Patent Publication Number: US-2015076827-A1

Title: Energy harvesting systems for power take-off (pto) modules

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is:
         a continuation-in-part of U.S. application Ser. No. 13/361,806 (docket no. OSC-P008), filed Jan. 30, 2012, which claims the benefit of:
           U.S. Provisional Application No. 61/437,586 (docket no. OSC-P008P), filed Jan. 28, 2011;   
           a continuation-in-part of U.S. application Ser. No. 13/541,250 (docket no. OSC-P006C1), filed Jul. 3, 2012, which is:
           a continuation of U.S. application Ser. No. 13/016,895 (docket no. OSC-P006), filed Jan. 28, 2011, which claims the benefit of priority of:
               U.S. Provisional Application No. 61/328,396 (docket no. OSC-P006P), filed on Apr. 27, 2010, and   U.S. Provisional Application No. 61/300,438 (docket no. OSC-P004P), filed on Feb. 1, 2010;   
               a continuation-in-part of U.S. application Ser. No. 13/016,828 (docket no. OSC-P004), filed on Jan. 28, 2011;   a continuation-in-part of U.S. application Ser. No. 13/336,843 (docket no. OSC-P004CIP), filed on Dec. 23, 2011;   a continuation-in-part of U.S. application Ser. No. 13/333,173 (docket no. OSC-P007), filed on Dec. 21, 2011, which claims the benefit of priority of:
               U.S. Provisional Application No. 61/425,753 (docket no. OSC-P007P), filed on Dec. 21, 2010, and   U.S. Provisional Application No. 61/482,146 (docket no. OSC-P009P), filed on May 3, 2011;   
               
               

     Each of these patent applications is incorporated by reference herein in its entirety. 
    
    
     STATEMENT OF FEDERALLY SPONSORED RESEARCH 
     This invention was made in part with Government support under Grant No: IIP-1014346 awarded by the National Science Foundation (NSF) and Contract No: WC133R-10-CN-0220 from the National Oceanographic and Atmospheric Administration (NOAA). The Government has certain rights to this invention. 
    
    
     SUMMARY 
     Embodiments of systems are described. In one embodiment, the system is a system for harvesting electrical power from mechanical energy. The system includes a buoy, a tether, and a plurality of power take-off (PTO) modules. The tether is coupled between the buoy and a fixed location below the buoy. The PTO modules are coupled in series to one another along the tether. Each PTO module is configured to generate induced electrical energy in response to forces transferred from the tether to the PTO module. 
     In another embodiment, the system includes a buoy, a plurality of tethers, and a power take-off (PTO) module. The tethers are coupled between the buoy and at least one fixed location below the buoy. The PTO module is coupled to multiple tethers of the plurality of tethers. The PTO module is configured to generate induced electrical energy in response to forces transferred from the tether to the PTO module. 
     In another embodiment, the system includes a plurality of buoys, a power take-off (PTO) module, and a tether. The PTO module is coupled to multiple buoys of the plurality of buoys. The PTO module is configured to generate induced electrical energy in response to forces transferred from the buoy to the PTO module. The tether is coupled between the PTO module and at least one fixed location below the PTO module. 
     In another embodiment, the system includes a buoy, a plurality of tethers, and a power take-off (PTO) module. The tethers are coupled between the buoy and at least one fixed location below the buoy. The tethers are arranged to angle away from the buoy in different radial directions around a circumference of the buoy. The PTO module is coupled to at least one of the plurality of tethers. The PTO module is configured to generate induced electrical energy in response to forces transferred from the tether to the PTO module. 
     Other embodiments of the system are also described. Other aspects and advantages of embodiments of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrated by way of example of the principles of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1-1  illustrates one embodiment of an energy generating device for use in a downhole drilling application. 
         FIG. 1-2  illustrates another embodiment of an energy generating device for use in a downhole drilling application. 
         FIG. 1-3  illustrates another embodiment of an energy generating device for use in a downhole drilling application. 
         FIGS. 1-4 ,  1 - 5 , and  1 - 6  illustrate other embodiments of an energy generating device that converts the movement of the drill string into electrical energy. In particular,  FIGS. 1-4  and  1 - 5  illustrate side views, and  FIG. 1-6  illustrates a cross-sectional or end view. 
         FIGS. 1-7  and  1 - 8  illustrates tables with calculations related to an embodiment of a lateral bending vibration energy harvester. 
         FIG. 1-9  illustrates a cross-sectional or end view of another embodiment of an energy generating device for converting lateral bending vibration energy into electrical energy. 
         FIG. 2-1  illustrates one embodiment of a wave energy harvesting device based on the principle of reverse magnetostriction. 
         FIG. 2-2  illustrates one embodiment of tether systems to secure magnetostrictive elements to buoys. 
         FIG. 2-3  illustrates another embodiment of tether systems to secure magnetostrictive elements to buoys. 
         FIG. 2-4  illustrates another embodiment of tether systems using multiple groups of parallel tethers extending from the buoys. 
         FIG. 2-5  illustrates a table of alloy compositions and magneto-mechanical/electrical properties for measurements of corresponding alloy flux density, as well as the maximum change in flux density for each alloy composition. 
         FIG. 2-6  illustrates one embodiment of a hydraulic loading system to compress a magnetostrictive element. 
         FIG. 2-7  illustrates a graph of one embodiment of test results for the change in magnetic flux density for a change in applied load. 
         FIG. 2-8  illustrates a table of a sample calculation of the elastic energy, magnetic energy and estimated mechanical to magnetic energy conversion efficiency for an embodiment of an energy harvesting device. 
         FIG. 2-9  illustrates before and after images of four corrosion coupons before and after 21 day ocean water exposure. 
         FIG. 2-10  illustrates one embodiment of a power take-off (PTO) module for magnetostrictive performance testing. 
         FIG. 2-11   a  illustrates a graph of wave-tank measurements of load and voltage, as well as voltage calculated from measured load. 
         FIG. 2-11   b  illustrates a graph of a correlation between measured and calculated data. 
         FIG. 2-12  illustrates a graph of single-sided amplitude spectra of wave height and tether tension. 
         FIG. 2-13  illustrates one embodiment of a spar buoy, tethers, and PTO modules (located serially within the tether lengths) modeled in OrcaFlex. 
         FIG. 2-14   a  illustrates a graph of tether tensions of nine tethers connected to a 6 m draft buoy under a wave condition with 5.2 m wave height and 5.6 s period. 
         FIG. 2-14   b  illustrates a graph of a correlation of tether tension between the top and bottom of the tether. 
         FIGS. 2-15   a  and  2 - 15   b  illustrate a cost model based on results from hydrodynamic testing. 
         FIG. 3-1  illustrates three embodiments of flux path configurations with (a) one, (b) two, and (c) three flux paths. 
         FIG. 3-2  illustrates a graph of magnet thickness effects for the arrangement of  FIG. 3-1  having two flux paths. 
         FIG. 3-3  illustrates a graph of an effect of magnet cross-section for the two flux-path case from  FIG. 3-1 . 
         FIG. 3-4  illustrates a graph of an effect of number of flux paths for 2″×1″×0.125″ magnet. 
         FIG. 3-5  illustrates a graph of a demonstration of 1 Tesla flux change using commodity Fe—Al alloys. 
         FIG. 3-6  illustrates a graph of a maximum change in flux density per strain cycle vs. number of flux paths for 2″×0.5″×0.0625″ magnets. 
         FIG. 3-7  illustrates a graph of flux density change per strain cycle vs. applied load for varying flux path materials. 
         FIG. 3-8  illustrates a test embodiment which includes a magnetic circuit with an unloaded Fe—Al rod as flux path component. 
         FIG. 3-9  illustrates a graph of test results for voltage output of a coil on magnetostrictive and flux path elements with load applied only to one element. 
         FIG. 3-10  illustrates a graph of test results for voltage output of a coil on magnetostrictive and flux path elements with load applied both elements. 
         FIG. 3-11  depicts an image of one embodiment of the sub-scale compression fixture design of  FIG. 2-10 . 
         FIG. 3-12  illustrates a graph of predicted and measured results of bench testing of the compression fixture of  FIG. 3-11 . 
         FIG. 3-13  illustrates a schematic circuit diagram to show how the magnets, flux path components and magnetic components are treated in the magnetic circuit. 
         FIG. 3-14  illustrates a graph of one set of measured data for the change in permeability with stress of the magnetic circuit of  FIG. 3-13 . 
         FIG. 3-15  illustrates a graph of a change in flux density with stress for flux paths with 2″×0.5″×0.0625″ magnets predicted by magnetic circuit based modeling. 
         FIG. 3-16  illustrates a graph of a change in flux density with stress for flux paths with 2″×1″×0.0625″ magnets predicted by magnetic circuit based modeling. 
         FIG. 4-1  shows an embodiment of a device with a moving mass and springs that may be used for harvesting energy from vibrations of machinery. 
         FIG. 4-2  shows an embodiment of a device with one or more magnetostrictive elements that may be used for harvesting energy from vibrations of machinery. 
     
