unconvential structures
due to their three dimensional flux paths. The design and the construction of a transverse
flux machine can become difficult, resulting in higher design and implementation costs. Due
to the intricate structure of a transverse flux machine, inherent vibration is known to occur
[16]. As the generator design is geared toward integration into a cylindrical point absorber
and consideration has been taken into the survivability and robustness of the generator,
a longitudinal flux design is more appealing. A longitudinal flux generator can be broken
down into a two dimensional solution, such as the one shown in Figure 2.1.
15
Figure 2.1: Longitudinal Flux Path
2.2 Unique VRPM properties
The purpose of a generator is to convert mechanical energy into electric energy. Energy
generation via a generator is a result of the interaction between a stationary section, the
stator, and a moving section, the rotor, within a magnetic field. The operation for a
variable reluctance permanent magnet generator is unique. The permanent magnets act as
a magnetic battery to some degree as they are the source of the magnetic flux path and
thus the magnetic field. The magnetic field induces a potential within the windings. As the
rotor moves into and out of position (minimizing and maximizing the air gap), a rotational
path through which the flux can travel is repetitively formed as the intensity and polarity
of the magnetic field varies and alternates, respectively. The alternating field results in
an alternating flux path which generates a closed loop electric field in the same location.
16
Thus, the electric field induces a potential upon the windings located on the stator. As
a result, the applied mechanical force from the permanent magnets utilizes Faraday’s law
of electromagnetic induction to convert the applied force into electricity seen upon the
windings.
17
Chapter 3 – Design
In addition to selecting the appropriate generator topology to operate in a point-absorber,
customizations to the linear generator were chosen to optimize the design. The design
strategy begins by identifying the minimum amount of specific torque, or shear stress,
necessary to produce the peak power rating of the generator. The process continues by
appropriately sizing the permanent magnets to achieve the recently discovered minimum
shear stress. The analytically chosen magnetic geometry would then be modeled with finite
element analysis, or FEA, to verify the generator produces the necessary force. Following
the FEA, the remaining components of the design are modified to ensure the generator
operates without saturation occurring through the longitudinal flux path.
3.1 Novel Longitudinal Scheme
Optimizing present day VRPM machine designs can be performed by a novel restructuring
which minimizes the overall volume of the costly components; the permanent magnets and
phase windings. This reduction in cost and volume can be done by locating the windings
and the permanent magnets on the same section of the generator, the stator. Therefore,
the length of the rotor can be expanded in order to utilize a larger wave stroke without a
significant increase in the cost of the generator.
In as recently as 2007, it has been thought that a major disadvantage of the longitudinal, when compared to the transverse, machines is the existence of end windings [15].
End windings are undesired as they increase the cost of the device and the stator resis-
18
tance of each phase without providing a useful advantage. The generator design discussed
throughout the chapter utilizes a magnetic flux path, as shown in Figure 2.1, that can be
done in a manner to form a cylinder. This eliminates all end windings that currently both
longitudinal and transverse flux machines experience. The 100 kW machine was designed
in this manner. The 100 W design was built as a way to verify the accuracy of the design
process, simulations, and modeling. As such, modifications were made from the generator
layout discussed in this section.
Figure 3.1: Cylindrical Equivalent of a 1 phase Stator
One module, or bobbin, of the cylindrical equivalent stator is shown in Figure 3.1.
The figure includes two sets of permanent magnets in a ring orientation placed around
the endpoints, or salient poles, of the stator. In addition to the permanent magnets are
sections of a soft iron core designed to provide a flux path around the windings. The sections
consist of one long yet skinny hollow cylinder connected to two wider and shorter cylinders
protruding from each end, or salient poles. To reduce eddy currents from forming, the
sections of soft iron core can be supplemented with sets of laminations cut parallel to the
19
direction of the flux path. In the case of the 100 W generator, radial laminations would be
used. For a cylindrically formed stator, the flux travels through a radial path resulting in
the necessity of radial laminations. The area within both salient poles is spaced to include
the appropriately sized coils with the amount of turns necessary to achieve the peak output
voltage with the peak input wave velocity.
The rotor takes on a cylindrical form as well. While the outer diameter remains consistent, the inner diameter of the rotor varies. Teeth and gaps are formed on the inner section
of the rotor to regulate the flow of the flux between the stator and the rotor. The diameter
between every set of teeth is consistent, and the same follows for every set of gaps. The
size and spacing of these teeth and gaps are dictated by the geometry of the permanent
magnets. Figure 2.1 is a side profile of the 100 W configuration. It is also a cross sectional
viewpoint of the cylindrical configuration of the Figure 3.2.
With the novel orientation of the components for a longitudinal flux design, the previous
advantages of a transverse flux design are no longer as significant. Table 3.1 compares
the typical comparison between a transverse and longitudinal flux generator to the novel
longitudinal flux generator.
1
2
3
4
5
6
Table 3.1: Flux Path Comparison
Longitudinal
Transverse
End-Winding Exist
Ring-Shaped End-Winding
(High loss) [15]
(low loss) [15]
Large Magnet Quantity
Large Magnet Quantity
Simplistic Flux Path
Complex Flux Path
Medium Power Density [14]
High Power Density [14]
Low Power Factor [14]
Low Power Factor [14]
Normal Construction
Complex Construction
Novel Longitudinal
Ring-Shaped Winding
(no loss)
Small Magnet Quantity
Simplistic Flux Path
Medium Power Density
Low Power Factor
Simplistic Construction
The elimination of end windings as well as the reduction of the costly components are
only two of the advantages that this new structure incorporates. In addition to develop-
20
Figure 3.2: Cylindrical Rotor
21
ing ease for the power take off connection, locating these components on the spar of the
point-absorber increases the long term reliability as this separates the components from
the moving portion of the generator. Restructuring the typical variable reluctance machine
also allows for better utilization of the existing components. The longitudinal flux path
and cylindrical shape allows one hundred percent utilization for the volume of the current
induced coils. Isolation between phases also occurs. Isolating each phase into individual
modules, or bobbins, increases the safety conditions of the machine, improves the commercialization of the device, and reduces noise and vibration issues.
Safety is a concern in all engineering applications. The likelihood of a phase to phase
fault is reduced due to the segregation of each module. One must look into more than
the price of materials and energy production to stream line a machine into commercial
applications. With the ability to construct several similarly shaped smaller components
rather than large and unique shaped ones, the design and construction times are reduced.
Additionally, the smaller components of the generator can be broken down into sections
that can be built independently and simultaneously, reducing the development time of an
individual product. Cogging torque is known for producing noise and vibrations in PM
machines [17]. The spacing between the salient poles of each module, or bobbin, can reduce
the magnitude of the cogging torque. Reduction of the cogging torque, the torque which
causes a resistance towards free-flowing movement, is another novel application applied to
this generator design. This occurs when the salient poles of one module are properly spaced
for a particular orientation of the permanent magnets.
The modular design of each module, or bobbin, provides additional benefits beyond isolation between phases. Modulating each phase of the machine into multiple series connected
phase equivalents reduces the diameter of the rotor, or more specifically the back iron, resulting in a reduction of the diameter of the generator. An added bonus to the modulated
22
phase, or bobbins, is ease of customization. If a four phase design is more appealing for a
particular application, then the modular units could be connected in a manner to produce
a four phase generator rather than three. The output characteristics will vary, but the only
necessary physical modification between the three phase equivalent and four phase equivalent generator would be the quantity of modular connections of the windings. If twice the
current is desired for each phase, then one can double the quantity of bobbins and connect
them in parallel to the existing configuration for each phase.
When there is a constraint on the diameter of the generator it would require multiple
bobbins to be built and connected in a series configuration. Simply speaking, the generator
would remain a three phase device, but each of the three phases would have multiple
modules, equivalent to a phase, connected in a series formation. This would allow the
diameter constraint to be met while achieving minimum required force to produce a peak
power of one hundred eighteen kilowatts for each phase. The design reduces the diameter
while streamlining the generator into a more industrially feasible design.
3.2 Identify Design Parameters
There are many parameters involved in calculating the specific geometry of a longitudinal
flux variable reluctance permanent magnet generator, and the process of determining each
can become cumbersome. Thankfully, identification of a few parameters can greatly simplify
this process. If one were to identify the specific design parameters of certain characteristics
about the desired output of the generator as well as an expected profile of the inputted
force, then identifying the process between the two becomes quite feasible.
23
3.2.1 Input Variations
Equation 3.1 demonstrates a typical wave profile where Hs is the significant wave height
and Ts is the significant wave period [18, 19]. The typical resultant wave velocity used to
define the geometry appropriate for proper magnetic characteristics can be extracted from
this equation. The problem lies in the fact that the wave profile is a typical case where
individual waves can take on completely random profile. So the characteristics of the wave,
such as magnitude, velocity, and frequency, are changing as well. While the characteristics
of the wave environment for a given location are consistently altering, there is a cyclic
manner to the variations. Equation 3.1 and 3.2 represent the generic equation of an average
sinuosidal wave and its peak to peak velocity [18, 19]. For this reason, the design of a
generator would depend on the location in which it shall operate. With close proximity
to the Oregon shoreline, this particular VRPM machine was designed for utilization at the
Oregon coast.
2πt
Hs
sin
2
Ts
X(t) =
|V pp| =
2πHs
Ts
(3.1)
(3.2)
With data on ten year averages of the waves off of the Oregon coast [1, 20], a profile of
the average wave characteristics was estimated. This estimation allows researchers with the
opportunity to extract the optimal design parameters. Essentially, the ideal performance of
the generator is designed to operate during the most frequently occurring wave properties.
Therefore, the wave parameters extracted are depending on the desired performance from
the generator. The optimal design parameters for the 100 W and 100 kW generators can
24
be found in Table 1.1.
3.2.2 Mechanical Clearance and Air Gap
The mechanical clearance has one main role for the point absorber design. It is referred to as
the spacing physically between the stationary component, the stator and spar, and a moving
portion, the rotor and float. The air gap is a magnetic parameter which consists of the sum
of the mechanical clearance and the magnet thickness. From a mechanical perspective, the
mechanical clearance has to be large enough to not create excessive friction between the
spar and the float. Unfortunately, the larger the mechanical clearance is between the spar
and float, the larger the reluctance will be. This has an effect on the the total real power
from the generator. Initially from a magnetic perspective, a minimal mechanical clearance
is preferred as shown in Figure 3.3.
140
120
100
Real Power (Watts)
80
60
40
20
c=1mm
c=2mm
c=3mm
c=4mm
c=5mm
0
-20
0
1
2
3
4
5
6
7
Permanent Magnet Thickness, h (in mm)
8
9
10
Figure 3.3: Power Generated for Various Mechanical Clearances
25
There are two ways to increase the air gap; the mechanical clearance can be increased
and the thickness of the magnet can be lengthened. An evaluation of the 100 W data can
identify the relationship between these parameters. Figure 3.3 shows this case. The power
generated decreases if the mechanical clearance increases. At the same time, the figure
displays how increasing the magnet thickness while maintaining a width to thickness ratio,
or w/h ratio, increases the output power. In those cases, it would be necessary to increase
the thickness of the permanent magnets in order to produce the same output power.
Besides the mechanical advantage of friction reduction, there is an additional advantage
that was originally overlooked in the 100 W generator design. In order to output the same
total real power from the generator with a larger mechanical clearance, the size of the
magnets must be increased. Larger magnets incur greater cost, so one may consider this
to be a nondesirable modification. However, this process reduces the reactive component
of the total power. Figure 3.4 demonstrates that with the same output power, the smaller
mechanical clearance contains more reactive power. While there is an additional cost to the
price of the larger volume magnets, the power factor of the system is significantly increased.
This can be seen in Figure 3.5. The same real power can be produced with a significantly
smaller reactive component thus resulting in a PF increase.
3.2.3 Construction Constraints
There are many elements that play a role in the design of the generator. Generally, the larger
a device, the more difficult it is to build. While there are electrical, magnetic, and geometric
considerations, other elements require additional forethought. Ease of commercialization
and safety considerations are just as important as constraints to the sizing of the device. In
the case of the point absorber technology, the cylindrical shape of the rotor and the stator
26
2500
c=1mm
c=2mm
c=3mm
c=4mm
c=5mm
Reactive Power (in VAR)
2000
1500
1000
500
0
-100
0
100
200
300
Real Power (in Watts)
400
500
600
Figure 3.4: Real vs. Reactive Power
0.9
0.8
0.7
0.6
PF
0.5
0.4
0.3
0.2
c=1mm
c=2mm
c=3mm
c=4mm
c=5mm
0.1
0
-0.1
0
1
2
3
4
5
6
7
Permanent Magnet Thickness, h (in mm)
8
9
10
Figure 3.5: Power Factor at Various Mechanical Clearances
27
would be one constraint. Lack of maintaining concentric shapes between the spar and float
would alter the performance of the generator. The machining tolerances for large diameter
devices as well as developing concentric cylinders becomes increasingly difficult. Due to
this, there is a limitation for the 100 kW generator of around one meter for the diameter
of the stator.
3.3 Permanent Magnet Selection
In order to properly select a permanent magnet for the 100 W and 100 kW linear generator
applications, one must first become aware of the parameters used to classify them. The
remanence flux density (Br), intrinsic coercive force (iHc), coercive force (Hc), maximum
energy product (BHmax), the intrinsic BH curve, and the BH curve are the most prudent
characteristics in this situation used to classify magnetic materials. Figure 3.6 represents
how each correlate in a plot of the magnetic flux density and magnetic field intensity. The
shaded region in the figure represents the demagnetization curve. Ideally, the shape of the
demagnetization curve would match the intrinsic curve as the maximum BH would notably
increase.
A magnet’s composition, the grade of it’s particular composition, and the physical dimensions all determine the amount of force, resulting in energy, a generator is capable of
producing. Besides determining the material and grade of the magnet, the appropriate
sizing of the permanent magnets must be identified. Then there are two steps involved
in determining the dimensions of the permanent magnets; a mathematical calculation of
the appropriate size must be performed and verified via finite element analysis. Table 3.2
identifies the geometric nomenclature for the permanent magnets while Figure 3.7 displays
the orientation of each in relation to the stator and rotor.
