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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 41 44 45 48 56 60 Modeling and Simulation . . . . . . . . . . 63 TABLE OF CONTENTS (Continued) Page 5 100 W Hardware Build and Testing Equipment . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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. 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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