    
    
     Throughout the description, similar reference numbers may be used to identify similar elements. 
     DETAILED DESCRIPTION 
     It will be readily understood that the components of the embodiments as generally described herein and illustrated in the appended figures could be arranged and designed in a wide variety of different configurations. Thus, the following more detailed description of various embodiments, as represented in the figures, is not intended to limit the scope of the present disclosure, but is merely representative of various embodiments. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated. 
     The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. 
     Reference throughout this specification to features, advantages, or similar language does not imply that all of the features and advantages that may be realized with the present invention should be or are in any single embodiment of the invention. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present invention. Thus, discussions of the features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment. 
     Furthermore, the described features, advantages, and characteristics of the invention may be combined in any suitable manner in one or more embodiments. One skilled in the relevant art will recognize, in light of the description herein, that the invention can be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments of the invention. 
     Reference throughout this specification to “one embodiment,” “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the indicated embodiment is included in at least one embodiment of the present invention. Thus, the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment. 
     Embodiments described herein include a method and device for harvesting energy or generating electricity. In one embodiment, the device includes at least one magnetostrictive element and one or more electrically conductive coils or circuits. The device also includes one or more magnetic circuits which are coupled with one or more electrical circuits to increase or maximize power production. When the magnetostrictive element is deployed in a body of water, the motion of and/or the hydrodynamic forces applied by the body of water, including wave motion, acting on a component mechanically coupled to a structure comprising the magnetostrictive element, causes changes in the stress and/or strain of the magnetostrictive element. Alternatively, the magnetostrictive element may be deployed in a different fluid. The electrically conductive coil or circuit is within the vicinity of the magnetostrictive element. A corresponding change in magnetic flux density passing through the magnetostrictive element, as magnetic permeability of the magnetostrictive element changes with stress, generates an electric voltage and/or electric current in the electrically conductive coil or circuit. 
     The embodiments include a device for generating electricity, the device at least one magnetostrictive element and one or more electrically conductive coils or circuits. The magnetostrictive element, when deployed as a part of a structure in a body of water, the motion of the body of water, including wave motion, or hydrodynamic interaction of waves with a component mechanically coupled with the structure comprising the magnetostrictive element, causes changes in the strain of one or more magnetostrictive elements. The one or more electrically conductive coils or circuits are within the vicinity of one or more of the magnetostrictive elements. A corresponding change in magnetic flux density in the one or more magnetostrictive elements generates an induced electric voltage and/or electric current in the one or more electrically conductive coils or circuits. In some embodiments, there is no substantial relative motion between the one or more magnetostrictive elements and the one or more electrically conductive coils or circuits. 
     Other embodiments include a device where the magnetic flux is directed through one or more magnetostrictive elements by one or more “flux paths” composed of, in addition to the one or more magneto strictive elements themselves, a combination of magnetically permeable material and one or more permanent magnets. Permeable materials include magnetostrictive materials. In other embodiments, the magnetostrictive element includes a magnetostrictive core, which may be part of the flux path. The magnetostrictive core, permeable materials, and the permanent magnets may experience changes in stress, experience at least part of the applied load on a structure comprising the flux path, (e.g., a tether), and/or share other functions with the magnetostrictive element. In some embodiments, the applied load on a structure comprising the flux path is substantially shared between one or more magnetostrictive elements, and brittle components such as the permanent magnets will not experience any changes in load/stress. 
     Other embodiments of the device include at least one electrically conductive coil or circuit that is in the vicinity of the flux paths and/or magnetostrictive material. The electrically conductive coil or circuit may include, or be substantially made of, an electrically conductive material such as copper or aluminum, which may have an insulating coating on the wire. 
     An embodiment may include a fixture for applying a pre-stress load, either compressive or tensile, to the magnetostrictive element. The fixture may be made of magnetically permeable and/or impermeable material and may include flux paths and permanent magnets, or electromagnets. In one embodiment, a bias magnetic field is also applied to one or more materials described in this disclosure. The fixture may include design considerations that reduce the occurrence of magnetic saturation and overall magnetic reluctance of the device. The fixture is also designed to transfer applied external loads to the magnetostrictive element to cause a change in magnetic properties of the element. The design of the fixture may seek to increase or maximize the amount of load transferred to the magnetostrictive element. The method for applying the pre-stress may be through the use of bolts, or other means to make a rigid connection to the magnetostrictive element, which may or may not have low magnetic permeability to reduce magnetic flux leakage. The fixture for applying the pre-stress load may include bolts. The bolt material may also be chosen to have a low Young&#39;s modulus and high yield strength. The bolt diameter may be chosen to decrease the stiffness of the bolts relative to that of the magnetostrictive element(s). The fixture may also include aluminum brackets (or brackets of another material) for locating the permanent magnets. The fixture may include two or more flat bars (or structural plates) of metal with holes drilled in them for threaded rods and nuts. The flat bars may or may not be made of a magnetically permeable alloy such as mild steel, or a relatively impermeable alloy such as stainless steel. The use of magnetically permeable flat bars may include additional bars to create a closed flux path. 
     An embodiment of the device may include one or more magnetostrictive elements that are a binary alloy of iron and aluminum, with an atomic percentage of aluminum between about 14 and 21%. Another embodiment of the device may include one or more magnetostrictive elements that are a binary alloy of iron and aluminum, with an atomic percentage of aluminum between about 18% and 19%. The elements may also be a ternary alloy of iron and aluminum with the third component being either manganese, cobalt, molybdenum, or tungsten with an atomic percentage between about 1% and 10%. Either the binary or ternary composition may include trace additives to improve mechanical properties such as ductility and machinability. Trace additives that serve this role include, but are not limited to: niobium, titanium, vanadium, boron, carbon, or any other element demonstrated to reduce grain growth or grain boundary fracture. In other embodiments, the magnetostrictive element includes different materials from those named, above. In other embodiments, the magnetostrictive element includes a combination of materials from those named above and other materials. 
     Embodiments of the device may include an external enclosure to protect the device from the effects of the external environment, e.g., salt-water corrosion or other corrosive fluids. The external enclosure may include components designed as seals and gaskets, and may include a structural element for transferring the load to the internal compression fixture and magnetostrictive element. These components may include deformable seals or constituent parts. The enclosure may also have leak-tight electrical connections to connect internal and external electrical systems. The enclosure may also include structural elements for attaching the device to one or more tethers and/or buoys and/or other devices. In other embodiments, the enclosure may include other materials or other structures. 
     While examples of ocean applications are provided above for the magnetostrictive devices, at least some of the embodiments described can be used in drilling applications. The drilling applications may include downhole drilling applications. Some embodiments are suitable for downhole drilling applications, including but not limited to oil and gas applications or for geothermal applications. 
     Embodiments described herein include a method and device for converting the mechanical energy from vibration and impact loads that are generated during a drilling operation into magnetic and electrical energy using a novel design that utilizes magnetostrictive elements. Such devices may be useful in powering a variety of different types of equipment that may be located on the drill string and/or the bottom hole assembly (BHA). These include, but are not limited to measurement while drilling (MWD) tools, logging while drilling (LWD) tools, sensors, transmitters, receivers, repeaters etc. Embodiments of the design combine proven concepts from existing technologies with technology proven on the bench scale for energy generation using magnetostrictive devices to create a powerful solution for harvesting energy from drilling operations. Embodiments include designs that can convert the energy from axial, lateral or torsional vibrations to electrical energy. Some embodiments may help to reduce usage of or eliminate use of batteries downhole. Embodiments of the design are expected to have relatively low capital costs and very good survivability during downhole drilling operations. Some embodiments may include power management strategies to optimize the delivered power from a suite of devices distributed across the length of the drill string and/or BHA. Some embodiments will include components for applying a pre-stress to the magnetostrictive elements, or other materials described in embodiments, herein, which may be either tensile or compressive. Other embodiments will convert the mechanical energy from vibration and impact loads from other mechanical energy besides the mechanical energy generated from drilling operation. Other embodiments will convert hydrodynamic energy in combination with, or replacement of, the mechanical energy generated from vibration and impact loads. 
     Vibration Energy Harvesting Applications 
       FIG. 1-1  illustrates one embodiment of an energy generating device  100  for use in a downhole drilling application. In this embodiment the energy generating device  100  is mounted on the outer surface of a pipe  102  that is part of the drill string (not shown). Attached to the surface of the pipe  102  in a radial direction is a magnetostrictive alloy rod  104  that is contained within a “cage”  106 . The cage  106  consists of magnetically permeable material  104  and bias magnets  108 . The cage  106  serves to create a closed path flux loop that includes the magnetostrictive alloy rod  104 . On the top surface of the magnetostrictive alloy rod  104  and flux cage  106  is a mechanism  110  for generating load changes on the magnetostrictive alloy rod  104 . This loading mechanism  110  includes an impact head  112  that makes contact with the rock wall (not shown) in the drill hole and a compression spring  114 . As the distance between the central drill pipe  102  and the rock wall changes, the force being applied to the compression spring  114  changes. When the magnetostrictive alloy rod  104  experiences a load change generated by the compression spring  114  and impact head  112 , there is a corresponding change in magnetic permeability in the magnetostrictive material  104 . This results in a change in magnetic flux density passing through the magnetostrictive material  104  as the load from the compression spring  114  changes. This change in magnetic flux causes electrical energy to be generated in the coil  118  that surrounds the magnetostrictive alloy rod  104 . 
     The size and spring constant of the compression spring  114 , along with the diameter of the magnetostrictive alloy material  104  can all be adjusted to create a design that is suitable for a given drilling operation and/or power requirement. In addition, the number of energy generating devices  100  installed at a particular location, or along a particular drill string, can be varied to produce different power levels.  FIG. 1-1  shows a single energy generating device  100 . However, multiple energy generating devices  100  can be spaced along the length and/or circumference of the central drill pipe  102  to generate more power than a single energy generating device  100  can generate. The spacing of the energy generating devices  100  along the drill pipe  102  can be done in such a way as to not impede the return flow of the drilling mud that typically flows back up the annular hole between the outside surface of the drill pipe  102  and inside surface of the rock drill hole (i.e., the space in which the energy generating device  100  is installed). 
       FIG. 1-2  illustrates another embodiment of an energy generating device  120  for use in a downhole drilling application. In this example, a similar “shock absorber” type mechanism is used to capture the mechanical energy from impact loads from collisions with the rock wall during drilling. However, in this case, the impact force load from contacting the rock wall is used to drive a piston rod  122  in an oscillating linear motion. Then, a gear system or lever arm  124  is used to transfer this oscillating motion into the tensioning of a high tension spring  126 . The oscillating motion of the piston rod  122  results in changes in the tensioning force being applied to the magnetostrictive rod assembly  128 . The changes in tensile force being applied to the magnetostrictive alloy rod  104  result in the generation of electrical power in the coil  118  that surrounds the magnetostrictive alloy rod  104 . One potential advantage to this embodiment is that it allows for using a longer magnetostrictive rod  104  that may be useful for generating higher power levels for some applications. In both of these embodiments described, where an impact head  112  is contacting the surface of the rock wall, some embodiments may include bearings or roller bearings (not shown) in the surface of the impact head  112  where it makes contact with the rock wall so that the frictional losses will be reduced or minimized and, therefore, have less influence on the drilling operation. 
       FIG. 1-3  illustrates another embodiment of an energy generating device  140 . The illustrated energy generating device  140  utilizes the energy contained in the torsional modes of vibration, i.e. “stick-slip.” Looking axially down the drill-string, the energy generating device  140  has magnetostrictive elements  104  in a tangential direction, as indicated by the cross-hatched elements. As the string rotates clockwise, the blue (“B”) brackets, which are connected to the upper part of the drill-string (towards the top of the well), will transfer the torque to the red (“R”) brackets, which are connected to the lower part of the drill string (towards the bottom of the well), by axially loading the magnetostrictive rod  104 . The stick-slip will cause large changes in the axial loads of the magnetostrictive rod  104 , which are then converted into magnetic energy through magnetostriction and subsequently electrical energy through induction. The energy generating device  140  may include any number of magnetostrictive elements  104  at a single axial location along the drill string, and any number of groups of magnetostrictive elements  104  along the axial dimension (i.e., length) of the drill string. In one embodiment, the energy generating device  140  has a central hole  142  through which drilling mud may flow. 
       FIGS. 1-4 ,  1 - 5 , and  1 - 6  illustrate another embodiment of an energy generating device  160  that converts the bending in the drill string  162  due to lateral vibrational loads into electrical energy. As the drill head  164  is penetrating the rock, the drill string  162  experiences vibrations in lateral, axial, and torsional directions. The lateral vibrations impose bending loads along the length of the drill string  162 . In this embodiment, the energy generating device  160  has magnetostrictive material  104  around the circumference of the drill collar  166  or other external surface along the length of the drill string  162 . Different angular positions along the circumference of the drill collar  166  will capture the loading along different lateral directions. The changes in load experienced by the drill collar  166  will also be experienced by the magnetostrictive material  104  which will result in changes in magnetic flux through reverse magnetostriction. The changes in magnetic flux are then converted to electrical energy through induction in a coil  118  surrounding the magnetostrictive material  104 . The magnetostrictive material  104  may be in the vicinity of bias magnets (not shown) and flux paths to increase or maximize the changes in flux due to the changing stress state in the magnetostrictive material  104 . The magnetostrictive material  104  may be in a state of pre-stress that is caused by a pre-stress fixture  168 , such as a compression fixture. The standard geometry of the drill collar  166  may be used, allowing mud to flow through the center. The outer envelope of the magnetostrictive material  104  will be sufficiently smaller than the bore-hole diameter to allow mud to adequately flow out of the hole. 
     For reference, some calculations of bending stresses in magnetostrictive materials mounted to drill collar are provided below. These calculations assume a simple supported beam with a point load applied at the midpoint. The beam has length L, the point load P is applied at x=L/ 2 . The reaction forces at the ends of the beam are R=P/ 2  and act in the opposite direction of P. The bending moment equations for the beam are: 
       0&lt;= x&lt;=L/ 2:  M ( x )=( P/ 2)* x    
         L/ 2&lt;= x&lt;=L: M ( x )=( P/ 2)*( L−x ) 
     The second derivative of deflection with respect to x is related to the moment equation as follows: 
         v″=M ( x )/( E*I )  E —modulus of elasticity,  I —second moment of area
 