28
Figure 3.6: Generic B-H Curve
Table 3.2: Magnetic Symbols Classification
Name
Symbol
Magnet Width
wm
Magnet Thickness
hm
Mechanical Clearance/Gap
c
3.3.1 Magnetic Material
While there exists an array of permanent magnet materials, the properties of each help
identify which material is applicable in certain conditions. Temperature considerations,
surface treatment, cost, availability, customized geometry, and magnet strength are a few
of the properties which aid in the material selection process. There are three general
classifications for the various materials, and depending upon which elements one considers,
the permanent magnet would be considered a ceramic, alnico, or rare earth magnet.
29
Figure 3.7: PM, Stator, and Rotor Dimensions
Ceramic magnets are commonly referred to as ferrite magnets. The two main type
are made of a composite of iron oxide and barium carbonate or strontium carbonate [2].
These are widely available products which consist of compressed powder. As such, these
magnets are typically brittle. A ceramic magnet generally can handle large variations in
temperature, but the maximum energy product, commonly referred to as the BH product,
are relatively low [2]. Alnico magnets are alloys of aluminum, nickel, and cobalt. These
magnets have a high mechanical strength and are very corrosion resistant while also having
a large temperature stability [2]. However, they also contain a low BH product and are
prone to demagnetization.
Rare earth magnets are alloys of the lanthanide group [2], and they are known as the
30
Table 3.3: Typical Magnet
Material
BHmax
MGOe
Ceramic
3-5
Alnico
5 - 10
Samarium Cobalt
20 - 32
Neodymium Iron Boron 30 - 50
Material
Br
kGs
3-6
7 - 11
8 - 12
11 - 14
Properties [2]
Hc
Temperature
kOe
deg C
2-3
400 - 800
0.5 - 2
500 - 1000
8 - 11
250 - 675
10 - 13
80 - 400
superior material when as high energy product is desired. There are numerous forms of
rare earth magnets, but the most prevalent are samarium cobalt, or SmCo, and neodymium
iron boron, or NdFeB. Both forms contain a BH product five to ten times that of ceramic
and alnico permanent magnets. Samarium cobalt has better temperature resistance and
corrosion resistance in comparison to neodymium iron boron. However, neodymium iron
boron was selected for the 100 W and 100 kW generators because the pitfalls of the device
are manageable. Neodymium iron boron contains a larger remanence flux density, or Br,
and a larger coercive force, or Hc, resulting in a larger BH product, and there is a linear
relationship between the coercive force of the permanent magnet and the magnitude of
shear stress that is capable of being produced.
After input from Columbia Power Technologies, the operating temperature to which
this magnets will be exposed were found not significant enough to prevent neodymium
iron boron as an option. Lastly, corrosion issues are mitigated for the 100 W generator
by properly plating the permanent magnets with a nickel-copper-nickel compound. Other
coating compounds are also available. This material is one of the most corrosion resistant
and durable plating [2].
31
3.3.2 Permanent Magnet Grade
The preferred composition and grade is determined from a trade-off between price, volume,
availability, and the maximum desired energy product of the magnets. The grade of a
magnet refers to the product of the remanence flux density and the coercive force, and
this maximum energy product is typically represented in units of mega Gauss Oersteds, or
MGOe. A large coercivity, or Hc, is highly preferred, as shown in Equation 3.11, due to the
direct effect on the shear stress produced [13]. For the design of the 100 W and 100 kW
linear generators, grade 45 was the chosen material type which provides a coercivity in the
range of 875 to 950 kA/m, or 11 KOe to 12 KOe [21].
Table 3.4: Typical NdFeB
Grade BHmax
MGOe
N35
35
N38
38
N40
40
N42
42
N45
45
N48
48
N50
50
Grade
Br
kGs
12.1
12.6
12.9
13.3
13.6
14
14.3
Properties [2]
Hc
kOe
11.4
11.7
11.9
12.3
12.1
12.1
12.1
Table 3.4 displays the difference in properties between the different grades. From a
volume and energy production standpoint, the highest grade would be most preferred. The
selection of grade 50 rather than the chosen grade 45 would provide eleven percent more
shear stress for the same volume. More realistically, the large grade would result in the
reduction of the overall volume of the permanent magnets. As the volume of the magnets
dictates the dimensions of several components on the stator and rotor, the reduction in
magnet volume would equally result in a reduction of generator volume. In the case of the
32
100 W generator, commercially available grade 45 magnets are far more common to find;
the cost of custom ordering a small quantity of high grade rare earth magnets was identified
to not outweigh the advantages of grade 45 magnets available off-the-shelf.
3.3.3 Defining Magnetic Requirements
The high power density that variable reluctance PM machines produce is a result of a large
torque density, or shear stress, formed from the magnetomotive force, MMF. Therefore,
achieving the desired torque density, based upon wave characteristics and target power
production, is the critical factor in designing the hardware to meet the specifications. Once
a target peak vertical wave velocity has been chosen, the minimum requirements of a linear
generator to achieve the target output power can be identified. The specifications listed in
Table 3.5 provide the means to determine the requirements of the linear generator.
Table 3.5: Design Specifications
Initial Specifications
Peak Power
P
Peak Vertical Velocity
vwave
Maximum Spar/Stator Diameter
d
Number of stator bobbins per phase
Nb
Utilizing the variables from Table 3.5, one can arrive at Equation 3.3 to achieve the
minimum shear stress necessary to achieve the desired output power. The shear stress can
be viewed as the linear equivalent to torque. The minimum linear force per unit area, or
shear stress, necessary to achieve the desired output power when given a particular input
velocity is used to check whether the magnet geometry, designed in the following section, is
capable of producing enough power.
33
P
τminshear =
F
N v
= b wave
A
wm (πd)
(3.3)
As this value is dependent upon the cross sectional area of the permanent magnets,
the minimum shear stress extensively reduces. Figure 3.8 illustrates how the minimum
shear stress reduces for the 100 W generator as the thickness and width are increased. As
described later in the chapter, the width, w, of the permanent magnet was adjusted along
with the thickness, h, by a factor of seven to account for an optimal combination of the
produced power and power factor. Therefore, an increase in magnet volume will reduce the
required energy density of the magnet.
6
x 10
5
Minimal Shear Stress (N/m)
5
4
3
2
1
0
0
1
2
3
4
5
6
7
Permanent Magnet Thickness, h (in mm)
8
9
10
Figure 3.8: Minimum Shear Stress
If the peak vertical wave velocity and desired peak power generated are known, then
the minimum shear stress, or specific torque, upon the permanent magnets necessary for
the device to produce the rated output power can be identified. The minimum shear stress
34
indicates the value of increased magnet volume. If the volume of the magnets where to
remain constant yet the output rating were increased from 100 W to 100 kW, then Figure 3.8
would have the identical shape at a magnitude one thousand times the current value. To
develop a linear generator with an output one thousand times larger, the cross sectional
area of the 100 kW generator was increased by a factor of roughly twelve hundred.
3.3.4 Magnet Geometry
With the projected wave statistics, the desired output characteristics, and the physical
design constraints all identified, the sequential step of the design process is to evaluate the
possible permanent magnet geometries that, when interacting with the radial laminations
of the stator and the rotor, will produced a shear stress, or specific torque, exceeding that
of the minimum required shear stress. Identification of the geometry of the permanent
magnets and the prevention of saturation for each magnetic hardware component are the
additional considerations necessary to finalize the generator design of the variable reluctance
linear PM generator. These additional considerations require more specifications listed in
Table 3.6.
Table 3.6: Design Specifications
Additional Specifications
Coercive Force
Hc
Remanence Flux Density
Br
Quantity of Phases
Magnet Width to Thickness Ratio w/h
Peak Current
Iout
Peak Voltage
Vout
Mechanical Clearance
c
Spooner and Haydock utilized the techniques of Lorentz’s force to identify the shear
35
stress in terms of the stator and rotor geometry. Lorentz’s force, shown in Equation 3.4,
states that a force is equal to the cross product of the product of the length of a wire and
the current flowing through it with a magnetic field in its presence.
F = i`B
(3.4)
The source of the magneto motive force would be the permanent magnets. As shown
in Equation 3.5, the mmf is determined by magnetic field intensity and thickness of the
magnets. The same equation also shows how the magnet can be replaced by coil with
a given number of turns and current. When taking into consideration the conditions of
the lorentz force as a force on a point charge, the current can be found by representing
the magnets as a coil with a single turn. With this representation, the amount of current
expected to be generated is equivalent to the intrinsic coercivity multiplied by the thickness,
or h, of the magnet. The length of the wire is a factor that is yet to be determined. It is
dependent upon the diameter of the stator and the number of turns. While the magnetic
field is the magnetic field present in a salient pole, or tooth, of the rotor minus the magnetic
field in the slot between the adjacent salient poles. With the combination of these formulas,
the force and the areas of the magnetic geometry will provide a value for the shear stress
generated.
mmf = N i = Hc hm
(3.5)
B = Btooth − Bslot
(3.6)
36
τshear =
F
Hc hm `B
=
A
wm (πd)
(3.7)
Equation 3.7 is an undesirable method of achieving shear stress as the variables within
are dependant upon the position of the rotor. In addition to being dynamic values, the
magnetic field for the salient poles and the neighboring slots are not known quantities. The
sum of them, however, is fixed value that can be supplemented into the equation, the root
magnetic field density. The magnetic field within a tooth and the magnetic field in the
neighboring slot can be rewritten in a manner as to develop a ratio between the slot and
the tooth.
Br = Btooth + Bslot
Bslot
Hc hm
Btooth 1 −
=
wm
Btooth
τshear
(3.8)
(3.9)
With the use of conformal mapping done by Spooner and Haydock [13], Equation 3.10
demonstrates the ratio between the slot and the tooth can be represented in terms of the
magnet thickness, magnet width, and mechanical clearance. Inserting this ratio along with
the root magnetic field density provides a usable formula to evaluate the shear stress of a
variable reluctance PM machine based upon the geometry of the magnets and the size of
the mechanical clearance.
hm + c
Bslot
'q
Btooth
(hm + c)2 + ( w2m )2
(3.10)
37
q
τshear = Hc Br
hm (hm + c)2 + ( w2m )2 − (hm + c)
q
wm (hm + c)2 + ( w2m )2 + (hm + c)
(3.11)
As shown in Equation 3.11 [13], the shear stress is dependent upon the coercive force (or
magnetic field intensity) of the permanent magnets, Hc, the remanence flux density through
the magnetic circuit, Br, magnet thickness, h, the magnet width, w, and the mechanical
clearance, c (or air gap). With the same parameters and the permeability constant, Spooner
and Haydock developed an equation similar to Equation 3.12, to identify the power factor,
or PF, for a variable flux permanent magnet machine [13].
1
PF = r
1+
πBr (hm +c)
2µ0 Hc hm
2 1+
m +c 2
8( hw
)
m
2
(3.12)
A common standard in the geometry selection is to consider the ratio between the
width and thickness, the width-thickness ratio. To determine the width and thickness of
the magnets, it is best to correlate the ratio between the two by investigating their effect on
the shear stress and power factor, as these two values will determine the real power produced
from the linear generator. The power factor and shear stress have different profiles with
the width-thickness ratio. The shear stress has a local maximum while the power factor
continues to rise as the ratio increases. By sweeping various magnet width-to-thickness
ratios and viewing the crossover point between the power factor and shear stress, it can be
seen in Figure 3.9 that an a magnet width to thickness ratio around 7 would provide a fair
compromise between the force produced and the power factor of the system.
With a fixed relationship between the width and thickness of the magnet, the geometry
of the shear stress and power factor equations can be reduced to only the thickness and the
mechanical clearance. These are the same two parameters discussed previously that, for an
38
1
0.9
Normalized PF and Normalized Shear Stress
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
Magnet Width - to - Thickness Ratio
8
9
10
11
Figure 3.9: Power Factor and Shear Stress Crossover Point
increase in cost and volume, can also be modified to achieve the same output power with a
significantly greater power factor. After substituting the width to thickness ratio into the
previous shear stress and power factor equations, the resultant equations are used to design
begin the design of the variable reluctance permanent magnet generator.
p
τshear
hm (hm + c)2 + (3.5hm )2 − (hm + c)
p
= Hc Br
(7hm ) (hm + c)2 + (3.5hm )2 + (hm + c)
1
PF = r
1+
πBr (hm +c)
2µ0 Hc hm
2 m +c 2
1 + 8( h7h
)
m
2
(3.13)
(3.14)
The final stage of the magnet design is to combine the three key design elements to
discern which geometry would be most preferred. Overlapping the new equations for the
shear stress with the knowledge of the minimum shear stress allows one to select the dimen-
39
sion of the magnet which will appropriately provide the desired output. If NdFeB35 were
chosen rather than NdFeB45, the identical minimum shear stress would remain and the
produced shear stress curves would take on a similar shape, however, the magnitude of the
output power would be reduced. For this reason, larger volume magnets would be required
to meet the intersection of the minimum shear stress curve with the produced shear stress.
As the thickness of the permanent magnet increases, the width increases accordingly by a
factor of seven. The increased cross sectional area reduces the required shear stress. The
magnet thickness is increased until the produced shear stress reaches that of the minimum
desired amount. When the shear stress is evaluated at various mechanical clearances, one
can consider additional geometric solutions. This process opens the door to provide the
same total power while increasing the power factor of the generator. As the cross sectional
area increases, the reduced minimum shear stress allows one to utilize an increased mechanical clearance and still achieve the desired output power of 100 W or 100 kW. As shown
in Figure 3.4, an increased mechanical clearance contributes to a reduction in the reactive
component thus increasing the power factor.
For the 100 W generator, the improved power factor consideration was overlooked. A
mechanical clearance of 1 mm was used. The 100 kW generator later produced incorporated
the advantages of an increased mechanical clearance. A mechanical clearance of 3 mm was
used to increase the power factor by up to 0.2. Unless a large volume custom order were to
be taken, commercially available rare earth magnets today do not provide a wide selection
in geometries. Instead, the thickness, width, and depth of the magnets chosen for the 100 W
generator was 2 mm by 14.3 mm by 31.75 mm, respectively. Ideally, the magnet geometry
would match that found from Figure 3.10 to ensure that the desired output of the generator
would be achieved.