     Integrating twice and solving for the constants of integration, the deflection equation for the beam is derived as: 
       0&lt;= x&lt;=L/ 2:  v ( x )=1/( E*I )*[( P*x̂ 3)/12−( P*L̂ 2* x )/16]
 
         L/ 2&lt;= x&lt;=L: v ( x )=1/( E*I )*[( P*x̂ 3)/12−( P *( x−L/ 2)̂3)/6−( P*L̂ 2* x )/16]
 
     The maximum deflection and bending moment occurs at x=L/2: 
         v ( L/ 2)=( P*L̂ 3)/(48* E*I ) 
         M ( L/ 2)=( P*L )/4 
     The drill collar has a tubular cross section with outer diameter D and inner diameter d. Given a deflection at x=L/2, the load P can be calculated as can the moment M(L/2). 
     A cylindrical magnetostrictive rod of diameter dm is attached at the top and bottom of the drill collar. Assume the same loading conditions are present and that the magnetostrictive rods have negligible effect on the bending moment equation. It is possible to calculate the bending stresses which occur at the center of the magnetostrictive rods. 
       6=( M ( L/ 2)* c )/ I    
         c —distance from the neutral axis to the center of the magnetostrictive rod
 
         c=D/ 2+ dm/ 2 
         I —second moment of area of the drill collar and magnetostrictive rods
 
         I =(π/64)*( D̂ 4− d̂ 4)+2*[(π/64)* dm̂ 4+(π/4)* dm̂ 2*( D/ 2+ dm/ 2)̂2]
 
       FIGS. 1-7  and  1 - 8  illustrates tables with calculations of the bending stress and power production capability of the lateral bending vibration harvester. The configuration is as stated above, with 8 rods spaced equidistant around the circumference of the drill pipe, as shown in  FIG. 1-9 . This means that two are located at zero degrees relative to the bending plane, 4 are 45° out of plane, and two are 90° out of plane (which don&#39;t contribute significantly to the stiffness or power generation). 
     Ocean Energy Harvesting Applications 
     Portions of this section describe activities demonstrating aspects of the technical and economic viability of a magnetostrictive wave energy harvester (MWEH). Some embodiments herein utilize magnetostrictive alloy compositions with appropriate magneto-mechanical properties that enable low-cost energy production from ocean waves. Wave-tank testing of a sub-scale device and hydrodynamic modeling of the system can be used to more accurately predict power generation capacity and durability. In some embodiments, new materials compositions are used to provide a 40% improvement in magnetic flux density obtainable relative to conventional materials. While tertiary alloy additions do not necessarily enhance corrosion resistance of the magnetostrictive alloys significantly, alloy corrosion through direct sea-water exposure is not a significant concern because at least one embodiment of a no-moving-parts system is able to use highly reliable sealing techniques routinely used in the marine environment. The hydrodynamic modeling indicates that embodiments of the system can result in relatively stable and consistent operation in the ocean environment while generating electric power at a cost of under $0.10/kwh when used at utility-scale. Finally, wave tank testing demonstrates a high correlation between test results and results obtained from predictive models. 
       FIG. 2-1  illustrates one embodiment of a wave energy harvesting device  200  based on the principle of reverse magnetostriction. A stress or strain imposed on a magnetostrictive material  202  causes its magnetic properties (e.g., magnetic permeability) to change significantly. In one embodiment, the magnetic property is a magnetic flux density of a magnetostrictive component  202 . In the presence of a bias magnetic field, a closed-loop magnetic circuit can be designed in which changes in load on the magnetostrictive material result in changes in magnetic flux density. The hydrodynamic loads caused by the wave/buoy interaction result in corresponding load changes in the magnetostrictive alloy rods  202  which are embedded in the taut tethers  204  connecting the buoy  206  to its anchor  208 ; these in turn result in a constantly changing magnetic flux through the rods  202  with only minimal elastic deformation (100&#39;s of ppm) of the alloy rods  202 . If coils  210  are wrapped around (or otherwise deployed around) any part of the magnetic circuit, a voltage will be induced in the coils  210  according to Faraday&#39;s law of induction. This principle allows construction of a wave energy harvesting device  200  with no moving parts. The use of low-cost commodity metals as the magnetostrictive alloy constituents can lead to energy costs that are competitive with conventional power sources. In some embodiments, the magnetostrictive rod  202  is mounted in a compression device  212 , and the magnetostrictive rod  202  and the electrical coil  210  are enveloped in a protective casing  214 . In some embodiments, at least a portion of the compression device  212  provides a flux path  216  within the wave energy harvesting device. 
     The buoys  206  may be designed to have a draft sufficient to provide stability and large buoyant forces. The buoy  206  may have connections for one or more tethers  204  that extend from the buoy  206  to the anchor  208  at the ocean floor. The tethers  204  may extend from the buoy  206  in one or more radial directions and at one or more inclination angles relative to the ocean floor to increase buoy stability. Each tether  204  may include one or more magnetostrictive devices  200  and other load-bearing members. An example of this embodiment is shown in  FIG. 2-2 , which illustrates one embodiment of tether systems to secure magnetostrictive elements  200  to buoys  206 .  FIG. 2-2  also illustrates a specific embodiment of one of the magnetostrictive devices  200 , which includes a magnetostrictive rod (core)  202 , electrical coil  210 , protective casing  214 , external electrical connections  218 , and structural attachment elements  220 . 
     In some embodiments, the tethers  204  might be at an inclination angle from 1° to 89° relative to the ocean floor, and will likely be from 30° to 60°, as shown in  FIG. 2-3 . This angle leads to improved hydrodynamic stability of the buoy  206 , and less motion, which equates to better load transfer to the tethers  204  and consequently the energy harvesting device  200 . Hydrodynamic modeling of the buoy  206 /tether  204 /energy harvester system  200  may be used to determine specific installation angles for a given installation location and environment. In some embodiments, the groups of one or more tethers  204  may extend from the corresponding buoy  206  in approximately the same radial direction, with the tether system comprising multiple such groups of parallel tethers  204 , as shown in  FIG. 2-4 . Another embodiment includes another type of water flotation device in addition to, or instead of, the one or more buoys  206 . 
     Experiments were performed to measure alloy flux density change. Candidate alloys were selected based on literature results that showed a peak in magneto-mechanical coupling for iron-aluminum alloys at an atomic Al percentage between 16 and 19 and maximum energy density for iron-gallium alloys at an atomic Ga percentage in a similar range. Tests were performed to determine if, based on their position in the periodic table, Fe—Al performs similarly to Fe—Ga in reverse magnetostriction. Other sources have demonstrated that adding a tertiary element could also be beneficial: Co and C to improve the magneto-mechanical coupling coefficient and magneto-elastic coupling, Mn to increase the electrical resistivity of the alloy and thereby decrease losses due to eddy currents, and Mo to reduce corrosion weight loss while increasing strength and ductility. Based on these previous findings, processes and tests were performed on five binary compositions of Fe—Al and seven tertiary compositions in which a third element was added to an Fe—Al base composition. These alloy compositions are summarized in the table shown in  FIG. 2-5 . Also included in the table are three other alloys (marked with an asterisk) that were tested previously. 
     The alloys were cast by Sophisticated Alloys, Inc. (Butler, Pa.) using a vacuum-induction technique that produced 14″ long rods with a 1.25″ diameter. These rods were machined through either centerless grinding or turning on a lathe to a final diameter of 0.96″ and cut to a length of 6.25″. 
     To determine the reverse magnetostrictive performance of each alloy, the change in magnetism (ΔB) of each specimen was quantified as a function of change in compressive loading. In each test, a bias magnetic field was applied to the magnetostrictive element  202 , which was then compressed in a hydraulic loading system  230 , as shown in  FIG. 2-6 . Neodymium rare-earth magnets provided the magnetomotive force (MMF), which was directed through the specimen by flux paths  216  composed of mild steel (1018) bars. The results presented here are for a configuration with two flux paths, each with one 2″×0.5″×0.0625″ NdFeB magnet, and these paths were magnetically isolated from the steel frame of the loading system using aluminum separators. The compressive load was quickly released, and the change in magnetic flux induced a voltage in a copper-wire coil  210  around the specimen, which was recorded with a data-acquisition system (not shown). The voltage change as a function of time was then used to calculate the change in magnetism. 
     The magneto-mechanical performance was a strong function of the alloy composition.  FIG. 2-7  shows the change in magnetic flux density for a change in applied load. The maximum change in flux density for each alloy composition is also summarized in the table shown in  FIG. 2-5 . 
     The 18.5% Al alloy demonstrated the highest change in flux density, while the 18.0% Al alloy had the highest value of dB/dσ. All of the ternary compounds, with the exception of the 2.0% Mn alloy, showed significantly reduced values for both ΔB and dB/dσ. It should be noted that the absolute magnitude of ΔB and dB/dσ are dependent on the particulars of the configuration being tested, e.g., the number of flux paths, magnet thickness and cross-sectional area, etc., but the relative performance seems to hold over the configurations tested. 
     The resistivity of each alloy, which is important because higher resistance levels reduce eddy currents and thus increase efficiency, was tested with a four-point resistance measurement. The results of these measurements are also summarized in the table shown in  FIG. 2-5 . All of the alloys have a resistivity between those of iron (1.0×10 −7  Elm) and aluminum (2.8×10 −8  Ω·m), as would be expected. Consistent with conventional teachings, the addition of 8.0% Mn nearly doubled the electrical resistance. However, the reduction in magnetic flux density likely offsets the potential benefit for low frequency applications such as the ocean wave harvester. However, the Mn-doped material may be of interest in other high-frequency applications such as vibration energy harvesters. 
     Corrosion coupons were machined from six alloys for salt-water testing. One alloy was a representative binary alloy, and the others were ternaries chosen to evaluate the effect of the tertiary compound on corrosion resistance. The coupons were nominally 1.25″ diameter with a 0.25″ thickness. 
     The 17.5% Al was chosen as the baseline binary composition, to which the Mn, Mo and Co ternaries were compared. Stainless steel (316) was also tested as a control sample. Mild steel (1018), which is the material used in some embodiments for flux paths, was also tested. Three coupons of each alloy were tested. The weight of each coupon was measured after which it was suspended in a separate container of filtered, sterilized and pH buffered ocean water (specific gravity=1.025, pH=8.3) for 21 days. Upon removal from the salt water, the coupons were rinsed and scrubbed to remove corrosion products, and then weighed to determine the corrosion rate per unit area that is summarized in the table shown in  FIG. 2-5 . 
     The stainless steel had a very low corrosion rate as expected (−0.4 g/m 2 ·yr), while the mild steel had moderate weight loss (48.0 g/m 2 ·yr). All of the Fe—Al alloys exhibited weight gain except for the 8.0% Mo specimen. This is likely due to the formation of a surface scale that is sufficiently adherent to the alloy coupons that it could not be washed off by rinsing. While this may be studied in more detail, such scale formation could result in a passivation layer formation that reduces corrosion rate over time. A visual inspection was also performed where each coupon was qualitatively rated in terms of appearance. Before and after images of four of the corrosion coupons (labeled a through d) are shown in  FIG. 2-9 . The five alloys with tertiary elements had very little visual difference, and so are represented by the 2.0% Mn alloy. The stainless steel (316) coupons show almost no corrosion; otherwise the 17.5% Al alloy appears to have performed the best. It should also be noted that while the surface corrosion is visually obvious, the largest change in weight observed was 0.1% for the 8.0% Mn alloy, which is nearly twice that of any of the other alloys. It is quite possible that this would likely mean that small leaks, even if they occur, will not result in catastrophic failure of the alloy rods, and is more likely to result in a slow decline in alloy rod power production. 
     The observation that corrosion of the alloys was significant, and could not be significantly mitigated by small alloying additions, necessitates a fail-safe sealing mechanism that ensures that the elements are not directly exposed to sea-water over the lifetime of the product. 
     The results from the magnetostrictive performance testing were incorporated into a sub-scale power take-off (PTO) module  240 , which was bench and wave-tank tested.  FIG. 2-10  illustrates one embodiment of a PTO module  240 . The illustrated PTO module  240  includes a larger (11″ long, 1.125″ diameter) magnetostrictive rod  202  in a compression fixture  242  (i.e., load-bearing structure). The compression fixture  242  included four flux paths  216 , each of which included a 2″×1″×0.0625″ rare-earth magnet  244 , and stainless-steel bolts  246  to apply a bias compressive force to the magnetostrictive alloy  202 . The system was designed such that an external tensile load would relieve the pre-compression, causing a magnetic flux change and an attendant voltage change. This fixture was housed inside a PVC enclosure  248  designed to transfer external mechanical loads to the internal compression fixture with watertight electrical connections  250  for taking measurements. 
     Bench testing of the sub-scale PTO module  240  was accomplished by applying a cyclic tensile load to the PTO module  240  while measuring the open-circuit voltage output. The force was applied by hand using a lever arm that allowed load changes of about 300 pounds, which were measured with a load cell (not shown). While this load was more than an order of magnitude lower than what an alloy rod of this diameter would be designed for and would be expected in ocean operation with an appropriately sized buoy, it was representative of the load changes that would be experienced in the wave tank, and it could be applied in a more controlled manner than that of the electro-hydraulic press shown in  FIG. 2-6 , which is limited to square-wave loading. 
     The measured load and voltage of bench testing results of the assembled device  240  were low-pass filtered at 55 Hz to remove the noise associated with line voltage. The predicted voltage was calculated using Faraday&#39;s law of induction, 
         V=N ( dB/d σ)( dσ/dt ),
 