40
10
x 10
4
9
8
Shear Stress (N/m)
7
6
c=1mm
c=2mm
c=3mm
c=4mm
c=5mm
Minimal Shear Stress
5
4
3
2
1
0
0
1
2
3
4
5
6
7
Permanent Magnet Thickness, h (in mm)
8
Figure 3.10: Minimal vs. Produced Shear Stress
9
10
41
3.4 Additional Magnetic Dimensions
There are several additional elements to the design of a magnetic circuit which will adversely affect the performance of the generator. A few of the concerns for these additional
components are the material, geometry, and spacing. The density of the flux path, the
amount of cogging force, the operational frequency, and the system inductance are just a
few of the conditions which hinder the production of power. Therefore, the limitations to
the characteristics of the stator, rotor, and windings must be considered for the following
stage of design.
3.4.1 Stator and Rotor Geometry
A significant portion of the hardware for the magnetic circuit is contained within the stator.
It includes radial laminations, windings wrapped around the center of the laminations, and
rows of permanent magnets encased around the edges of the salient poles. The shape of
the radial laminations of one phase of the stator, as shown in Figure 3.1, is essentially two
equally shaped cylinders with a thinner and elongated cylinder connected between the two.
The thinner elongated cylinder consisting of the core, and the two equally shaped cylinders
as the salient poles. On the outer edges of the two primary cylinders, or endpoints, are
rows of magnets with each row alternating in polarity where one row is polarized towards
the center of the cylinder while the neighboring row or rows are polarized radially outward.
The sizing of these components is limited by various constraints. There is a correlation
between the sizing of the magnets with sizing of the rotor and the stator. This relationship
can be observed in Figure 3.11. The generator has been broken down into individual
sections explicitly for the purpose of proper sizing. These sections are further broken down
42
into correlating dimensions labeled as ’a’ through ’f’.
Figure 3.11: Stator and Rotor Sizing Dimensions
The size of dimension ’a’ is dictated solely by the geometry of the magnets. It is
equivalent to twice the width of the permanent magnet previously designed. Dimension ’b’,
however, is limited only by the desired maximum diameter of the stator. If the maximum
diameter is not achieved, then one can also modify dimension ’b’ based upon the volume
constraints for the windings. Dimension ’c’ is limited to discrete variations in size as this
component dimension determines the spacing between the two salient poles. This dimension
is the primary component in providing enough volume for the windings to be wrapped
around a portion of the flux path and remain completely contained within the stator. When
the necessary volume of the windings has been calculated, the size of dimension ’c’ can be
43
chosen.
While providing room for the coils to be wound around one section of the flux path,
the third cylinder is shaped in a manner which allows an spacing of a half period between
the two endpoints. This is done to allow for a cogging reduce technique, discussed later
in the chapter, to be achieved. One would prefer to limit the vertical lengh of the stator,
as a longer stator requires a longer rotor. The maximum limit for dimension ’c’, therefore,
would be determined by the largest desired size of the stator. The minimum spacing of
dimension ’c’ is done using Equation 3.15 which shows how the width of the magnet, or w,
corrolates with the spacing as the with is equivalent to one half of a. Iterations of x can be
chosen to identify appropriate spacing considerations which do not conflict with the volume
constraint. It was not until the third iteration until this was achieved for the 100 W design.
c=
a 2
[x − (x − 1)2 ]
2
(3.15)
Ideally, all dimensions would be reduced to the minimal allowable size that the above
listed constraints will allow. Often the minimal sizing for the majority of the dimensions
is limited by an additional factor, flux saturation. Both dimensions ’d’ and ’e’ are strongly
influenced by this factor. Additionally, the volume of the windings places a maximum
limitation on dimension ’d’. This is a flexible constraint as dimensions ’c’ and ’d’ can be
modified in a manner to account for the volume of the windings. The maximum limit for
dimension ’e’, would be determined by the largest desired size of the rotor. The minimum
size of dimension ’f’ is chosen by the vertical velocity and stroke of the wave along with the
vertical length of the stator. For the 100 W generator, there were three phases separated
by six hundred electrical degrees resulting in a length of nearly one half of a meter. With
the parameters from Table 1.1, the stroke and the velocity would require the rotor to move
44
four tenths of a meter in order to fully utilize the energy from the wave. Therefore, the
summation of the two would require at nearly a meter in length for the rotor.
3.4.2 Flux Density and Saturation
Like the relationship between the magnetic field intensity, or Hc, and the amount of produced shear stress, the amount of shear stress generated is linearly affected by the density
of flux. For this reason, a smaller flux path would seem more preferable as it would increase
the flux density. However, if the density becomes too significant, it could limit amount of
flux flowing through the path. The permanent magnet acts as the source with the capability
to produce a certain amount of flux. This flux then travels through the various components
within the magnetic loop. As the cross sectional area changes, the amount of flux remains,
therefore, changing the density of the flux. If the density becomes too significant for a given
material, the amount of flux flowing through the entire system is hindered. This condition
is commonly referred to as flux saturation, and in this case, the potential of the permanent
magnets to produce flux is being limited. Thus, the remaining components of the system are
designed to allow the maximum amount of flux, produced by the magnets, to flow through
the loop in an alternative manner as to induce a field onto the windings.
Ferromagnetic materials, like laminations, are commonly the limiting factor in the flux
saturation limit. Laminations and windings are composed of iron which is a ferromagnetic
material that has a maximum saturation limit around 2.2 tesla or 21,500 gauss [22]. The 100
W and 100 kW linear generators were designed with a consideration of up to 2.1 tesla as the
saturation limit for all ferromagnetic components. This would account for any discrepancies
such as impurities in the material. In order to appropriately size the geometry of the rotor
and stator, all components were selected at their maximum constraints and then evaluated
45
using finite element analysis to verify saturation has not occurred. Finite element analysis
models the change in the magnetic density through the various components. This is an
essential design tool as it identifies the locations where the size can be reduced without
affecting the system’s performance. Multiple iterations were done with the 100 W and 100
kW model to reduce the stator and rotor components.
3.4.3 Windings
The arrangement of the windings is equally as important as the magnet selection. Without
winding, there would be no transfer to electrical power, and improper sizing can either
produce undesired effects or cause the generator to not operate at all. The location the size
and the number of turns are the three topics to keep in mind when designing the windings.
In order to induce a magnetic field onto the windings, the windings must be placed in a
location to allow the alternating flux to flow through the center. This permits the windings
to be placed anywhere along the rotor or stator. Typically windings are located on the
rotor in the gaps between the salient poles, or teeth. This is not the case for the 100 W
and 100 kW designs. One of the novel modifications is to orient the windings in a central
location on the stator for multiple benefits. With the windings on the stator, the amount
of wire required for the overall generator is reduced which results in a reduction of weight,
cost, and losses due to resistance. As the windings are on the stationary section of the
generator, the reliability and survivability of the generator increases. Additionally, there is
an ease to the transportation of power as the power take off is routed from the sea floor,
up the mooring system, and directly to the stator.
Proper sizing of the wire is necessary to prevent the deterioration of the windings. Wire
sizes are identified by an American Wire Gauge, or AWG, standard. This standard identifies
46
the size, maximum current carrying capabilities, and the resistance and weight per a given
distance of wire. The minimum wire size is determined by the peak output current and the
current density of the particular sizes. Table 3.7 represents the AWG rating, resistances,
and maximum current densities of certain wire sizes. The 100 W generator has a peak
output current of 5.65 Amps, and the 100 kW generator has a peak output current of 178.2
Amps. As a result the 100 W generator would be limited to at least a 14 AWG wire. The
current of the 100 kW generator is large enough to where multiple bobbins are connected
in parallel with each other to reduce the amount of current passing through the windings.
With four bobbins per phase, the current reduces to 44.55 Amps which requires a minimum
wire size of 5 AWG.
AWG
4
5
6
11
12
13
14
15
Table 3.7: AWG Copper Wire Table [3]
Ohms/1000ft Current Capacity (Amps)
0.2533
59.6
0.3915
47.3
0.4028
37.5
1.284
11.8
1.619
9.33
2.042
7.4
2.575
5.87
3.247
4.65
Ft/lb
7.914
9.98
12.58
40.12
50.59
63.8
80.44
101.4
The maximum size of wire that can be used for the windings is determined by the cost,
weight, and space constraints within the stator. When considers the losses of a system, a
larger wire size, or lower AWG, is more preferred. This will reduce the amount of resistance
in the windings which reduces the losses in the generator. The minimal allowable size, 14
AWG, was chosen for 100 W linear generator, a decision that perhaps was not taken with
enough consideration. If the wire were to be replaced with 12 AWG, then there would be
a thirty seven percent reduction in the resistance. The 100 W linear generator contained
47
a significant amount of loss due to the resistance of the windings. Therefore, if a length
of wire was reduced and/or the size of wire was increased, then the losses would not have
impeded the output performance.
R = rrelative π`N
X=π
v
φ
N
wm i
(3.16)
(3.17)
Equations 3.16 and 3.17 are used to determine the real and reactive phase resistance
present for the 100 W generator, respectively. The resistance of the windings, therefore,
becomes nearly 1.17 ohms when using a 14 AWG wire, at a diameter of 0.1 m and 450 turns,
and the reactance is 3.751 ohms with a wave velocity of 0.8 m/s, magnet with of 0.0143 m,
450 turns, a peak output current of 5.65 amps, and a flux of 0.000134 Vs. If the windings
were replaced with 12 AWG wire, the resistance would be reduced to 0.07 ohms.
The number of turns is the third design element to the windings. The number of turns
that make up one phase of the winding dictates what range of output voltages will be
present. It also contains a squared relationship with the inductance of the overall system,
therefore, significantly affecting the power factor and system losses. The number of turns
is determined by a relation between the desired output voltage, the vertical velocity of the
waves, the width of the permanent magnets, and the amount of flux present as shown in
Equation 3.18.
N=
Vout
Vout wm
=
φ2πfe
φπvwave
(3.18)
For the most part, these values are predetermined by the components of the system.
48
The voltage and wave velocity are desired inputs and outputs while the frequency and flux
are determined by the rotor, stator, and magnets. The electrical frequency is determined by
the width of the magnets and the velocity of the waves. Later in the chapter, a technique
is described which would allow a modification of the frequency by modifying the magnet
width. The flux is produced by the permanent magnets and passes through the rotor and
stator. Therefore, ensuring no saturation occurs through the flux path or receiving higher
grade magnets would increase the flux.
An desired output voltage of 21 volts with a 0.8 m/s wave velocity and a chosen magnet
width of 0.0143 m would produce a flux of 0.000134 Vs according to simulations with finite
element analysis. This would require 450 turns for the 100 W linear generator. In the
100 kW case, only 18 turns are necessary. With the desired output voltage of 560, a wave
velocity of 1.2 m/s, a magnet thickness of 0.068625 m, and a flux density of 0.07079 Vs, the
number of turns is dramatically reduced.
3.4.4 Reluctance and Inductance Calculations
While in operation, every device experiences some degree of loss. The same holds for
a linear generator. In order to accurately model the expected power produced from the
variable reluctance permanent magnet linear generator, the amount of power created and
lost through the generation process must be determined. The power created is primarily
determined by the shear force produced when sizing the permanent magnets; the shear
stress multiplied with the cross sectional area of the magnets and the vertical wave velocity
provides the created power of the generator. As a result, Equation 3.19 describes the
resultant electrical power generated.
49
Pe = Pcreated − Ploss
(3.19)
The amount of real power produced is effected by the desired output current and the
winding resistance. Equally so, the amount of real power produced from the apparent
power is hindered by the desired output current as well as the electrical frequency and
the system inductance. Taking into consideration Equation 3.20, one can identify some
of the dictating factors of the reactive energy shown in Equation 3.24. Equations 3.23
and 3.24 identify the resistance of the windings and the system inductance as two significant
variables which, when modified, can alter the performance of the generator. Equation 3.20
also demonstrates how the reluctance of the 100 W generator inversely effected the system
inductance. Reluctance is comparable to resistance in the sense that reluctance can be
described as the prevention of flux flow. Nevertheless, reluctance stores energy rather than
dissipating it.
L=
φ
N 2 µA
N2
=N =
<
i
`
(3.20)
Ideally, this reactive component would be reduced. If the same amount of apparent
power is generated by the generator but the reactive component is reduced, then Equation 3.21 shows that the amount of real power generated must increase. However, losses
are incurred which reduce the amount of real power produced. The length of the windings
contribute to the loss of the machine. The implementation of the 100 W linear generator
proves that overlooking the losses due to the winding resistance will result in a generator
not achieving an ideal performance.
| S |=
q
P 2 + Q2
(3.21)
50
The power created is resolved into conditions that can be determined, before the use
of simulations and modeling, by the geometry of the permanent magnets, the properties of
the magnet, and the input velocity. The same can be done with all of the real and reactive
parameters before the modeling process begins. The real losses would be the product of
the output current with the resistance per length and the length of the wire. The reactive
power consists of the velocity of the wave, the width of the magnets, the number of turns
and the system reluctance.
Pcreated = τshear vwave A = τshear vwave (wd)
(3.22)
As previously mentioned, the amount of apparent power produced is total power of the
system, and the apparent power consists of the real power and the reactive power while
ideally a generator and motors would have no reactive power. If this scenario were the case,
the total amount of power produced would equal the real power. In this scenario, the losses
from Equation 3.23 would be the only detriment to the created power. Unfortunately, this
is not the case. Equation 3.24 identifies the reactive contribution of the apparent power.
1
1
r
P loss = (Ipeak )2 Rs = (Ipeak )2 ( `wire/turn N )
2
2
m
(3.23)
!