     where N is the number of turns of the coil, A is the cross-sectional area of the rod, B is the magnetic flux density, and σ is the applied load. The value of dB/dσ was found by minimizing the standard deviation of the difference between the actual and calculated voltages. The predicted voltage has excellent agreement with the measured output, with an R-squared of 0.98. The magnitude of dB/dσ is roughly one third of the value arrived at through magneto-mechanical performance testing. This is due to load sharing between the magnetostrictive rod and the bolts in the compression fixture. Before testing it was predicted that only 30% of the applied load would be felt by the magnetostrictive, which agrees well with this testing. An analysis shows that through optimization of the compression fixture it should be possible to push this value to 90%. 
     PTO module testing was conducted both with and without the PVC enclosure  248  to verify that the enclosure  248  did not adversely affecting load transfer. Despite the use of static seals, dB/dσ decreased by only 2% with the enclosure  248 . With further optimization through the use of a bellows seal, it appears that this loss can be reduced even further. Finally, the device was successfully leak-tested by submerging it in a tub of water overnight, to verify its leak-tightness prior to the wave-tank testing. 
     Wave-tank testing was performed at the UC-Berkeley Marine Mechanics Wave Flume, located at the Richmond Field Station in Berkeley, Calif. The work was performed in collaboration with Marine Innovation and Technology (MI&amp;T, Berkeley, Calif.), a naval architecture and offshore platform consultancy. One end of the PTO module  240  was attached to a cylindrical buoy  206  with a fully submerged buoyancy of 600 lbs. The other end of the PTO module  240  was attached to a rope that ran through an anchored pulley and up to a movable carriage. A load cell was placed in series with the PTO module  240  to measure line tension. Output voltage and wave height were also measured. Waves with crest-to-trough heights ranging from 6″ to 10″ and periods ranging from 0.75 s to 2.0 s were generated over the course of the test. 
     The results from a typical run are shown in  FIGS. 2-11   a  and  2 - 11   b . These results correspond to a particular test with 10″ waves with a period of 1.1 s. The predicted voltage was arrived at using the value of dB/dσ found during bench testing, which provides an excellent fit to the measured voltage (R 2 =0.94). This is important because it provides confidence in an ability to predict performance in wave environments based on previous bench-top results. 
     An interesting observation from the data presented in  FIGS. 2-11   a  and  2 - 11   b  is that the tether tension, while periodic, is clearly different than the nearly sinusoidal wave profile. There is a significant amount of energy contained at higher frequencies, as can be seen in the amplitude spectra of the tension, which is shown in  FIG. 2-12 . While almost all of the frequency content of the wave-gauge signal occurs at 0.571 Hz (1.75 s period) and its first harmonic, 1.14 Hz, the tension measurements have appreciable peaks at 2.29 and 2.84 Hz. A similar frequency multiplication has been found through hydrodynamic modeling, and these results suggest that a significant increase in power generation could be observed and defined, since the power output is proportional to the square of dσ/dt. 
     MI&amp;T also performed a hydrodynamic analysis of the MWEH system. MI&amp;T used OrcaFlex, an industry-standard tool for static and dynamic analysis of a wide range of offshore systems, for this task. OrcaFlex is a fully 3D non-linear time domain finite element program that is capable of dealing with arbitrarily large deflections. OrcaFlex provides fast and accurate analysis of catenary systems such as flexible risers and umbilical cables under wave and current loads and externally imposed motions. Wave profiles used in the OrcaFlex modeling were determined using the Joint North Sea Wave Project (JONSWAP) wave spectrum model, and were based on actual wave conditions off the coast of Oregon.  FIG. 2-13  illustrates one embodiment of a spar buoy, tethers, and PTO modules (located serially within the tether lengths) modeled in OrcaFlex. 
     The buoy was modeled as a series of co-axial cylinders mounted end to end along the local z-axis as shown in  FIG. 2-13 . This allowed execution of the model with changes to the buoy geometry, by specifying the number of cylinders and their lengths and diameters. Heave stiffness and righting moments in pitch and roll were determined by calculating the intersection of the water surface with each of the cylinders making up the buoy, allowing for the instantaneous position and attitude of the buoy in the wave. Hydrodynamic loads on the buoy were calculated using Morison&#39;s equation and added mass and damping were calculated by WAMIT, a computer program based on the linear and second-order potential theory for analyzing floating or submerged bodies. Drag forces in the model were applied only to submerged parts of the buoy. Added mass and drag were proportioned based on the submerged fraction of the buoy. Each of the tethers was modeled as a “Line” in OrcaFlex as shown in  FIG. 2-13 . In OrcaFlex, lines are flexible linear elements used to model cables, hoses, chains or other similar items, and are represented using a lumped mass model. 
     The main results of the dynamic modeling activities were:
         1. Buoy “draft”—the length of buoy under water—is a key factor that determines the nature of buoy motion and tether loading in the system. For the Oregon wave spectra used, a buoy draft of 6 m provided stability of the buoy across all the wave conditions experienced. Instability in the tether was never seen except in a simulation of a 100-year wave (which may be addressed through system design optimization).   2. With a 6-meter draft with nine tethers, there was a very strong correlation (R 2 =0.89-1.00) between top line tensions on the five tethers on the same side of the buoy relative to the wave direction, and a comparatively weaker, but positive, correlation between tethers on opposite sides relative to the wave direction (0.3-0.7). In the sample data shown in  FIG. 2-14   a , the line tensions of nine tethers connected to a buoy with a 6 m draft, in a wave condition with significant wave height of 5.2 m and average period of 5.2 seconds is presented.   3. With a 6-meter buoy draft, there was a very high correlation coefficient (R 2 =1.00) between top line tensions and bottom line tensions on each tether as shown in  FIG. 2-14   b . The magnitude of the tensions at the top and bottom of each tether was offset slightly due to the weight of the PTOs and chains on the tether itself.   4. For a given buoy, the stress scaled fairly predictably with the number of tethers. Analysis of a 6 m draft buoy with 9 and 6 tethers, respectively, was performed, and as expected the line tensions increased. There was good correlation between the tensions in each case, but the average line tension was about 10% higher than the expected factor of 1.5, presumably due to the greater range of motions possible for the buoy due to the reduced tether stiffness (this load increase may be beneficial from a power production stand-point).       

     The results of the hydrodynamic modeling were incorporated into a cost model to determine the levelized cost of energy (LCOE); previous LCOE projections were based on sinusoidal waveforms. 
     A detailed cost model for the MWEH is built upon the validated performance model described above, and utilizing cost methodologies developed by NREL for the evaluation of new technologies for the wind industry. A summary of the cost model is shown in  FIGS. 2-15   a  and  2 - 15   b . In addition to the alloy material itself, all of the other associated components (e.g., copper coils, mooring chain link, buoys, anchors, power-electronics, sealing systems, engineering, installation, maintenance, permits, depreciation) are considered, and a general principle of conservatism was employed across the board. Significant project uncertainty (10% of capital costs) was also built in for conservatism. This model incorporates the results of hydrodynamic modeling into the cost model. The results show that the technology should be quite attractive for utility scale power production and can deliver levelized costs of energy of $0.10-0.20/kWh for initial deployments and under $0.10/kWh for larger farms. 
     While the corrosion testing has indicated that the low cost magnetostrictive alloys studied are susceptible to surface corrosion, design and testing of prototype units has significantly reduced the impact of this finding on overall product success. After a full day of submersion in a proprietary lab and two days of submersion in the Berkeley wave tank under load, the low cost commercial compression seals used on the prototype units held up very well. The use of these extremely reliable seals (PTFE gaskets between flanges and compression fittings) is unique to embodiments of the device described herein due to the ability to make electric power without significant relative motion. The ability to use these sealing techniques, well proven in the marine environment, provides confidence that the Fe—Al alloys can be used, despite their surface corrosion characteristics, without compromising product lifetime. However, some embodiments may include redundancy in corrosion protection for longer periods of testing under more aggressive conditions. 
     Alloys 13, 14 and 15 listed in the table shown in  FIG. 2-5  have no magneto-mechanical or electrical properties reported because the parts broke during machining. It was a concern that certain compositions could not survive machining. While an increase in the percentage of Al in Fe—Al alloys has been shown to make the alloy more brittle, it is not clear that the failures were driven by that factor alone. It is possible that this is due to a problem in the processing of the rods as the more recent alloys have been centerless-ground to the desired outer diameter, whereas the earlier rods were turned on a lathe. To determine if the particular machining operation was indeed the problem, one rod each from the same cast batch of 18.5% Al was machined using each method. The rod that underwent centerless grinding fractured, but the rod that was lathed did not and could be tested. While centerless grinding may not be the sole cause of all the failures, it does appear responsible for many of the failed parts. Further, the failures in centerless grinding are likely a result of pre-existing flaws, which may be at least partially addressed by changes to the manufacturing process. 
     While some problems were identified during the course of the testing (e.g., surface corrosion characteristics of iron aluminum alloys, brittle fracture during machining of some Fe—Al alloys), work-around solutions for each of these have been identified as indicated below. 
     The testing has demonstrated the unique potential of the MWEH to generate power from ocean waves by de-risking key technology elements. In particular, the alloys tested in this project have shown a significant increase (&gt;40%) in magneto-mechanical performance over those used previously and as such have been shown through detailed cost modeling to be able to provide electricity costs under $0.10/kWh in large wave farms. While the alloys do show lower corrosion resistance than stainless steel, it is relatively simple to design an enclosure that will transfer load to the magnetostrictive element while also sealing very effectively against the ocean environment, because embodiments of the design have no moving parts. The following can also result in improved performance and/or lower cost of the PTO and MWEH system.
         1. Designing the PTO module with significant redundancy so that the corrosion risk factor can be effectively eliminated, while maintaining the cost advantage and not compromising performance (e.g., PVC or polyurethane spray coatings on the alloys).   2. Evaluating manufacturing process improvements (e g, minimizing temperature variations to reduce grain size) and minor compositional improvements (e.g., trace alloying additions to reduce grain size) to increase reliability of the alloy rods, while not compromising performance.   3. Designing, building and testing the reliability and performance of a significantly scaled up PTO module lab conditions that simulate and exceed specific expected operating environments in the ocean (e.g., high pressure leak testing, accelerated cyclic fatigue testing).   4. Enhancing the system performance through a targeted hydrodynamic modeling effort that can further reduce costs by increasing the energy transfer characteristics from the buoy to the tether (e.g., tethers may be at a slight angle to reduce buoy motion and increase tether loads).   5. Testing the optimized PTO in a wave tank environment that can produce waves of sufficient height so as to produce stresses that are similar to those experienced by the full-scale PTO in an ocean environment (e.g., open air wave tank at Ohmsett).       