1
1
vwave N 2
Q = (Ipeak )2 (ωL) = (Ipeak )2 2π(
)(
)
2
2
2wm
<
(3.24)
As a result of Equations 3.22, 3.23, and 3.24, the real power generated can be calculated
through either input and output parameters discussed in section 3.3.3 or through generator
characteristics which can be calculated previous to modeling. When the generator is in
operation, variable reluctance machines are known for storing a significant portion of the
51
energy in the form of inductance. Ideally, the stored energy would be greatly reduced or
eliminated. Since stored energy diminishes the efficiency of the overall system, reducing the
amount of power loss would be of concern, and there appears to be a number of variables
which, if modified, would aid in the reduction of power loss. The number of turns is
typically dictated by the desired output voltage, and the current by the desired output
currents; however, the reluctance of the system is a parameter to which generator designers
have more flexibility in modifying. For this reason, it appears to be ideal to reduce the
system inductance by maximizing the reluctance of magnetic circuit through modification
of the hardware geometry for the stator and rotor. Equation 3.20 shows the reluctance of
the generator is linearly dependent upon the length of the flux path and inverse linearly
dependent upon the cross-sectional area. Therefore, the amount of real power produced
appears to increase by reducing the length and increasing the cross-sectional area throughout
the flux path.
What will be noted later in this section is that the change is reluctance is dominated
by the air gap. Therefore, a change in the reluctance would result in a starting back with
new magnet geometry. In this case, there are alternative methods to additionally aid in
increasing the real power. The number of turns has a squared relationship to the inductance
and a linear effect on the output voltage. While the generator’s output voltage is directly
affected by the number of turns for each phase, Equation 3.18 demonstrates the the number
of turns can be reduced while maining the output voltage by appropriate modifying the
electrical frequency. Later in the chapter, an adjustable frequency technique is described in
detail.
52
3.4.4.1 Sectionally Equivalent Components
Finite Element Analysis, or FEA, is an accurate method to identify the reluctance and
inductance of a system once the desired material and geometry is determined for all components. However, a calculation of the approximate geometry can identify a range of values to
expect while still in the development process. This process is useful as it aids in forecasting
the amount of stored energy that will be present in the generator. One can break down the
hardware into individual components and evaluate each component in order to obtain an
equivalent magnetic circuit. This magnetic circuit can then be transformed into an electrical equivalent, therefore, identifying the system inductance. With reference to Figure 3.12,
Table 3.8 identifies each of the relevant components along with their dimensions and the
resultant reluctance for a given flux path and a given stator-to-rotor position.
Table 3.8: Flux Path Geometry
Shape 1a, 1b
d = 31.75mm W1 = 75mm ` = 65mm
h = 28.6mm
W2 = 55mm A = 908.05mm2
Shape 2
d=
31.75mm h1 = 128.7mm ` = 100.1mm
W = 20mm
h2 = 71.5mm
A = 635mm2
Shape 3a, 3b
d = 31.75mm W1 = 34.5mm ` = 24.4mm
h = 14.3mm
W2 = 14.3mm A = 454.025mm2
Shape 4
d=
31.75mm h1 = 128.7mm ` = 114.4mm
W = 20.2mm
h2 = 100.1mm A = 641.3mm2
Shape 5a, 5b
d=
31.75mm h + c = 3mm ` = 3mm
W = 14.3mm
A = 454.025mm2
µr =
<=
5000
11392.6
1
H
µr =
<=
5000
25088.8
1
H
µr =
<=
5000
8553.23
µr =
<=
5000
2838.91 H1
µr =
<=
1
H
1
5.258x106 H1
In order to identify the reluctance seen through one flux path of the generator, the flux
53
path needs to be broken down into sectional equivalents. The reluctance of each sectional
is independently evaluated based upon the geometry and direction of the flux path. From
there, the reluctance of the system is simply the summation of each sectional equivalent.
Figure 3.12: Sectionally Equivalent Components of a Flux Path
The separation between sections is identified by a change in the flux path direction or
a change in material. For the development of the 100 W and 100 kW linear generators,
Figure 3.12 breaks down the components of one flux path into twelve independent sections.
Due to the inherent symmetry of the stator and rotor, the sectional equivalent shape for
the 100 W can be simplified into only five relevant shapes. The geometric dimensions of
each relevant shape for the 100 W is further listed in Table 3.8.
54
3.4.4.2 Equivalent Magnetic Circuit
Looking into the minimized structure for the flux path from Figure 3.12, one can obtain
the equivalent magnetic circuit, or simplified reluctance model. The reluctance of each
individual component is calculated from the length, area, and relative permeability, using
Equation 3.25, and then placed into the appropriate position in the reluctance model.
Figure 3.13 identifies the associated magnetic circuit, or reluctance model, of the geometry
and configuration of the components in Figure 3.12.
Ʀ
Ʀ
Ʀ 5a
1a
3a
Ʀ
Ʀ2
4
mmf
Ʀ
Ʀ1b
Ʀ
5b
3b
Figure 3.13: Equivalent Magnetic Circuit
`1
`i
=2
µo µr Ai
µ o µ r A1
Σ<path = Σ
`2
`3
+2
µ o µ r A2
µ o µ r A3
+
`4
`5
+2
µ o µ r A4
µ o µ r A5
(3.25)
+
With the length of the flux path, the cross-sectional area, and the relative permeability of
each sectional, one can use Equation 3.25 to evaluate the component and system reluctance
for one given position of the rotor relative to the stator. The resultant reluctance of each
component for the 100 W generator can be found in Table 3.8. The system reluctance,
55
therefore, comes to <P AT H = 10,583,820
1
H.
One can deduce that due to the low relative
permeability of the air gap, the length of the air gap will remain the dominating factor
in the reluctance of the overall system. This indicates that the reluctance throughout the
ferromagnetic material can be neglected, and that the length and cross sectional area of the
air gap is of great concern.
During the identification of the design parameters, it was mentioned that an increase
in the magnet thickness and mechanical clearance, or air gap, would result in an improved
power factor. This would be the reason behind why that is the case. As the reluctance of
the air gap dictates over ninety nine percent of the system’s reluctance, an increase in the
air gap would significantly increase the reluctance of the system. This would result in a
decrease in the system inductance; therefore, providing a greater power factor.
3.4.4.3 Equivalent Electrical Circuit
The duality between magnetic and electric circuits allows a conversion between the two to
be possible. E. Colin Cherry published an article which entails the relationship between the
two and how one circuit can convert into another[23]. The process of converting a circuit
is similar to inverting the connections and relationships of each component. Nodes, series
elements, open, current source, and reluctance from a magnetic circuit becomes meshes, parallel elements, short, voltage source, and inductance (or permeance ideally speaking) for an
electrical circuit, respectively [23]. As the magnetic circuit of the 100 W model contains all
magnetic elements in series, the resultant electrical circuit will contain all parallel-connected
elements as expressed in Figure 3.14.
The conversion involves two stages; the first stage is to change each element from reluctance to inductance values, and the second stage entails how to alter the connection
56
points of each element. Using Equation 3.20 along with the number of turns, the reluctance of each component in the magnetic circuit of the 100 W generator can be converted
to inductance. Altering the connection of each inductance simply involves converting all
series connections to parallel connections and vice versa. Another viewpoint that may be
preferred is to convert every node into a mesh loop[23]. In the case of the 100 W linear generator design, all components are series connected; therefore, all series connections become
parallel-connected.
Figure 3.14: Equivalent Electrical Circuit
As a result of the electrical circuit from Figure 3.14, the system inductance of the 100 W
longitudinal flux variable reluctance PM linear generator for a given flux path and a given
stator-to-rotor position would be roughly around 19mH.
3.4.5 Cogging Torque
Cogging torque resists the linear interaction between the stator and rotor. If the magnitude
of the cogging torque becomes large enough, the vertical velocity of the rotor no longer
mirrors the vertical velocity of the waves. Therefore, the potential for energy generation is
reduced. Depending on the location and orientation of the permanent magnets in coordination with the remaining components in the magnetic circuit, the cogging torque can be
reduced to a level which would be more manageable.
57
When the force of the waves is applied to the float, the rotor will begin transitioning
through multiple electric cycles. For a given position, one cycle will consist of one rotor
pole and one rotor gap passing through this position. Conventionally, linear generator
designs space the two endpoints of the stator in a manner which provides a spacing of a
full period between the two as shown in Figure 3.15. However, this arrangement creates an
asynchronous attractive and repelling force between the stator and the rotor. As the rotor
passes the two endpoints of the stator, the cogging torque will introduce one cycle where
attractive and repelling forces are introduced by only one rotor tooth. On the previous
and subsequent cycles, however, the cogging forces nearly doubles as two rotor teeth are
contributing. This relationship between two analytically determined cycles can be seen from
the 100 W generator in Figure 3.16 as the typical configuration.
If there were to be a half period spacing between the two endpoints of the stator, as
shown in Figure 3.15, this asynchronous cogging torque can be reduced. With the endpoints
of the stator spaced in a manner to create half of a cycle between them, the cogging torque
remains consistent between cycles. While one endpoint is affected by the attractive and
repelling forces of one rotor tooth, the other endpoint experiences the affects from two. As
shown in Figure 3.16, the improved configuration takes on a more symmetric shape with
consistent magnitudes for the peaks and nulls. Equation 3.15 represents how this half cycle
spacing can be achieved.
The combination of these attractive and repelling forces can reduce the peak cogging
torque for single phase machine by 27 percent of that which is expected from the typical
stator design and an 18 percent reduction for a three phase machine [24]. As a result, the
rms equivalent of the cogging torque from a single phase and three phase machine is reduced
by 9 percent and 14 percent respectively [24]. Figure 3.17 displays the absolute value of the
cogging torque for a single phase along with the RMS value for the typical and improved
58
Figure 3.15: Full Period and Half Period Spacing of the Stator Endpoints
59
3000
Typical
Improved
2000
Force (Nm)
1000
0
-1000
-2000
-3000
0
5
10
15
Position (mm)
20
25
Figure 3.16: Typical and Improved Single Phase Cogging Force
30
60
configurations.
3000
Typical
Typical RMS
Improved
Improved RMS
2500
abs[Force (Nm)]
2000
1500
1000
500
0
0
5
10
15
Position (mm)
20
25
30
Figure 3.17: Absolute and RMS Values of the Single Phase Cogging Force
3.4.6 Adjustable Frequency
One significant advantage of a variable reluctance machine is the ability to adjust the
frequency at which the machine operates to a rate higher than that of the input frequency.
A variable reluctance machine has the ability to be modified in a manner which imposes
an electrical frequency different from the rest of the system. The mechanical frequency to
which the generator operates is dependent upon the period of the wave. This can be seen
61
in Equation 3.26.
fmech =
1
Twave
(3.26)
The electrical frequency, however, is dependent upon more considerations. As the rotor
moves at a specific linear velocity, the electrical frequency is determined by the geometry of
the teeth and gaps on the rotor with respect to the geometry of the permanent magnets on
the endpoints of the stator. As shown in Equation 3.27, the quantity of rows of permanent
magnets on the primary cylinder can be determined by the desired output frequency, the
typical input frequency of the waves, and the width of the magnets and poles on the rotor.
A one hundred watt and one hundred kilowatt generator was designed at the minimum
condition with two rows per salient pole.
fe =
vwave
2wm
(3.27)
The most basic configuration of magnet, teeth, and gap configuration is shown on the
left in Figure 3.18. If the quantity of magnets on one endpoints of the stator were to double
from two to four while the width of the magnets, teeth, and gaps were to reduce by half
their current size, then the frequency at which the generator operates would double. A
modified viewpoint of the dimensions is shown on the right in Figure 3.18. This type of
modification is irrelevant to the input velocity of the wave, and therefore an essential design
factor in reducing the inductance of the overall system. A point of concern to remember is
the half period spacing between the two endpoints to reduce cogging effects. As the change
in frequency and number of turns occurs, the geometry of the stator may require a change
to reduce cogging torque and account for spacing of the windings.
62
Figure 3.18: Frequency Modified Stator and Rotor Dimensions
63
Chapter 4 – Modeling and Simulation
Validation of the initial assumptions and the expected outcomes are the primary goals for
the process of modeling and simulating the linear generator. While achieving these goals,
there are two stages to the modeling and simulations of the linear generator. The first
stage involves the use of finite element analysis, or FEA, to analyze the magnetic effects of
the system. Here is where the accuracy of the magnetics is verified. FEA is a numerical
technique for finding approximate solutions to differential equations. In the case of the
linear generator design, FEA is used to analyze the magnetostatic effects upon the stator,
the permanent magnets, and the rotor. This is done at various rotor positions in order to
identify how the generator will perform.
The three primary roles of a finite element analysis on the magnetic effects is to verify
the flux does not achieve saturation as it travels around the path, identify the reduced
lamination size and shape, and verify the force produced will exceed that of the minimum
force necessary. The second stage involves developing a generic model that will account
for accurately predict how the variable reluctance permanent magnet linear generator will
operate when various waves are applied. A simulink model was developed for this stage.
While the previous chapter describes how to utilize formulas to develop a generator specific
for a particular output, this model is designed without a desired output in mind. Rather
than utilizing solely the formulas from the previous chapter, the information from the FEA
was incorporated to more accurately predict the system’s response. From the finite element
analysis, look up tables, or LUTs, can be generated to compare the applied current and
position to the amount of generated flux and force. These look up tables were then included
64
integrated with the design formulas to generate a generic model.
FEA, or finite element analysis, provides the opportunity to vary an applied current as
well as the position between devices, such as a rotor and stator. As the name inherently
states, the reluctance varies with position; therefore, the flux will equally vary with position.
While the machine operates in a generating mode, the position and flux will vary inducing
a voltage on the windings. During simulation, however, the reverse is done. To perform a
magnetic analysis of the generator in the same manner as the 100 W and 100 kW analysis,
a current is applied through the windings of one bobbin and the flux and force produced are
measured. The process would be equivalent to motoring a generator, or running a generator
as if it were meant to be a motor.
Obtaining the maximum applied force via magnetic modeling can become a tedious
process. By injecting into the windings the peak desired current, the process consists
of a finite element analysis in 0.5 mm increments. The increments must continue for a
complete electric cycle in order to evaluate the maximum and minimum force generated.
Then verification that the peak force generated exceeds the minimum shear stress must be
done. At the same time, the geometry of the magnetic components is optimized to ensure
saturation will not occur.
The first look up table, shown in Figure 4.1, determines the current from the flux and
current position. The following look up table, shown in Figure 4.2, identifies the phase
specific forces from the current and the position. In order to obtain the information for
both of the look up tables, a sweep of multiple positions at given current values were
simulated to identify the various flux values.
iR = φ<
(4.1)
65
Equation 4.1 shows, there is a linear relationship between the current and flux. For this
reason, linear interpolation can be done between multiple sweeps of current and position
values to identify the remaining flux values. The darkened lines throughout the figure show
actual results of the sweeps modeled through FEA, and the remaining portion of the chart
was taken through linear interpolation.
Figure 4.1: Current Generated given Flux and Position
The flux and position from Figure 4.1 is then used in the next stage of modeling to
identify what the resultant current would become. Through the various sweeps, the force
produced was also obtained. The combination of the current and position is used to determine the output force in a look up table for the next stage of modeling and simulation.
66
Figure 4.2 displays the correlation between the current, position, and force. It can be seen
that in addition to the current and flux relationship, the current and force take on a linear
relationship as well.
Figure 4.2: Generated Force given Current and Position
Due to symmetry of the phases in the variable reluctance PM linear generator, a finite
element analysis is only preformed on one stator bobbin. How the results of one stator
bobbin are interpreted for the entire system, however, depends on the quantity of phases
for the system and the quantity of series and/or parallel connected bobbins per phase. For
a three phase machine with four bobbins per phase, similar to the configuration of the 100
kW generator, the force generated from the analysis would equivalently become one fourth
67
of the force seen upon each of the three phases.
Figure 4.3: Radial Simulation Represented as Two-Dimensions
Figure 4.3 represents four seperate simulations of the magnetic field density taken with
the same current applied at four separate positions. The magnitude of the flux density is
represented by an increasing darkness of the material. It can be seen in Figure 4.3 that
as the position varies, the flux density varies dramatically. In certain locations, the flux
intensity may become too intense causing saturation to occur. In these situations, the
geometry of the stator or rotor must be increased to prevent saturation from occurring. In
the case of the 100 W and 100 kW generators, saturation was not an issue. Instead, the
stator and rotor geometry was reduced in order to lower the size and cost of the device.
After each sweep through one magnetic cycle is complete, modifications can be made yet
again to the previously chosen dimensions.
The dynamics of a variable reluctance linear generator can be modeled via a block
68
level schematic as shown in Figure 4.4. While typical block level diagrams consist of the
mathematical correlations between the inputs and outputs, this schematic incorporates the
magnetic modeling, via FEA, with the mathematical models to more accurately predict how
a variable reluctance permanent magnet machine will operate. The three phase sequence
utilizes two look up tables, or LUTs, to correlate the results of the magnetic modeling
into the model. One particular LUT identifies the current based upon position and flux
while the other uses the current and the position to identify the applied force. With the
simulated data in these LUTs, the block level three phase schematic can determine the
position, velocity, acceleration, phase voltage, phase current, and phase force.
Figure 4.4: Three Phase Simulink Schematic
The next step in the completion of the variable reluctance permanent magnet linear
generator model is to validate its performance to actual data taken from the hardware. The
100 W generator is built and given particular inputs to observe how the hardware responds.
69
Those same inputs are applied to the simulink model, and then compared to the results of
the hardware. As a result, the linear generator designed independently to the output power,
which utilizes the design formulas along with the magnetic effects from FEA, is verified to
an actual linear generator built to produce 100 W. The comparison either validates the
accuracy of the model or provides methods of improvement to further extend the accuracy
of the model. If necessary, as it was in this design, new parameters can be included after
the experimental results. Once this process was complete, the 100 kW linear generator was
designed and modeled with FEA to identify the hardware necessary to construct a device
capable of producing one thousand times the amount of power.
70
Chapter 5 – 100 W Hardware Build and Testing Equipment
While the process of physically constructing of the VRPM machine involves multiple topics
of consideration, the process can be classified into three primary concerns. The development
of the windings for each phase, the alignment of each phase with respect to the others as well
as the rotor, and the various assembly constraints are all necessary to consider before the
development starts. This chapter elaborates on these concerns throughout the development
of the 100 W variable reluctance permanent magnet generator.
5.1 Development of Windings
While the alignment may be the most critical stage in the 100 W build, a high regard for
care should be also taken while developing the windings as they play a significant role in
the energy generation. The windings will dictate the output voltage as well as the power
factor. A significant portion of the build time involves developing and securing this section
of the generator.
5.1.1 Winding the Coils
In order to ensure the geometric shape and proper tension was applied to the windings was
consistently throughout each phase, a winding mechanism was constructed. The winding
mechanism, shown in Figure 5.1, consisted of two horizontally placed rods, an adjustable
tension mechanism, a starting block, two side mounted blocks, and a rotary handle.
71
Figure 5.1: Winding Mechanism
One horizontally placed rod stores the coils yet to be used while the other is used to
mount the starting block and two side mounted blocks. The coils are sent through the
adjustable tension mechanism and to the starting block. A recommendation would be to
lubricate the starting block then reverse applying tape. A starting block is dimension critical. It is made to match the desired shape of the air gap in the center of the windings,
laminations later will be placed through the gap, as well as the desired height of the windings. The material chosen for the block must allow for some flexibility without comprising
the overall dimensions.
Mask the block with tape in a reverse manner as to allow the tape to move freely on
the block while sticking to the first row of windings. This will provide protection for the
insulation on the coils during the removal of the windings from the starting block. As the
second rod is rotated by the connected rotary handle, the windings begin to form around
72
the starting block and between the two side mounted blocks. After every row of windings
have been wound, a layer of glass cloth electrical tape, insolution type H, was applied as an
insulating barrier to reduce the liklehood of a major short occuring. As the winding took
place, the tension upon the coils was regulary checked.
5.1.2 Coil Tension
The amount of tension applied to coils during the winding process will determine the coil
density of the windings. An adjustable tension device was placed in-line with the windings
and the wire spool. While a large density will reduce the volume, the tension must be
adjusted to account for the later included resin. It can be seen in the cross-sectional view of
the windings, shown in Figure 5.2, that with too much tension, the resin is not allowed to
evenly flow between all of the coils. When this occurs air gaps are present around various
coils which will increase the vibration between coils and reduce heat dissipation.
Figure 5.2: Windings with High Tension (Left) and Appropriate Tension (Right)
Rather than surrounding each individual coil, a large portion of the resin surrounds
significant sections of air between the coils as when a high level of tension was applied while
73
winding the mold. While the appropriate tension Figure 5.2 displays some of the same signs
in select portions of the cross-section, the majority of the individual coils are surrounded
within the resin.
5.1.3 Polyepoxide Application
There are a few main benefactors for applying polyepoxide, or epoxy/resin, to the windings
of each phase. Resin prevents unwanted vibration between each of the windings as well as
the associated components. It acts as an insolating barrier to prevent deteriation of the
isolation on the windings due to harsh weather conditions. Additionally, epoxy is known to
dissipate heat from the windings better than if the windings were exposed to air.
The final dimensions with the windings after resin is applied must adhere to stringent
geometric requirements. The windings must fit exactly into the volume allotted by the
stator geometry to ensure the machine will be properly assembled and operate without
incurring a great deal of vibration. The windings with the epoxy must form to a somewhat
tubular shape where the height must be as close as possible to 71.5mm while the inner
diameter is a 40mm x 31.75mm rectangle and the outer diameter cannot exceed 75mm.
In order to ensure such critical dimensions were met, a epoxy mold was constructed out
of polyethylene which is also known as ultra high molecular weight polyethylene, or UMHW.
While resin will form a strong bond with the windings, polyethylene acts as a barrier. The
coils are placed into the mold, the resin is poured into the gaps, the mold is screwed closed,
and the mold remains until the resin is fully hardened. Once this has taken place, the resin
sealed windings are extracted from the mold and ready for use.
74
Figure 5.3: Epoxy Mold
5.1.4 Vacuum Sealing Chamber
When the two solutions, a polymer and a catalyt, are mixed to form epoxy, air pockets
become traped within the mixture. While the epoxy is still in a liquid form, before the
solution has hardened to a solid, a percentage of the air pockets can still be extracted. This
can be done with the utilization of a vacuum sealed chamber. By placing the epoxy mold
into a chamber and apply a vacuum seal, the air pockets will be forced to excape while
the mixture has not yet hardened. There are two main approaches which a vacuum sealed
chamber can be implemented. The chamber could be used after the epoxy has mixed with
the windings or it could be used during the mixing process.
One method would be to have the coils preplaced into the epoxy mold which is within a
vacuumed chamber. This chamber is then used to supply resin, in the liquid form, into one
side of the mold and out another. The alternative solution would be to mix the resin, pour
the resin into the epoxy mold which is housing the windings, and then place the unit into
75
Figure 5.4: Typical Windings without a Vacuum Seal Method
76
a chamber to be used. The ladder solution was used in the 100 W build for ease of various
researching techniques. Multiple resin encased windings were made each a new method
of extracting air pockets from the epoxy mixture. Figure 5.4 displays one set of windings
without any vacuum method applied. It is clearly apparent that the presence of air pockets
within the epoxy is prominant.
Figure 5.5: Windings with a Partial Vacuum Seal Method
Through the various trials of many air extraction techniques, it was found that the ideal
method is to only partially apply a vacuum seal, upon the windings, while the epoxy is still
in liquid form. If a long term vacuum is applied, the act of the vacuum upon the hardening
epoxy can cause pressure changes between the epoxy and air pockets which are significant
77
enough to expand the air pockets without allowing the expanded air pockets to escape. In
this case, the quantity of pockets will remain constant; however, the volume of space they
take up within the windings after the epoxy has hardened will increase. For this reason, a
partial vacuum procedure, only while the epoxy is clearly in liquid form, is most preferred.
Figure 5.5 demonstrates the improvements upon one set of windings when such a procedure
is implemented.
5.2 Alignment
One downfall of the VRPM machine is the necessity for critical alignment. Not only does
the alignment between each phase must match, but the air gap between the stator and the
translator, or rotor, must be maintained within tenths of millimeters throughout the entire
time the rotor is in motion. The alignment of the 100 W system is convoluted with the
assembly of the machine.
The position of the first phase was calibrated to a reference point along the path taken by
the linear bearings. The key point is to align the two endpoints of the phase to the reference
point as motion of the generator, along the linear bearings, takes place. The necessity for
accuracy is again expressed as all future steps rely on the precision of the initial step. The
following stages involve aligning each subsequent phases with the previously alligned phase.
To do so, two aspects are kept in mind; the distance on the new phase with respect to the
previous phase and the alignment to the reference point utilized in the first step must be
reviewed. Each phase was separated by 600 electrical degrees from the subsequent phase.
Spacers are a useful tool for alignment. Spacer were built and used for the 100 W generator
in order to ensure proper separation between the stator and rotor occured. Once all the
phases are properly aligned with each other as well as the reference point, the translator
78
is included by aligning with reference to the air gap requirements. The consistency of the
1 mm air gap for the 100 W generator is then verified through the entire motion of that
which the rotor will allow.
5.3 Assembly Constraints
A necessary factor to consider when developing any device is the assembly process. The
100 W generator build is a perfect example how consideration of the assembly is equally
as important as the design specifications. The device assembly must be taken into consideration during, rather than after, the design process. The difficulty of assembling the
machine can become a commercially limiting factor as it plays a significant role in the
design, development time, and cost of the product.
Without consideration of the device assembly, dilemmas such as the combination of
resin, windings, and stator laminations arise. For this reason, ideas such as stator lamination overlapping have been integrated into the 100 W VRPM machine. Having the stator
laminations as one unit poses issues when trying to integrate the windings into the situation. The common solution is to seperate the laminations into multiple shapes. Having two
seperately shaped stator laminations typically involves a mounting system to ensure the
connection between the two shapes does not create an additional air gap into the magnetic
circuit.
At the same time, eddy current losses are prevalent due to the sharp transition between
components. Developing the iron core into two sections, which when combined overlap each
other, mitigates the previous issues that typically arrise. The overlapping solution allows
for the independent development of the epoxy infused windings while providing a smoother
transition between the components. With this arrangement and the mounting hardware
79
Figure 5.6: Visual of Overlapping Laminations
typically used for the laminations, air gaps between the laminations is less likely and, if
occuring, less severe to the magnetic circuit.
5.4 Integration to the LTB
While typically the stator is the stationary portion of a generator and the rotor is the section
consistently in movement, the roles of each can be replaced and still allow the generator to
operate as expected. In the case of testing the 100 W generator, this reverse implementation
of the stator and rotor was utilized. The components of the stator were attached to a plate
which was driven to move in an vertical direction by a linear test bed, or LTB. Conversely,
the components of the rotor were mounted onto another plate which was firmly secured to
the base of the LTB and remained stationary throughout the testing.
Figures 5.7 and 5.8 demonstrates the layout of the stator and rotor relative to each
other. As a result from the mounting, the LTB was able to receive the same diagnostics as
if the stator were still and the rotor was moving. The exact dimensions of each component
shown in Figures 5.7 and 5.8 are visually shown in the appendix.
80
Figure 5.7: Isometric View of the 3-Phase 100 W Generator
5.4.1 Stator
The stator for the 100 W linear generator consists of three independant modular units, one
for each phase of the three phase machine. Each phase consists of I - shaped laminations
with two sets of magnets at each of the four salient poles. As shown in Figures 5.9 and 5.10,
mounting hardware is used to secure the magnets to the laminations as well as to secure
the windings. The mounting hardware consists of non-magnetic stainless steel c - shaped
clamps and non-magnetic stainless steel screws chosen to not alter the magnetic flux path.
In addition to the previous mounting hardware, there are mounting mechanisms used to
interconnect each phase while remaining electrically isolated. A nonconductive material and
stainless steel mounting hardware are used to physically separate the sets of overlapping
laminations from the interconnecting hardware such as the backing plate to which each
phase is mounted. This backing plate not only secures each phase relative to the subsequent
81
(a) Front View
(b) Top View
Figure 5.8: Front and Top Views of the 3-Phase 100 W Generator
82
(a) Isometric View
(b) Front View
Figure 5.9: Isometric and Front Views of a 1-Phase 100 W Stator
83
phases, but it contains linear guides which dictates the interaction between the rotor and
the stator. With the addition of a block of metal to maintain the rigidity of the backing
plate, the 3 - phase 100 W stator can be viewed in Figures 5.11, 5.12, 5.13, and 5.14.