     Using a combination of external flux paths and bias magnetic fields has a positive impact on performance of the magnetostrictive alloy. As such, optimizing the flux path configuration in terms of the number of flux paths, cross-sectional area of flux paths and bias field magnets, bias field magnet thickness, and material composition of the flux paths may have further impacts on performance of the magnetostrictive alloy. Changes in these parameters can be directly tied to changes in either the magnetic reluctance and permeability or the magneto-motive force (MMF) of the magnetic circuit. Each configuration was evaluated based on the change in flux density per strain cycle as a function of change in load. 
     For each test, the bias field was applied to the magnetostrictive element using rectangular neodymium rare-earth permanent magnets. The magnetostrictive rod  202  was then compressed in the hydraulic loading system  230 , as shown in  FIG. 2-6 . The rare-earth magnets provided the MMF, which was directed through the magnetostrictive rod by flux paths  216  composed of mild steel (1018) that formed a closed magnetic circuit. The circuit was magnetically isolated from the steel frame of the hydraulic press  230  by large aluminum spacers. The compressive load was quickly released, and the change in magnetic flux induced a voltage in a copper-wire coil  210  around the magnetostrictive element  202 , which was recorded with a data-acquisition system. The voltage change as a function of time was then integrated to calculate the change in magnetic flux density. For all tests the magnetostrictive element  202  was a 6.25″ long, 0.956″ diameter Fe—Al rod. 
     In order to maximize the change in flux per strain cycle (ΔB), a parametric study of the configuration was performed in which the magnet geometry and the corresponding flux path geometry were varied. The magnet geometry is defined by the cross-sectional area, which is the area normal to the flux paths, and the magnet thickness, which is the dimension along the flux path. Three different cross-sectional areas were tested, with different thicknesses for each. For each of these eight magnet sizes, the configuration was altered to have 1, 2, or 3 flux paths with a single magnet on each path. These tests were performed with a binary iron-aluminum alloy with 19% atomic aluminum.  FIG. 3-1  shows the three different flux path configurations for a given magnet size. In particular, image (a) of  FIG. 3-2  shows a single flux path; image (b) shows two flux paths; and image (c) shows three flux paths. When the number of flux paths and bias field magnets, as well as the magnet cross-section, is held constant, an increase in the thickness of the magnets decreases the maximum flux change for a given change in load, as shown in  FIG. 3-2 . 
     This is attributed to the fact that thicker magnets have a proportionately greater MMF, and at lower applied loads, the changes in magnetic permeability of the magnetostrictive rod with stress are too small to reduce the flux density significantly below saturation. This explains the flat regions at low stresses in the  FIG. 3-2  plots, and that this flat region becomes progressively more prominent at greater magnet thickness. Further, the increase in MMF, which increases linearly with magnet thickness, is countered by the increase in internal reluctance of the rare-earth magnets as their thickness increases, relative to the reluctance of the rest of the magnetic circuit. Magnetic reluctance is equal to R=L/(μA) where R is the magnetic reluctance, L is the length dimension along the direction of the magnetic flux lines within the body (i.e. the thickness of the magnet for a rectangular magnet that is magnetized so that the poles are on the large area faces), μ is the magnetic permeability and A is the area of cross-section. The reluctance therefore scales linearly with the thickness of the magnets, and since μ for rare-earth permanent magnets is only about 1.1 times greater than that of air, the effect of increasing magnet thickness is effectively the same as adding an air gap. The increase in magnet thickness is also observed to shift the flux change curve towards higher loads, i.e., a thicker magnet will require a higher change in load to achieve the same flux change as a thinner magnet. These phenomena are not, however, observed for the single flux path consisting of 2″×0.5″ cross-section magnets. For this particular configuration, an increase in magnet thickness increases the maximum flux change without any apparent shift in the curve. This is likely due to the lower flux caused by the single, relatively small magnet. 
     A similar shift in the curves is seen in  FIG. 3-3  for an increase in magnet cross-section for a given thickness and number of flux paths. While this shift is consistent for all of the magnets tested, this shift does not necessarily correspond to a decrease in the maximum change in flux. For each of the configurations tested, the 2″×1″ magnets appear to give the highest change in flux, with a maximum of 0.953 T for the two flux path configuration at 0.0625″ magnet thickness. 
     Increasing the number of flux paths for a given magnet geometry again causes the flux change curve to shift towards higher loads and the maximum flux change to decrease for a given load, as shown in  FIG. 3-4 . The exception to this again occurs with the 2″×0.5″ magnets. For the 0.0625″ and 0.125″ thicknesses, an increase in the number of flux paths causes an increase in the maximum flux change, up to a point. 
     It is possible increase the maximum ΔB even higher by using smaller 2″×0.5″ cross-section magnets with vertical flux paths of the same cross-section and top and bottom flux paths with twice that cross-section, at 2″×1″. The increase in ΔB is attributed to the increased area of the horizontal portions of the paths, which are shared for all legs of the circuit; that is, for each flux path the top and bottom pieces are shared and thus should have a larger area to pass the larger flux without saturating. With this enhancement, and using an optimized alloy composition of 18.5% Al, ΔB values over 1 T can be achieved, as shown in  FIG. 3-5 . The addition of a second flux path increases the maximum ΔB by 71% over that of a single flux path, but the gains for additional paths fall off rapidly thereafter: 8% increase for a third path, 2% increase for a fourth, 1% for a fifth, and 0.7% for a sixth (See  FIG. 3-6 ). As a result, the increase in device cost and complexity begins to quickly outpace any gains in ΔB beyond 1 Tesla. 
     The choice of material for the flux paths has a marked effect on the performance of the device. Three different materials for the flux path with different materials characteristics are listed below, along with their impact on overall system performance.
         1. Cast iron: High saturation magnetization (&gt;2.2 T), high relative permeability (2000-5000)   2. Mild steel (1018): High saturation magnetization (&gt;2.1 T), moderate relative permeability (200-500)   3. Duplex stainless steel (2025)—Low saturation magnetization (&lt;1.5 T), moderate relative permeability (50-100).       

     Mild steel gave the most desirable performance characteristics with the greatest overall flux change as shown in  FIG. 3-7 . Cast iron also performed well, but not as well as the mild steel in terms of maximum ΔB observed; its curve also had a lower slope (dB/dσ), which affects the net power generation capacity of the system. Duplex stainless steel performed very poorly due to its low saturation magnetization. 
     In addition, improved performance was demonstrated through the use of unloaded magnetostrictive rods as flux paths. The Fe—Al alloys have a permeability that is about half that of mild steel. In some embodiments, the vertical flux path components may be replaced with one or more magnetostrictive rods while using mild steel for the top and bottom flux paths.  FIG. 3-8  illustrates an embodiment of a device  300  which includes a magnetostrictive rod  302  under load within the flux path and a second magnetostrictive rod  304  that is not under load, but is used within the flux path. For this setup, there are two magnetostrictive rods  302  and  304  making up a single closed flux path, but only one rod  302  is under load. This use of one or more unloaded Fe—Al magnetostrictive elements resulted in a performance improvement of about 10% over that of mild steel alone. 
     The voltage that each device produces is directly proportional to the number of turns of wire through which the flux passes. In an effort to maximize the number of turns, it may be possible to have a coil around the flux path components in addition to the coil around the loaded magnetostrictive rod. As a demonstration of this concept, a coil may be placed around the unloaded Fe—Al flux path component  304  in the single flux-path configuration shown in  FIG. 3-8 , and a compressive load may be applied to the other magnetostrictive rod  302 . The resulting open-circuit voltage for both coils can be measured to infer flux change (proportional to the area under the voltage curve, shown in  FIG. 3-9 ). These waveforms were measured with identical 1400 turn coils. Assuming that the flux path was a closed circuit, it could be expected that they should measure the same value. This was not, however, what was observed. The change in flux measured on the flux-path rod  304  is 0.55 T, 40% less than the 0.91 T measured on the loaded magnetostrictive rod  302 . 
     The first measurements showing this discrepancy were taken with the coils connected to a load, and the difference was originally attributed to an inductance difference. It was clear in that measurement that inductance was playing a role, as the peak of the voltage waveform from the flux-path coil measurement occurred nearly a tenth of a second later than the peak of the magnetostrictive coil voltage. The cause for the difference could be that the inductance of a coil is directly proportional to the relative permeability of the core material, and as the magnetostrictive rod is loaded, its relative permeability, and therefore the coil inductance, decreases. A less inductive coil provides less opposition to the change in current, causing its voltage to peak more quickly. While this explains the temporal shift in voltage peaks, the resulting flux change measured by each coil was the same as that of the respective open-circuit voltage measurements, where inductance would not have been an issue due to the lack of current. 
     To explore whether this observation was a result of the change in inductance in the loaded rod, the load was applied to both rods  302  and  304 . This would cause the permeability, and therefore the inductance, to change in both rods  302  and  304  at the same time. The voltage waveforms were approximately the same, as expected (see  FIG. 3-10 ), but the change ΔB in total flux density did not decrease, even with the lower stress. This implies that it may be possible to design the flux paths in such a way that a lower applied stress can produce the same amount of power, and thus increase device reliability without sacrificing performance. These measurements also support the notion that having coils around a larger portion of the magnetic circuit can lead to large gains in power generation. 
     In some embodiments, aluminum coils may be used as a substitute for copper (Cu) coils. The two main advantages for using Al for the coils are cost and weight. The density of Al is less than a third of that of Cu, and, based on commodity pricing, aluminum is one-third as expensive per ton, and therefore aluminum commodity costs per unit volume are around one-ninth of that of copper. Even after incorporating Al&#39;s 1.67 times higher resistance, it appears that use of Al coil could result in lower costs. Testing shows that this increase in internal resistance of the coil leads to a reduction in energy produced per strain cycle of 10-15% for the same load resistance. Additionally, the lighter aluminum coil would reduce the weight of the full-scale device, which would translate into savings on installation costs. Also, a cost model indicates that once increased scale drives the aluminum wire manufacturing cost multiplier (i.e., manufactured cost as a multiple of the commodity metal cost) to be closer to that of copper (1.2-1.3)), there may be a significant benefit in using Al wire in at least some embodiments. 
     In one embodiment, the PTO module  240  (see the sub-scale compression fixture design of  FIG. 2-10 ) includes a compression fixture  242  to apply a bias compressive load to the magnetostrictive rod  202 . This bias load will then be partially relieved when a tensile force, such as that from the wave/buoy interaction, is applied to the PTO module  240 , and this change in load is what is converted into magnetic energy. The fixture also includes considerations for the flux paths  216 , and in some embodiments is integrated with the flux paths  216 . As such, the design criteria for at least one embodiment of the compression fixture are that the fixture maintains a bias compressive load while transferring the large majority of load changes to the magnetostrictive rod  202 , and the fixture incorporates flux paths  216 . 
     The magnetostrictive element  202  was 11″ long with a 1.125″ diameter. The fixture  242  was made out of mild steel and had four flux paths  216 , each of which included a 2″×1″×0.0625″ NdFeB magnet  244 , and had four stainless steel bolts  246  to apply and hold the bias compressive stress to the magnetostrictive element  202 . The magnetostrictive element  202  had an internal thread machined into each end, into which a stainless steel eye-bolt  252  was threaded and the tensile load applied. The internal thread removed a large fraction of the mating surface between the compression fixture end-plates and the magnetostrictive rod  202 , and this smaller area could lead to a flux density large enough to reach saturation. To address this concern, shoulders were machined onto the ends of the rod  202  and counter-bores were machined into the end-plates so that the magnetostrictive rod  202  would slip-fit into the end plates of the compression fixture  242 , thereby increasing the contact area between them. Careful consideration was given to the fixture design to maintain the integrity of the magnetic circuit; the compression bolts  246  were made from very low permeability stainless steel, and the magnets  244  were held in place with small aluminum brackets (not shown), which were bolted to the flux paths with nylon bolts (not shown), all to avoid any potential shorts in the magnetic circuit. The compressive stress applied to the magnetostrictive rod  202  was calibrated against bolt torque, which allowed flexibility to change the applied stress to the desired value by simply tightening or loosening the bolts  246 . For at least some of the tests, the device is configured to operate in a region with maximum dB/dσ, which corresponded to a bias load of 5,000 lbs. 
     Bench testing of the compression fixture was performed by applying a cyclic tensile load to the device while measuring both the applied load and the open-circuit output voltage. The force was applied by hand using a lever arm that achieved load changes on the order of 300 pounds. In other embodiments, a load that is more than an order of magnitude higher than this may be applied using an electro-hydraulic press. The application of the relatively smaller load by hand allowed a loading pattern that is more consistent with the load changes that would be experienced in the ocean environment, albeit at a much lower amplitude.  FIG. 3-11  depicts an image of one embodiment of the sub-scale compression fixture design of  FIG. 2-10 . 
       FIG. 3-12  illustrates a graph of results of bench testing of the compression fixture of  FIG. 3-11 . The measured load and voltage were low-pass filtered at 55 Hz to remove the noise associated with line voltage. The predicted voltage was calculated using Faraday&#39;s law of induction, 
         V=NA ( dB/d σ)( dσ/dt ),
 