When the 100 W generator is integrated into the LTB, or linear test bed, the stator
contains a connection rod which links the backing plate of the stator to the yoke of the
LTB. As the LTB manipulates the movement of previously determined waves heights, the
LTB adjusts the vertical position of the yoke which therefore moves all phases of the stator
congruently and relative to the stationary rotor.
5.4.1.1 Phase Separation and Magnet Arrangement
The separation between each of the phases as they are connected to the backing plate must
be taken into consideration. Appropriate separation prevents flux leakage between the end
of one phase and the start of another. The exact position of the separation is essential. The
orientation of the magnets and the separation between the phases upon the backing plate
are chosen to create a three phase sinusoidal output that is equally spaced by one hundred
twenty degrees. The configuration is done in a manner where the top phase represents phase
c, the middle phase represents phase a, and the bottom phase represents phase b.
The configuration of the stator shown in Figure 5.15 is separated by six hundred electrical
degrees or five time one hundred twenty electrical degrees. This provides a two hundred
forty degree electrical separation between neighboring phases while providing an additional
360 mechanical degrees needed during building for properly mounting and spacing each
phase.
The vertical distance between phases is the summation of a multiple and two thirds of
the vertical distance of one salient pole and one gap on the rotor. The factor of two thirds
84
(a) Top View
(b) Side View
Figure 5.10: Top and Side Views of a 1-Phase 100 W Stator
85
Figure 5.11: Isometric View of the 3-Phase 100 W Stator
Figure 5.12: Front View of the 3-Phase 100 W Stator
86
Figure 5.13: Top View of the 3-Phase 100 W Stator
Figure 5.14: Side View of the 3-Phase 100 W Stator
87
develops a two hundred forty degree spacing between the neighboring phase. Equally so,
the orientation of the magnets on the middle phase, phase a, are reversed in comparison to
the others. This reduces the likelihood of leakage flux between phases as it creates a like
polarity between the two magnets on the edge of the previous phase and upcomming phase.
The force that would that would either repel or attract the magnets onto or away from
the endpoints of the salient poles on the stator was small enough to allow the magnets to
be mounted by convential adhesive glue. In fact the force acted in favor of mounting the
magnets as it was an attractive force.
Figure 5.15 contains arrows identifying the north and south orientation of the magnets
at the endpoint of each salient pole for every phase of the 100 W linear generator. The
orientation from a top down perspective is as follows; phase one: north south north south,
phase two: south north south north, and phase three: north south north south.
5.4.2 Rotor
The rotor for the 100 W linear generator consists of laminations, electrically isolating components, mounting hardware, a backing plate, linear rails, and a framing hardware. To the
left and right are a series of laminations joined to form the poles and gaps that form a rotor.
In order to develop the mechanical clearance consistently throughout the operation of the
generator, additional mounting hardware positions the laminations to a particular location
relative to the movement of the stator when located within Oregon State’s Linear Test Bed.
On both ends of the laminations are nonconductive material used to ensure that isolation
between the phases occurs. Mounting hardware and stainless steel screws were introduced
to provide a way to connect to the backing plate.
The backing plate provides the opportunity for the stator and the rotor to interact
88
Figure 5.15: Phase Separation and Permanent Magnet Orientation
89
(a) Isometric View
(b) Front View
Figure 5.16: Isometric and Front Views of the 3-Phase 100 W Rotor
90
together while maintaining the one milimeter mechanical clearance. This is done by the
attached linear rails which interact with the vertical guides on the stator. The backing plate
maintains rigidity while being firmly mounted to the base of the LTB through the use of
the framing hardware.
(a) Top View
(b) Side View
Figure 5.17: Top and Side Views of the 3-Phase 100 W Rotor
91
5.5 Testing Apparatus
The design technique described throughout the thesis was implemented for the construction
of a 100 W 3-phase linear generator. The 100 W 3-phase linear generator was designed as
a proof-of-concept. Therefore rather than developing a fully cylindrical linear generator, a
sectional equivalent version of the design was produced as a proof-of-concept. Essentially,
the 100 W design was developed to prove the concept of the linear generator would operate
as designed and to verify the accuracy of the VRPM model developed in simulink. It
is important to note that the production of a sectional equivalent reduces many of the
benefits previously listed. While modularity is maintained, the optimization of the coils for
each bobbin no longer exists, therefore, resulting in a reduced power factor. The sectional
equivalent version of a one hundred watt three phase linear generator is shown in Figure 5.19.
Figure 5.18: Three-phase Converter for Power Generation
As shown in Figure 5.18, the variable reluctance linear generator was connected to a
power electronics board, or HiRel board, that interfaces with a DC supply, a dSPACE based
control system, and the load. The HiRel board has two 3-phase inverters with an inverter
bus voltage at 42V. To counter-act the poor power factor of variable reluctance machines,
reactive power is applied as a compensation; a technique known as power factor correction.
92
Source of power factor correction is applied via a DC power supply. The DC supply, set to
42V, provided the bus voltage for the inverters while the dSPACE control system dictated
the control of the generator and load based upon the ocean wave’s information.
Figure 5.19: Sectional Equivalent of a 3-Phase 100 W Linear Generator
The rotor laminations shown are at a height of 1001.1mm, 31.75mm deep, and 34.5mm
wide with teeth and gaps at a height and width of 14.3mm. The each phase of the stator
laminations have two endpoints 28.6mm in height and 150mm in width with a 71.5mm tall
and 40mm wide core section allowing for a 71.5mm by 55mm spacing for windings. The magnets attached to the stator endpoints were commercially distributed grade 45 Neodymium
93
Iron Boron, NdFeB45, with dimensions of 14.3mm x 31.75mm x 3.175mm.
(a) Sectional of the Stator Lamination
(b) Sectional of the Stator Lamination
The variable reluctance linear generator was tested in the Linear Test Bed, or LTB, at
the Wallace Energy Systems and Renewables Facility, or WESRF, as shown in Figure 5.21.
The LTB is a unique laboratory testing tool that has the ability to apply a vertical force
equivalent to any sea stat or programmed position. This tool allows researchers to model
the effects which the ocean will impose onto a generator. With the previously gathered
wave information (wave height, period, and velocity), a wave profile was generated by the
LTB and applied to the linear generator.
The LTB is a 17 ft tall x 9 ft wide x 5.5 ft deep device that is capable of controling a
6.5 ft stroke relative stroke via position, velocity, and force control. The LTB creates an
scenerio where the device under test will heave and fall as if the device was acutally in a
wave environment. Depending on the device under test, the LTB can provide 1 m/sec at
20,000 N thrust, 2 m/sec at 10,000 N thrust, or up to 19kW at 95 percent efficiency. The
LTB is designed to create a linear motion between centrally-oriented vertically spar and the
surrounding float shown as in Figure 5.22. [25]
94
Figure 5.20: Rotor Lamination
95
Figure 5.21: Linear Test Bed
Figure 5.22: CAD viewing of the LTB
96
Chapter 6 – Experimental Results
While the non-cylindrical shape of the linear generator simplifies its design, it was this
modification that ultimately caused the poor performance of the maschine. When the
output voltage and output current remain consistent between a 100 W cylindrically shaped
generator and a 100 W sectional equivalent generator, the number of turns with the coils
will change. As a result, the generator inductance for both designs is not the same. If
the sectional equivalent 100 W generator was modified to contain the same magnitude
of inductance as the cylindrically shaped generator, the modification would result in a
reduction of generated power. The large inductance on the sectional equivalent model
resulted in the significantly larger reactive power which further diminished the already low
expected power factor.
It is inherently known that the variable reluctance machines will produce a low power
factor. At one time, the low power factor was the primary reason such machines were
not an appealing topology. However, the advancements in power electronics provided a
technique to counter-act the effects of a power factor machine. In this particular case, the
large number of turns also created a large resistance for this topology which results a small
counter-electromotive force and the machine not achieving the expected performance.
As the 100 W generator is only a portion of the cylindrical shape, only a portion of the
flux seen by a cylindrical generator would be present. In order to reach the desired output,
Equation 3.18 shows that a reduced flux would require an increase in the number of turns.
Unfortunately, the real and reactive power of the generator is directly related to the number
of turns. As the number of turns is modified, Equation 3.23 shows that the stator resistance
97
increases linearly and Equation 3.24 demonstrates that the reactive component increases
by a squared relationship. Therefore, additional power is lost through the windings and a
more significant portion of the maintained level of apparent power becomes reactive.
At the lower speeds rather than producing power, Table 6.1 shows the machine required
power with the active load to achieve higher applied forces. A notable detail from the
experiment is the omission of values for the higher velocities and larger applied forces on
Table 6.1. This data does not exist due to the limited capabilities of the hardware. The
voltage limitation on the power electronics prevented the experiment from going forward
with larger applied forces.
Table 6.1: VRPM Machine 100 W Active Loading
Applied Force
25%
50%
75%
At of 25% of the peak velocity
Ave LTB Power In (W)
6.2
12.7
18.7
VRPM Output Power (W)
2.8
4.3
2.1
Efficiency (%)
45.2
33.9
11.3
At of 50% of the peak velocity
Ave LTB Power In (W)
12.6
24.9
37.4
VRPM Output Power (W)
6.1
13.3
16.7
Efficiency (%)
48.4
53.6
44.7
At of 75% of the peak velocity
Ave LTB Power In (W)
18.9
37.2
VRPM Output Power (W)
8.7
22.1
Efficiency (%)
46.1
59.5
At of 100% of the peak velocity
Ave LTB Power In (W)
25.0
50.4
VRPM Output Power (W)
10.8
31.5
Efficiency (%)
43.0
62.5
At of 125% of the peak velocity
Ave LTB Power In (W)
31.4
VRPM Output Power (W)
12.4
Efficiency (%)
39.4
100%
25.1
-4.8
-19.19
98
Chapter 7 – Conclusion
With the potential and accessibility of wave energy, it is capable of becoming the next major
alternative energy source. There are a few new technologies emerging to harness the wave
potential and convert it into wave energy. A point absorber is one of those technologies.
While multiple machine (motors/generator) topologies exist, a variable reluctance permanent magnet machine, VRPM, would be the most applicable method of generating energy
from ocean waves via a point absorber. A variable reluctance machine is a robust generator
that can reliably operate at low speeds with consistently variable input amplitudes and
frequencies in the harsh conditions of an ocean environment. A longitudinal flux VRPM
linear generator can be redesigned in a cylindrical manner to reduce or eliminate issues that
a conventional longitudinal flux generator would experience.
When considering the VRPM machine, the amount of energy extracted from the waves
are strongly influenced by the type and shape of the permanent magnets as well as the
mechanical clearance between the rotor and stator. The interaction between the two will
modify the amount of apparent power produced along with the power factor. The dimensions of the remaining linear generator components are dictated by the geometry of the
permanent magnets, the mechanical clearance, and any physical constraints that may arise
due to the cost and construction associated with the commercialization of this product.
While a generator may be capable of producing a certain amount of apparent power,
losses and the inductive nature of the VRPM machine prevents the amount of real power
outputted from the device. The performance of the generator can be improved by reducing
the losses and the reactive component of the apparent power. This can be done by increasing
99
the electrical frequency, increasing the quantity of permanent magnets, and increasing the
size of the wire used for the windings. Each of these techniques can be independently carried
out or a combination of each can be implemented.
7.1 Future Work
There are various techniques, which can be implemented during the design of the linear
generator, that would provide improvements to the performance of the generator. Of these
techniques, four in particular are worth taking into consideration during future designs.
Increasing the cross sectional area, or equivalently the quantity, of permanent magnets
can be accomplished by increasing the width of the salient poles, therefore, allotting additional space for magnets to be mounted. This technique is fairly straight forward as it
reduces the minimum shear stress requirement while increasing the amount of shear stress
produced. This concept opens up the consideration for additional techniques.
The second technique emerges as an expansion from the original. Figure 3.5 demonstrates that an increase in the thickness of the permanent magnets results in an increase
in the generator’s power factor. Additionally, Figure 3.10 identifies that an increase in the
mechanical clearance between the rotor and stator would reduce the produced shear stress.
Therefore, one can increase the mechanical clearance of the device while increasing the geometry of the permanent magnets, to maintain the generator output specifications, in order
to increase the power factor of the generator.
Both techniques increase the amount of flux flowing through the flux path which provides
an additional benefit. As the flux increases, Equation 3.18 identifies that the amount of
turns necessary to produce the desired output voltage can be reduced. Equation 3.23
demonstrates how a linear decrease in the number of turns results in a linear reduction in
100
the real power loss. The reactive power shown in Equation 3.24 also demonstrates a linear
reduction. As the apparent power remains consistent, this reduction increases the amount
of real power produced.
The downfall of the first two techniques is that an increase in the volume of permanent
magnets results in an increase in the stator and rotor geometry of the device. There is an
additional way to improve the performance by modifying the geometry of the magnets while
maintaining the existing volume. This can be done due to an electrical gearing effect which
this generator topology possesses. This technique is similar to the previous one as it reduces
the number of turns which reduces the real power loss and reactive power. Equation 3.18
demonstrates how an increase in the electrical frequency will provide the same advantages
as if the flux were to increase. Section 3.4.6 discusses the intricate details on how to modify
the geometry of the VRPM machine to increase the electrical frequency.
The final, and relatively straight forward, technique which can be used to reduce real
power losses would be to increase the size of the wire used for the windings as an increase
in the wire size would reduce the amount of resistive losses. Table 3.7 demonstrates that an
increase in wire size from 14 AWG to 12 AWG would result in a 36 to 37 percent reduction
in the resistive losses. A large wire size additionally permits higher currents to flow for
cases when the wave velocity exceeds the predicted values. Pending there is space available
to accommodate for an increased wire size, a larger wire size may be one of the preferred
techniques as it would benefit the performance of the generator without significant design
modifications.
101
Bibliography
[1] National Data Buoy Center. Station 46050 - stonewall banks - 20nm west of newport,
or. http://www.ndbc.noaa.gov/station_history.php?station=46050, 2009.
[2] Magcraft. Permanent magnet selection and design handbook. National Imports, April
2007.
[3] Howard W. Sams. Handbook of Electronic Tables and Formulas. Howard W. Sams and
Company, fifth edition, 1979.