     where N is the number of turns of the coil, A is the cross-sectional area of the rod, and a is the applied load. The value of dB/dσ was found by minimizing the standard deviation of the difference between the actual and calculated voltages. The predicted voltage closely matches the measured output, with an R-squared of 0.88. The magnitude of dB/dσ is roughly one third of the value arrived at through magneto-mechanical performance testing. This is due to load sharing between the magnetostrictive rod  202  and the bolts  246  in the compression fixture  242 . Test results confirmed predictions that only 30% of the applied load would be felt by the magnetostrictive rod  202 . 
     Analysis shows that careful design of the compression fixture  242  can result in load transfers to the magnetostrictive rod  202  of over 90%. This can be achieved by decreasing the effective stiffness of the bolts  246  relative to that of the magnetostrictive alloy  202 , either by using a material  202  with a lower Young&#39;s modulus or by decreasing the combined cross-sectional area of the bolts  246 . As an example, if we were to use two 0.375″ bolts  246  with a Young&#39;s modulus (E) of 100 GPa to apply a 100 MPa strain to a 1″ diameter Fe—Al rod (E=160 GPa), then 89.5% of an applied tensile load would be transferred to the magnetostrictive rod  202 . For an application such as this, the choice of bolt material may be very important. Titanium alloys seem to be the best candidates owing to their low tensile modulus and high yield strength, but this must be balanced against the substantially higher cost for these components. Brass and bronze may offer good solutions as relatively low cost options that can still achieve over 85% load transfer to the magnetostrictive alloy rods  202 . 
       FIG. 3-13  illustrates a schematic circuit diagram to show how the magnets, flux path components and magnetic components are treated in the magnetic circuit. This circuit diagram may be used to model the behavior of the MWEH PTO. Magnetic circuit analysis is analogous to electrical circuit analysis—the magnetic flux is similar to current, the MMF is similar to voltage and the reluctance is similar to resistance. The flux paths are assumed to be closed with no leakage reluctances in this analysis. The MMF of the rare-earth magnets was calculated from the geometry (thickness) and the coercivity of the material. The first step was to estimate the change in permeability of the alloy rods as a function of stress. This was done by measuring the flux change data and using a simple one flux path circuit to assess permeability. A sample calculation based on one set of measured data is shown in  FIG. 3-14 . This data was fitted to a third-order polynomial, which we then used to predict the changes in permeability with stress for more complex configurations. 
     In order to model more complex configurations, this permeability analysis can be used to solve for flux in the magnetostrictive rod knowing all the other circuit parameters on a spreadsheet-based model. The model was very successful in predicting general trends in the data despite its simplicity. For example,  FIG. 3-15  shows the predicted flux in one and two flux path configurations for 2″×0.5″×0.0625″ magnets, and  FIG. 3-16  shows the shows the predicted flux in one and two flux path configuration for 2″×1″×0.0625″ magnets. Both the trends in the data and shapes of the curves are very similar to the observed results. The slight changes in actual flux density measured are likely due to the fact that the simple model assumes that the saturation magnetization is achieved at a fixed stress level, while in reality this is likely approached asymptotically. Also, the model does not consider the variations of permeability as a function of the internal flux—only as a function of stress. However, considering this, the power of this simple model to predict performance fairly closely to the measured results is very encouraging and should be a powerful tool for us going forward. 
     The foregoing demonstrates a 1 T change in magnetic flux density per strain cycle and a component fabrication process that will allow for high-throughput manufacturing. 
       FIG. 4-1  shows an embodiment of a device  400  with a moving mass  402  and springs  404  that may be used for harvesting energy from vibrations of machinery  406 , such as drills. The device  400  may be incorporated into the machinery  406  or coupled mechanically otherwise to vibrate with at least one component in the machinery  406 . In a drilling application, the device  400  may be part of the drill string or incorporated within or outside a drill collar. In some embodiments, the device  400  may be used for harvesting energy from the lateral vibrations of a drill string or drill collar. As the drill string or drill collar vibrates, one or more moving masses  402  may move in phase with or out of phase (or in an unsynchronized manner) with the vibrating part and/or result in extension of compression of one or more springs  404  which transfer a load to a magnetostrictive element  402 . The element  402  may have other associated components such as a flux path, pre-compression fixture, magnets etc, arranged in a configuration such that the changes in stress experienced by the element may be converted into changes in magnetic flux through the element, and electric current/voltage being produced in one or more coils that may be around or near the element or flux paths. Many such devices may be arranged in a variety of ways, including along the circumference or length of the drill or vibrating machinery  406 . 
       FIG. 4-2  shows an embodiment of a device  410  with one or more magnetostrictive elements  402  that may be used for harvesting energy from vibrations of machinery  406 , such as drills. The device  400  may be incorporated into the machinery  406  or coupled mechanically otherwise to vibrate with at least one component in the machinery  406 . In a drilling application, the device  400  may be part of the drill string or incorporated within or outside a drill collar. In some embodiments, the device  400  may be used for harvesting energy from the bending of a drill string or drill collar as it vibrates. As the drill string or drill collar vibrates in a lateral mode, it may bend, one or more magnetostrictive elements  402  extending or contracting in phase with or out of phase (or in an unsynchronized manner) with the vibrating part. The element or elements  402  may have other associated components such as a flux path, pre-compression fixture, magnets etc, arranged in a configuration such that the changes in stress experienced by the element may be converted into changes in magnetic flux through the element, and electric current/voltage being produced in one or more coils that may be around or near the element or flux paths. Many such devices  400  may be arranged in a variety of ways, including along the circumference or length of the drill or vibrating machinery  406 . 
     In a similar manner to the embodiments shown in  FIGS. 4-1  and  4 - 2 , embodiments of the devices  400  and  410  may be coupled to any elongated structure of a piece of machinery that experiences vibrational movement. In some embodiments, the elongated structure is a component of a drill string or bottom hole assembly of a drilling rig. However, in other embodiments and applications, the elongated structure may be a different type of components of a drilling rig or other machinery.