[4] European Wind Energy Association. Statistics. http://www.ewea.org/index.php?
id=1486, 2009.
[5] Ocean Energy Council. Wave energy. http://www.oceanenergycouncil.com/index.
php/Wave-Energy/Wave-Energy.html, 2008.
[6] Dr. Ted K. Brekken. Personal interview, 2008. Oregon State University.
[7] US Department of Energy. Energy efficiency and renewable energy. http://www.
energysavers.gov/renewable_energy/ocean/index.cfm/mytopic=50010, 2009.
[8] Mike Robinson. Renewable energy technologies for use on the outer continental shelf. http://ocsenergy.anl.gov/documents/docs/NREL_Scoping_6_06_2006_
web.pdf, 2006.
[9] University Corporation for Atmospheric Research. Density of ocean water. http://
www.windows.ucar.edu/tour/link=/earth/Water/density.html&edu=high, 2001.
[10] WESRF. Wave energy presentation. http://eecs.oregonstate.edu/wesrf/, 2009.
[11] Pelamis. Pelamis wave power. http://www.pelamiswave.com/index.php, 2009.
[12] Sonal Patel. A new wave: Ocean power. Electric Power Conference and Exhibition,
May 2008.
[13] E. Spooner and L. Haydock. Vernier hybrid machines, pages 655–662. IEE Proc.
Electr. Power Appl., 2003.
[14] P.R.M. Brooking and M.A. Mueller. Power conditioning of the output from a linear vernier hybrid permanent magnet generator for use in direct drive wave energy
converters. IEE Proc.-Gener. Transm. Distrib., 152(5), September 2005.
102
[15] Berkeley Mechanics Research Group.
Transverse flux machine.
e-driveonline.com/images/Presentations/, February 2007.
[16] Wolfgang Hill.
6043579.
Permanently excited transverse flux machine, 1996.
http://
US Patent
[17] E. Muljadi and J. Green. Cogging torque reduction in a permanent magnet wind turbine generator. American Society of Mechanical Engineers Wind Energy Symposium,
21(CP-500-30768), January 2002.
[18] Al Schacher. Novel control design for point absorber wave energy convertors, 2007.
Thesis for Master of Science.
[19] Joseph Prudell. Novel design and implementation of a permanent magnet linear tubular
generator for ocean wave energy conversion, 2007. Thesis for Master of Science.
[20] Roger Bedard.
Oregon offshore wave power demonstration project.
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Final_RB_121305.pdf, 2005.
[21] BBAutomacco. Ndfeb magnets - neodymium iron boron. http://www.bbautomacao.
com/Mag_NdFeB.htm, 2009.
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Prop, 2003.
[23] E. C. Cherry. The Duality Between Electric and Magnetic Circuits and the Formation
of Transformer Equivalent Circuits, pages 101–111. Proc. Physical Soc. London, 1949.
[24] Zuan Yen. Personal interview, 2008. Oregon State University.
[25] A. VanderMeulen E. Amon C. York A. Schacher T. Brekken A. von Jouanne P. Hogan,
K. Rhinefrank and B. Paasch. A unique wave energy linear test bed design and control.
AiAA Aerospace Sciences Meeting and Exhibit, January 2008.
103
APPENDICES
104
The MATLAB code used to solely for the purpose of developing a significant portion of
the plots throughout the thesis is shown below. The performance for the constructed 100
W variable reluctance permanent magnet linear generator was intially calculated. The code
follows with by modifying certain design parameters to identify methods of improvement
for the 100 W generator.
1
2
% 100 W 3PH RMS Power and Loss Calculations
3
clear;
4
clc;
5
6
c = 1;
% Mechanical clearance, units: mm
7
h = 2;
% Magnet thickness, units: mm
8
w = 14.3*10ˆ−3;
% Magnet width, units: m
9
%w = h*7;
% Magnet width (with w/h ratio), units: m
10
th = 31.75*10ˆ−3;
% Magnet depth (into paper of a 2D view), units: m
11
d = 100*10ˆ−3;
% Windings diameter, units: m
13
uo = 4*pi*10ˆ−7;
% Permeability of free space, units: H/m
14
ur = 1;
% Relative permeability, unitsless
16
A100 = 4*th*w;
% Cross sectional area, units: mˆ2
17
Acyc = 2*pi*d*w;
% Area (cylindrical form), units: mˆ2
19
Hc = 890000;
% Magnetic field intensity, units: A/m
20
Br = 1.23;
% Magnetic flux density, units: N/Am
21
v = 0.8;
% Vertical wave velocity, units: m/s
12
15
18
22
23
% −−−−−−−−− Calculations Specifically for the 100 W generator −−−−−−−−−
105
24
25
vout = 20;
% Desired output voltage, units: volts
26
iout = 5.6;
% Desired output current, units: amps
27
fm = 1/1.9;
% Mechanical operating frequency (0.5263 Hz)
28
f = v/(2*w);
% Electrical operating frequency (27.9720 Hz)
29
flux = 0.000253;
% −−−−−−−−− SIMULATED VALUE −−−−−−−−−
30
N = vout/(flux*2*pi*f); % Number of turns for the windings (449.7857)
31
r100 = ((h*10ˆ−3)+(c*10ˆ−3)) / (uo*ur*A100);
32
L = Nˆ2/r100;
% Phase Inductance (0.1539 H)
33
rpf = 0.008286;
% Resistance/meter of 14 AWG
34
Rs = rpf*(pi*d)*N;
% Coil Resistance (1.1708 ohms)
35
ploss100 = ioutˆ2*(Rs); % Peak Power Loss (36.7178 Watts)
% reluctance (1314500 1/H)
36
37
tau100num = (Hc*Br)*((h*10ˆ−3)/w)*(sqrt(((h*10ˆ−3)+(c*10ˆ−3))ˆ2+(w/2)ˆ2)
− ((h*10ˆ−3)+(c*10ˆ−3)));
38
39
tau100den = (sqrt(((h*10ˆ−3)+(c*10ˆ−3))ˆ2+(w/2)ˆ2)+((h*10ˆ−3)+(c*10ˆ−3)));
40
tau100 = tau100num / tau100den;
41
preftau100 = (100 / v) / A100;
42
P100 = tau100 * A100 * v − ploss100; % Peak Real Power (61.6157 Watts)
43
Q100 = ioutˆ2 *2*pi*f * L;
% Peak Reactive Power (848.2416 VAR)
44
Smag100 = sqrt(P100ˆ2 + Q100ˆ2);
% Apparent Power (850.4765 VA)
45
S100 = P100 + j*Q100;
% Complex Power (61.6157+850.4765i)
% Peak Preferred Shear Stress (68829 N/m)
46
47
Prms3phase = 3*P100/2;
% 3 Phase RMS Real Power (92.4235 W)
48
Qrms3phase = 3*Q100/2;
% 3 Phase RMS Reactive Power (1272.4 VAR)
49
% −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
50
51
x2 = 20;
% sweep of h, from 1 to x2
52
x3 = 4;
% accuracy per mm
53
for c = 1:5
106
for h = 1:x2
54
55
w = ((h/x3)*10ˆ−3)*7; % Maintain the w−to−h Ratio
56
A = 4*th*w;
57
f = v/(2*w);
% New Electrical Frequency
58
N = 450;
% Evaluated with a contant number of turns
59
r(c,h) = (((h/x3)*10ˆ−3)+(c*10ˆ−3)) / (uo*ur*A); % Reluctance
60
L(c,h) = Nˆ2/r(c,h);
61
ploss(c,h) = ioutˆ2*(Rs); % Peak Losses
% New Cross sectional Area
62
taunum(c,h) = (Hc*Br)*(((h/x3)*10ˆ−3)/w)*(sqrt((((h/x3)*10ˆ−3)
63
+ (c*10ˆ−3))ˆ2+(w/2)ˆ2)−(((h/x3)*10ˆ−3)+(c*10ˆ−3)));
64
taudem(c,h) = (sqrt((((h/x3)*10ˆ−3)+(c*10ˆ−3))ˆ2+(w/2)ˆ2)
65
+ (((h/x3)*10ˆ−3)+(c*10ˆ−3)));
66
67
tau(c,h) = taunum(c,h) / taudem(c,h);
68
preftau(c,h) = (100 / v) / A;
% Desired Shear Stress
69
Pwoloss(c,h) = tau(c,h)*A*v;
% Peak Real Power before losses
70
P(c,h) = tau(c,h)*A*v−ploss(c,h);
% Peak Real Power
71
Q(c,h) = ioutˆ2*2*pi*f*L(c,h);
% Peak Reactive Power
72
Smag(c,h) = sqrt(P(c,h)ˆ2+Q(c,h)ˆ2); % Apparent Power
73
S = P(c,h)+j*Q(c,h);
% Complex Power
74
PF(c,h) = (P(c,h))/(Smag(c,h));
% Power Factor
end
75
76
end
77
% −−−−−−−−−−−−−−−−−−−−−− PLOTTING −−−−−−−−−−−−−−−−−−−−−−
78
79
% −−−−−−−−−−−−−−−−−−−−−− 2−D Plots −−−−−−−−−−−−−−−−−−−−−
80
% Plotting Shear Stress
81
figure
82
plot([1:x2]/x3, tau(1,:),'−ro');
83
hold on
107
84
plot([1:x2]/x3, tau(2,:), '−*');
85
hold on
86
plot([1:x2]/x3, tau(3,:), 'b');
87
hold on
88
plot([1:x2]/x3, tau(4,:), 'g');
89
hold on
90
plot([1:x2]/x3, tau(5,:), 'r');
91
hold on
92
plot([1:x2]/x3, preftau(1,:),'−−r');
93
xlabel('Permanent Magnet Thickness, h (in mm)')
94
ylabel('Shear Stress (N/m)')
95
legend('c=1mm','c=2mm','c=3mm','c=4mm','c=5mm','Desired Shear Stress')
96
97
% Plotting Power from Permanent Magnets (Before Losses)
98
figure
99
plot([1:x2]/x3, Pwoloss(1,:),'−ro');
100
hold on
101
plot([1:x2]/x3, Pwoloss(2,:), '−*');
102
hold on
103
plot([1:x2]/x3, Pwoloss(3,:), 'b');
104
hold on
105
plot([1:x2]/x3, Pwoloss(4,:), 'g');
106
hold on
107
plot([1:x2]/x3, Pwoloss(5,:), 'r');
108
xlabel('Permanent Magnet Thickness, h (in mm)')
109
ylabel('Power Generated (Watts)')
110
legend('c=1mm','c=2mm','c=3mm','c=4mm','c=5mm')
111
112
% Plotting Desired Shear Stress
113
figure
108
114
plot([1:x2]/x3, preftau(1,:),'−ro');
115
hold on
116
plot([1:x2]/x3, preftau(2,:), '−*');
117
hold on
118
plot([1:x2]/x3, preftau(3,:), 'b');
119
hold on
120
plot([1:x2]/x3, preftau(4,:), 'g');
121
hold on
122
plot([1:x2]/x3, preftau(5,:), 'r');
123
xlabel('Permanent Magnet Thickness, h (in mm)')
124
ylabel('Desired Shear Stress (N/m)')
125
126
% Plotting Reluctance
127
figure
128
plot([1:x2]/x3, r(1,:),'−ro');
129
hold on
130
plot([1:x2]/x3, r(2,:), '−*');
131
hold on
132
plot([1:x2]/x3, r(3,:), 'b');
133
hold on
134
plot([1:x2]/x3, r(4,:), 'g');
135
hold on
136
plot([1:x2]/x3, r(5,:), 'r');
137
xlabel('Permanent Magnet Thickness, h (in mm)')
138
ylabel('Reluctance (1/H)')
139
legend('c=1mm','c=2mm','c=3mm','c=4mm','c=5mm')
140
141
% Plotting Real Power Output
142
figure
143
plot([1:x2]/x3, P(1,:),'−ro');
109
144
hold on
145
plot([1:x2]/x3, P(2,:), '−*');
146
hold on
147
plot([1:x2]/x3, P(3,:), 'b');
148
hold on
149
plot([1:x2]/x3, P(4,:), 'g');
150
hold on
151
plot([1:x2]/x3, P(5,:), 'r');
152
hold on
153
xlabel('Permanent Magnet Thickness, h (in mm)')
154
ylabel('Real Power (Watts)')
155
legend('c=1mm','c=2mm','c=3mm','c=4mm','c=5mm')
156
157
% Plotting Reactive Output
158
figure
159
plot([1:x2]/x3, Q(1,:),'−ro');
160
hold on
161
plot([1:x2]/x3, Q(2,:), '−*');
162
hold on
163
plot([1:x2]/x3, Q(3,:), 'b');
164
hold on
165
plot([1:x2]/x3, Q(4,:), 'g');
166
hold on
167
plot([1:x2]/x3, Q(5,:), 'r');
168
hold on
169
xlabel('Permanent Magnet Thickness, h (in mm)')
170
ylabel('Reactive Power (VAR)')
171
legend('c=1mm','c=2mm','c=3mm','c=4mm','c=5mm')
172
173
% Comparision between Real and Reactive Output Power
110
174
figure
175
plot(P(1,:),Q(1,:),'−ro');
176
hold on
177
plot(P(2,:),Q(2,:), '−*');
178
hold on
179
plot(P(3,:),Q(3,:), 'b');
180
hold on
181
plot(P(4,:),Q(4,:), 'g');
182
hold on
183
plot(P(5,:),Q(5,:), 'r');
184
hold on
185
xlabel('Real Power (in Watts)')
186
ylabel('Reactive Power (in VAR)')
187
legend('c=1mm','c=2mm','c=3mm','c=4mm','c=5mm')
188
189
% Plotting Apparent Power
190
figure
191
plot([1:x2]/x3, Smag(1,:),'−ro');
192
hold on
193
plot([1:x2]/x3, Smag(2,:), '−*');
194
hold on
195
plot([1:x2]/x3, Smag(3,:), 'b');
196
hold on
197
plot([1:x2]/x3, Smag(4,:), 'g');
198
hold on
199
plot([1:x2]/x3, Smag(5,:), 'r');
200
hold on
201
xlabel('Permanent Magnet Thickness, h (in mm)')
202
ylabel('Apparent Power (in VA)')
203
legend('c=1mm','c=2mm','c=3mm','c=4mm','c=5mm')
111
204
205
% Plotting Power Factor
206
figure
207
plot([1:x2]/x3, PF(1,:),'−ro');
208
hold on
209
plot([1:x2]/x3, PF(2,:), '−*');
210
hold on
211
plot([1:x2]/x3, PF(3,:), 'b');
212
hold on
213
plot([1:x2]/x3, PF(4,:), 'g');
214
hold on
215
plot([1:x2]/x3, PF(5,:), 'r');
216
hold on
217
xlabel('Permanent Magnet Thickness, h (in mm)')
218
ylabel('PF')
219
legend('c=1mm','c=2mm','c=3mm','c=4mm','c=5mm')
220
221
% −−−−−−−−−−−−−−−−−−−−−− 3−D Plots −−−−−−−−−−−−−−−−−−−−−
222
% Plotting Shear Stress vs. h vs. c
223
[h,c]=meshgrid([1:x2],1:5);
224
surf(h,c,tau)
225
xlabel('Magnet Thickness, h (in mm)')
226
ylabel('c (in mm)')
227
zlabel('Shear Stress (N/m)')
228
229
% Plotting Apparent Power vs. h vs. c
230
figure
231
[h,c]=meshgrid([1:x2],1:5);
232
surf(h,c,Smag)
233
xlabel('Magnet Thickness, h (in mm)')
112
234
ylabel('c (in mm)')
235
zlabel('Apparent Power (N/m)')
236
237
% Plotting Real Power vs. h vs. c
238
figure
239
[h,c]=meshgrid([1:x2],1:5);
240
surf(h,c,P)
241
xlabel('Magnet Thickness, h (in mm)')
242
ylabel('c (in mm)')
243
zlabel('Real Power (N/m)')
113
The contents enclosed below are the specific dimensions the major components of the
100 W linear generator that was designed, built, and tested at OSU’s WESRF Facility.
The formation of the 100 W linear generator lead way to the development guidelines listed
throughout the thesis. Machine tolerances for each component are listed for each drawing.
The majority of the units are metric as listed on each document; however, some drawings
are found in inches.
Figure 1: Back Plate
PROPRIETARY AND CONFIDENTIAL
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
NEXT ASSY
4
APPLICATION
1500
USED ON
150
150
150
150
150
150
300
70.8
438.80
199.4
3
DO NOT SCALE DRAWING
FINISH
STEEL
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
CHECKED
DATE
QUANTITY = 1
2
COMMENTS: 6.35mm (0.25in) THICKNESS
Q.A.
MFG APPR.
ENG APPR.
SGE
NAME
28X THRU
5.25
DRAWN
48.90
UNLESS OTHERWISE SPECIFIED:
48.90
REV
SCALE: 1:16 WEIGHT:
1
SHEET 1 OF 1
A BackPlate 1.0
SIZE DWG. NO.
TITLE:
114
Figure 2: BarStock 075x075
PROPRIETARY AND CONFIDENTIAL
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
NEXT ASSY
4
APPLICATION
USED ON
28.44
28.44
635
3
DO NOT SCALE DRAWING
FINISH
STEEL
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
112.69
176.37
176.37
112.69
9.525
19.05
SGE
NAME
DATE
QUANTITY = 1
2
SCALE: 1:8 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
BarStock075x075
SIZE DWG. NO.
TITLE:
5.11 THRU ALL
11.11
5.08
COMMENTS: 19.05MM (0.75") THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
5X
115
Figure 3: Magnet Clamp
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
NEXT ASSY
15
3.90 THRU
PROPRIETARY AND CONFIDENTIAL
2X
4
APPLICATION
USED ON
3
DO NOT SCALE DRAWING
FINISH
ALUMINUM
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
55
SGE
NAME
QUANTITY = 12
COMMENTS: 15MM THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
2
DATE
11.50
5.75
15
SCALE: 2:1 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
MagnetClamp
SIZE DWG. NO.
TITLE:
7.50
7.50
116
Figure 4: Magnet Clamp 2
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
15
15
NEXT ASSY
4
APPLICATION
11.50
USED ON
3
DO NOT SCALE DRAWING
FINISH
ALUMINUM
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
55
SGE
NAME
QUANTITY = 12
COMMENTS: 15MM THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
5.75
2
DATE
SCALE: 2:1 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
MagnetClamp2
SIZE DWG. NO.
TITLE:
HOLES TAPPED FROM THIS SURFACE
7.50
7.50
2X
2.71 THRU ALL
6-32 UNC THRU ALL
117
Figure 5: Phase Arm Clamp
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
2X
NEXT ASSY
4
USED ON
7.50
7.50
APPLICATION
5.25 THRU
45
3
DO NOT SCALE DRAWING
FINISH
ALUMINUM
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
58.50
SGE
NAME
QUANTITY = 12
COMMENTS: 15MM THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
11.75
15
2
DATE
SCALE: 1:1 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
Phase_ArmClamp
SIZE DWG. NO.
TITLE:
118
Figure 6: Phase Back Plate
112.690
176.370
176.370
112.690
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
635
28.440
NEXT ASSY
75
4
APPLICATION
BACK VIEW
USED ON
7.10
38
59.80
38
30
5.25 THRU
3
DO NOT SCALE DRAWING
FINISH
STEEL
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
14.90
24x
SGE
NAME
DATE
150
94
FRONT VIEW
QUANTITY = 1
2
COMMENTS: 6.35MM (0.25IN) THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
43.500
43.500
43.500
43.500
43.500
43.500
16 X
3.80 THRU ALL
10-24 UNC THRU ALL
5X
3.80 THRU ALL
10-24 UNC THRU ALL
SCALE: 1:1 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
Phase_BackPlate
SIZE DWG. NO.
TITLE:
28
66.880
61.500
27.870
61.500
27.870
61.500
119
Figure 7: Phase Clamp
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
NEXT ASSY
5.25 THRU
PROPRIETARY AND CONFIDENTIAL
2X
4
APPLICATION
USED ON
3
DO NOT SCALE DRAWING
FINISH
ALUMINUM
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
SGE
NAME
QUANTITY = 6
COMMENTS: 15 MM THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
5
5
70
7.50
7.50
2
DATE
SCALE: 1:1 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
Phase_clamp
SIZE DWG. NO.
TITLE:
45
15
120
Figure 8: Phase Spacer 2.5 Inch
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
110
NEXT ASSY
8
4
10
USED ON
43.50
4.76
9.65
APPLICATION
4X
3.80
10-24 UNC
3
DO NOT SCALE DRAWING
FINISH
STEEL
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
63.50
SGE
NAME
8
QUANTITY = 6
4.76
9.65
2
DATE
19.50
43.50
10
SCALE: 1:1 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
SIZE DWG. NO.
Phase_spacer2andhalfinch
Phase_spacer2andhalfinch
55
4.76
9.65
TITLE:
19.50
COMMENTS: 3.175MM THICKNESS
(0.125IN)
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
63.50
2X
3.80
10-24 UNC
4X
3.80
10-24 UNC
121
Figure 9: Phase Bottom PVC Spacer
43.50
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
63.50
10
8
NEXT ASSY
4
APPLICATION
USED ON
19.50
3
DO NOT SCALE DRAWING
FINISH
PLASTIC
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
55
110
SGE
NAME
QUANTITY = 6
COMMENTS: 6.35MM THICKNESS
(0.25IN)
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
19.50
2
DATE
5.25 THRU
SCALE: 1:1 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
SIZE DWG. NO.
PhaseBottomPVCspacer
PhaseBottomPVCspacer
TITLE:
6X
122
28.60
10
UNDESIRABLE
LOCATIONS
LOCATION
FOR TAB INSERTS
150
40
Figure 10: Lamination Part B
M19
C4
.1MM
DO NOT SCALE DRAWING
FINISH
MATERIAL
+
UNLESS OTHERWISE NOTED
TOLERANCES
ALL DIMENSIONS IN MM
1
REV #
QUANTITY
200
THICKNESS 24 GAUGE
COMMENTS:
DATE
11/28/2007
TOP BOT LAM B
PART NAME:
SE/JY
DESIGNER
55
A
SHEET
OREGON STATE UNIVERSITY
SIZE DWG. NO.
123
28.60
61.50
55
150
Figure 11: Lamination Part C
55
C4
M19
.1MM
DO NOT SCALE DRAWING
FINISH
MATERIAL
+
UNLESS OTHERWISE NOTED
TOLERANCES
ALL DIMENSIONS IN MM
UNDESIRABLE
LOCATION
LOCATIONS
FOR TAB INSERTS
1
REV #
QUANTITY
200
THICKNESS 24 GAUGE
COMMENTS:
DATE
11/28/2007
TOP BOT LAM C
PART NAME:
SE/JY
DESIGNER
A
SHEET
OREGON STATE UNIVERSITY
SIZE DWG. NO.
124
Figure 12: Translator
34.50
1101.10
14.30
M19
C4
.1MM
DO NOT SCALE DRAWING
FINISH
MATERIAL
+
UNLESS OTHERWISE NOTED
TOLERANCES
ALL DIMENSIONS IN MM
1
REV #
QUANTITY
170
DATE
11/28/2007
THICKNESS 24 GAUGE
COMMENTS:
TRANSLATOR
PART NAME:
SE/JY
DESIGNER
UNDESIRABLE
SIDE
FOR TAB INSERTS
14.30
14.30
A
SIZE DWG. NO.
SHEET
OREGON STATE UNIVERSITY
125
Figure 13: Translator Spacer
1.319
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
1.319
9.525( 0.2)
NEXT ASSY
4
APPLICATION
USED ON
35.75
3
DO NOT SCALE DRAWING
FINISH
PLASTIC
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN INCHES
TOLERANCES: +/- 0.01 IN UNLESS
OTHERWISE SPECIFIED
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
24.49
SGE
NAME
QUANTITY = 4
2
DATE
18.86
COMMENTS: 3/8 IN THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
30.12
0.221 THRU
UNLESS OTHERWISE SPECIFIED:
41.38
43.35 ±.20
8X
SCALE: 1:8 WEIGHT:
A
1
1.0
REV
.262
SHEET 1 OF 1
TranslatorSpacer
SIZE DWG. NO.
TITLE:
13.23
7.60
1.97
126
Figure 14: Tubing 2x1x337mm
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
4X
NEXT ASSY
4
APPLICATION
5.25 THRU
USED ON
3
DO NOT SCALE DRAWING
FINISH
STEEL
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
25.40
50.80
SGE
NAME
DATE
QUANTITY = 1X WITH HOLES
4X WITHOUT HOLES
2 INCH BY 1 INCH TUBING
2
COMMENTS: 6.35 (0.25 IN) THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
20
48.90
199.40
48.90
SCALE: 1:4 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
Tubing2x1x337mm
SIZE DWG. NO.
Tubing2x1x337mm
TITLE:
127
Figure 15: Tubing 2x1x800mm
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
NEXT ASSY
4
APPLICATION
USED ON
3
DO NOT SCALE DRAWING
FINISH
STEEL
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
50.80
800
SGE
NAME
DATE
QUANTITY = 2X
2 INCH BY 1 INCH TUBING
2
COMMENTS: 6.35 (0.25IN) THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
SCALE: 1:8 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
Tubing2x1x800mm
SIZE DWG. NO.
Tubing2x1x800mm
TITLE:
128
Figure 16: Angle Tubing 2x1x894mm
PROPRIETARY AND CONFIDENTIAL
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
NEXT ASSY
4
APPLICATION
USED ON
50.80
894.427
50.80
3
DO NOT SCALE DRAWING
FINISH
STEEL
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
25.40
101.60
SGE
NAME
DATE
QUANTITY = 2X
2 INCH BY 1 INCH TUBING
2
COMMENTS: 6.35 (0.25IN) THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
SCALE: 1:8 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
Tubing2x1x894mmAngle
SIZE DWG. NO.
Tubing2x1x894mmAngle
TITLE:
129
Figure 17: Tubing 2x1x1500mm
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
NEXT ASSY
4
APPLICATION
USED ON
25.40
3
DO NOT SCALE DRAWING
FINISH
STEEL
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN MM
TOLERANCES: +/- 0.1MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
SGE
NAME
DATE
QUANTITY = 2X
2 INCH BY 1 INCH TUBING
2
COMMENTS: 6.35 (0.25IN) THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
50.80
UNLESS OTHERWISE SPECIFIED:
1500
SCALE: 1:16 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
Tubing2x1x1500mm
SIZE DWG. NO.
Tubing2x1x1500mm
TITLE:
130
Figure 18: Tubing 35x35x1200mm
5
THE INFORMATION CONTAINED IN THIS
DRAWING IS THE SOLE PROPERTY OF
OREGON STATE UNIVERSITY. ANY
REPRODUCTION IN PART OR AS A WHOLE
WITHOUT THE WRITTEN PERMISSION OF
OREGON STATE UNIVERSITY IS
PROHIBITED.
PROPRIETARY AND CONFIDENTIAL
1200
NEXT ASSY
88.90
41.050
7.125
143
143
143
143
143
143
143
99.50
4
APPLICATION
USED ON
FRONT VIEW
3
DO NOT SCALE DRAWING
FINISH
STEEL
MATERIAL
INTERPRET GEOMETRIC
TOLERANCING PER:
DIMENSIONS ARE IN INCHES
TOLERANCES: +/- 0.1 MM
FRACTIONAL
ANGULAR: MACH
BEND
TWO PLACE DECIMAL
THREE PLACE DECIMAL
UNLESS OTHERWISE SPECIFIED:
16X
3.797
15
10-24 UNC
9.650
SGE
NAME
DATE
QUANTITY = 2X
3.5 INCH BY 3.5 INCH TUBING
2
COMMENTS: 6.35 (0.25IN) THICKNESS
Q.A.
MFG APPR.
ENG APPR.
CHECKED
DRAWN
48.90
20
150
150
150
150
150
150
150
BACK VIEW
12.830
9.650
SCALE: 1:1 WEIGHT:
A
1
1.0
REV
SHEET 1 OF 1
Tubing35x35x1200mm
SIZE DWG. NO.
Tubing35x35x1200mm
TITLE:
14X
3.797
10-24 UNC
131